{ "Math": [ { "Question": "At which value of x is f continuous but not differentiable?\n\nA. a\nB. b\nC. c\nD. d\nE. e", "Answer (final answer highlighted)": "D", "ImagePath": "Math/1" }, { "Question": "The table shows values of $f'$, the derivative of function $f$. Although $f'$ is continuous over all real numbers, only selected values of $f'$ are shown. If $f'$ has exactly two real zeros, then $f$ is increasing over which of the following intervals?\n\nA. $ 15$\nC. $x > 5$ only\nD. $x > 1$\nE. $x > 3$", "Answer (final answer highlighted)": "B", "ImagePath": "Math/2" }, { "Question": "Shown is a graph of $f''$, the second derivative of function $f$. The curve is given by the equation $f'' = (x - a)^2 (x - d)$. The graph of $f$ has inflection points at which values of $x$?\n\nA. b only\nB. c only\nC. a and d\nD. a and c\nE. d only", "Answer (final answer highlighted)": "E", "ImagePath": "Math/3" }, { "Question": "Shown in the diagram is a graph of $f'$, the derivative of function $f$. If $f(3) = 3$, then $f(1)=$?\n\nA. \\frac{10}{3}\nB. \\frac{13}{3}\nC. -\\frac{5}{3}\nD. 4\nE. 6", "Answer (final answer highlighted)": "B", "ImagePath": "Math/4" }, { "Question": "Shown is a graph of $f'$, the derivative of function $f$. Which of the following statements is true?\n\nA. $f$ is not differentiable at $x = -2$.\nB. $f$ has a local minimum at $x = -1$.\nC. $f$ is increasing from $x = 1$ to $x = 3$.\nD. $f$ is increasing from $x = -3$ to $x = -1$.\nE. $f$ is decreasing from $x = -2$ to $x = 1$.", "Answer (final answer highlighted)": "D", "ImagePath": "Math/5" }, { "Question": "Which of the graphs shown does the $\\lim_{x \\to 3} f(x)$ exist?\n\nA. I only\nB. II only\nC. I and II only\nD. III only\nE. I and III only", "Answer (final answer highlighted)": "E", "ImagePath": "Math/6" }, { "Question": "A graph of function $f(x)$ on the interval $[-1, 4]$ is shown. Regions A, B, and C have areas of 1, 2, and 3 respectively. What is $\\int_{-1}^{4} (f(x) + 2) dx$?\n\nA. 2\nB. 4\nC. 10\nD. 12\nE. 16", "Answer (final answer highlighted)": "D", "ImagePath": "Math/7" }, { "Question": "Shown above is a slope field for which of the following differential equations?\n\nA. $\\frac{dy}{dx} = \\frac{x}{y}$\nB. $\\frac{dy}{dx} = xy$\nC. $\\frac{dy}{dx} = x + y$\nD. $\\frac{dy}{dx} = x - y$", "Answer (final answer highlighted)": "C", "ImagePath": "Math/8" }, { "Question": "The graph of a piecewise linear function $f(x)$ is above. Evaluate $\\int_{3}^{8} f'(x) , dx$.\n\nA. 2\nB. -2\nC. 5\nD. 0", "Answer (final answer highlighted)": "B", "ImagePath": "Math/9" }, { "Question": "The table above gives selected values for the twice-differentiable function f. In which of the following intervals must there be a number c such that $f'(c) = -2$.\n\nA. (0,2)\nB. (2,4)\nC. (4,6)\nD. (6,8)", "Answer (final answer highlighted)": "B", "ImagePath": "Math/10" }, { "Question": "The graph of a function, $f$, is shown above. Let $h(x)$ be defined as $h(x) = (x + 1) \\cdot f(x)$. Find $h'(4)$.\n\nA. -6\nB. -2\nC. 4\nD. 14", "Answer (final answer highlighted)": "A", "ImagePath": "Math/11" }, { "Question": "Two differentiable functions, $f$ and $g$ have the property that $f(x) \\geq g(x)$ for all real numbers and form a closed region $R$ that is bounded from $x = 1$ to $x = 7$. Selected values of $f$ and $g$ are in the table above. Estimate the area between the curves $f$ and $g$ between $x = 1$ and $x = 7$ using a Right Riemann sum with the three sub-intervals given in the table.\n\nA. 13\nB. 19\nC. 21\nD. 27", "Answer (final answer highlighted)": "B", "ImagePath": "Math/12" }, { "Question": "The table above gives values of a differentiable function $f(x)$ at selected $x$ values. Based on the table, which of the following statements about $f(x)$ could be false?\n\nA. There exists a value $c$, where $-5 < c < 3$ such that $f(c) = 1$\nB. There exists a value $c$, where $-5 < c < 3$ such that $f'(c) = 1$\nC. There exists a value $c$, where $-5 < c < 3$ such that $f(c) = -1$\nD. There exists a value $c$, where $-5 < c < 3$ such that $f'(c) = -1$", "Answer (final answer highlighted)": "B", "ImagePath": "Math/13" }, { "Question": "The function $f$ is continuous on the closed interval $[-2,2]$. The graph of $f'$, the derivative of $f$, is shown above. On which interval(s) is $f(x)$ increasing?\n\nA. $[-1,1]$\nB. $[-2, -1]$ and $[1, 2]$\nC. $[0, 2]$\nD. $[-2, 0]$", "Answer (final answer highlighted)": "C", "ImagePath": "Math/14" }, { "Question": "The graph of $f$ is shown above. Which of the following statements is false?\n\nA. $f(1) = \\lim_{x \\to 1} f(x)$\nB. $f(3) = \\lim_{x \\to 3} f(x)$\nC. $f(x)$ has a jump discontinuity at $x = 2$\nD. $f(x)$ has a removable discontinuity at $x = 4$", "Answer (final answer highlighted)": "A", "ImagePath": "Math/15" }, { "Question": "Consider the following back-to-back stemplot:\nWhich of the following are true statements?\nI. The distributions have the same mean.\nII. The distributions have the same range.\nIII. The distributions have the same standard deviation.\n\nA. II only\nB. I and II\nC. I and III\nD. II and III\nE. I, II, and III", "Answer (final answer highlighted)": "D", "ImagePath": "Math/16" }, { "Question": "The graph below shows cumulative proportions plotted against land values (in dollars per acre) for farms on sale in a rural community. What is the median land value?\n\nA. $2000\nB. $2250\nC. $2500\nD. $2750\nE. $3000", "Answer (final answer highlighted)": "A", "ImagePath": "Math/17" }, { "Question": "Following is a histogram of ages of people applying for a particular high-school teaching position. Which of the following statements are true?\nI. The median age is between 24 and 25.\nII. The mean age is between 22 and 23.\nIII. The mean age is greater than the median age.\n\nA. I only\nB. II only\nC. III only\nD. All are true\nE. None is true", "Answer (final answer highlighted)": "C", "ImagePath": "Math/18" }, { "Question": "A study was conducted to determine the effectiveness of varying amounts of vitamin C in reducing the number of common colds. A survey of 450 people provided the following information:\n\nIs there evidence of a relationship between catching a cold and taking vitamin C?\n\nA. The data prove that vitamin C reduces the number of common colds.\nB. The data prove that vitamin C has no effect on the number of common\ncolds.\nC. There is sufficient evidence at the 1% significance level of a relationship\nbetween taking vitamin C and catching fewer colds.\nD. There is sufficent evidence at the 10% significance level, but not at the 1%\nsignificance level, of a relationship between taking vitamin C and catching\nfewer colds.\nE. There is not sufficient evidence at the 10% level of a relationship between\ntakng vitamin C and catching fewer colds.", "Answer (final answer highlighted)": "E", "ImagePath": "Math/19" }, { "Question": "The boxpolts below summarize the distribution of SAT verbal and math scores among students at an upstate New York high school. Which of the following statements are true?\nI. The range of the math scores equals the range of the verbal scores.\nII. The highest math score equals the median verbal score.\nIII. The verbal scores appear to be roughly symmetric, while the math scores appear to be skewed to the right.\n\n(A) I only\n(B) III only\n(C) I and II\n(D) II and III\n(E) I, II, and III", "Answer (final answer highlighted)": "C", "ImagePath": "Math/20" }, { "Question": "The prices, in thousands of dollars, of 304 homes recently sold in a city are summarized in the histogram below. Based on the histogram, which of the following statements must be true? \n\n(A) The minimum price is $250,000. \n(B) The maximum price is $2,500,000. \n(C) The median price is not greater than $750,000. \n(D) The mean price is between $500,000 and $750,000. \n(E) The upper quartile of the prices is greater than $1,500,000. ", "Answer (final answer highlighted)": "C", "ImagePath": "Math/21" }, { "Question": "As part of a study on the relationship between the use of tanning booths and the occurrence of skin cancer, researchers reviewed the medical records of 1,436 people. The table below summarizes tanning booth use for people in the study who did and did not have skin cancer. Of the people in the study who had skin cancer, what fraction used a tanning booth? \n\n(A) 190/265\n(B) 190/896 \n(C) 190/1,436 \n(D) 265/1,436 \n(E) 896/1,436", "Answer (final answer highlighted)": "B", "ImagePath": "Math/22" }, { "Question": "In northwest Pennsylvania, a zoologist recorded the ages, in months, of 55 bears and whether each bear was male or female. The data are shown in the back-to-back stemplot below. Based on the stemplot, which of the following statements is true?\n \n(A) The median age and the range of ages are both greater for female bears than for male bears. \n(B) The median age and the range of ages are both less for female bears than for male bears. \n(C) The median age is the same for female bears and male bears, and the range of ages is the same for female bears and male bears. \n(D) The median age is less for female bears than for male bears, and the range of ages is greater for female bears than for male bears. \n(E) The median age is greater for female bears than for male bears, and the range of ages is less for female bears than for male bears. ", "Answer (final answer highlighted)": "A", "ImagePath": "Math/23" }, { "Question": "Nutritionists examined the sodium content of different brands of potato chips. Each brand was classified as either healthy or regular based on how the chips were marketed to the public. The sodium contents, in milligrams (mg) per serving, of the chips are summarized in the boxplots below. \n\nBased on the boxplots, which statement gives a correct comparison between the two classifications of the sodium content of the chips? \n(A) The number of brands classified as healthy is greater than the number of brands classified as regular. \n(B) The interquartile range (IQR) of the brands classified as healthy is greater than the IQR of the brands classified as regular. \n(C) The range of the brands classified as healthy is less than the range of the brands classified as regular. \n(D) The median of the brands classified as healthy is more than twice the median of the brands classified as regular. \n(E) The brand with the least sodium content and the brand with the greatest sodium content are both classified as healthy. ", "Answer (final answer highlighted)": "B", "ImagePath": "Math/24" }, { "Question": "A factory has two machines, A and B, making the same part for refrigerators. The number of defective parts produced by each machine during the first hour of operation was recorded on 19 randomly selected days. The scatterplot below shows the number of defective parts produced by each machine on the selected days. Which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days? \n\n(A) Machine A always produced the same number of defective parts as machine B. \n(B) Machine A always produced fewer defective parts than machine B. \n(C) Machine A always produced more defective parts than machine B. \n(D) Machine A usually, but not always, produced fewer defective parts than machine B. \n(E) Machine A usually, but not always, produced more defective parts than machine B. ", "Answer (final answer highlighted)": "D", "ImagePath": "Math/25" }, { "Question": "A state educational agency was concerned that the salaries of public school teachers in one region of the state, region A, were higher than the salaries in another region of the state, region B. The agency took two independent random samples of salaries of public school teachers, one from region A and one from region B. The data are summarized in the table below. Assuming all conditions for inference are met, do the data provide convincing statistical evidence that the salaries of public school teachers in region A are, on average, greater than the salaries of public school teachers in region B? \n\n(A) Yes, there is evidence at the significance level of a= 0.001. \n(B) Yes, there is evidence at the significance level of a=0.01 but not at a=0.001. \n(C) Yes, there is evidence at the significance level of a=0.05 but not at a=0.01. \n(D) Yes, there is evidence at the significance level of a=0.10 but not at a=0.05. \n(E) No, there is no evidence at the significance level of a=0.10. ", "Answer (final answer highlighted)": "C", "ImagePath": "Math/26" }, { "Question": "As part of a community service program, students in three middle school grades (grade 6, grade 7, grade 8) each chose to participate in one of three school-sponsored volunteer activities. The graph below shows the distribution for each class for the three activities. Based on the graph, which statement must be true? \n\n(A) Of all the students who chose activity B, the greatest number of students were in grade 6. \n(B) Grade 7 and grade 8 had the same number of students who did not choose activity A. \n(C) The grade with the greatest percentage of students who chose activity C was grade 8. \n(D) For students in grade 7, the number who chose activity C was greater than the number who chose activity B. \n(E) For students in grade 8, the number who chose activity A was greater than the number who chose activity B. ", "Answer (final answer highlighted)": "D", "ImagePath": "Math/27" }, { "Question": "The number of siblings was recorded for each student of a group of 80 students. Some summary statistics and a histogram displaying the results are shown below. An outlier is often defined as a number that is more than 1.5 times the interquartile range below the first quartile or above the third quartile. Using the definition of an outlier and the given information, which of the following can be concluded? \n\n(A) The median is greater than the mean, and the distribution has no outliers. \n(B) The median is greater than the mean, and the distribution has only one outlier. \n(C) The median is greater than the mean, and the distribution has two outliers. \n(D) The median is less than the mean, and the distribution has only one outlier. \n(E) The median is less than the mean, and the distribution has two outliers. ", "Answer (final answer highlighted)": "E", "ImagePath": "Math/28" }, { "Question": "Extra study sessions were offered to students after the midterm to help improve their understanding of statistics. Student scores on the midterm and the final exam were recorded. The following scatterplot shows final test scores against the midterm test scores. Which of the following statements correctly interprets the scatterplot?\n\nA. All students have shown significant improvement in the final exam scores as a result of the extra study sessions.\nB. The extra study sessions were of no help. Each student\u2019s final exam score was about the same as his or her score on the midterm.\nC. The extra study sessions further confused students. All student scores decreased from midterm to final exam.\nD. Students who scored below 55 on the midterm showed considerable improvement on the final exam; those who scored between 55 and 80 on the midterm showed minimal improvement on the final exam; and those who scored above 80 on the midterm showed almost no improvement on the final exam.\nE. Students who scored below 55 on the midterm showed minimal improvement on the final exam; those who scored between 55 and 80 on the midterm showed moderate improvement on the final exam; and those who scored above 80 on the midterm showed considerable improvement on the final exam.", "Answer (final answer highlighted)": "D: The scatterplot shows three different groups. The group of students on the far left of the scatterplot scored lowest on the midterm, in a range of 30-50, but then scored in a range of 65-85 on the final, showing considerable improvement. The middle group scored between 55-80 on the midterm and then between 60-85 on the final, showing very little improvement. The third group, the one on the far right of the scatterplot, scored above 85 on the midterm and then above 85 on the final, showing almost no improvement. To assist you in seeing this, you can add a straight line to the graph, going from a point on the x-axis at 50 (midterm = 50) and the bottom of the y-axis (final = 50) to a point at midterm = 100 and final = 100. Then, people on the upper left of that line did better on the final, whereas those on the lower right did better on the midterm.", "ImagePath": "Math/29" }, { "Question": "A resident of Auto Town was interested in finding the cheapest gas prices at nearby gas stations. On randomly selected days over a period of one month, he recorded the gas prices (in dollars) at four gas stations near his house. The boxplots of gas prices are as follows: Based on this display, which of the stations had the closest mean and median during the month?\n\nA. Station 1\nB. Station 2\nC. Station 3\nD. Station 4\nE. We cannot tell without knowing the standard deviation of the gas prices from each station.", "Answer (final answer highlighted)": "B The mean is strongly affected by skew and outliers, while the median is not. Therefore the mean will be closest to the median when the box-and-whisker plot is most symmetric; the most symmetric of the box-and-whisker plots is from station 2.", "ImagePath": "Math/30" }, { "Question": "During flu season, a city medical center needs to keep a large supply of flu shots. A nurse\u2019s aid compiles data on the number of flu shots given per day in the past few years during flu season. A cumulative probability chart of the collected data is as follows: How many flu shots should the center store every day to meet the demand on 95 percent of the days?\n\nA. At most 190\nB. At most 140\nC. Exactly 170\nD. At least 150\nE. At least 200", "Answer (final answer highlighted)": "E Look closely at the chart. For example, the point (160, 0.4) indicates that on 40 percent of the days, up to 160 shots were given. To find the number of shots needed to meet the demand on 95 percent of the days, we need to find the 95th percentile. Draw a horizontal line from the cumulative probability of 0.95 to the curve. From the point at which the line meets the curve, draw a vertical line down to the x-axis, and then read the number of flu shots given there. It should be approximately 200.", "ImagePath": "Math/31" }, { "Question": "In the northern United States, schools are sometimes closed during winter due to severe snowstorms. At the end of the school year, schools have to make up for the days missed. The following graph shows the frequency distribution of the number of days missed due to snowstorms per year using data collected from the past 75 years. Which of the following should be used to describe the center of this distribution?\n\nA. Mean, because it is an unbiased estimator\nB. Median, because the distribution is skewed\nC. IQR, because it excludes outliers and includes only the middle 50 percent of data\nD. First quartile, because the distribution is left skewed\nE. Standard deviation, because it is unaffected by the outliers", "Answer (final answer highlighted)": "B IQR, first quartile, and standard deviation are not measures of central tendency. Median and mean are measures of central tendency. The mean is affected by extreme observations\u2014large observations tend to make the mean higher. Because this distribution is skewed, the median should be used to describe the center of the distribution. Note that the median is not affected by the extreme measurements.", "ImagePath": "Math/32" }, { "Question": "X and Y are independent random variables; the probability distributions for each are given in the table above. Let Z = X + Y. What is P(Z \u2264 2)?\nA. 0.07\nB. 0.15\nC. 0.24\nD. 0.40\nE. 0.80", "Answer (final answer highlighted)": "B There are three mutually exclusive ways to get a sum less than or equal to two: x = 0 and y = 1, x = 0 and y = 2, x = 1 and y = 1. Since the random variables are independent, we can multiply each pair\u2019s probabilities to get the probability of the pair. That is:\n\nP(x = 0 and y = 1) = P(x = 0) \u00d7 P(y = 1) = 0.4 \u00d7 0.1 = 0.04", "ImagePath": "Math/33" }, { "Question": "Two hundred students were classified by sex and hostility level (low, medium, high), as measured by an HLT-test. The results were the following. If the hostility level among students were independent of their sex, then how many female students would we expect to show the medium HLT score?\n\nA. 25\nB. 45\nC. 54\nD. 60\nE. 75", "Answer (final answer highlighted)": "C The total number of females in the sample = 120.\n\nThe total number of students with medium HLT score = 90.\n\nThe total number of students in the sample = 200.\n\nThe expected number of females with medium = (120)*(90)/200 = 54", "ImagePath": "Math/34" }, { "Question": " The following boxplot summarizes the prices of books at a bookstore. Which of the following is true about the prices of books at this store?\n\nA. This store carries more books priced above the mean than below the mean.\nB. This store carries more books priced below the mean than above the mean.\nC. This store carries about the same number of books at different prices in the entire price range.\nD. The mean price of books at this store is the same as the median price of books.\nE. The mean price of books at this store is lower than the median price of books.", "Answer (final answer highlighted)": "\nB This boxplot is highly \nright-skewed. The book prices range from about $8 to $80, but the median\n price is around $12. This means that 50 percent of the books are priced\n around $12 or lower. Even the third quartile is around $25, which means\n that about 75 percent of the books are priced at $25 or below. When a \ndistribution is right-skewed, the mean is above the median, and \ntherefore, more books are below the mean than above it.", "ImagePath": "Math/35" }, { "Question": "The following graph summarizes data collected on annual rainfall in two cities for the past 150 years. Which of the following conclusions can be made from this graph?\n\nA. The cities have different mean annual rainfalls, but the range of their annual rainfalls is approximately the same.\nB. On average, City B gets more rain than City A, but it has a smaller range of annual rainfall.\nC. On average, City B gets more rain than City A, and it has a larger range of annual rainfall.\nD. On average, City A gets more rain than City B, but it has a smaller range of annual rainfall.\nE. On average, City A gets more rain than City B, and it has a larger range of annual rainfall.", "Answer (final answer highlighted)": "B The approximate range of annual rainfall for City A is five to 45 inches, with a mean of approximately 23 inches. The approximate range of annual rainfall for City B is 20 to 40 inches, with a mean of approximately 30 inches. This means that, on the average, City B gets more rain than City A, but the range for City A is larger than that for City B.", "ImagePath": "Math/36" }, { "Question": "The following cumulative graph gives the electricity demand of a certain town.The power plant that provides electricity to this town is capable of generating 12,000 kW daily. On what percent of days will the power plant not be able to meet the demand for electricity?\n\nA. About 3 percent\nB. About 60 percent\nC. About 80 percent\nD. About 92 percent\nE. About 97 percent", "Answer (final answer highlighted)": "A In this cumulative graph, we need to find P(Demand > 12,000), because that is the point at which the power company will not be able to meet the demand for electricity. Draw a vertical line at 12,000 until it reaches the curve. From the point at which it crosses the curve, draw a horizontal line to the Y-axis. The line reaches the Y-axis at approximately 97 percent, which means that on 97 percent of days the demand for electricity will be, at most, 12,000. In other words, on about 3 percent of days, the power plant will have more demand for electricity than what they produce. Because none of the other choices are close to 3 percent, you do not need to be accurate with your drawing.", "ImagePath": "Math/37" }, { "Question": "Sixty pairs of measurements were taken at random to estimate the relation between variables X and Y. A least squares regression line was fitted to the collected data. The resulting residual plot is as follows. Which of the following conclusions is appropriate?\n\nA. A line is an appropriate model to describe the relation between X and Y.\nB. A line is not an appropriate model to describe the relation between X and Y.\nC. The assumption of normality of errors has been violated.\nD. The assumption of constant sample standard deviations has been violated.\nE. The variables X and Y are not related at all.", "Answer (final answer highlighted)": "B The curvature in the residual plot indicates that a line is not an appropriate model to describe the relation between X and Y. If a line is an appropriate model, then the residual plot will show randomly scattered residuals without any pattern.", "ImagePath": "Math/38" }, { "Question": "Use the following computer output for a least-squares regression for Questions below. What is the equation of the least-squares regression line?\nA. \u0177= -0.6442x+ 22.94\nB. \u0177= 22.94 + 0.5466x\nC. \u0177= 22.94 + 2.866x\nD. \u0177= 22.94 - 0.6442x\nE. \u0177= -0.6442 + 0.5466x", "Answer (final answer highlighted)": "D The correct answer is (d). The slope of the regression line. \u20130.6442, can be found under \u201cCoef\u201d to the right of \u201cx.\u201d The intercept of the regression line, 22.94, can be found under \u201cCoef\u201d to the right of \u201cConstant.\u201d", "ImagePath": "Math/39" }, { "Question": "Given that the analysis is based on 10 datapoints, what is the P-value for the t-test of the hypothesis $H_0 : \\beta = 0$ vesus $H_A : \\beta \u2260 0$.\n\nA. 0.02 < P < 0.03\nB. 0.20 < P < 0.30\nC. 0.01 < P < 0.05\nD. 0.15 < P < 0.20\nE. 0.10 < P < 0.15", "Answer (final answer highlighted)": "B The correct answer is (b). The t statistic for H0: \u03b2 = 0 is given in the printout as \u20131.18. We are given that n = 10 \u21d2 df = 10 \u2013 2 = 8. From the df = 8 row of Table B (the t Distribution Critical Values table), we see, ignoring the negative sign since it\u2019s a two-sided test,\n\n1.108 < 1.18 < 1.397 \u21d2 2(0.10) < P < 2(0.15),\n\nwhich is equivalent to 0.20 < P < 0.30.", "ImagePath": "Math/40" }, { "Question": "If three fair coins are flipped, P(0 heads) = 0.125, P(exactly 1 head) = 0.375, P(exactly 2 heads) = 0.375, and P(exactly 3 heads) = 0.125. The following results were obtained when three coins were flipped 64 times. What is the value of the X2statistic used to test if the coins are behaving as expected, and how many degrees of freedom does the determination of the P-value depend on?\n\nA. 3.33, 3\nB. 3.33, 4\nC. 11.09, 3\nD. 3.33, 2\nE. 11.09, 4", "Answer (final answer highlighted)": "A $\\chi^2 = \\frac{(10-8)^2}{8} + \\frac{(28-24)^2}{24} + \\frac{(22-24)^2}{24} + \\frac{(4-8)^2}{8} = 3.33$In a chi-square goodness-of-fit test, the number of degrees of freedom equals one less than the number of possible outcomes. In this case, df = n\u20131 = 4 \u2013 1 = 3.", "ImagePath": "Math/41" }, { "Question": "For the histogram pictured above, what is the class interval (boundaries) for the class that contains the median of the data?\n\nA. (5, 7)\nB. (9, 11)\nC. (11, 13)\nD. (15, 17)\nE. (7, 9)", "Answer (final answer highlighted)": "E The correct answer is (e). There are 101 terms, so the median is located at the 51st position in an ordered list of terms. From the counts given, the median must be in the interval whose midpoint is 8. Because the intervals are each of width 2, the class interval for the interval whose midpoint is 8 must be (7, 9).", "ImagePath": "Math/42" }, { "Question": "Thirteen large animals were measured to help determine the relationship between their length and their weight. The natural logarithm of the weight of each animal was taken and a least-squares regression equation for predicting weight from length was determined. The computer output from the analysis is given below. Give a 99% confidence interval for the slope of the regression line. Interpret this interval.\n\nA. (0.032, 0.041); the probability is 0.99 that the true slope of the regression line is between 0.032 and 0.041.\nB. (0.032, 0.041); 99% of the time, the true slope will be between 0.032 and 0.041.\nC. (0.032, 0.041); we are 99% confident that the true slope of the regression line is between 0.032 and 0.041.\nD. (0.81, 1.66); we are 99% confident that the true slope of the regression line is between 0.032 and 0.041.\nE. (0.81, 1.66); the probability is 0.99 that the true slope of the regression line is between 0.81 and 1.66.", "Answer (final answer highlighted)": "C The correct answer is (c). df = 13 \u2013 2 = 11 \u21d2 t* = 3.106 (from Table B; if you have a TI-84 with the invT function, t* = invT(0.995,11)). Thus, a 99% confidence interval for the slope is:\n\n0.0365 \u00b1 3.106(0.0015) = (0.032, 0.041).\n\nWe are 99% confident that the true slope of the regression line is between 0.032 units and 0.041 units.", "ImagePath": "Math/43" }, { "Question": "For the following observations collected while doing a chi-square test for independence between the two variables Aand B, find the expected value of the cell marked with \"X.\"\n\nA. 4.173\nB. 9.00\nC. 11.56\nD. 8.667\nE. 9.33", "Answer (final answer highlighted)": "D The correct answer is (d). There are 81 observations total, 27 observations in the second column, 26 observations in the first row. The expected number in the first row and second column equals 27/81*26=8.667.", "ImagePath": "Math/44" }, { "Question": "The following is a probability histogram for a discrete random variable X. What is $\\mu_x$.\n\nA. 3.5\nB. 4.0\nC. 3.7\nD. 3.3\nE. 3.0", "Answer (final answer highlighted)": "D The correct answer is (d). 2(0.3) + 3(0.2) + 4(0.4) + 5(0.1) = 3.3.", "ImagePath": "Math/45" }, { "Question": "You are developing a new strain of strawberries (say, Type X) and are interested in its sweetness as compared to another strain (say, Type Y). You have four plots of land, call them A, B, C, and D, which are roughly four squares in one large plot for your study (see the figure below). A river runs alongside of plots C and D. Because you are worried that the river might influence the sweetness of the berries, you randomly plant type Xin either A or B (and Yin the other) and randomly plant type Xin either C or D (and Yin the other). Which of the following terms best describes this design?\n\nA. A completely randomized design\nB. A randomized study\nC. A randomized observational study\nD. A block design, controlling for the strain of strawberry\nE. A block design, controlling for the effects of the river", "Answer (final answer highlighted)": "E The correct answer is (e). The choice is made here to treat plots A and B as a block and plots C and D as a block. That way, we are controlling for the possible confounding effects of the river. Hence the answer is (c). If you answered (e), be careful of confusing the treatment variable with the blocking variable.", "ImagePath": "Math/46" }, { "Question": "A set of test scores has the following 5-number summary. Which statement about outliers must be true?\n\nA. There is exactly one outlier on the lower end.\nB. There is at least one outlier on the lower end.\nC. There is exactly one outlier on the higher end.\nD. There is at least one outlier on the higher end.\nE. There are no outliers.", "Answer (final answer highlighted)": "B Using the outlier guideline, any value above Q3 + 1.5 \u22c5 IQR = 28.5 + 1.5 \u22c5 10.5 = 44.25, or below Q1 \u2212 1.5 \u22c5 IQR = 18 \u2212 1.5 \u22c5 10.5 = 2.25, is considered an outlier. Because the maximum is 33, there are no values above 44.25. The minimum of 2 is an outlier. There may be more than one value below 2.25, so all we can say is that there is at least one outlier on the lower end.", "ImagePath": "Math/47" }, { "Question": "The table above shows the regression output for predicting the number of calories from the number of milligrams of sodium for items at a fast-food chain. What percent of the variation in calories is explained by the regression model using sodium as a predictor?\n\nA. 7.36%\nB. 54.2%\nC. 53.8%\nD. 73.4%\nE. 73.6%", "Answer (final answer highlighted)": "B You should recognize that this is the interpretation of $r_2$. According to the printout, that value is 0.542313, or about 54.2%.", "ImagePath": "Math/48" }, { "Question": "Researchers in the Southwest are studying tortoises-a species of animal that is affected by habitat loss due to human development of the desert. A total of 78 tortoises are being studied by researchers at several sites. The data on gender and species of all these tortoises is organized in the table shown below. If a tortoise from this study is to be selected at random, let A = the tortoise is femaleand B = the tortoise is a Morafka. Which of the following appropriately interprets the value of P(B|A)?\n\nA. 31.3% is the probability that a randomly selected Morafka tortoise is a female tortoise.\nB. 31.3% is the probability that a randomly selected female tortoise is a Morafka tortoise.\nC. 19.2% is the probability that a randomly selected Morafka tortoise is a female tortoise.\nD. 19.2% is the probability that a randomly selected female tortoise is a Morafka tortoise.\nE. 31.3% is the probability that a randomly selected tortoise is a Morafka tortoise.", "Answer (final answer highlighted)": "B This is asking for a conditional probability. P(Morafka|Female). Out of the 48 female tortoises, 15 are Morafka. 15/48 = 0.3125, or about 31.3%.", "ImagePath": "Math/49" }, { "Question": "Breakfast cereals have a wide range of sugar content. Some cereals contain High Fructose Corn Syrup (HFCS) as a source of sugar and some do not. The boxplots above show the total sugar content of different types of cereal for those containing HFCS and for those that do not. Which statement is true based on the boxplots?\n\nA. The number of cereals with HFCS is about the same as the number of cereals without HFCS.\nB. The cereals with HFCS have a greater interquartile range than the cereals without HFCS.\nC. The cereals without HFCS have a greater range than the cereals with HFCS.\nD. About half the cereals without HFCS have less sugar than about three-fourths of the cereals with HFCS.\nE. About half the cereals with HFCS have more sugar than about three-fourths of the cereals without HFCS.", "Answer (final answer highlighted)": "E The median of the HFCS group is the same as Q3 of the No HFCS group.", "ImagePath": "Math/50" }, { "Question": "Researchers were gathering data on alligators in an attempt to estimate an alligator's weight from its length. They captured 29 alligators and measured their length and weight. They created three regression models. Each model, along with its residual plot, is shown below. yrepresents the weight in pounds and xrepresents the length in inches.Which statement is true?\n\nA. There is a linear relationship between weight and length, and model I is most appropriate.\nB. There is a linear relationship between weight and length, and model II is most appropriate.\nC. There is a nonlinear relationship between weight and length, and model I is most appropriate.\nD. There is a nonlinear relationship between weight and length, and model II is most appropriate.\nE. There is a nonlinear relationship between weight and length, and model III is most appropriate.", "Answer (final answer highlighted)": "D Because there is a curve in residual plot I, which is for weight vs. length, the relationship between those two variables is not linear. Because residual plot II shows a no curve and plot III does, plot II represents a better model.", "ImagePath": "Math/51" }, { "Question": "Listed above are the summary statistics for the daily high temperatures (in degrees F) for the month of September in a Midwestern U.S. city. One particular day has a z-score of 0.70. What was the likely temperature that day?\n\nA. 68\nB. 70\nC. 74\nD. 76\nE. 80", "Answer (final answer highlighted)": "E z = 0.70 = (x-74.9)/7.29, x = 80.", "ImagePath": "Math/52" }, { "Question": "In American football, the running back carries the football forward in a quest to score points. Many people create fantasy football teams by selecting players as their \"team.\" These fans analyze data to judge which players are outstanding. The following regression output analyzes the linear relationship between the number of times a running back is given the football (carries) and the total number of yards that player gains in a season for a random sample of 18 running backs. The appropriate calculation for a 99% confidence interval for the slope of the least squares regression line for the total yards gained versus number of carries in a season for all running backs is:\n\nA. 4.3441 \u00b1 2.576.(1.811)\\sqrt{18}\nB. 4.3441 \u00b1 2.921.(1.811)\nC. 4.3441 \u00b1 2.921.(1.811)\\sqrt{18}\nD. 4.3441 \u00b1 2.898.(1.811)\nE. 4.3441 \u00b1 2.898.(1.811)\\sqrt{18}", "Answer (final answer highlighted)": "B The formula for the confidence interval for the slope is $b_1 \u00b1 t* \u00b7 s_{b1}$. From the printout b1 = 4.3441 and sb1 = 1.811. t* for 18 \u2013 2 = 16 degrees of freedom and 99% confidence is 2.921.", "ImagePath": "Math/53" }, { "Question": "Above is a cumulative relative frequency plot for the scores of a large university class on a 90-point statistics exam. Which of the following observations is correct?\n\nA. The median score is at least 60 points.\nB. The distribution of scores is skewed to the right.\nC. The distribution of scores is skewed to the left.\nD. The distribution is roughly symmetric.\nE. If a passing score is 60, most students passed the test.", "Answer (final answer highlighted)": "B The steeper part of the graph corresponds to the higher bars on a histogram. So the higher bars would be on the left with a tail stretching toward the right.", "ImagePath": "Math/54" }, { "Question": "Some health professionals suspect that doctors are more likely to order cardiac tests for men than women, even when women describe exactly the same symptoms. Young doctors, training to work in the emergency room, were randomly assigned to two groups-Group A and Group B-and presented with the exact same description of common symptoms of heart disease. However, those in Group A were told that the patient was a 55-year-old female and those in Group B were told that the patient was a 55-year-old male. All other patient characteristics were exactly the same. Which of the following is the appropriate statistic to test whether doctors are less likely to order cardiac tests when the patient is female?\n\nHere's the content with the mathematical expressions enclosed in dollar signs:\n\nA.$ z = \\frac{(0.70) - (0.85)}{\\sqrt{(0.70)(0.85)\\left(\\frac{1}{60} + \\frac{1}{40}\\right)}} $\n\nB.$ z = \\frac{(0.70) - (0.85)}{\\sqrt{(0.76)(0.24)\\left(\\frac{1}{60} + \\frac{1}{40}\\right)}} $\n\nC.$ z = \\frac{(0.70) - (0.85)}{\\sqrt{(0.76)(0.24)\\left(\\frac{1}{42} + \\frac{1}{34}\\right)}} $", "Answer (final answer highlighted)": "B Under the null hypothesis, the proportions are the same, so the standard error formula is based on the pooled proportion (x1+x2)/(n1+n2)", "ImagePath": "Math/55" }, { "Question": "The graph of the function \\( f \\) is shown below:\n\nIf $g(x) = \\int_{0}^{x^2} f(t) \\, dt$, what is $g'(2)$?\n\nA. 32\nB. 16\nC. 8\nD. 4\n", "Answer (final answer highlighted)": "C: The Second Fundamental Theorem of Calculus says that $\\frac{d}{dx} \\int_{c}^{x} f(t)dt = f'(x)$. Here, we get: $g'(x) = \\frac{d}{dx} \\int_{0}^{x^2} f(t)dt = f(x^2) \\cdot 2x$ (the $2x$ term comes from applying the Chain Rule to the limit in the integral). Therefore, $g'(2) = f(4) \\cdot 2 \\cdot 2$. From the graph, we can see that $f(4) = 2$, so $g'(2) = 2 \\cdot 2 \\cdot 2 = 8$.", "ImagePath": "Math/56" }, { "Question": "The graph of $f'$ is shown above. Which statements about $f$ must be true for $a < x < b$?\nI. $f$ is increasing.\nII. $f$ is continuous.\nIII. $f$ is differentiable.\n\nA. all three\nB. II only\nC. I and II only\nD. I and III only\n", "Answer (final answer highlighted)": "A: $f'(x) > 0$; the curve shows that $f'$ is defined for all $a < x < b$, so $f$ is differentiable and therefore continuous.", "ImagePath": "Math/57" }, { "Question": "The table shows some of the values of differentiable functions $f$ and $g$ and their derivatives. If $h(x) = f(g(x))$, then $h'(2)$ equals\nA. -2\nB. -1\nC. 0\nD. 1", "Answer (final answer highlighted)": "B: Since $h(x) = f(g(x))$, $h'(x) = f'(g(x))g'(x)$ and $h'(2) = f'(g(2))g'(2) = f'(3) \\cdot 1 = -1$.", "ImagePath": "Math/58" }, { "Question": "The graph of $f$ is shown above, and $f$ is twice differentiable. Which of the following has the largest value?\nI. $f(0)$\nII. $f'(0)$\nIII. $f''(0)$\n\nA. I\nB. II\nC. III\nD. I and II", "Answer (final answer highlighted)": "C: Since $f$ is decreasing, $f' < 0$ and since $f$ is concave up, $f'' > 0$. The graph also shows that $f(0) < 0$. Thus $f''(0)$ has the largest value.\n\n\n\n\n\n", "ImagePath": "Math/59" }, { "Question": "A slope field for a differential equation is shown above. Which of the following could be the differential equation?\nA. $ \\frac{dx}{dy} = 2x $\nB. $ \\frac{dx}{dy} = -2x $\nC. $ \\frac{dx}{dy} = y $\nD. $ \\frac{dx}{dy} = x - y $", "Answer (final answer highlighted)": "B: Note that for each column, all the tangents have the same slope. For example, when $ x = 0 $ all tangents are horizontal, which is to say their slopes are all zero. This implies that the slope of the tangents depends solely on the $ x $-coordinate of the point and is independent of the $ y $-coordinate. Also note that when $ x > 0 $ slopes are negative, and when $ x < 0 $ slopes are positive. Thus, the only differential equation that satisfies these conditions is $ \\frac{dy}{dx} = -2x $.\n\n\n\n\n\n", "ImagePath": "Math/60" }, { "Question": "The graph of $f''$, the second derivative of $f$ is shown above. The graph of $f''$ has horizontal tangents at $x = -2$ and $x = 2$. For what values of $x$ does the graph of the function $f$ have a point of inflection?\n\nA. $-4$, $0$ and $4$\nB. $-2$, $0$ and $2$\nC. $-4$ and $4$ only\nD. $0$ only\n", "Answer (final answer highlighted)": "A: Note that $f'' > 0$ on the intervals $(-\\infty, -4)$ and $(0, 4)$. Thus the graph of the function $f$ is concave up on these intervals. Similarly, $f'' < 0$ and concave down on the intervals $(-4, 0)$ and $(4, \\infty)$. Therefore $f$ has a point of inflection at $x = -4$, $0$, and $4$.", "ImagePath": "Math/61" }, { "Question": "The domain of the function $f$ is $0 \\leq x \\leq 9$ as shown above. If $g(x) = \\int_{0}^{x} f(t) , dt$, at what value of $x$ is $g(x)$ the absolute maximum?\nA. 0\nB. 1\nC. 2\nD. 8\n\n", "Answer (final answer highlighted)": "C: First, the graph of $f(x)$ is above the x-axis on the interval $[0, 2]$ thus $f(x) \\geq 0$, and $\\int_{0}^{x} f(t) , dt > 0$ Secondly, $f(x) \\leq 0$ on the interval $[2, 8]$ and $\\int_{2}^{8} f(x) , dx < 0$, and thus $\\int_{0}^{2} f(t) , dt$ maximum. Note that the area of the region bounded by $f(x)$ and the x-axis on $[2, 8]$ is greater than the sum of the areas of the two regions above the x-axis. Therefore,\n\n$\\int_{0}^{2} f(x) , dx + \\int_{2}^{8} f(x) , dx + \\int_{8}^{x} f(x) , dx < 0$ and $\\int_{0}^{x} f(x) , dx < 0$ and\n\nConsequently, $\\int_{0}^{x} f(x) , dx$ is the absolute maximum value.", "ImagePath": "Math/62" }, { "Question": "The graph of a function $f$ is shown above. Which of the following statements is/are true?\n\nI. $\\lim_{x \\to 1} f(x)$ exists\n\nII. $f(1)$ exists\n\nIII. $\\lim_{x \\to 1} f(x) = f'(1)$\n\nA. I only\n\nB. II only\n\nC. I and II only\n\nD. I, II, and III", "Answer (final answer highlighted)": "C: Since $\\lim_{x \\to 1^+} f(x) = \\lim_{x \\to 1^-} f(x) = 4$, $\\lim_{x \\to 1} f(x)$ exists. The graph shows that at $x = 1$, $f(x) = 1$ and thus $f(1)$ exists. Lastly, $\\lim_{x \\to 1} f(x) \\neq f'(1)$.", "ImagePath": "Math/63" }, { "Question": "The base of a solid is a region bounded by the lines $y = x$, $y = -x$, and $x = 4$, as shown above. What is the volume of the solid if the cross sections perpendicular to the x-axis are equilateral triangles?\n\nA. $\\frac{16\\sqrt{3}}{3}$\n\nB. $\\frac{32\\sqrt{3}}{3}$\n\nC. $\\frac{64\\sqrt{3}}{3}$\n\nD. $\\frac{256\\pi}{3}$", "Answer (final answer highlighted)": "C: Area of a cross section $= \\frac{\\sqrt{3}}{4} (2x)^2 = \\sqrt{3}x^2$.\n\nUsing your calculator, you have:\n\nVolume of solid $= \\int_{0}^{4} \\sqrt{3}(x^2)dx = \\frac{64\\sqrt{3}}{3}$.\n\n\n", "ImagePath": "Math/64" }, { "Question": "Let $f$ be a continuous function on $[0, 6]$ and have selected values as shown below.\nIf you use the subintervals $[0, 2]$, $[2, 4]$, and $[4, 6]$, what is the trapezoidal approximation of $\\int_{0}^{6} f(x) , dx$?\n\nA. 9.5\n\nB. 12.75\n\nC. 19\n\nD. 25.5", "Answer (final answer highlighted)": "B: $\\int_{0}^{6} f(x)dx \\approx \\frac{6 - 0}{2} \\left[ 0 + 2(1) + 2(2.25) + 6.25 \\right] \\approx 12.75$", "ImagePath": "Math/65" }, { "Question": "The graph of $f$ for $-1 \\leq x \\leq 3$ consists of two semicircles, as shown above. What is the value of $\\int_{-1}^{3} f(x) , dx$?\n\nA. 0\n\nB. $\\pi$\n\nC. $2\\pi$\n\nD. $4\\pi$\n", "Answer (final answer highlighted)": "A: $\\int_{-1}^{3} f(x) , dx = \\int_{-1}^{1} f(x) , dx + \\int_{1}^{3} f(x) , dx = \\frac{1}{2} \\pi (1)^2 - \\frac{1}{2} \\pi (1)^2 = 0$", "ImagePath": "Math/66" }, { "Question": "The graph of the polar curve $r = 3 - \\sin \\theta$ is shown above. Which of the following expressions gives the area of the region enclosed by the curve?\n\nA. $\\frac{1}{2} \\int_{0}^{2\\pi} (3 - \\sin \\theta) d\\theta$\n\nB. $\\frac{1}{2} \\int_{0}^{2\\pi} (3 - \\sin \\theta)^2 d\\theta$\n\nC. $\\int_{0}^{2\\pi} (3 - \\sin \\theta) d\\theta$\n\nD. $\\int_{0}^{2\\pi} (3 - \\sin \\theta)^2 d\\theta$", "Answer (final answer highlighted)": "B: To enclose the area, $\\theta$ must sweep through the interval from $0$ to $2\\pi$. The area of the region enclosed by $r = 3 - \\sin \\theta$ is $A = \\frac{1}{2} \\int_{0}^{2\\pi} (3 - \\sin \\theta)^2 d\\theta$.", "ImagePath": "Math/67" }, { "Question": "The graph of the velocity function of a moving particle is shown above. What is the total displacement of the particle during $0 \\leq t \\leq 20$?\n\nA. $20 , \\text{m}$\n\nB. $50 , \\text{m}$\n\nC. $100 , \\text{m}$\n\nD. $500 , \\text{m}$\n", "Answer (final answer highlighted)": "B: $\\int_{0}^{20} v(t)dt = \\frac{1}{2}(40)(5) + \\frac{1}{2}(10)(-20) + \\frac{1}{2}(5)(20) = 50$", "ImagePath": "Math/68" }, { "Question": "A particular solution of the differential equation whose slope field is shown abovecontains point $P$. This solution may also contain which other point?\n\nA. E\nB. B\nC. C\nD. D\n", "Answer (final answer highlighted)": "A: The slope field suggests the curve shown above as a particular solution.", "ImagePath": "Math/69" }, { "Question": "Using the left rectangular method and four subintervals of equal width, estimate $\\int_{0}^{8} |f(t)| , dt$, where $f$ is the function graphed below.\n\nA. 16\n\nB. 5\n\nC. 8\n\nD. 15", "Answer (final answer highlighted)": "A: $2(3) + 2(0) + 2(4) + 2(1)$.\n\n", "ImagePath": "Math/70" }, { "Question": "Use the graph of $f$ shown on $[0,7]$. Let $G(x) = \\int_{2}^{3x-1} f(t) , dt$.\n\n$G'(1)$ is\n\nA. 1\n\nB. 2\n\nC. 3\n\nD. 6\n", "Answer (final answer highlighted)": "D: $G'(x) = f(3x - 1) \\cdot 3$.", "ImagePath": "Math/71" }, { "Question": "Use the graph of $f$ shown on $[0,7]$. Let $G(x) = \\int_{2}^{3x-1} f(t) , dt$.\n\n$G$ has a local maximum at $x =$\n\nA. 1\n\nB. $\\frac{4}{3}$\n\nC. 2\n\nD. 5", "Answer (final answer highlighted)": "B: Since $f$ changes from positive to negative at $t = 3$, $G'$ does also where $3x - 1 = 3$.", "ImagePath": "Math/72" }, { "Question": "Use the graph below, consisting of two line segments and a quarter-circle. The graph shows the velocity of an object during a 6-second interval.\n\nDuring what time interval (in sec) is the speed increasing?\n\nA. $0 < t < 3$\n\nB. $3 < t < 5$\n\nC. $3 < t < 6$\n\nD. $5 < t < 6$", "Answer (final answer highlighted)": "B: Speed is the magnitude of velocity; its graph is shown in the answer explanation for question 20.", "ImagePath": "Math/73" }, { "Question": "The graph of $f$ is shown above. Let $G(x) = \\int_{0}^{x} f(t)dt$ and $H(x) = \\int_{2}^{x} f(t) dt$. Which of the following is true?\n\nA. $G(x) = H(x) + 3$\n\nB. $G'(x) = H'(x + 2)$\n\nC. $G(x) = H(x + 2)$\n\nD. $G(x) = H(x) - 2$\n", "Answer (final answer highlighted)": "A: $G(x) = H(x) + \\int_{0}^{2} f(t) dt$, where $\\int_{0}^{2} f(t) dt$ represents the area of a trapezoid.\n\n", "ImagePath": "Math/74" }, { "Question": "Which function could be a particular solution of the differential equation whose slope field is shown above?\nA. $y = x^3$\nB. $y = \\frac{2x}{x^2 + 1}$\nC. $y = \\frac{x^2}{x^2 + 1}$\nD. $y = \\sin x$", "Answer (final answer highlighted)": "B: Solution curves appear to represent odd functions with a horizontal asymptote. In the figure above, the curve in (B) of the question has been superimposed on the slope field.", "ImagePath": "Math/75" }, { "Question": "The work done in lifting an object is the product of the weight of the object and the distance it is moved. A cylindrical barrel 2 feet in diameter and 4 feet high is half-full of oil weighing 50 pounds per cubic foot. How much work is done, in foot-pounds, in pumping the oil to the top of the tank?\n\nA. $100\\pi$\n\nB. $200\\pi$\n\nC. $300\\pi$\n\nD. $400\\pi$", "Answer (final answer highlighted)": "D: The graph shown has the x-axis as a horizontal asymptote. ", "ImagePath": "Math/76" }, { "Question": "The graph below shows the velocity of an object moving along a line, for $0 \\leq t \\leq 9$.\n\nThe object is farthest from the starting point at $t =$\n\nA. 2\n\nB. 5\n\nC. 6\n\nD. 8\n", "Answer (final answer highlighted)": "C: Velocity $v$ is the derivative of position; because $v > 0$ until $t = 6$ and $v < 0$ thereafter, the position increases until $t = 6$ and then decreases; since the area bounded by the curve above the axis is larger than the area below the axis, the object is farthest from its starting point at $t = 6$.", "ImagePath": "Math/77" }, { "Question": "The equation of the curve shown below is $y = \\frac{4}{1+x^2}$. What does the area of the shaded region equal?\n\nA. $4 - \\frac{\\pi}{4}$\n\nB. $8 - 2\\pi$\n\nC. $8 - \\pi$\n\nD. $8 - \\frac{\\pi}{2}$", "Answer (final answer highlighted)": "B: The required area, $A$, is given by the integral\uff1a$2 \\int_{0}^{1} \\left( \\frac{4}{1+x^2} \\right) dx = 2[4 \\arctan(x)]_{0}^{1} = 2 \\left( 4 - \\frac{\\pi}{4} \\right)$\n\n", "ImagePath": "Math/78" }, { "Question": "Use the following table, which shows the values of the differentiable functions $f$ and $g$.\nThe average rate of change of function $f$ on $[1,4]$ is\n\nA. $\\frac{7}{6}$\n\nB. $\\frac{4}{3}$\n\nC. $\\frac{15}{8}$\n\nD. $\\frac{9}{4}$", "Answer (final answer highlighted)": "B: $f(4) - f(1) = \\frac{6 - 2}{4 - 1} = \\frac{4}{3}$", "ImagePath": "Math/79" }, { "Question": "Use the following table, which shows the values of the differentiable functions $f$ and $g$f $h(x) = g(f(x))$ then $h'(3) =$\n\nA. $\\frac{1}{2}$\n\nB. $1$\n\nC. $4$\n\nD. $6$", "Answer (final answer highlighted)": "B: $h'(3) = g'(f(3)) \\cdot f'(3) = g'(\\frac{1}{4}) \\cdot f'(3) = \\frac{1}{2} \\cdot 2$.", "ImagePath": "Math/80" }, { "Question": "Which equation has the slope field shown below?\n\nA. $\\frac{dy}{dx} = \\frac{5}{y}$\n\nB. $\\frac{dy}{dx} = \\frac{5}{x}$\n\nC. $\\frac{dy}{dx} = \\frac{x}{y}$\n\nD. $\\frac{dy}{dx} = 5y$", "Answer (final answer highlighted)": "A: Note that (1) on a horizontal line the slope segments are all parallel, so the slopes there are all the same and $\\frac{dy}{dx}$ must depend only on $y$; (2) along the x-axis (where $y = 0$) the slopes are infinite; and (3) as $y$ increases, the slope decreases.", "ImagePath": "Math/81" }, { "Question": "The graph below shows the velocity of an object moving along a line, for $0 \\leq t \\leq 9$.\n\nAt what time does the object attain its maximum acceleration?\n\nA. $8 < t < 9$\n\nB. $5 < t < 8$\n\nC. $t = 6$\n\nD. $t = 8$", "Answer (final answer highlighted)": "A: Acceleration is the derivative (the slope) of velocity $v$; $v$ is largest on $8 < t < 9$.", "ImagePath": "Math/82" }, { "Question": "\nHere is the content from the image with the mathematical parts denoted by $:\n\nWater is poured at a constant rate into the conical reservoir shown above. If the depth of the water, $h$, is graphed as a function of time, the graph is\n\nA. concave downward\n\nB. constant\n\nC. linear\n\nD. concave upward", "Answer (final answer highlighted)": "A; As the water gets deeper, the depth increases more slowly. Hence, the rate of change of depth decreases: $\\frac{d^2 h}{dt^2} < 0$.", "ImagePath": "Math/83" }, { "Question": "If $P(x) = g^2(x)$, then $P'(3)$ equals\n\nA. 4\n\nB. 6\n\nC. 9\n\nD. 12", "Answer (final answer highlighted)": "D: $P'(x) = 2g(x) \\cdot g'(x)$", "ImagePath": "Math/84" }, { "Question": "In the table above, if $h(x) = g(f(x))$, then $h'(2) =$\n\nA. 4\n\nB. 2\n\nC. -6\n\nD. -18", "Answer (final answer highlighted)": "D: We can find $h'(x)$ using the Chain Rule. We get: $h'(x) = g'(f(x)) \\cdot f'(x)$. Now, we just have to evaluate $h'(2)$. We get: $h'(2) = g'(f(2)) \\cdot f'(2) = 6 \\cdot -3 = -18$.", "ImagePath": "Math/85" }, { "Question": "Using the subintervals $[0, 2]$, $[2, 5]$, $[5, 7]$, and $[7, 10]$, approximate $\\int_{0}^{10} f(x)dx$ using a left Riemann sum.\n\nA. 102\n\nB. 204\n\nC. 176\n\nD. 242", "Answer (final answer highlighted)": "C: We need to add up the areas of the four rectangles whose widths are the distances between the x-coordinates and whose heights are determined by evaluating $f$ at the left coordinate of each interval. We get: $R = (2)f(0) + (3)f(2) + (2)f(5) + (3)f(7)$. Now we can use the table to find the appropriate values of $f$. We get: $R = (2)(8) + (3)(11) + (2)(20) + (3)(29) = 16 + 33 + 40 + 87 = 176$.", "ImagePath": "Math/86" }, { "Question": "Which of the following is the differential equation of the slope field above?\n\nA. $\\frac{dy}{dx} = x^2 + y^2$\n\nB. $\\frac{dy}{dx} = x^2 - y^2$\n\nC. $\\frac{dy}{dx} = x - y$\n\nD. $\\frac{dy}{dx} = (x + y)^2$", "Answer (final answer highlighted)": "A: We can find the correct differential equation by testing some values of $x$ and $y$ and seeing what the slope is at those values. At the origin, the slope is $0$, which unfortunately, does not eliminate any of the choices. At $(1, 1)$, the slope is positive, which eliminates (B) and (D). At $(-1, -1)$, the slope is again positive, which eliminates (C). This leaves (A).", "ImagePath": "Math/87" }, { "Question": "If $g(x) = \\int_{0}^{x^2} f(t) , dt$, what is $g'(2)$?\n\nA. 32\n\nB. 16\n\nC. 8\n\nD. 4", "Answer (final answer highlighted)": "C: The Second Fundamental Theorem of Calculus says that $\\frac{d}{dx} \\int_{c}^{x^2} f(t),dt = f'(x)$. Here, we get: $g'(x) = \\frac{d}{dx} \\int_{0}^{x^2} f(t),dt = f'(x) \\cdot x^2$. Therefore, $g'(2) = f'(4) \\cdot 4$. From the graph, we can see that $f(4) = 2$, so $g'(2) = 2 \\cdot 4 = 8$.", "ImagePath": "Math/88" }, { "Question": "The graph of $f$ is shown in the figure above. If $g(x) = \\int_{0}^{x} f(t) , dt$, for what positive value of $x$ does $g(x)$ have a minimum?\n\nA. 1\n\nB. 2\n\nC. 3\n\nD. 4", "Answer (final answer highlighted)": "D: If we want to find where $g(x)$ is a minimum, we can look at $g'(x)$. The Second Fundamental Theorem of Calculus tells us how to find the derivative of an integral: $\\frac{d}{dx} \\int_{c}^{x} f(t) , dt = f(x)$, where $c$ is a constant. Thus, $g'(x) = f(x)$. The graph of $f$ is zero at $x = 0$, $x = 2$, and $x = 4$. We can eliminate $x = 0$ because we are looking for a positive value of $x$. Next, notice that $f$ is negative to the left of $x = 4$ and positive to the right of $x = 4$. Thus, $g(x)$ has a minimum at $x = 4$.\n\nWe also could have found the answer geometrically. The function $g(x) = \\int_{0}^{x} f(t) , dt$ is called an accumulation function and stands for the area between the curve and the x-axis to the point $x$. Thus, the value of $g$ grows from $x = 0$ to $x = 2$. Then, because we subtract the area under the x-axis from the area above it, the value of $g$ shrinks from $x = 2$ to $x = 4$. The value begins to grow again after $x = 4$.", "ImagePath": "Math/89" }, { "Question": "In the northern United States, schools are sometimes closed during winter due to severe snowstorms. At the end of the school year, schools have to make up for the days missed. The following graph shows the frequency distribution of the number of days missed due to snowstorms per year using data collected from the past 75 years. Which of the following should be used to describe the center of this distribution?\n\nA. Mean, because it is an unbiased estimator\nB. Median, because the distribution is skewed\nC. IQR, because it excludes outliers and includes only the middle 50 percent of data\nD. First quartile, because the distribution is left skewed\nE. Standard deviation, because it is unaffected by the outliers\n", "Answer (final answer highlighted)": "B:QR, first quartile, and standard deviation are not measures of central tendency. Median and mean are measures of central tendency. The mean is affected by extreme observations\u2014large observations tend to make the mean higher. Because this distribution is skewed, the median should be used to describe the center of the distribution. Note that the median is not affected by the extreme measurements.\n", "ImagePath": "Math/90" }, { "Question": "2. The table shows some of the values of differentiable functions $f$ and $g$ and their derivatives. If $h(x) = f(g(x))$, then $h'(2)$ equals\n\n\nA. -2\n\nB. -1\n\nC. 0\n\nD. 1\n\n", "Answer (final answer highlighted)": "B: The correct answer is (B). Since $h(x) = f(g(x))$, $h'(x) = f'(g(x)) \\cdot g'(x)$ and $h'(2) = f'(g(2)) \\cdot g'(2) = f'(3) \\cdot 1 = -1.", "ImagePath": "Math/91" }, { "Question": "The graph of $f$ is shown above, and $f$ is twice differentiable. Which of the following has the largest value?\n\nI. $f(0)$\nII. $f'(0)$\nIII. $f''(0)$\n\nA. I\nB. II\nC. III\nD. I and II\n\n\n", "Answer (final answer highlighted)": "C: Since $f$ is decreasing, $f' < 0$ and since $f$ is concave up, $f'' > 0$. The graph also shows that $f(0) < 0$. Thus $f''(0)$ has the largest value.", "ImagePath": "Math/92" }, { "Question": "A slope field for a differential equation is shown above. Which of the following could be the differential equation?\n\nA. $\\frac{dx}{dy} = 2x$\n\nB. $\\frac{dx}{dy} = -2x$\n\nC. $\\frac{dx}{dy} = y$\n\nD. $\\frac{dx}{dy} = x - y$\n\n\n\n", "Answer (final answer highlighted)": "B: Note that for each column, all the tangents have the same slope. For example, when $x = 0$ all tangents are horizontal, which is to say their slopes are all zero. This implies that the slope of the tangents depends solely on the $x$-coordinate of the point and is independent of the $y$-coordinate. Also note that when $x > 0$ slopes are negative, and when $x < 0$ slopes are positive. Thus, the only differential equation that satisfies these conditions is $\\frac{dy}{dx} = -2x$.\n", "ImagePath": "Math/93" }, { "Question": "The graph of $f''$, the second derivative of $f$ is shown above. The graph of $f''$ has horizontal tangents at $x = -2$ and $x = 2$. For what values of $x$ does the graph of the function $f$ have a point of inflection?\n\nA. -4, 0 and 4\n\nB. -2, 0 and 2\n\nC. -4 and 4 only\n\nD. 0 only", "Answer (final answer highlighted)": "A: Note that $f'' > 0$ on the intervals $(-\\infty, -4)$ and $(0, 4)$. Thus the graph of the function $f$ is concave up on these intervals. Similarly, $f'' < 0$ and concave down on the intervals $(-4, 0)$ and $(4, \\infty)$. Therefore $f$ has a point of inflection at $x = -4, 0$, and $4$.\n", "ImagePath": "Math/94" }, { "Question": "The figure below shows the portions of the graphs of the ray $\\theta = \\frac{\\pi}{4}$ and the curve $r = 2 \\cos \\theta + \\sin \\theta$ that lie in the first quadrant. Which of the following integrals expresses the area of the shaded region $R$?\nA. $\\int_{0}^{\\frac{\\pi}{4}} (\\frac{\\pi}{4} - r) d\\theta$\n\nB. $\\int_{0}^{\\frac{\\pi}{4}} r^2 d\\theta$\n\nC. $\\int_{0}^{\\frac{\\pi}{4}} \\frac{r^2}{2} d\\theta$\n\nD. $\\int_{0}^{1.6} (\\frac{\\pi}{4} - \\frac{r^2}{2}) d\\theta$\n", "Answer (final answer highlighted)": "C: The area of a simple region enclosed by a polar curve $r$ between two rays $\\theta = \\alpha$ and $\\theta = \\beta$ is $\\int_{\\alpha}^{\\beta} \\frac{r^2}{2} d\\theta$.\n\nIn our case, the simple polar region $R$ is enclosed by $r$ and the rays $\\theta = 0$ and $\\theta = \\frac{\\pi}{4}$; therefore, the integral in answer (C) expresses the area of $R$.\n", "ImagePath": "Math/95" }, { "Question": "The graphs of the polar curves $r = 2 + \\cos \\theta$ and $r = -3 \\cos \\theta$ are shown on the graph below. The curves intersect when $\\theta = \\frac{2\\pi}{3}$ and $\\theta = \\frac{4\\pi}{3}$. Region $R$ is in the second quadrant, bordered by each curve and the y-axis.\nSet up but do not evaluate a formula to find the area of $R$.\n\nA. $\\frac{1}{2} \\int_{\\frac{2\\pi}{3}}^{\\frac{4\\pi}{3}} ((2 + \\cos \\theta)^2 - (-3 \\cos \\theta)^2) d\\theta$\n\nB. $\\int_{\\frac{2\\pi}{3}}^{\\frac{4\\pi}{3}} ((2 + \\cos \\theta)^2 - (-3 \\cos \\theta)^2) d\\theta$\n\nC. $\\frac{1}{2} \\int_{\\frac{2\\pi}{3}}^{\\frac{4\\pi}{3}} ((-3 \\cos \\theta)^2 - (2 + \\cos \\theta)^2) d\\theta$\n\nD. $\\frac{3}{4} \\int_{\\frac{2\\pi}{3}}^{\\frac{4\\pi}{3}} ((-3 \\cos \\theta)^2 - (2 + \\cos \\theta)^2) d\\theta$", "Answer (final answer highlighted)": "C: When you see sine and cosine, most of the time it will involve the Pythagorean theorem, which states $\\sin^2 x + \\cos^2 x = 1$. You will want to solve for sine and cosine: $\\frac{x}{2} = \\sin t$ and $\\frac{y}{3} = \\cos t$. Now square both to get $\\frac{x^2}{4} = \\sin^2 t$ and $\\frac{y^2}{9} = \\cos^2 t$. Add the equations and simplify.\n\n$\\frac{x^2}{4} + \\frac{y^2}{9} = \\sin^2 t + \\cos^2 t = 1$\n\nHence, (C) is correct.", "ImagePath": "Math/96" }, { "Question": "The graph of the function $f$ is shown above. Which of the following statements is false?\n\nA. $\\lim_{x \\to 1} f(x) = \\infty$\n\nB. $\\lim_{x \\to 3} f(x) = 1$\n\nC. $\\lim_{x \\to 4} f(x) = 6$\n\nD. $\\lim_{x \\to 5} f(x) = 4$", "Answer (final answer highlighted)": "D: The limit of a function exists at $x = a$ if both one-sided limits approach the same value. The limit does not have to equal the actual value of the function at that point. For this function, the limit from the left and from the right of $x = 1$ is $+\\infty$ (because the graph increases without bound on both sides of the vertical asymptote), so the limit equals $\\infty$ and you can eliminate (A). The limit from the left and from the right of $x = 3$ is 1 (even though $f(3)$ is 0), so eliminate (B). The limit from the left and from the right of $x = 4$ is 6, so eliminate (C). This means (D) must be correct. (The limit from the left of $x = 5$ is 4, while the limit from the right is 3, so the limit does not exist.)\n\n", "ImagePath": "Math/97" }, { "Question": "Let $h(x)$ be continuous on $[-5, -2]$ with some of the values shown in the following table:\nIf $h(x) = -1$ has no solutions on the interval $[-5, -2]$, which of the following values are possible for $a$?\n\nI. -4\nII. -3\nIII. 0\n\nA. I only\nB. II only\nC. III only\nD. I and II only", "Answer (final answer highlighted)": "D: Since the function is continuous and never attains a value of $-1$ on the interval, neither will it attain any value greater than $-1$. Therefore, only $-4$ and $-3$ are possible values for $a$. See the discussion of the intermediate value theorem in 20.\n", "ImagePath": "Math/98" }, { "Question": "The function $f$ is continuous and differentiable on $0 < x < 10$. Use the table of values to determine an interval for which according to the mean value theorem $f'(c) = 0$ for some $c$ on the interval.\n\nA. $6 < x < 7$\n\nB. $5 < x < 7$\n\nC. $1 < x < 7$\n\nD. $5 < x < 6$\n", "Answer (final answer highlighted)": "C: The mean value theorem requires two points whose secant line has a slope equal to the slope of the tangent line. The slope of the tangent line is $f'(1, 5)$ and $(7, 5)$ are the only two points which qualify. The interval is $a < x < b$ or $1 < x < 7$.\n", "ImagePath": "Math/99" }, { "Question": "The table below includes all critical points of the continuous function $g(x)$. Use the table to determine where the function $g(x)$ is increasing within the interval $-2 < x < 20$.A. $0 < x < 9.08$ and $14 < x < 20$\n\nB. $-2 < x < 0$ \nC. $-2 < x < -0.94$\n\nD. $-2 < x < -0.94$ and $14 < x < 20$", "Answer (final answer highlighted)": "A: Notice that the information given is about $g(x)$, not $g'(x)$. A function can only change from increasing to decreasing or from decreasing to increasing at a critical point. $g(x)$ increases from $-0.33$ to $0$ on the interval $0 < x < 9.08$ and from $-7.3$ to $-4.4$ on the interval $14 < x < 20$. $g(x)$ is increasing on $0 < x < 9.08$ and $14 < x < 20$.\n", "ImagePath": "Math/100" }, { "Question": "Which of the following statements are true of the graph of $f$ below?www.apstudy.net\nI. $f' \\geq 0$ on the interval from D to F\nII. $f'' = 0$ at points B, D, and F\nIII. $f'' > 0$ on the interval from A to B\nIV. $f'' > 0$ on the interval from D to F\n\nA. I and II\nB. I and III\nC. II and IV\nD. II, III, and IV", "Answer (final answer highlighted)": "A\uff1a Statement I is correct since $f$ is strictly increasing on the interval from D to F. Statement II is true since there is a horizontal tangent to the curve at points B, D, and F, implying $f' = 0$. Statement III is false since $f$ is concave downward on the interval from A to B. Statement IV is false since $f$ is concave upward only on the interval from D to E. The function is concave downward from E to F, so $f'' < 0$ for that interval.\n", "ImagePath": "Math/101" }, { "Question": "Given the table below, find the slope of the tangent line of $\\frac{f(x)}{g(x)}$ at the point $x = 2$.\n\n \nA. $\\frac{5}{7}$\n\nB. $\\frac{19}{9}$\n\nC. $-\\frac{55}{9}$\n\nD. Undefined\n\n", "Answer (final answer highlighted)": "C: At $x = 2$, $\\left(\\frac{f}{g}\\right)'$ is $\\frac{f'(2)g(2) - f(2)g'(2)}{(g(2))^2}$, which equals $\\frac{5(3) - 10(7)}{9}$, which simplifies to $-\\frac{55}{9}$.", "ImagePath": "Math/102" }, { "Question": "Find the area of the region bounded by the graphs of $f(x) = x^3$ and $g(x) = 3x^2 - 2x$ shown below.The graph of the acceleration function of a moving particle is shown below. On what intervals in $[0, 20]$ does the particle have a positive change in velocity, and what is the change in velocity of the particle over the entire interval $[0, 20]$?\n\nA. $[5, 15]$ and $-\\frac{25}{2}$ m/s\n\nB. $[5, 15]$ and $\\frac{25}{2}$ m/s\n\nC. $[0, 10]$ and $1$ m/s\n\nD. $[0, 10]$ and $\\frac{125}{2}$ m/s", "Answer (final answer highlighted)": "A: Recall that $a(t) = \\int v(t) dt$ and integrals represent net change, so the area under the curve represents change in velocity. This area is positive for $[5, 15]$. To find the total change in velocity you calculate the area under the curve. Area above the x-axis is positive, and area below the x-axis is negative.\n\nTotal change in velocity is $= -(5)(10) \\left(\\frac{1}{2}\\right) + (10)(5) \\left(\\frac{1}{2}\\right) - (5)(5) \\left(\\frac{1}{2}\\right) = -\\frac{25}{2}$ m/s.", "ImagePath": "Math/103" }, { "Question": "The graph of the acceleration function of a moving particle is shown below. On what intervals in $[0, 20]$ does the particle have a positive change in velocity, and what is the change in velocity of the particle over the entire interval $[0, 20]$?\n\nA. $[5, 15]$ and $-\\frac{25}{2} \\text{ m/s}$\n\nB. $[5, 15]$ and $\\frac{25}{2} \\text{ m/s}$\n\nC. $[0, 10]$ and $1 \\text{ m/s}$\n\nD. $[0, 10]$ and $\\frac{125}{2} \\text{ m/s}$\n", "Answer (final answer highlighted)": "A: Recall that $a(t) = \\int v(t) , dt$ and integrals represent net change, so the area under the curve represents change in velocity. This area is positive for $[5, 15]$. To find the total change in velocity you calculate the area under the curve. Area above the x-axis is positive, and area below the x-axis is negative.\n\nTotal change in velocity is $= -(5)(10) \\left(\\frac{1}{2}\\right) + (10)(5) \\left(\\frac{1}{2}\\right) - (5)(5) \\left(\\frac{1}{2}\\right) = -\\frac{25}{2} \\text{ m/s}$.\n\n\n\n\n\n\n", "ImagePath": "Math/104" }, { "Question": "A particle is moving along a straight line, and its acceleration is shown below. Assuming the particle started at rest, calculate the speed of the particle after 3 s.\n\nA. $-3$ m/s\n\nB. $\\frac{3}{2}$ m/s\n\nC. $0$ m/s\n\nD. $3$ m/s", "Answer (final answer highlighted)": "E: The integral of acceleration is velocity. The area under the curve in the interval $[0,3]$ is triangular and below the x-axis:\n$-\\left(\\frac{3}{2}\\cdot 2.5\\right) = -3$ m/s\n\nSince speed is the absolute value of velocity, the correct answer is $3$ m/s.\n", "ImagePath": "Math/105" }, { "Question": "The graph of the function f is shown above. For how many values of x in the open interval (-3, 6) is f discontinuous?\nA. two\nB. three\nC. four\nD. five\n", "Answer (final answer highlighted)": "B A function is continuous at a value of x (e.g., x = 2) if https://img.apstudy.net/ap/calculus-bc/kp21/390ef1efbadf4286bccf10941a7dbb44.png . Graphically, this means that a function is continuous if you can draw its graph without lifting up your pencil. Here, you would have to lift your pencil at x = -1.5, at x = 3, and again at x = 4. Thus, the function is not continuous (and therefore discontinuous) for three values of x in the interval (-3, 6), making (B) the correct answer.", "ImagePath": "Math/106" }, { "Question": "Let g be defined as shown above. If g is continuous for all real numbers, what is the value of k ?\nA. -6\nB. -10\nC. 0\nD. 4\n", "Answer (final answer highlighted)": "A You are given a piecewise function g and told that it is continuous for all real numbers. Both individual \"pieces\" of the function are continuous on their own, so all you need to check is where the function breaks, which is at x = 3. To be continuous at x = 3, https://img.apstudy.net/ap/calculus-bc/kp21/3533b661ae60464eb24f291bb8f73ee5.png must equal https://img.apstudy.net/ap/calculus-bc/kp21/6d035923cc8d461493a40c448da2968a.png", "ImagePath": "Math/107" }, { "Question": "Part of the graph of f on the closed interval [-5, 5] is shown above. If f is discontinuous for only one value of x in the open interval (-5, 5), then what must f(1) equal?\nA. -4\nB. 4\nC. f(1) can take on any value.\nD. f(1) cannot be determined.\n", "Answer (final answer highlighted)": "A The graph shown has a gap at x = -2 and a hole at x = 1. For there to be only one discontinuity, one of the apparent discontinuities needs to be continuous. It's not possible to make the gap continuous, but if f(1) = -4, the discontinuity is eliminated, leaving f with only one discontinuity. Thus, (A) is correct.", "ImagePath": "Math/108" }, { "Question": "A. 0\nB. 10\nC. 25\nD. nonexistent\n", "Answer (final answer highlighted)": "B Memorize the limit definition of the derivative before Test Day: https://img.apstudy.net/ap/calculus-bc/kp21/e7acb89e5c1040249ad62f7f9e17b1a4.png . Notice that both terms in the numerator are being squared, so https://img.apstudy.net/ap/calculus-bc/kp21/5bdc8a4e04ee4f4389deaf873a8c8eb3.png (B) is correct. Note that you could also use L'H\u00f4pital's rule to find the limit.", "ImagePath": "Math/109" }, { "Question": "The graph of f(x) is given above. Which of the following statements is true about f\"(x) ?\nA. f\"(x) > 0 for all values of x \nB. f\"(x) < 0 for all values of x \nC. f\"(x) < 0 for -2 < x < -1 and f\"(x) > 0 for -1 < x < 1 and x > 2\nD. f\"(x) > 0 for -2 < x < 0 and x > 2, and f\"(x) < 0 for 0 < x < 2\n", "Answer (final answer highlighted)": "D This question is all about knowing what the second derivative tells you about a graph: f\"(x) > 0 means the second derivative is positive, which tells you the graph of f is concave up (a cup that opens up). Similarly, f\"(x) < 0 means the second derivative is negative, which tells you the graph of f is concave down (a cup that opens down). The concavity of this graph changes, so eliminate (A) and (B). The graph is concave up in the range -2 < x < 0 and x > 2, and concave down in the range 0 < x < 2, so (D) is correct.", "ImagePath": "Math/110" }, { "Question": "Consider the graph of f(x) shown above. Which of the following statements is true about f ?\nA. f\"(x) > 0 for 1 < x < 2\nB. f\"(x) < 0 for 1 < x < 2\nC. f'(x) > 0 for 0 < x < 1 and 2 < x < 3\nD. f'(x) < 0 for 0 < x < 1 and 2 < x < 3\n", "Answer (final answer highlighted)": "A This question is all about knowing what the first and second derivatives tell you about a graph. Examine each statement, one at a time. Cross out false statements as you go. (A): The given graph is of the function itself. If f\"(x) > 0, the second derivative is positive, and the graph is concave up (a cup that opens up). This graph is indeed concave up for 1 < x < 2, so (A) is correct. There is no need to check the other statements unless you're not sure of your answer, but just in case you're curious ... (B): f\"(x) < 0 means the graph is concave down (a cup that opens down). This graph is concave up, not down, between 1 < x < 2, so this statement is false. (C): f'(x) > 0 means the graph is increasing. This graph increases for approximately the first half of the interval 0 < x < 1, but then decreases for the second half of the interval, so this statement is false. (D): f'(x) < 0 means the graph is decreasing. This graph increases for approximately the first half of the interval 0 < x < 1, so this statement is false.", "ImagePath": "Math/111" }, { "Question": "The graph of a piecewise-defined function f is shown above. The graph has a vertical tangent at x = 3 and horizontal tangent lines at x = 1.5 and x = 4.5. What are all values of x, for -4 < x < 6, at which f is continuous but not differentiable?\nA. x = 0\nB. x = -2 and x = 3\nC. x = 1.5 and x = 4.5\nD. x = -2, x = 0, and x = 3\n", "Answer (final answer highlighted)": "B The question is asking for points at which f is continuous but not differentiable. That means you need to identify the points where you would not lift up your pencil if you were drawing the graph (so f is continuous), but where the derivative is undefined. This occurs at sharp turns or corners, like those at the vertex of an absolute value function, and at points where the tangent line is vertical. Here, you have two such points: a corner point at x = -2 and a vertical tangent at x = 3. This means (B) is the correct answer. Be careful of (D). While the function is not differentiable at x = 0, it is also not continuous there.", "ImagePath": "Math/112" }, { "Question": "The graph of a function g is shown above. At which of the following points is g'(x) positive and decreasing?\nA. a\nB. b\nC. c\nD. d\n", "Answer (final answer highlighted)": "A This question is asking where the first derivative is positive and decreasing. A positive first derivative, or g'(x) > 0, is represented graphically by a positive slope. Only the points at a and c have positive slopes, so eliminate (B) and (D). For the first derivative to be decreasing, g\"(x) must be negative. In other words, the graph must be concave down. This is true at a, but not at c, so (A) is the correct answer.", "ImagePath": "Math/113" }, { "Question": "The graph of y = f(x) is shown above. For which of the following values of x is f'(x) negative and increasing?\nA. a\nB. b\nC. c\nD. d\n", "Answer (final answer highlighted)": "D This problem is asking where the first derivative of f is negative and increasing. A negative first derivative, or f'(x) < 0, is represented graphically by a negative slope. The points at a, c, and d have negative slopes, so eliminate (B). For the first derivative to be increasing, f\"(x) must be positive. In other words, the graph must be concave up. This is true at d, but not at a or c, so (D) is the correct answer.", "ImagePath": "Math/114" }, { "Question": "The graph of the derivative of f, f\u00e2\u0080\u00b2, is shown above. If f(0) = 7, what is f(6) ?\nA. 9\nB. 12\nC. 14\nD. 15\n", "Answer (final answer highlighted)": "D To find f(6), compute f(6) = f(0) + total change in f on 0 \u00e2\u0089\u00a4 x \u00e2\u0089\u00a4 6. The area under the graph of f\u00e2\u0080\u00b2 from x = 0 to x = 6 gives the total change in f on 0 \u00e2\u0089\u00a4 x \u00e2\u0089\u00a4 6. Express this as the definite integral: https://img.apstudy.net/ap/calculus-bc/kp21/02e8c4b4a8dd45aa8fb2f6f81feb177e.png The definite integral https://img.apstudy.net/ap/calculus-bc/kp21/93a029f7799b4d32b4b0439c8608aa1c.png is the area under the graph of f\u00e2\u0080\u00b2. To compute this area, break it into three regions, as shown below: https://img.apstudy.net/ap/calculus-bc/kp21/chapter14_ch22_figure_text_un418.png The area under the curve is therefore Area of rectangle A + Area of triangle B - Area of triangle C. Note that the area of triangle C is subtracted because the definite integral considers the area beneath the x-axis to be negative. This gives: https://img.apstudy.net/ap/calculus-bc/kp21/dfbc5d1d557a49d39339539847427da6.png Adding this to f(0) = 7 yields (D). https://img.apstudy.net/ap/calculus-bc/kp21/538c1ff8dd2a44919391339c3f1aba6d.png", "ImagePath": "Math/115" }, { "Question": "The acceleration of an airplane from the moment of liftoff (t = 0) to 20 minutes into the flight is shown above. If the speed at liftoff is 900 ft/min, what is the speed of the plane after 20 minutes?\nA. 610 ft/min\nB. 900 ft/min\nC. 1,510 ft/min\nD. 1,800 ft/min\n", "Answer (final answer highlighted)": "C Think of this as an accumulation problem. The speed of the airplane 20 minutes after liftoff is the initial speed plus the change in speed on 0 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 20. The change in speed is given by the definite integral https://img.apstudy.net/ap/calculus-bc/kp21/f61cdc87ac3d436fbca818bac205266d.png Therefore: https://img.apstudy.net/ap/calculus-bc/kp21/9fb433ccddc1470abd4e1345eff78aa3.png The definite integral https://img.apstudy.net/ap/calculus-bc/kp21/4587a96ef2a449eb866dadf87b9542d4.png is the area under the acceleration curve on 0 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 20. Break this area into two regions: trapezoid A and rectangle B: https://img.apstudy.net/ap/calculus-bc/kp21/chapter14_ch22_figure_text_un421.png https://img.apstudy.net/ap/calculus-bc/kp21/06373c3cd4654018b18eaa7828668217.png Therefore, the speed at t = 20 is s(20) = 900 + 610 = 1,510 ft/min, which is (C).", "ImagePath": "Math/116" }, { "Question": "The graph of a function f is shown above. Which of the following statements about f is true?\nA. An infinite discontinuity occurs at x = 4.\nB. A jump discontinuity occurs at x = 3.\nC. A removable discontinuity occurs at x = 2.\nD. A jump discontinuity occurs at x = 1.\n", "Answer (final answer highlighted)": "D Examine the discontinuity at each value of x. The graph is continuous at x = 4, so (A) is not correct. The discontinuity at x = 3 is a removable discontinuity (a hole), so (B) is not correct. The discontinuity at x = 2 is an infinite discontinuity (a vertical asymptote), so (C) is not correct. That leaves (D) as the correct choice. The discontinuity at x = 1 is a jump discontinuity because there is a gap in the graph there.", "ImagePath": "Math/117" }, { "Question": "Let g be the function given above. If g is continuous for all real numbers, what is the value of k ?\nA. -6\nB. -3\nC. 0\nD. 2\n", "Answer (final answer highlighted)": "A You are given a piecewise function g and told that it is continuous for all real numbers. Both individual functions, or \"pieces,\" are continuous on their own, so all you need to check is where the function potentially splits, which is at x = 2. To be continuous at x = 2, https://img.apstudy.net/ap/calculus-bc/kp21/286a8054549e49a492a6109d34629fec.png must equal https://img.apstudy.net/ap/calculus-bc/kp21/f49b21b013d14fdeb79c48cf223216ee.png", "ImagePath": "Math/118" }, { "Question": "The graph of f(x) appears above. Which of the following could be the zeros of the derivative function f\u00e2\u0080\u00b2(x) ?\nA. x = -2, 2.5\nB. x = -3, 1, 4\nC. x = -2, -1, 2.5\nD. x = -4, -1, 3, 5\n", "Answer (final answer highlighted)": "B The zeros of the derivative function f\u00e2\u0080\u00b2(x) are the values of x at which f(x) has a horizontal tangent, in this case at the relative minimums and maximums. Here, this occurs at x = -3 (a relative minimum), x = 1 (a relative maximum), and x = 4 (a relative minimum). That's (B).", "ImagePath": "Math/119" }, { "Question": "The position of a particle, s, is given above for 0 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 10. On what interval(s) is the particle slowing down?\nA. 2 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 6\nB. 0 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 4\nC. 0 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 2 UU 4 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 6\nD. 2 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 6 U 6 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 10\n", "Answer (final answer highlighted)": "C A particle is slowing down when the velocity and acceleration have opposite signs. This means you need to take the derivative of s to find velocity, v, and the second derivative to find acceleration, a. The result is v(t ) = s\u00e2\u0080\u00b2(t) = t2 - 8t + 12 and a(t) = v\u00e2\u0080\u00b2(t) = 2t - 8. The easiest way to determine where v and a have opposite signs is to graph their equations on your calculator. You're only interested in the interval from 0 to 10, so adjust your window accordingly. The graph should look like this: https://img.apstudy.net/ap/calculus-bc/kp21/chapter23_pt1_q83_a_e.png Examine the graph to find that the velocity and acceleration have opposite signs (one is above the x-axis while the other is below) on the intervals 0 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 2 and 4 \u00e2\u0089\u00a4 t \u00e2\u0089\u00a4 6, which is (C). Note that you could also find where v and a are equal to zero and where they are positive and negative by hand, but using your calculator is the more efficient method.", "ImagePath": "Math/120" }, { "Question": "The graph of a function f is given above. Based on the graph, which of the following statements is true?\nA. f is continuous and differentiable everywhere and f\u00e2\u0080\u00b2(2) = 0.\nB. f is continuous everywhere and differentiable everywhere except at x = 2.\nC. f is discontinuous at x = 2 and f is differentiable everywhere except at x = 2.\nD. f is discontinuous at x = 2, f is differentiable everywhere, and f\u00e2\u0080\u00b2(2) = 0.\n", "Answer (final answer highlighted)": "B This question is testing your knowledge of what continuity and differentiability mean graphically. Continuity is the more intuitive concept: You don't need to take your pencil off the page to trace the graph where it is continuous. This means you can immediately eliminate (C) and (D). Next, recall that the derivative of a function at a point corresponds to the slope of the tangent line to the graph at that point. There is no tangent line to the function at the point where x = 2 (because there is a sharp corner), but there is a tangent line at every other point. From this, you can eliminate (A), leaving (B) as the correct answer. Careful-don't be fooled into thinking that f\u00e2\u0080\u00b2(2) = 0 just because the graph has a minimum there. It would have to be differentiable there too, and it is not.", "ImagePath": "Math/121" }, { "Question": "The graph above shows the polar curve r = 3\u00ce\u00b8 + sin \u00ce\u00b8 for 0 \u00e2\u0089\u00a4 \u00ce\u00b8 \u00e2\u0089\u00a4 \u00cf\u0080 . Let R be the region bounded by the polar curve and the x-axis. What is the area of R?\nA. 16.804\nB. 20.923\nC. 56.720\nD. 113.439\n", "Answer (final answer highlighted)": "C The equation for finding a region bounded by a polar curve is https://img.apstudy.net/ap/calculus-bc/kp21/79539ab614b74eb89e67f41e0a480ba5.png https://img.apstudy.net/ap/calculus-bc/kp21/403a2365da3640efa865d151aca09780.png Hence, (C) is correct.", "ImagePath": "Math/122" }, { "Question": "Question: 17\nWhat is the purpose of the chart shown below?\n \nA. To identify the standard deviation of revenue compared to profit\nB. To identify whether the mean profit is larger than the mode revenue\nC. To make a multivariate projection of sales based on revenue and profit\nD. To determine whether there is any correlation between revenue and profit\nE. To observe whether there is any causation going from revenue to profit\n", "Answer (final answer highlighted)": "(D) The chart shown is a scatter plot, and its function is to show the values of up to two variables. It can also be used to observe whether there is any correlation if two variables are plotted.", "ImagePath": "Math/123" }, { "Question": "Question: 21\nDescribe the shape of the histogram below.\n \nA. Normal\nB. Bimodal\nC. Skewed right\nD. Skewed left\nE. Uniform\n", "Answer (final answer highlighted)": "(E) Uniform describes the shape of this histogram because the bars are approximately the same height, which represents approximately equal frequencies.", "ImagePath": "Math/124" }, { "Question": "Question: 22\nTwo college professors are grading several papers and are required to draw histograms to show the grade distribution at the end of the semester. The test scores are graded on a range of 0 to 100 points. Which of the following claims is correct?\n \nA. The exam results graded by the first professor have a right-skewed distribution because the median is different from the standard deviation.\nB. The exam results graded by the second professor have a normal distribution because the mode and mean are equal.\nC. The exam results graded by the first professor have a normal distribution because the mean, median, and average are the same.\nD. The exam results for the first professor cannot be visually represented because two of the students achieved all of the points available.\nE. The exam results for the second professor have a right-skewed distribution because the mode and mean are larger than the median.\n", "Answer (final answer highlighted)": "(C) The exam results for the first professor, as can be seen from the table, follow a normal distribution where the median, mode, and mean are all the same.", "ImagePath": "Math/125" }, { "Question": "Question: 24\nFind the mean and the median in the dot plot below (n = 20).\n \nA. Mean: 12.9; median: 13\nB. Mean: 12.4; median: 13\nC. Mean: 12.9; median: 13.5\nD. Mean: 12.9; median: 14\nE. Mean: 12.4; median: 14\n", "Answer (final answer highlighted)": "(C) Recall that in a dot plot, each dot represents a single data value. Thus the mean is (5 + 7 + 8 + 9 + 10 + 10 + 11 + 11 + 12 + 13 + 14 + 14 + 14 +15 + 16 + 17 + 17 +18 + 18 19)/20 = 12.9. The median is 13.5 = (13 + 14)/2, since the number of data points is even.", "ImagePath": "Math/126" }, { "Question": "Question: 25\nFind the number of data values represented and the median for the stem plot below.\n \nA. n = 13; median: 36.5\nB. n = 20; median: 36.56\nC. n = 24; median: 32\nD. n = 13; median: 34\nE. n = 20; median: 34\n", "Answer (final answer highlighted)": "(E) In a stem plot, each leaf represents a single value. Counting the number of leaves, there are a total of 20, so n = 20.; The median is 34 = (34 + 34)/2 since the number of data points is even.", "ImagePath": "Math/127" }, { "Question": "Question: 26\nData values represented by the bar labeled \"10\" in the histogram below fall into which range?\n \nA. 7.5 up to 12.5\nB. 7.25 up to 12.75\nC. 8.5 up to 11.5\nD. 8.75 up to 11.75\nE. 8.75 up to 11.25\n", "Answer (final answer highlighted)": "(E) The boundaries are midway between the bar labels: left boundary: (7.5 + 10)/2 = 8.75; right boundary: (10 + 12.5)/2 = 11.25. Values represented by the bar therefore lie in the range 8.75 up to 11.25.", "ImagePath": "Math/128" }, { "Question": "Question: 27\nThe variable marked with x in the table below is of an unknown value. If the mean of the dataset is 15, what is the value of x?\n \nA. The value of x is 1.\nB. The value of x is 3.\nC. The value of x is 21.\nD. The value of x is 7.5.\nE. The value of x is 5.\n", "Answer (final answer highlighted)": "(C) To calculate the value of x, we must understand that the mean is calculated by the sum of all of the figures divided by the number of figures. The sum of the values shown in the table is 104. As there are 6 known values and x, making a total of 7, this means that: With a simple multiplication of both sides of the equation with 7, we can conclude that: 104 + x = 105 Meaning that x has the value of 1.", "ImagePath": "Math/129" }, { "Question": "Question: 28\nThe variable marked with y has the smallest value of the dataset. If the range of the dataset is 23, what is the value of y and what is the mean?\n \nA. The value of y is 11, while the mean is 19.\nB. The value of y is 57, while the mean is 28.2.\nC. The value of y is 23, while the mean is 21.4.\nD. The value of y is 26, while the mean is 22.\nE. The value of y is 29, while the mean is 22.75.\n", "Answer (final answer highlighted)": "(A) The range is defined as the maximum minus the minimum value of the dataset. As the largest value is 34 and y is defined as the lowest value, meaning the minimum, this means that x = 34 - 23, which is equal to 11. Calculating the mean simply requires summing all of the values and dividing them by 5, which yields a mean value of 19.", "ImagePath": "Math/130" }, { "Question": "Question: 33\nFind the five-number summary from the box plot and calculate the interquartile range.\n \nA. Min: 4; Q1: 5.75; Med: 9.5; Q3: 13.75; Max: 16; IQR: 8\nB. Min: 3; Q1: 5.75; Med: 10.5; Q3: 13.75; Max: 16; IQR: 8\nC. Min: 3; Q1: 5.75; Med: 9.5; Q3: 13.75; Max: 15; IQR: 8\nD. Min: 3; Q1: 5.75; Med: 9.5; Q3: 13.75; Max: 16; IQR: 8\nE. Min: 3; Q1: 5.75; Med: 9.5; Q3: 13.75; Max: 16; IQR: 9\n", "Answer (final answer highlighted)": "(D) Reading from the graph, Min: 3; Q1: 5.75; Med: 9.5; Q3: 13.75; Max: 16. Calculating the interquartile range = Q3 - Q1 = 13.75 - 5.75 = 8.", "ImagePath": "Math/131" }, { "Question": "Question: 34\nWhich statement is true of the dataset summarized by this five-number summary?\n \nA. There are no outliers.\nB. 3 is a mild outlier and 20 is an extreme outlier.\nC. 3 and 20 are mild outliers.\nD. 20 is an extreme outlier.\nE. 20 is a mild outlier. There are no extreme outliers.\n", "Answer (final answer highlighted)": "(E) Interquartile range (IQR) is 10.5 - 4.5 = 6. To find the boundary for mild outliers, multiply the IQR by 1.5:6(1.5) = 9. Any values that are less than Q1 - 9 or greater than Q3 + 9 are considered mild outliers (but not more than 3(IQR), which is considered extreme). 20 is a mild outlier because it is greater than 10.5 + 9 = 19.5 and less than 10.5 + 18 = 28.5.", "ImagePath": "Math/132" }, { "Question": "Question: 39\nThe range of a dataset is 20 and x has the highest value of the variables provided. What is the value of y and the standard deviation of the dataset if rounded to two decimals?\n \nA. The value of y is 32, and the standard deviation is 7.\nB. The value of y is 30, and the standard deviation is 6.41.\nC. The value of y is 35, and the standard deviation is 7.92.\nD. The value of y is 20, and the standard deviation is 4.03.\nE. The value of y is 2, and the standard deviation is 5.76.\n", "Answer (final answer highlighted)": "(B) Because the minimal value in the dataset is 10, the maximum can be obtained from the formula for the range y - 20 = 10. Through this equation, it is clear that y = 30. After calculating the mean by calculating the sum and dividing it by the number of values, we can see that the mean is 13. The standard deviation is then calculated by subtracting the mean from each value, and this new value then needs to be squared. After calculating the mean of the squared values, we see that the standard deviation is the root of this value and is 6.41.", "ImagePath": "Math/133" }, { "Question": "Question: 41\nFor the probability density curve below, which of the following statements is true?\n \nI. The area is exactly 1 underneath it.\nII. It does not model the distribution of the data.\nIII. It is a function that is always positive.\nA. I only\nB. I and III only\nC. II and III only\nD. II only\nE. III only\n", "Answer (final answer highlighted)": "(B) All probability density curves are mathematical models of probability distributions. Probability distributions are proportional distributions of data, and the area underneath them sums to 1. They are also always above the horizontal axis because probability is nonnegative.", "ImagePath": "Math/134" }, { "Question": "Question: 42\nWhy is the following not an example of a valid probability density curve?\n \nA. Because the curve does not follow a normal distribution\nB. Because such a function is by definition either constantly positive or negative\nC. Because such a function has to have at least two maximum values and one minimum value\nD. Because the function cannot be negative\nE. Because the function cannot be positive\n", "Answer (final answer highlighted)": "(D) A valid probability density curve has to be nonnegative, and the area between the curve and the x-axis should be equal to 1.", "ImagePath": "Math/135" }, { "Question": "Question: 44\nThe following box plot illustrates the movement of two variables, A1 and B1. Which of the following assumptions is correct?\n \nA. A1 has smaller outliers compared to B1.\nB. The value of the median is higher for B1.\nC. The range of the data is larger in A1.\nD. The two variables have medians of the same value.\nE. A1 has problems with outliers that are larger compared to most of the dataset, while B1 has outliers that are smaller than most of the dataset.\n", "Answer (final answer highlighted)": "(C) It is clear that the values for the dataset labeled A1 have a larger range and a larger median compared to B1; the outliers are more pronounced than in B1.", "ImagePath": "Math/136" }, { "Question": "Question: 46\nThe histograms below show the number of cat and dog owners based on the number of each animal owned. Choose the best description from the statements below.\n \nA. There are more cat owners than dog owners. There are more cats than dogs.\nB. There are more cat owners than dog owners. There are more dogs than cats.\nC. There are more dog owners than cat owners. There are more cats than dogs.\nD. There are more dog owners than cat owners. There are more dogs than cats.\nE. The cat owners are equal to dog owners. There are more cats than dogs.\n", "Answer (final answer highlighted)": "(A) There are more cat owners than dog owners. There are more cats than dogs. This can be estimated by the relative heights of the bars labeled 1, 2, 3, 4, and 5. Notice that there are more households that own greater quantities of cats.", "ImagePath": "Math/137" }, { "Question": "Question: 52\nThe cumulative frequency distribution of airfares is displayed in the ogive. What airfares correspond to the 20th percentile, the 50th percentile, and the 80th percentile?\n \nA. P20 = 95; P50 = 102; P80 = 106\nB. P20 = 96; P50 = 103; P80 = 106\nC. P20 = 96; P50 = 102; P80 = 106\nD. P20 = 96; P50 = 102; P80 = 100\nE. P20 = 96; P50 = 102; P80 = 107\n", "Answer (final answer highlighted)": "(C) Reading from the vertical axis the percentages and down to the horizontal axis, P20 = 96; P50 = 102; P80 = 106.", "ImagePath": "Math/138" }, { "Question": "Question: 53\nThe histogram represents the heights of males in the United States between the ages 20\u00e2\u0080\u009329. The mean is 69.6 inches, and the standard deviation is 2.6 inches. Since the heights are approximately normal, find the height that represents the 20th percentile. How should this be interpreted?\n \nA. 60 inches. 20% of the population of males between the ages 20\u00e2\u0080\u009329 are shorter than approximately 60 inches.\nB. 68.6 inches. 20% of the population of males between the ages 20\u00e2\u0080\u009329 are shorter than approximately 68 inches.\nC. 67.4 inches. 20% of the population of males between the ages 20\u00e2\u0080\u009329 are shorter than approximately 68 inches.\nD. 67.4 inches. 20 males between the ages 20\u00e2\u0080\u009329 are shorter than approximately 67 inches.\nE. 60 inches. 20 males between the ages 20\u00e2\u0080\u009329 are shorter than approximately 60 inches tall.\n", "Answer (final answer highlighted)": "(C) The z-score associated with 20% to the left of it is -0.84. To find the height associated with that z-score: z \u00cf\u0083 + \u00ce\u00bc = - 0.84(2.6) + 69.6 = 67.4. That means that 20% of the population is shorter than 68 inches tall.", "ImagePath": "Math/139" }, { "Question": "Question: 54\nThe histogram represents the heights of males in the United States between the ages 20\u00e2\u0080\u009329. The mean is 69.6 inches, and the standard deviation is 2.6 inches (approximately normal). Three adult males are selected from the group. Their heights are 75 inches, 63 inches, and 79 inches. Determine which heights, if any, are unusual.\n \nA. The 79-inch height is the only one that is unusual because it is more than three standard deviations above the mean. The z-scores, respectively, are: 2.08, \u00e2\u0080\u00932.54, and 3.62.\nB. The 79-inch and 63-inch heights are the only ones that are unusual because they are more than two standard deviations from the mean. The z-scores, respectively, are: 2.00, \u00e2\u0080\u00932.54, and 3.62.\nC. All heights are unusual since they are more than two standard deviations from the mean. The z-scores, respectively, are: \u00e2\u0080\u00932.08, \u00e2\u0080\u00932.54, and 3.62.\nD. All heights are unusual since they are more than two standard deviations from the mean. The z-scores, respectively, are: 2.08, \u00e2\u0080\u00932.54, and 3.62.\nE. All heights are unusual since they are more than two standard deviations from the mean. The z-scores, respectively, are: 2.08, 2.54, and 3.62.\n", "Answer (final answer highlighted)": "(D) http://img.apstudy.net/ap/statistics/a500/Ans_Eq_015.jpg Calculating for each height: 2.08, -2.54, and 3.62, respectively, shows that all are greater than two standard deviations from the mean.", "ImagePath": "Math/140" }, { "Question": "Question: 55\nThe dataset shown below has a mean value of 15. Based on this information, which of the following correctly identifies the unknown value x and the range of the dataset?\n \nA. The value of x is 3, and the range is 27.\nB. The value of x is 9, and the range is 25.\nC. The value of x is 5, and the range is 25.\nD. The value of x is 11, and the range is 19.\nE. The value of x is 18, and the range is 10.\n", "Answer (final answer highlighted)": "(B) By understanding that the mean is the sum of all of the elements divided by the number of the elements, it is possible to determine the value of x. The sum of the values shown in the table is 81. As there are 5 known values and x, making a total of 6, this means that: which when multiplying both sides of the equation leads to: 81 + x = 90 meaning that x has a value of 9. Because the range is the maximum minus the minimum, with the largest value being 30 and the smallest 5, the range is 25.", "ImagePath": "Math/141" }, { "Question": "Question: 58\nThe frequency distribution shows the number of magazine subscriptions per household in a random sample (n = 50). Find the mean number of subscriptions per household.\n \nA. Mean is 2.0\nB. Mean is 1.8\nC. Mean is 1.5\nD. Mean is 3.0\nE. Mean is 92\n", "Answer (final answer highlighted)": "(B) http://img.apstudy.net/ap/statistics/a500/Ans_Eq_019.jpg", "ImagePath": "Math/142" }, { "Question": "Question: 59\nThe table below shows the correct values of the mean and the standard deviation for four different datasets. Which of the following assumptions is most likely accurate?\n \nA. Dataset A has, on average, the smallest number of values that are different from the mean compared to the other datasets in the table.\nB. The maximum value of dataset B is 17.3.\nC. The maximum value of dataset D is 71.57.\nD. Dataset C has, on average, the smallest number of values that are different from the mean compared to the other datasets in the table.\nE. Dataset A has a variance of 2.53.\n", "Answer (final answer highlighted)": "(D) Because the standard deviation shows the dispersion of data within a certain dataset, it is most likely that the dataset with the smallest standard deviation compared to the size of the mean will, on average, be the dataset with the most consistent values. Answer choices (B) and (C) show incorrect calculations of the range, which is not calculated in such a manner. Answer choice (E) is not correct because variance is standard deviation squared, not the root of the standard deviation.", "ImagePath": "Math/143" }, { "Question": "Question: 63\nFive students had five tests in one semester, and every test was graded on a scale of 0 to 20 points. Based on information from the table, which of the following students had the largest variance in his or her results, and which student had the largest mean value?\n \nA. James had the largest variance, while Mike had the largest mean score.\nB. Mike had the largest mean score and the largest variance.\nC. Tina had the largest variance, while James had the highest mean score.\nD. Tina had the largest variance, while Mark had the largest mean score.\nE. Angela had the largest variance, while Mike had the largest mean score.\n", "Answer (final answer highlighted)": "(A) The dataset of the test scores for James had by far the highest variance, with a value of 40.3, because his results had the largest dispersion of data. Mike had the largest mean score because the sum of his results divided by the number of tests, which was 5, was the highest, with a mean score of 14.8.", "ImagePath": "Math/144" }, { "Question": "Question: 65\nWhat data point is indicated on the distribution?\n \nA. 61.9\nB. 64.5\nC. 67.0\nD. 72.1\nE. 77.2\n", "Answer (final answer highlighted)": "(D) The data point is at the point of inflection on the bell curve which is one standard deviation above the mean or X = 67 + 5.1 = 72.1.", "ImagePath": "Math/145" }, { "Question": "Question: 66\nWhich of the following statements best describes the scatter plot?\n \nI. A linear model would fit the data well.\nII. The bivariate data are positively correlated.\nIII. The linear relationship is weak\nA. I only\nB. I and III only\nC. I and II only\nD. II only\nE. III only\n", "Answer (final answer highlighted)": "(C) The data points are trending linearly with a positive slope.", "ImagePath": "Math/146" }, { "Question": "Question: 67\nThe scatter plot of study time in hours versus test scores in a statistics class is shown below. What can be said about the relationship between time spent studying and test scores?\n \nA. More time spent studying is related to lower test scores.\nB. Less time spent studying is related to higher test scores.\nC. More time spent studying is related to higher test scores.\nD. Higher test scores are caused by more time spent studying.\nE. There is no discernible relationship between study time and test scores.\n", "Answer (final answer highlighted)": "(C) The more time spent studying is related to a higher test scores since there is a positive linear relationship.", "ImagePath": "Math/147" }, { "Question": "Question: 70\nWhy does Chart 1 show a better fitting line than Chart 2? \n \nA. Because it has a negative correlation\nB. Because it shows a positive correlation\nC. Because it shows proof of causality\nD. Because it has a lower value of the sum of squares\nE. Because the value of the slope is negative\n", "Answer (final answer highlighted)": "(D) The best-fitting line is the least-squares regression line. The line in Chart 1 has a sum of squares of 3.6, which is smaller than 4.171.", "ImagePath": "Math/148" }, { "Question": "Question: 71\nBased on the data shown in the chart below, what is the most likely correlation between the two datasets shown?\n \nA. There is a correlation between the variables lower than -0.9.\nB. There is a correlation between the variables of -0.7.\nC. There is a correlation between the variables that is close to 0.\nD. There is a correlation between the variables that is around 0.65.\nE. There is a correlation between the variables higher than 0.9.\n", "Answer (final answer highlighted)": "(E) As can be seen, the two datasets tend to move in a highly similar manner. This indicates that there is a very strong positive correlation; the actual correlation between the two datasets is 0.97.", "ImagePath": "Math/149" }, { "Question": "Question: 72\nWhy does the following dataset most likely have a correlation of roughly 0.5?\n \nA. Because the two datasets move in opposite directions\nB. Because there is no connection between the datasets\nC. Because, at certain times, the increase in the value of one dataset is associated with the increase of the value of the second dataset\nD. Because, at certain times, as the value of one dataset increases, the other significantly decreases\nE. Because it is clear that the change of one variable causes a change in the other variable\n", "Answer (final answer highlighted)": "(C) The connection between the two datasets indicates that there is a positive correlation of roughly 0.5. This indicates that as the value of one variable increases, the value of the other variable is expected to increase as well.", "ImagePath": "Math/150" }, { "Question": "Question: 74\nIn the scatter plot, what effect does the indicated point have on the correlation coefficient and the slope of the least-squares regression line?\n \nA. The point is influential; r decreases and the slope increases.\nB. The point is influential; r decreases and the slope decreases.\nC. The point is influential; r decreases and the slope is unaffected.\nD. The point is not influential; therefore, r and the slope are unaffected.\nE. The point is influential; therefore, r and the slope are unaffected.\n", "Answer (final answer highlighted)": "(B) The point is influential; therefore, r decreases and slope decreases. Since this point is an outlier, r is reduced; because the outlier is above and to the left of the center of the data, the slope is tilted and flattened (smaller positive value).", "ImagePath": "Math/151" }, { "Question": "Question: 75\nIn the scatter plot, how could the data be transformed in order to do a linear regression?\n \nA. By squaring each data point y-value\nB. By taking the natural logarithm of each data point y-value\nC. By raising each data point y-value to the base 10\nD. By taking the square root of each data point y-value\nE. By cubing each data point y-value\n", "Answer (final answer highlighted)": "(D) The appropriate regression would be quadratic since the points are in a parabolic shape. Taking the square root of each data point y-value would be the appropriate transformation in order to perform a linear regression.", "ImagePath": "Math/152" }, { "Question": "Question: 77\nUsing the dataset, what can be said about the relationship between earnings and dividends?\n \nA. More earnings are related to more dividends.\nB. There is no discernible relationship between earnings and dividends.\nC. More earnings are related to less dividends.\nD. More dividends are caused by more earnings.\nE. Fewer earnings are related to more dividends.\n", "Answer (final answer highlighted)": "(B) The scatter plot and coefficient of determination indicate that earnings and dividends are unrelated. http://img.apstudy.net/ap/statistics/a500/03xAns82b.jpg Regression Analysis: Dividends versus Earnings The regression equation is: Dividends = 0.949 + 0.258 Earnings http://img.apstudy.net/ap/statistics/a500/f0234-02.jpg", "ImagePath": "Math/153" }, { "Question": "Question: 79\nFrom the regression output below, which type of variation does R-squared (R-Sq) pertain to?\n \nA. Total variation\nB. Unexplained variation\nC. Explained variation\nD. Least squares variation\nE. Error variation\n", "Answer (final answer highlighted)": "(C) R-squared is a measure of the explained variation in the response variable by the predictor variable.", "ImagePath": "Math/154" }, { "Question": "Question: 81\nFind the slope from the least-squares regression line for the data below of final grade as a percent and days absent. What does it tell us about the relationship?\n \nA. Slope is approximately 94.695. For each additional day absent, the student's final grade increases by about 0.947%.\nB. Slope is approximately -94.695. For each additional day absent, the student's final grade decreases by about 0.947%.\nC. Slope is approximately 6.767. For each additional day absent, the student's final grade increases by about 6.767%.\nD. Slope is approximately 6.767. For each additional day absent, the student's final grade decreases by about 6.767%.\nE. Slope is approximately -6.767. For each additional day absent, the student's final grade decreases by about 6.767%.\n", "Answer (final answer highlighted)": "(E) Slope is approximately -6.767 from the linear regression model for these data http://img.apstudy.net/ap/statistics/a500/Ans_Eq_039.jpg . For each day additional absent, the student's final grade decreases by about 6.767%.", "ImagePath": "Math/155" }, { "Question": "Question: 84\nCompare the two scatter plots. Which of the following statements is true about r ?\n \nA. r1 indicates a highly negative correlation, while r2 indicates a moderate positive correlation.\nB. The r value shows that there is causation between the datasets.\nC. r2 indicates a stronger correlation than r1.\nD. r cannot be used to find the percentage of variation that has been explained.\nE. The r value in this example is sensitive to outliers.\n", "Answer (final answer highlighted)": "(E) Due to the significant decrease from r1 to r2, it is clear that the value of r in this case is highly sensitive to outliers.", "ImagePath": "Math/156" }, { "Question": "Question: 87\nCompare the two regression outputs. Which regression equation explains more of the variation in y ?\n \nA. Regression 1, since R-Sq, unexplained variation, is the smaller.\nB. Regression 2, since R-Sq, total variation, is the smaller.\nC. Regression 1, since R-Sq, explained variation, is the greater.\nD. Regression 2, since R-Sq, explained variation, is the greater.\nE. Regression 1, since R-Sq, total variation, is the greater.\n", "Answer (final answer highlighted)": "(C) In Regression 1, R-sq, the explained variation by the predictor variable, is 81.5% while in Regression 2 the R-Sq is 80.7%. More of the variation in the response variable y is explained by x in Regression 1.", "ImagePath": "Math/157" }, { "Question": "Question: 88\nFind and interpret r for the dataset.\n \nA. r = 0.0903. There is a weak positive linear correlation.\nB. r = -0.0903. There is a weak negative linear correlation.\nC. r = 0.903. There is a strong positive linear correlation.\nD. r = -0.903. There is a strong negative linear correlation.\nE. r = 0.0903. There is no linear correlation.\n", "Answer (final answer highlighted)": "(D) r = -0.903. This indicates strong negative linear correlation.", "ImagePath": "Math/158" }, { "Question": "Question: 90\nFrom the time series data, find r. What does r tell us about the regression?\n \nA. r = 0.238. There is a very weak linear relationship.\nB. r = -0.238. There is a very weak linear relationship.\nC. r = 0.488. There is a very weak positive linear relationship.\nD. r = -0.488. There is a very weak negative linear relationship.\nE. r = -0.488. There is no discernible relationship.\n", "Answer (final answer highlighted)": "(C) r = 0.488 and is a measure of the strength and direction of a linear relationship; therefore, it indicates a weak positive linear relationship. The scatter plot indicates that a transformation would be appropriate before fitting a linear model to these data.", "ImagePath": "Math/159" }, { "Question": "Question: 91\nBased on the residuals shown in the chart below, what kind of transformation should be applied to better fit the dataset?\n \nA. The first difference should be used.\nB. A square transformation should be used.\nC. All of the values should be divided by 2.\nD. The root transformation should be used.\nE. The values should be transformed by multiplying them with an instrumental variable.\n", "Answer (final answer highlighted)": "(D) Based on the values in the chart, there are signs of a pattern that could be discovered by performing a root transformation.", "ImagePath": "Math/160" }, { "Question": "Question: 95\nCompare the two datasets below. Which statements are true?\n \nI. Absences are a better predictor of the final grade.\nII. The sum of the residuals is the same for both.\nIII. The unexplained variation in the final is much greater than in the midterm.\nA. I only\nB. I and III only\nC. I and II only\nD. II only\nE. III only\n", "Answer (final answer highlighted)": "(C) The coefficients of determination are 92.4% and 48.6%, respectively. That shows that absences explain more of the variation in the final then the midterm. Because the regression is a least-squares linear regression, the sum of the residuals is always zero, the same for both.", "ImagePath": "Math/161" }, { "Question": "Question: 96\nFrom the regression output below, calculate the coefficient of determination. What does it tell you about the relationship?\n \nA. r2 = 38.9%; that 38.9% of the variation of the residual error is explained by the regression\nB. r2 = 44.0%; that 44.0% of the variation of the difference of the regression and the residual error is explained by the total\nC. r2 = 28.0%; that 28.0% of the variation of the response variable is explained by the residuals\nD. r2 = 56.3%; that 56.3% of the variation of the explanatory variable is explained by the response variable\nE. r2 = 72.0%; that 72.0% of the variation of the response variable is explained by the explanatory variable\n", "Answer (final answer highlighted)": "(E) http://img.apstudy.net/ap/statistics/a500/Ans_Eq_047.jpg or 72.0%. The coefficient of determination is a measure of the variation of the dependent (response) variable that is explained by the regression line and the independent (explanatory) variable.", "ImagePath": "Math/162" }, { "Question": "Question: 97\nFrom the regression output below, calculate the percentage of unexplained variation in the dependent (response) variable.\n \nA. 1.8%\nB. 1.9%\nC. 96.4%\nD. 98.1%\nE. 98.2%\n", "Answer (final answer highlighted)": "(E) The percentage of unexplained variation in the dependent (response) variable is http://img.apstudy.net/ap/statistics/a500/Ans_Eq_048.jpg \u22c5 http://img.apstudy.net/ap/statistics/a500/Ans_Eq_049.jpg", "ImagePath": "Math/163" }, { "Question": "Question: 98\nUse the dataset to find the correlation coefficient. What would be the best explanation of the strength of this relationship?\n \nA. Correlation coefficient is -0.730. That higher grades are earned by more efficient study techniques.\nB. Correlation coefficient is 0.730. That students expecting higher grades study more hours per week.\nC. Correlation coefficient is -0.730. That less time spent studying results in better grades.\nD. Correlation coefficient is -0.730. That a higher expected GPA predicts a lower study time.\nE. Correlation coefficient is 0.730. That more time spent studying results in better grades.\n", "Answer (final answer highlighted)": "(D) r = -0.730. The best explanation for the relationship is that students expecting higher grades study fewer hours.", "ImagePath": "Math/164" }, { "Question": "Question: 109\nWhat statement is true about the two models for the dataset?\nCorrelations: Distress, Brain 1\nPearson correlation of Distress and Brain 1 = 0.878\nP-Value = 0.000\n \nA. Under both models, the correlation between the variables is the same.\nB. Model II is more appropriate since it has a larger residual error.\nC. Model I suggests a negative linear correlation between the variables.\nD. The residuals for the different data values will be the same under both models.\nE. The correlation should not be observed, as it is not statistically significant.\n", "Answer (final answer highlighted)": "(A) The correlation between the variables is the same. The only difference between Model I and Model II is what the dependent variable is. Otherwise, the strength of the correlation is identical.", "ImagePath": "Math/165" }, { "Question": "Question: 165\nThe probability of Bill serving an ace in tennis is 0.15, and the probability that he double faults is 0.25. What is the probability that Bill does not serve an ace or a double fault?\nA. 0.5\nB. 0.15\nC. 0.4\nD. 0.9\nE. 0.6\n", "Answer (final answer highlighted)": "(E) The probability distribution for Bill's serving in tennis is: P (not an Ace or Double Fault) = 1 - (0.15 + 0.25) = 0.6", "ImagePath": "Math/166" }, { "Question": "Question: 170\nCalculate the expected value and the variance of the following probability distribution.\n \nA. E(X ) = 2.0, V(X ) = 1.4\nB. E(X ) = 2.1, V(X ) = 1.0\nC. E(X ) = 2.1, V(X ) = 1.2\nD. E(X ) = 2.1, V(X ) = 1.4\nE. E(X ) = 2.0, V(X ) = 1.0\n", "Answer (final answer highlighted)": "(D) http://img.apstudy.net/ap/statistics/a500/f0247-01.jpg", "ImagePath": "Math/167" }, { "Question": "Question: 171\nThe probability distribution for the number of incidents occurring in a year is shown below. Calculate the expected value and the variance.\n \nA. E(X ) = 2.0, V(X ) = 2.0\nB. E(X ) = 1.9, V(X ) = 1.8\nC. E(X ) = 2.0, V(X ) = 1.8\nD. E(X ) = 2.0, V(X ) = 1.4\nE. E(X ) = 1.9, V(X ) = 1.4\n", "Answer (final answer highlighted)": "(C) http://img.apstudy.net/ap/statistics/a500/f0247-02.jpg", "ImagePath": "Math/168" }, { "Question": "Question: 172\nThe probability distribution for the frequency of an event occurring in five trials is shown below. Calculate the expected value and the standard deviation.\n \nA. E(X ) = 1.25, SD = 1.0\nB. E(X ) = 1.5, SD = 1.05\nC. E(X ) = 1.5, SD = 1.1\nD. E(X ) = 1.5, SD = 1.0\nE. E(X ) = 1.25, SD = 1.05\n", "Answer (final answer highlighted)": "(D) http://img.apstudy.net/ap/statistics/a500/f0247-03.jpg", "ImagePath": "Math/169" }, { "Question": "Question: 173\nThe probability distribution for the number of defects found in a sample is shown below. Calculate the expected value and the standard deviation.\n \nA. E(X ) = 0.9, SD = 0.8\nB. E(X ) = 0.9, SD = 0.6\nC. E(X ) = 0.9, SD = 0.7\nD. E(X ) = 1.0, SD = 0.6\nE. E(X ) = 1.0, SD = 0.7\n", "Answer (final answer highlighted)": "(A) http://img.apstudy.net/ap/statistics/a500/f0248-01.jpg", "ImagePath": "Math/170" }, { "Question": "Question: 175\nWhat should be the height of the missing bar in the histogram?\n \nA. 75\nB. 0.7\nC. 70\nD. 60\nE. 50\n", "Answer (final answer highlighted)": "(A) The scale of the vertical axis is in percents. The sum of the heights of the bars must equal 100. Let x be the unknown bar height. Then 100 = x + 15 + 5 + 5 and solving for x, x = 75.", "ImagePath": "Math/171" }, { "Question": "Question: 176\nSuppose a cell phone company manufactures cell phones and tablets in the following four states: Arizona, California, Washington, and Minnesota. The table below shows the percentage of total output by state, and within each state, the percentage output of each product. What is the probability that a randomly selected product will be a tablet manufactured in Minnesota? (Assume that all products are shipped from one distribution center.)\n \nA. 0.05\nB. 0.08\nC. 0.004\nD. 0.5\nE. 0.04\n", "Answer (final answer highlighted)": "(C) P (Minnesota & tablet) = 0.05(0.08) = 0.004", "ImagePath": "Math/172" }, { "Question": "Question: 198\nStudents in a biomedical statistics course take two tests before a final. The statistics from the first test for three different classes (May, June, and July) are shown. What would be the average and the standard deviation of the sum of the test scores?\n \nA. Mean of the sum: 51. Standard deviation: 10.51.\nB. Mean of the sum: 51. Standard deviation: 5.45.\nC. Mean of the sum: 51. Standard deviation: 3.24.\nD. Mean of the sum: 51. Standard deviation: 2.33.\nE. Mean of the sum: 50. Standard deviation: 3.24.\n", "Answer (final answer highlighted)": "(C) These classes are to be considered independent since the students are all different from class to class. With that assumption, http://img.apstudy.net/ap/statistics/a500/Ans_Eq_116.jpg and http://img.apstudy.net/ap/statistics/a500/Ans_Eq_117.jpg", "ImagePath": "Math/173" }, { "Question": "Question: 202\nGiven the following probability distribution, find P (1 \u00e2\u0089\u00a4 X \u00e2\u0089\u00a4 4).\n \nA. 0.01\nB. 0.08\nC. 0.20\nD. 0.58\nE. 0.70\n", "Answer (final answer highlighted)": "(C) Since this is a discrete random variable, the probability can be found using P(X = 1) + P(X = 2) + P(X = 3).", "ImagePath": "Math/174" }, { "Question": "Question: 204\nThe dataset below is based on a survey of 100 randomly selected travelers who were asked, \"How many trips per year do you typically take?\"\n \nWhat is the probability that a randomly selected survey participant is male or takes two or fewer trips per year?\nA. 0.17\nB. 0.18\nC. 0.36\nD. 0.69\nE. 0.86\n", "Answer (final answer highlighted)": "(D) P(male or takes fewer than two trips per year) = P(male) + P(takes fewer than two trips per year) - P(male and takes fewer than two trips per year) = 0.50 + 0.36 - 0.17.", "ImagePath": "Math/175" }, { "Question": "Question: 266\nIn a recent online survey of 1,700 adults, it was revealed that only 17% felt the Internet was secure. With what degree of confidence can you say that 17% \u00c2\u00b1 2% of adults believe that online security is secure?\nA. 72.9%\nB. 90%\nC. 95%\nD. 97.2%\nE. 98.6%\n", "Answer (final answer highlighted)": "(D) http://img.apstudy.net/ap/statistics/a500/f0268-03.jpg", "ImagePath": "Math/176" }, { "Question": "Question: 267\nOne of the students in the school council election wants to make healthy lunch menus her pitch to gain votes. What size voter sample would she need to obtain a 90% confidence that her support level margin of error is no more than 4%?\nA. 25\nB. 600\nC. 423\nD. 1691\nE. None of the above\n", "Answer (final answer highlighted)": "(C) http://img.apstudy.net/ap/statistics/a500/f0268-04.jpg", "ImagePath": "Math/177" }, { "Question": "Question: 279\nThe researchers conducting an experiment have obtained the results as shown in the table below. Which of the following correctly identifies the minimum and maximum values of the 95% confidence interval?\n \nA. 14.2\u00e2\u0080\u009320.2\nB. 11.151\u00e2\u0080\u009320.258\nC. 11.21\u00e2\u0080\u009323.21\nD. 9.652\u00e2\u0080\u009324.748\nE. 8.148\u00e2\u0080\u009325.184\n", "Answer (final answer highlighted)": "(D) The sample's size is 5 and the standard deviation can be calculated; it is 6.058. If we are searching for a 95% confidence interval, this means that we need to look at the critical t-values for 4 degrees of freedom at a 5% significance level, which is 2.776. The next step is to divide the standard deviation of the sample with the root of the sample size. This means that 6.058/2.236 = 2.719. This value then needs to be multiplied with the t-value, leading to the value of 7.548. The last step is determining the value of the mean, which is 17.2, and then subtracting and adding 7.548 to get the final confidence interval.", "ImagePath": "Math/178" }, { "Question": "Question: 282\nA team of researchers is testing a new drug. They have obtained the results as shown in the table below. What is the minimum and maximum value of the researchers' 95% confidence interval, rounded to one decimal?\n \nA. 8.7\u00e2\u0080\u009322.2\nB. 7.9\u00e2\u0080\u009323.2\nC. 5.4\u00e2\u0080\u009321.4\nD. 6.7\u00e2\u0080\u009324.7\nE. 3.4\u00e2\u0080\u009328.4\n", "Answer (final answer highlighted)": "(A) After we determine that the sample size is 9, we know that the degrees of freedom are 8. We need to find the value for the 5% level of statistical significance; this value is 2.306. After this, we need to determine the standard deviation, which is 8.791. By dividing the standard deviation with the root of the sample size, we find that 8.791/3 = 2.9303. By multiplying this value with the t-value, we find the value of 6.757. This value is then added to the value of the mean, which is 15.444.", "ImagePath": "Math/179" }, { "Question": "Question: 283\nWhile weighing five infants in the hospital we found their weights in kilograms to be 3.1, 3.5, 2.8, 3.2, and 3.4. What is a 90% confidence interval estimate of the infants' weights?\nA. 3.2 \u00c2\u00b1 0.202\nB. 3.2 \u00c2\u00b1 0.247\nC. 3.2 \u00c2\u00b1 0.261\nD. 4.0 \u00c2\u00b1 0.202\nE. 4.0 \u00c2\u00b1 0.261\n", "Answer (final answer highlighted)": "(C) df = 4 http://img.apstudy.net/ap/statistics/a500/f0270-01.jpg", "ImagePath": "Math/180" }, { "Question": "Question: 284\nA poll identifies the proportions of high-income and low-income voters who support a decrease in taxes. If we need to know the answer to be within \u00c2\u00b1 0.02 at the 95% confidence interval, what sample size should be taken?\nA. 3383\nB. 4803\nC. 7503\nD. 9453\nE. 4503\n", "Answer (final answer highlighted)": "(B) http://img.apstudy.net/ap/statistics/a500/f0270-02.jpg http://img.apstudy.net/ap/statistics/a500/f0270-03.jpg n \u00e2\u0089\u00a5 69.32 4802.5 and hence the poll would use the sample size of 4803.", "ImagePath": "Math/181" }, { "Question": "Question: 285\nA survey conducted on 1,000 Canadians found that 700 of them refused to receive the H1N1 vaccination. Construct a 95% confidence interval of the estimated proportion of Canadians who refused to receive the vaccination.\nA. (0.723, 0.777)\nB. (0.686, 0.714)\nC. (0.728, 0.672)\nD. (0.986, 0.914)\nE. (0.672, 0.728)\n", "Answer (final answer highlighted)": "(D) http://img.apstudy.net/ap/statistics/a500/f0270-04.jpg", "ImagePath": "Math/182" }, { "Question": "Question: 286\nFor a 95% confidence interval, you want to create a population proportion with a marginal error of no more than 0.025. How large of a sample would you need?\nA. 423\nB. 1537\nC. 385\nD. 2237\nE. 1082\n", "Answer (final answer highlighted)": "(B) For our problem, we will use p* = 0.5: http://img.apstudy.net/ap/statistics/a500/f0270-05.jpg", "ImagePath": "Math/183" }, { "Question": "Question: 287\nIn a random sample of 100 balloons, 30 of them are blue. Construct a 95% confidence interval for the true proportion of the blue balloons.\nA. (0.210, 0.399)\nB. (0.193, 0.407)\nC. (0.165, 0.334)\nD. (0.200, 0.380)\nE. (0.198, 0.378)\n", "Answer (final answer highlighted)": "(A) http://img.apstudy.net/ap/statistics/a500/f0270-06.jpg", "ImagePath": "Math/184" }, { "Question": "Question: 325\nIn a sample of 500 students from statistics courses in the fall semester, 312 earned a grade of C or higher. In the spring semester, 400 of the 525 students sampled earned a grade of C or higher. If we treat the fall semester as \"sample 1\" and the spring semester as \"sample 2,\" what is the appropriate standardized test statistic to determine whether a smaller proportion of students passed in the fall?\nA. z = -6.699\nB. z = -4.792\nC. z = 4.792\nD. z = 6.699\nE. The z-test statistic depends on the level of significance of the test\n", "Answer (final answer highlighted)": "(B) We are testing two proportions from two independent samples; therefore, the test statistic is http://img.apstudy.net/ap/statistics/a500/f0275-01.jpg This can also be found by performing a \"2-prop-z-test\" on the TI84 or 83 calculator as it gives both the test statistic and the p-value.", "ImagePath": "Math/185" }, { "Question": "Question: 336\nA survey of randomly selected visitors to a mall yielded the following data:\n \nBased on this sample, what would be the correct decision and conclusion of a test to determine whether the proportion who approve of a new design plan for the seating area in the food court is higher for women than it is for men at the 5% level?\nA. Reject the null hypothesis concluding that there is evidence the proportion is higher for women.\nB. Do not reject the null hypothesis concluding that there is no evidence that the proportion is higher for women.\nC. Reject the null hypothesis concluding that there is no evidence that the proportion is higher for women.\nD. Do not reject the null hypothesis concluding that there is no evidence that the proportion is higher for women.\nE. Conclude the proportion is higher for women since 199/301 > 152/254.\n", "Answer (final answer highlighted)": "(B) This is a two-sample proportion test, and the p-value can be calculated using the TI83 or 84 as 0.06345. (The test statistic is -1.526.) Since this is larger than 0.05, the null hypothesis is not rejected.", "ImagePath": "Math/186" }, { "Question": "Question: 340\nWhich of the following is a correct interpretation of the t-test shown below?\n \nA. There is a statistically significant difference between the means of the variables.\nB. There is a statistically significant difference when one is viewing the two-tailed test, but not for the one-tailed test.\nC. There is a weak negative correlation between the two variables.\nD. The results of the t-test suggest that the null hypothesis cannot be rejected.\nE. There is a statistically significant difference between the means of the sample.\n", "Answer (final answer highlighted)": "(D) As all of the p-values of the t-tests are higher than 0.05, this indicates that it is not possible to reject the null hypothesis.", "ImagePath": "Math/187" }, { "Question": "Question: 354\nA teacher is investigating the relationship between hours spent studying and exam scores (scale 0\u00e2\u0080\u0093100).\n \nBased on the computer output above, in a test of H0 : \u00ce\u00b2 = 0 versus Ha : \u00ce\u00b2 \u00e2\u0089\u00a0 0, which of the following would be correct?\nA. Reject H0 concluding that at the 5% level there is a linear relationship between hours spent studying and exam scores.\nB. Do not reject H0 concluding that at the 5% level there is a linear relationship between hours spent studying and exam scores.\nC. Reject H0 concluding that at the 5% level there is no evidence of a linear relationship between hours spent studying and exam scores.\nD. Do not reject H0 concluding that at the 5% level there is no evidence of a linear relationship between hours spent studying and exam scores.\nE. Based on the large value of the constant, conclude there is a linear relationship between hours spent studying and exam scores.\n", "Answer (final answer highlighted)": "(A) Based on the computer output, the p-value is zero, which would reject the null hypothesis for all of the usual significance levels. This is strong evidence of a linear relationship between the variables.", "ImagePath": "Math/188" }, { "Question": "Question: 357\nBased on a sample of 20 data values, the least-squares regression line to predict y from x is . If Sb = 0.76, find the t-test statistic for H0 : \u00ce\u00b2 = 0.\nA. 0.09\nB. 0.12\nC. 0.67\nD. 8.44\nE. 28.08\n", "Answer (final answer highlighted)": "(B) The test statistic for any test is always of the form http://img.apstudy.net/ap/statistics/a500/Ans_Eq_231.jpg Since we are testing whether the slope is zero, the test statistic is http://img.apstudy.net/ap/statistics/a500/Ans_Eq_232.jpg", "ImagePath": "Math/189" }, { "Question": "Question: 363\nA scientist is studying the relationship between the percentage of a particular type of nutrient in the soil and the eventual height of a plant.\nThe regression equation is: Height = 5.31 + 3.34 Percentage\n \nWhich of the following is true?\nA. Neither the constant nor the slope are statistically significant at the 1% significance level.\nB. The constant of the regression is 3.345.\nC. The regression can be interpreted as a 1% increase of the percentage of nutrients causing a 5.31 increase in the height of the plant.\nD. The lower the R-squared value, the stronger the connection between the two variables.\nE. The standard error of the slope is 1.316.\n", "Answer (final answer highlighted)": "(E) The only correct answer is that the standard error of the slope is 1.316, because its value is 3.345.", "ImagePath": "Math/190" }, { "Question": "Question: 365\nAs part of a project analyzing the relationship between the square footage of homes and their final sale price in thousands of dollars, a student performed a regression analysis.\nThe regression equation is: Sale Price = 179 + 0.0289 SqFt\n \nBased on the computer output above, what is the value for the t-test statistic to test H0 : \u00ce\u00b2 = 0?\nA. 1.53\nB. 4.42\nC. 3.06\nD. 8.84\nE. 40.52\n", "Answer (final answer highlighted)": "(A) Since \"square feet\" is used as the independent variable, that line provides information about the slope. Thus the t-test statistic is 1.53.", "ImagePath": "Math/191" }, { "Question": "Question: 375\nConsider the regression output provided below that considers the impact of height on weight. Which of the following is correct?\n \nA. The 95% confidence interval for the constant is from \u00e2\u0080\u00930.435 to 1.695.\nB. The regression output suggests that an increase in height is associated with a 0.219 increase in weight.\nC. The model is based on the comparison of seven observations.\nD. The R-squared value of the model suggests that the model may not be a good fit, and this is backed up by none of the coefficients being statistically significant at the 5% level.\nE. This model seems to be a good fit because it minimizes the value of the adjusted R-squared and because the intercept is not close to being equal to 0.\n", "Answer (final answer highlighted)": "(D) Both the value of the R-squared and the adjusted R-squared seem to indicate that the model has a limited ability to predict the value of the independent variable. As both the constant and the coefficient are not statistically relevant at the 5% level of statistical significance, it is clear that the model may not be properly specified. -0.435 to 1.695 is the confidence interval for the coefficient, not the constant.", "ImagePath": "Math/192" }, { "Question": "Question: 379\nThe plot below shows how well the unemployment rate predicts the result of the largest political bloc in Germany, CDU/CSU. The final equation is that votes for CDU/CSU = 0.0126 unemployment rate + 0.279. What can we infer from the results of this prediction?\n \nA. The regression line is not really accurate in predicting the results and there seem to be numerous outliers, some of which are not even captured by the 95% confidence interval.\nB. The regression model has a very high R-squared value, likely above 0.9, as almost all of the variables are within the 95% confidence interval.\nC. The fact that both the constant and the intercept have a value less than 1 means that they are both not statistically significant.\nD. The regression model is the best-fitting model because the intercept and the slope have similar values.\nE. The model is an excellent fit because all of the results are close.\n", "Answer (final answer highlighted)": "(A) This model, which has an R-squared value of 0.267, clearly does not fully capture the relevance of the dependent variable. The fact that the intercept and the slope have similar values does not hold any statistical significance.", "ImagePath": "Math/193" }, { "Question": "Question: 386\nWhich of the following datasets was used to gain the regression output below?\n \nA. Datasets A and B\nB. Datasets C and D\nC. Datasets E and F\nD. Datasets G and H\nE. Datasets C and G\n", "Answer (final answer highlighted)": "(A) Based on the value of the degrees of freedom, the only possible answers are (A) and (C). It is clear that the correlation is quite strong in (C), while the output shows a weak connection between the variables. Therefore, the correct answer is (A) because it shows the correct sample size and no strong correlation between the datasets.", "ImagePath": "Math/194" }, { "Question": "Question: 388\nA researcher is trying to determine the impact of the unemployment rate on the interest rate. Based on the values shown below, what can we conclude about the model?\n \nA. Based on the value of the Durbin-Watson coefficient and the R-squared value, it is clear that there is a strong predictability value of the model.\nB. Due to the fact that the R-squared value is very low, the predictability value of the model is high.\nC. Due to the fact that the value of the constant is larger than the intercept, the model is not statistically significant.\nD. Despite the fact that both the constant and the intercept are statistically significant at the 5% level, the predictability value of the model is low.\nE. Despite the fact that the value of the Akaike criterion is high, the low value of the Durbin-Watson statistic indicates that the model is stable.\n", "Answer (final answer highlighted)": "(D) Both the constant and the slope are statistically relevant at the 5% significance level, but the R-squared value indicates that the model does not have a high predictability value.", "ImagePath": "Math/195" }, { "Question": "Question: 399\nA student is studying the relationship between the number of hours students work and their final exam scores in statistics courses. A regression analysis resulted in the computer output below.\n \nWhat is the p-value that should be used to test H0 : \u00ce\u00b2 = 0 versus Ha : \u00ce\u00b2 > 0?\nA. 0\nB. 0.146\nC. 0.292\nD. 0.708\nE. 0.854\n", "Answer (final answer highlighted)": "(B) The predictor, or independent variable, in this situation is \"Hours.\" On the computer output, the p-value for this test can be found on the line for \"Hours.\"", "ImagePath": "Math/196" }, { "Question": "Question: 400\nA student is studying the relationship between the number of hours students work and their final exam scores in statistics courses. A regression analysis resulted in the computer output below.\n \nWhat is the t-test statistic that should be used to test H0 : \u00ce\u00b2 = 0 versus Ha : \u00ce\u00b2 \u00e2\u0089\u00a0 0?\nA. -3.22\nB. -1.61\nC. -0.805\nD. 5.655\nE. 11.31\n", "Answer (final answer highlighted)": "(B) The predictor, or independent variable, in this situation is \"Hours.\" On the computer output, the t-test statistic for this test can be found on the line for \"Hours.\"", "ImagePath": "Math/197" }, { "Question": "Question: 401\nA student is studying the relationship between the number of hours students work and their final exam scores in statistics courses. A regression analysis resulted in the computer output below.\n \nIf the student used a sample of 10, which of the following is the 95% confidence interval for the true slope of the regression line based on this dataset?\nA. -0.4195 \u00c2\u00b1 10.1695\nB. -0.4195 \u00c2\u00b1 23.451\nC. -0.4195 \u00c2\u00b1 0.2605\nD. -0.4195 \u00c2\u00b1 0.601\nE. -0.4195 \u00c2\u00b1 11.957\n", "Answer (final answer highlighted)": "(D) The critical value to find this interval is 2.306. From the output, the standard error of the estimate is 0.2605. Thus the margin of error is (2.306)(0.2605).", "ImagePath": "Math/198" }, { "Question": "Question: 413\nA public opinion poll surveyed a simple random sample of voters. Respondents were classified by gender and by voting preference (Republican, Democratic, or independent). Results are shown below.\n \nIf you conduct a chi-squared test for independence, what is the expected frequency count of male independents?\nA. 40\nB. 50\nC. 60\nD. 180\nE. 270\n", "Answer (final answer highlighted)": "(A) Using the formula for the expected frequency of this cell, http://img.apstudy.net/ap/statistics/a500/Ans_Eq_237.jpg", "ImagePath": "Math/199" }, { "Question": "Question: 420\nThe following data have been collected on the respondents' favorite type of sport:\n \nIf the expected frequencies rule for chi-square had been violated by the data, which categories could be combined together usefully in an attempt to increase the expected frequencies?\nA. Individual sport, team sport, and neither\nB. Males and females\nC. Individual sport and team sport\nD. Males and individual sport\nE. Team sport and neither\n", "Answer (final answer highlighted)": "(C) While possible, combining all of the levels of one category would possibly affect our analysis. For instance, if we were interested in gender differences, combining male and female would no longer allow us to do this. We could, however, combine the team and contact sport categories, since these are the most related, and still perform a similar analysis.", "ImagePath": "Math/200" }, { "Question": "Question: 423\nFor the following two-way table, compute the value of \u00cf\u00872.\n \nA. 1.45\nB. 4.167\nC. 5.2\nD. 5.55\nE. None of the above\n", "Answer (final answer highlighted)": "(B) The expected two-way table is given by the matrix http://img.apstudy.net/ap/statistics/a500/Ans_Eq_239.jpg http://img.apstudy.net/ap/statistics/a500/Ans_Eq_240.jpg", "ImagePath": "Math/201" }, { "Question": "Question: 424\nA toy company published an advertisement in the local newspaper of a major city and in a children's magazine to see which medium generated more advertising viewership. A random sample of families was taken, and each family was asked to indicate where they had seen the product's advertisement. The results are summarized below.\n \nThe advertiser decided to use a chi-square test to see whether there was a relationship between the newspaper and the magazine scores. What would be the degrees of freedom for this test?\nA. 3\nB. 4\nC. 7\nD. 8\nE. None of the above\n", "Answer (final answer highlighted)": "(A) Degrees of freedom = (rows - 1)(columns - 1) = (4 - 1)(2 - 1) = 3.", "ImagePath": "Math/202" }, { "Question": "Question: 425\nA physical education teacher at a middle school wanted to observe whether there was any association between the weight of a male student and how much weight he could lift. The following data were collected, and a chi-square test was performed. The output indicated a test statistic of 1.745 and a p-value of 0.1865.\n \nBased on the table above, which of the following is a correct statement?\nA. Since the value of the test statistic is so small, there is a significant relationship between the weight of an individual and the weight he can lift.\nB. The correlation coefficient from a linear regression analysis for these data would be less than 0.20.\nC. It is not possible to run a chi-square test on these data since the conditions for conducting this test are not met.\nD. The p-value of this test is large, which indicates that no significant relationship exists between the weight of an individual and the weight he can lift.\nE. The p-value of this test is small, which indicates that a significant relationship exists between the weight of an individual and the weight he can lift.\n", "Answer (final answer highlighted)": "(D) The p-value for the \u00cf\u00872 statistic is 0.1865, which is more than any reasonable alpha value. We would fail to reject the null hypothesis. There is insufficient evidence to conclude that an association or relationship exists between the weight of the individual and the weight he can lift.", "ImagePath": "Math/203" }, { "Question": "Question: 426\nA small college is expecting that the ratio of students that will pass compared to those that will fail will be 3 to 1. The college has 880 students. Despite these expectations, 639 students passed, while 241 failed. What is the correct chi-square statistic?\nA. 0.669\nB. 1.52\nC. 2.67\nD. 3.152\nE. 4.237\n", "Answer (final answer highlighted)": "(C) Once the data is placed in table form for clarity, it is clearly possible to see the difference between the actual and expected range and to calculate each step. The first step is determining the expected value. If the ratio of students expected to fail was meant to be 3 to 1, this means that 660 students were expected to pass, while 220 were expected to fail. The first step is to calculate the difference between the actual and the expected results. After squaring that value, it is necessary to divide this value with the expected value. By dividing this value with the expected results and then summing these two values, the chi-square statistic can be determined to be 2.67.", "ImagePath": "Math/204" }, { "Question": "Question: 431\nA recent study of accident records at a large engineering company in Europe reported the following number of injuries in each shift for one year.\n \nIs there sufficient evidence to say that the number of accidents during the three shifts are not the same? Test at the 0.05, 0.01, and 0.001 levels.\nA. There is sufficient evidence at all three levels to say that the number of accidents during each shift are not the same.\nB. There is sufficient evidence at both 0.05 and 0.01 levels but not at the 0.001 level.\nC. There is sufficient evidence at the 0.05 level but not at the 0.01 and 0.001 levels.\nD. There is sufficient evidence at the 0.001 level but not at the 0.05 and 0.01 levels.\nE. None of the above\n", "Answer (final answer highlighted)": "(A) http://img.apstudy.net/ap/statistics/a500/Ans_Eq_244.jpg http://img.apstudy.net/ap/statistics/a500/Ans_Eq_245.jpg With df = 3, the critical \u00cf\u00872-values for 0.05, 0.01, and 0.001 are 5.99, 9.21, and 13.82, respectively. Since 3.18 is less than each of those, there is sufficient evidence at all of these levels to say that the number of accidents on each shift is not the same.", "ImagePath": "Math/205" }, { "Question": "Question: 432\nA farm is expecting to have chickens hatched, where there will be an equal number of yellow, white, and mixed-color chickens. Despite these expectations, of the 900 chickens that were hatched, 276 of them were yellow, 294 of them were white, and 330 were mixed color. Which of the following is the correct chi-square statistic?\nA. 1.47\nB. 2.85\nC. 3.92\nD. 5.04\nE. 6.18\n", "Answer (final answer highlighted)": "(D) As a first step, it is important to identify the expected values. The farm was expecting an equal number of chickens of each type, which means that the expected value was 300 for each category. This is shown in the table below. The final result is gained from the sum of the individual statistics, which is 5.04.", "ImagePath": "Math/206" }, { "Question": "Question: 433\nA teacher at a community college is expecting that 10% of her class will get an A on their exam, 15% will get a B, 35% will get a C, 25% will get a D, while 15% will get an F. All of the students participated in the exam. The actual values were that 22 students got an A, 18 got a B, 25 got a C, 15 got a D, and 20 failed the test and got an F. Which of the following is the correct chi-square statistic?\nA. 1.92\nB. 5.47\nC. 17.25\nD. 21.24\nE. 23.52\n", "Answer (final answer highlighted)": "(E) The first step is determining the expected values. The total value can be gained by summing all of the students, since all students participated in the exam. The total is 22 + 18 + 25 + 15 + 20, which is equal to 100. The corresponding expected values and the calculations are shown in the table below. http://img.apstudy.net/ap/statistics/a500/f0288-02.jpg Based on calculating all of the steps required, the sum is therefore 23.52.", "ImagePath": "Math/207" }, { "Question": "Question: 434\nA building inspector inspects four major construction sites every day. In a sample of 100 days, the number of times each site passed inspection is shown in this chart.\n \nTest the hypothesis that Sites C and D pass inspection twice as often as Sites A and B; that is, that the frequency of passing inspection has the ratio 1:1:2:2.\nA. There is sufficient evidence at both the 10% and 5% significance levels that there is not a good fit with the indicated ratio.\nB. There is sufficient evidence at the 10% level, but not at the 5% level, that there is not a good fit with the indicated ratio.\nC. There is sufficient evidence at the 5% level, but not at the 10% level, that there is not a good fit with the indicated ratio.\nD. There is not sufficient evidence at either the 10% or 5% significance levels that there is not a good fit with the indicated ratio.\nE. There is not sufficient information to answer the question.\n", "Answer (final answer highlighted)": "(D) We have H0: good fit with a 1:1:2:2 ratio. Noting that 45 + 33 + 74 + 76 = 228, http://img.apstudy.net/ap/statistics/a500/Ans_Eq_249.jpg and http://img.apstudy.net/ap/statistics/a500/Ans_Eq_250.jpg", "ImagePath": "Math/208" }, { "Question": "Question: 437\nA school class is going on a class trip, and a vote is being taken of where the class wants to go. The school expects that half of the students would want to go to Disney World, while the other half would want to go to visit Washington, DC Despite these expectations, only 42 students wanted to go to Washington, DC, while twice as many wanted to go to Disney World. Which of the following correctly identifies the chi-square statistic?\nA. 4.1\nB. 7\nC. 14\nD. 17.4\nE. 22\n", "Answer (final answer highlighted)": "(C) If the number of students who want to go to Washington, DC, is 42, this means that 84 want to go to Disney World. This means that the school expected that 126/2 = 63 students would want to go on each trip. The final calculation is shown in the table below. This shows us that the final value of the chi-square statistic is 14.", "ImagePath": "Math/209" }, { "Question": "Question: 441\nA company decides to finance a trip as part of a team-building activity for its employees. All 135 employees could decide on whichever location they would visit, and the company expected that the same number of people would go to each of these locations. Despite this expectation, 43 people went to Paris, 59 to London, and 33 to Athens. Which of the following identifies the correct chi-square statistic between the expected and actual number of people?\nA. 3.62\nB. 5.18\nC. 7.64\nD. 9.18\nE. 11.31\n", "Answer (final answer highlighted)": "(C) Because the company expected each country to be visited by the same number of its employees, this means that it anticipated 135/3 = 45 employees would go to each city. From this information, it is easy to calculate the chi-square statistic as shown in the table below. http://img.apstudy.net/ap/statistics/a500/f0289-02.jpg When we round the result, it indicates that the correct chi-square statistic is 7.64.", "ImagePath": "Math/210" }, { "Question": "Question: 447\nUsing the given contingency table, determine whether there is evidence that the type of vote is dependent on gender at the 5% level.\n \nA. The null hypothesis is rejected, which implies there is evidence that the type of vote is dependent on gender.\nB. The null hypothesis is not rejected, which implies there is evidence that the type of vote is dependent on gender.\nC. The null hypothesis is rejected, which implies that there is no evidence that the type of vote is dependent on gender.\nD. The null hypothesis is not rejected, which implies that there is no evidence that the type of vote is dependent on gender.\nE. There is not enough information to determine whether the null hypothesis would be rejected.\n", "Answer (final answer highlighted)": "(D) To determine whether the two variables are related, we will use a chi-squared test of independence and get a test statistic of 2.78, which leads us to fail to reject the null hypothesis that the two variables are independent.", "ImagePath": "Math/211" }, { "Question": "Question: 449\nGiven the contingency table below, determine the expected frequency of cell 1, 3.\n \nA. 83.7\nB. 85\nC. 115\nD. 116.7\nE. 899\n", "Answer (final answer highlighted)": "(D) Cell 1,3 represents the value in the first row and third column. The expected frequency of this cell is http://img.apstudy.net/ap/statistics/a500/Ans_Eq_252.jpg", "ImagePath": "Math/212" } ], "Chemistry": [ { "Question": "Based on the strength of the intermolecular forces in each substance, estimate from greatest to smallest the vapor pressures of each substance in liquid state at the same temperature.\n\nA. propane > ethanal > ethene > methanol\nB. ethene > propane > ethanal > methanol\nC. ethanal > methanol > ethene > propane\nD. methanol > ethanal > propane > ethene", "Answer (final answer highlighted)": "B Vapor pressure is dependent on intermolecular forces. The weaker the IMFs are, the easier it is for molecules to escape from the surface of the liquid. To begin, polar molecules have stronger IMFs than nonpolar molecules. Methanol and ethanal are both polar, but methanol has hydrogen bonding meaning it has stronger IMFs (and thus a lower vapor pressure) than ethanal. Ethene and propane are both nonpolar, but propane is larger meaning it is more polarizable than ethene and thus has stronger IMFs and lower vapor pressure.", "ImagePath": "Chemistry/1" }, { "Question": "When in liquid state, which two substances are most likely to be miscible with water?\n\nA. propane and ethene\nB. methanol and propane\nC. ethene and ethanal\nD. methanol and ethanal", "Answer (final answer highlighted)": "D Water is polar, and using \"like dissolves like,\" we know that only polar solvents will be able to fully mix with it to create a homogenous solution.", "ImagePath": "Chemistry/2" }, { "Question": "Between propane and ethene, which will likely have the higher boiling point and why?\n\nA. propane, because it has a greater molar mass\nB. propane, because it has a more polarizable electron cloud\nC. ethene, because of the double bond\nD. ethene, because it is smaller in size", "Answer (final answer highlighted)": "B Both are nonpolar, but propane has a lot more electrons and thus is more polarizable than ethene.", "ImagePath": "Chemistry/3" }, { "Question": "The graph below shows the amount of potential energy between two hydrogen atoms as the distance between them changes. At which point in the graph would a molecule of $H_2$ be the most stable?\n\nA. Point A\nB. Point B\nC. Point C\nD. Point D", "Answer (final answer highlighted)": "C The molecule would be the most stable when it has the largest attractive potential energy, which is represented by a negative sign. While the magnitude of the potential energy may be larger at (A), it is repulsive at that point because the nuclei are too close together.", "ImagePath": "Chemistry/4" }, { "Question": "Two alloys are shown in the diagrams below\u2014bronze, and steel. Which of the following correctly describes the malleability of both alloys compared to their primary metals?\n\nA. Bronze's malleability would be comparable to that of copper, but steel's malleability would be significantly lower than that of iron.\nB. Bronze's malleability would be significantly higher than that of copper, but steel's malleability would be comparable to that of iron.\nC. Both bronze and steel would have malleability values similar to those of their primary metals.\nD. Both bronze and steel would have malleability values greater than those of their primary metals.", "Answer (final answer highlighted)": "C Alloys of any type generally have malleability that is very similar to the metals from which they are created.", "ImagePath": "Chemistry/5" }, { "Question": "The following diagram shows the relative atomic sizes of three different elements from the same period. Which of the following statements must be true?\n\nA. The effective nuclear charge would be the greatest in element X.\nB. The first ionization energy will be greatest in element X.\nC. The electron shielding effect will be greatest in element Z.\nD. The electronegativity value will be greatest in element Z.", "Answer (final answer highlighted)": "D Moving across a period, atomic size decreases. Therefore, atom Z will be farthest to the right (have the most protons), and thus will have the highest electronegativity value.", "ImagePath": "Chemistry/6" }, { "Question": "Two half-cells are set up as follows:\n\nHalf-Cell A: Strip of Cu(s) in $CuNO_3(aq)$\n\nHalf-Cell B: Strip of Zn(s) in $Zn(NO_3)_2(aq)$\n\nWhen the cells are connected according to the following diagram, the following reaction occurs. Correctly identify the anode and cathode in this reaction as well as where oxidation and reduction are taking place. \n A. Cu is the anode where oxidation occurs, and Zn is the cathode where reduction occurs. \n B. Cu is the anode where reduction occurs, and Zn is the cathode where oxidation occurs. \b C. Zn is the anode where oxidation occurs, and Cu is the cathode where reduction occurs. \n D. Zn is the anode where reduction occurs, and Cu is the cathode where oxidation occurs.", "Answer (final answer highlighted)": "C The oxidation state of copper changes from +1 to 0, meaning it has gained electrons and is being reduced, and reduction occurs at the cathode. Zinc's oxidation state changes from 0 to +2, meaning it has lost electrons and is being oxidized, which occurs at the anode.", "ImagePath": "Chemistry/7" }, { "Question": "Two half-cells are set up as follows:\n\nHalf-Cell A: Strip of Cu(s) in $CuNO_3(aq)$\n\nHalf-Cell B: Strip of Zn(s) in $Zn(NO_3)_2(aq)$\n\nWhen the cells are connected according to the following diagram, the following reaction occurs. How many moles of electrons must be transferred to create 127 g of copper?\n\nA. 1 mole of electrons\nB. 2 moles of electrons\nC. 3 moles of electrons\nD. 4 moles of electrons", "Answer (final answer highlighted)": "B 127 g is equal to 2 moles of copper, which is what appears on the balanced equation. To change one mole of copper from +1 to 0, 1 mole of electrons is required. Twice as many moles being created means twice as many electrons are needed.", "ImagePath": "Chemistry/8" }, { "Question": "Two half-cells are set up as follows:\n\nHalf-Cell A: Strip of Cu(s) in $CuNO_3(aq)$\n\nHalf-Cell B: Strip of Zn(s) in $Zn(NO_3)_2(aq)$\n\nWhen the cells are connected according to the following diagram, the following reaction occurs. If the $Cu^+ + e^- \u2192 Cu(s)$ half reaction has a standard reduction potential of +0.52 V, what is the standard reduction potential for the $Zn^{2+} + 2e^- \u2192 Zn(s)$ half reaction?\n\nA. +0.76 V\nB. -0.76 V\nC. +0.24 V\nD. -0.24 V", "Answer (final answer highlighted)": "B $ E_{\\text{cell}} = E_{\\text{red}} + E_{\\text{ox}} $\n$ 1.28 \\, V = 0.52 \\, V + E_{\\text{ox}} $\n$ E_{\\text{ox}} = 0.76 \\, V $\n$ -E_{\\text{ox}} = E_{\\text{red}} $\n$ E_{\\text{red}} = -0.76 \\, V $", "ImagePath": "Chemistry/9" }, { "Question": "Two half-cells are set up as follows:\n\nHalf-Cell A: Strip of Cu(s) in $CuNO_3(aq)$\n\nHalf-Cell B: Strip of Zn(s) in $Zn(NO_3)_2(aq)$\n\nWhen the cells are connected according to the following diagram, the following reaction occurs. As the reaction progresses, what will happen to the overall voltage of the cell?\n\nA. It will increase as [$Zn^{2+}$] increases.\nB. It will increase as [$Cu^{+}$] increases.\nC. It will decrease as [$Zn^{2+}$] increases.\nD. The voltage will remain constant.", "Answer (final answer highlighted)": "C As the reaction progresses, [Cu+] will decrease and [Zn2+] will increase. With a lower concentration on the reactants side and a higher concentration on the products side, the reaction will shift left, decreasing the overall potential of the reaction.", "ImagePath": "Chemistry/10" }, { "Question": "Two half-cells are set up as follows:\n\nHalf-Cell A: Strip of Cu(s) in $CuNO_3(aq)$\n\nHalf-Cell B: Strip of Zn(s) in $Zn(NO_3)_2(aq)$\n\nWhen the cells are connected according to the following diagram, the following reaction occurs. What will happen in the salt bridge as the reaction progresses?\n\nA. The Na+ ions will flow to the Cu/Cu+ half-cell.\nB. The Br- ions will flow to the Cu/Cu+ half-cell.\nC. Electrons will transfer from the Cu/Cu+ half-cell to the Zn/Zn2+ half-cell.\nD. Electrons will transfer from the Zn/Zn2+ half-cell to the Cu/Cu+ half-cell.", "Answer (final answer highlighted)": "A The electron transfer does not happen across the salt bridge, eliminating options (C) and (D). As the reaction progresses and [Cu+] decreases in the copper half-cell, positively charged sodium ions are transferred in to keep the charge balanced within the half-cell.", "ImagePath": "Chemistry/11" }, { "Question": "A solution of carbonic acid, $H_2CO_3$, is titrated with sodium hydroxide, NaOH. The following graph is produced. In addition to $OH^-$, what species are present in the solution during section III of the graph?\n\nA. $H_2CO_3$, $HCO_3^-$, and $CO_3^{2-}$\nB. $H_2CO_3$ and $HCO_3^-$\nC. $HCO_3^-$ and $CO_3^{2-}$\nD. $H_2CO_3$ and $CO_3^{2-}$", "Answer (final answer highlighted)": "C During sections I and II, the following reaction occurs: $H_2CO_3(aq) + OH^-(aq) \\leftrightarrow HCO_3^-(aq) + H_2O(l)$. The endpoint of that is reached when all $H_2CO_3$ has reacted, meaning that in sections III and IV the following occurs: $HCO_3^-(aq) + OH^-(aq) \\leftrightarrow CO_3^{2-}(aq) + H_2O(l)$.", "ImagePath": "Chemistry/12" }, { "Question": "A solution of carbonic acid, H2CO3, is titrated with sodium hydroxide, NaOH. The following graph is produced. What is the magnitude of the first dissociation constant?\n\nA. 10e-2\nB. 10e-4\nC. 10e-6\nD. 10e-8", "Answer (final answer highlighted)": "C During sections I and II, the following reaction occurs: $H_2CO_3(aq) + OH^-(aq) \\leftrightarrow HCO_3^-(aq) + H_2O(l)$. The endpoint of that is reached when all $H_2CO_3$ has reacted, meaning that in sections III and IV the following occurs: $HCO_3^-(aq) + OH^-(aq) \\leftrightarrow CO_3^{2-}(aq) + H_2O(l)$.", "ImagePath": "Chemistry/13" }, { "Question": "A solution of carbonic acid, H2CO3, is titrated with sodium hydroxide, NaOH. The following graph is produced. If the concentration of the sodium hydroxide is increased prior to repeating the titration, what effect, if any, would that have on the graph?\n\nA. The graph would not change at all.\nB. The pH values at the equivalence points would increase.\nC. The equivalence points would be reached with less volume of NaOH added.\nD. The slope of the equivalence points would decrease.", "Answer (final answer highlighted)": "C A more concentrated NaOH solution means more moles of NaOH are added per drop, so a lower volume of NaOH would be needed to add enough moles to reach the equivalence point.", "ImagePath": "Chemistry/14" }, { "Question": "Two solutions of potassium carbonate and sodium chloride are mixed together, and the particulate representation below shows what is present after the reaction has gone to completion. Which of the two original solutions is the limiting reagent and why?\n\nA. The potassium carbonate, because of the polyatomic anion\nB. The potassium carbonate, because there is no carbonate left after the reaction\nC. The calcium chloride, because there is an excess of calcium ions post-reaction\nD. The calcium chloride, because the component ions are smaller than those in potassium carbonate", "Answer (final answer highlighted)": "B If extra $Ca^{2+}$ ions are in solution, that means there were not enough $CO3^{2-}$ ions present for the $Ca^{2+}$ ions to fully react.", "ImagePath": "Chemistry/15" }, { "Question": " The structure of two oxoacids is shown below. Which would be a stronger acid, and why?\n\nA. HOCl, because the H\u2013O bond is weaker than in HOF as chlorine is larger than fluorine\nB. HOCl, because the H\u2013O bond is stronger than in HOF as chlorine has a higher electronegativity than fluorine\nC. HOF, because the H\u2013O bond is stronger than in HOCl as fluorine has a higher electronegativity than chlorine\nD. HOF, because the H\u2013O bond is weaker than in HOCl as fluorine is smaller than chlorine", "Answer (final answer highlighted)": "D The weaker the O-H bond is in an oxoacid, the stronger the acid will be because the H+ ions are more likely to dissociate. The O-F bond in HOF is stronger than the O-Cl bond in HOCl because fluorine is smaller (and thus more electronegative) than chlorine. If the O-F bond is stronger, the O-H bond is correspondingly weaker, making HOF the stronger acid.", "ImagePath": "Chemistry/16" }, { "Question": "The following diagrams show the Lewis structures of four different molecules. Which molecule would travel the farthest in a paper chromatography experiment using a polar solvent?\n\nA. Methanol\nB. Pentane\nC. Acetone\nD. Ether", "Answer (final answer highlighted)": "A In a polar solvent, polar molecules will be the most soluble (like dissolves like). Of the four options, methanol and acetone would both have dipoles, but those of methanol would be significantly stronger due to the H-bonding.", "ImagePath": "Chemistry/17" }, { "Question": "Four different acids are added to beakers of water, and the following diagrams represent the species present in each solution at equilibrium. Which acid has the highest pH?\n\nA. Acid 1\nB. Acid 2\nC. Acid 3\nD. Acid 4", "Answer (final answer highlighted)": "C The strength of an acid is dependent on the amount it dissociates in solution. A low dissociation is signified by a low presence of hydrogen ions. The weakest acid is choice (C).", "ImagePath": "Chemistry/18" }, { "Question": "Lewis diagrams for the nitrate and nitrite ions are shown below. Choose the statement that correctly describes the relationship between the two ions in terms of bond length and bond energy.\n\nA. Nitrite has longer and stronger bonds than nitrate.\nB. Nitrite has longer and weaker bonds than nitrate.\nC. Nitrite has shorter and stronger bonds than nitrate.\nD. Nitrite has shorter and weaker bonds than nitrate.", "Answer (final answer highlighted)": "C Nitrate has a bond order of 1.33. Nitite has a bond order of 1.5. A higher bond order means shorter and stronger bonds.", "ImagePath": "Chemistry/19" }, { "Question": "$NO_2$ gas is placed in a sealed, evacuated container and allowed to decompose via the following equation:\n\n$2NO_2(g) \u2194 2NO(g) + O_2(g)$\n\nThe graph below indicates the change in concentration for each species over time. What is happening to the rate of the forward reaction at t = 60 s?\n\nA. It is increasing.\nB. It is decreasing.\nC. It is remaining constant.\nD. It is zero.", "Answer (final answer highlighted)": "C At equilibrium, the concentrations of all species in the reaction are remaining constant, which shows up as a flat line on the graph. The rate of both the forward and reverse reactions are constant at equilibrium.", "ImagePath": "Chemistry/20" }, { "Question": "$NO_2$ gas is placed in a sealed, evacuated container and allowed to decompose via the following equation:\n\n$2NO_2(g) \u2194 2NO(g) + O_2(g)$\n\nThe graph below indicates the change in concentration for each species over time. As the reaction progresses, what happens to the value of the equilibrium constant Kp if the temperature remains constant?\n\nA. It stays constant.\nB. It increases exponentially.\nC. It increases linearly.\nD. It decreases exponentially.", "Answer (final answer highlighted)": "A The only factor that can affect the value of the equilibrium constant is temperature. If the temperature does not change, neither does the equilibrium constant.", "ImagePath": "Chemistry/21" }, { "Question": "$NO_2$ gas is placed in a sealed, evacuated container and allowed to decompose via the following equation:\n\n$2NO_2(g) \u2194 2NO(g) + O_2(g)$\n\nThe graph below indicates the change in concentration for each species over time. What would happen to the slope of the $NO_2$ line if additional $O_2$ were injected into the container?\n\nA. It would increase, then level off.\nB. It would decrease, then level off.\nC. It would remain constant.\nD. It would increase, then decrease.", "Answer (final answer highlighted)": "A If additional $O_2$ were injected into the container, the reaction would shift left, increasing the amount of $NO_2$ present. Eventually, the reaction would reach equilibrium again, meaning the lines would level out.", "ImagePath": "Chemistry/22" }, { "Question": "$NO_2$ gas is placed in a sealed, evacuated container and allowed to decompose via the following equation:\n\n$2NO_2(g) \u2194 2NO(g) + O_2(g)$\n\nThe graph below indicates the change in concentration for each species over time. Using the graph, how could you determine the instantaneous rate of disappearance of $NO_2$ at t = 30 s?\n\nA. By determining the area under the graph at t = 30 s\nB. By taking the slope of a line tangent to the $NO_2$curve at t = 30 s\nC. By using the values at t = 30 s and plugging them into the Kp expression\nD. By measuring the overall gas pressure in the container at t = 30 s.", "Answer (final answer highlighted)": "B To determine the change in concentration at a specific time, we would need the slope of the line at that point. As the line is curved, the only way to do that (without calculus) is to draw a line tangent to the curve at that point and measure its slope.", "ImagePath": "Chemistry/23" }, { "Question": "The reaction shown in the following diagram is accompanied by a large increase in temperature. If all molecules shown are in their gaseous state, which statement accurately describes the reaction?\n\nA. It is an exothermic reaction in which entropy increases.\nB. It is an exothermic reaction in which entropy decreases.\nC. It is an endothermic reaction in which entropy increases.\nD. It is an endothermic reaction in which entropy decreases.", "Answer (final answer highlighted)": "A The temperature increase is indicative of energy being released, meaning the reaction is exothermic. The entropy (disorder) of the system is increasing as it moves from three gas molecules to five.", "ImagePath": "Chemistry/24" }, { "Question": "The contents in the three containers on the left in the diagram above are transferred to the container on the right. The volumes of the original containers are exactly the values indicated. The pressure in the first three containers is 1.0 atm. What is the pressure in the container on the right?\n\nA. 3.0 atm\nB. 4.0 atm\nC. 1.1 atm\nD. 0.50 atm\n", "Answer (final answer highlighted)": "C: There are several ways of solving this problem. One way is to determine the moles present in the original containers, which must be the same as in the final container. In each case, moles = n = PV/RT. Numbering the containers from left to right as 1, 2, 3, and 4 gives: https://img.crackap.com/ap/chemistry/a5/Image00498.jpg", "ImagePath": "Chemistry/25" }, { "Question": "The diagram above shows the structure of molecules of CS2 and COS. The boiling point of COS is 223 K, and the boiling point of CS2 is 319 K. Which of the following is the best explanation of why the boiling point of CS2 is higher?\n\nA. The molar mass of CS2 is greater.\nB. COS has weaker covalent bonds than CS2.\nC. Only CS2 can form intermolecular dipole-dipole forces.\nD. COS has stronger intermolecular forces because it is polar and CS2 is not.", "Answer (final answer highlighted)": "A: Stronger intermolecular forces lead to higher boiling points. Even though COS has dipole-dipole forces, which are usually stronger than the London dispersion forces present in CS2, the greater molar mass of CS2 leads to a London dispersion force contribution that is sufficient to compensate for the general trend of dipole-dipole forces being stronger than London dispersion forces. This is why comparisons should only be made between molecules of similar molecular masses.", "ImagePath": "Chemistry/26" }, { "Question": "Which of the following best explains why the boiling point of 2-propanol is lower than the other two compounds in the diagram and table above?\n\nA. Larger molecules get tangled and cannot escape each other.\nB. It has weaker hydrogen bonds.\nC. It is the lightest of the three.\nD. It is a more symmetrical molecule.", "Answer (final answer highlighted)": "C: All three compounds are capable of hydrogen bonding; therefore, this cannot be the cause of difference. In general, all other things being equal, it takes less energy to move a lighter molecule from the liquid state to the gaseous state.w", "ImagePath": "Chemistry/27" }, { "Question": "The Dumas method is a procedure for determining the molar mass of a gas. In this procedure the mass of a gas is divided by the moles of gas determined from the ideal gas equation (n = PV/RT). The molar masses of some compounds, such as acetic acid, illustrated above, show significant deviations from the \u201ccorrect\u201d values. Why does the presence of dimers as illustrated make it unlikely to obtain an accurate molar mass of acids, such as acetic acid?\n\nA. Acetic acid, like all acids, will lose a hydrogen ion, so the molar mass is that of the acetate ion, which is less than that of acetic acid.\nB. Acetic acid is a liquid at room temperature, and its boiling point is too high to get accurate results.\nC. Acids are too reactive to give accurate results.\nD. The presence of strong intermolecular forces (hydrogen bonding) makes the gas nonideal; therefore the ideal gas law is not applicable.", "Answer (final answer highlighted)": "D: Strong hydrogen bonds hold two molecules of acetic acid together. Ideal gases have no intermolecular forces. Therefore, the ideal gas law used in experiment is invalid.", "ImagePath": "Chemistry/27" }, { "Question": "Which of the labeled arrows in the diagram above represents the strongest intermolecular force?\n\nA. A\nB. B\nC. C\nD. D", "Answer (final answer highlighted)": "B-This is a dipole-dipole force, which is stronger than a dipole-induced dipole (A and C) or a London dispersion force (D).", "ImagePath": "Chemistry/28" }, { "Question": "pH versus volume of titrant added\nThe diagram above represents the idealized titration curve for the reaction of pure sodium carbonate, Na2CO3, with a strong acid such as hydrochloric acid, HCl. E and F represent the pH at the endpoints corresponding to the formation of HCO3- and H2CO3, respectively. G and H correspond to the quantity of acid required to reach the endpoints.\nA trial run used a sample of pure sodium carbonate. How does the volume of acid necessary to reach G from 0 compare to the volume of acid necessary to get from G to H?\n\nA. They are the same.\nB. It takes more to reach point G.\nC. It takes more to get from G to H.\nD. It is impossible to determine", "Answer (final answer highlighted)": "A: At point G, all the $CO3^{2-}$ has been converted to $HCO^{3-}$ and the moles of $ HCO^{3-}$ will equal the moles of $CO3^{2-}$ originally present plus the quantity of $HCO^{3-}$ originally present. It will require a greater volume of acid to titrate a greater number of moles of $HCO^{3-}$ as required for the $CO3^{2-}$.", "ImagePath": "Chemistry/29" }, { "Question": "pH versus volume of titrant added\nThe diagram above represents the idealized titration curve for the reaction of pure sodium carbonate, Na2CO3, with a strong acid such as hydrochloric acid, HCl. E and F represent the pH at the endpoints corresponding to the formation of HCO3- and H2CO3, respectively. G and H correspond to the quantity of acid required to reach the endpoints.\nThe analysis of a sample contaminated with NaHCO3 gave slightly different results. How does the volume of acid necessary to reach G from 0 compare to the volume of acid necessary to get from G to H for the second sample?\n\nA. It takes more to get from G to H.\nB. It takes more to reach point G.\nC. They are the same.\nD. It is impossible to determine.", "Answer (final answer highlighted)": "C: It would be necessary to titrate the strong base and the $CO3^{2-}$ to reach G. However, it is only necessary to titrate the $HCO_{3-}$ to reach H, which means less acid is necessary.\n\n", "ImagePath": "Chemistry/30" }, { "Question": "pH versus volume of titrant added\nThe diagram above represents the idealized titration curve for the reaction of pure sodium carbonate, Na2CO3, with a strong acid such as hydrochloric acid, HCl. E and F represent the pH at the endpoints corresponding to the formation of HCO3- and H2CO3, respectively. G and H correspond to the quantity of acid required to reach the endpoints.\nHow could a student determine if there was a strong acid or a strong base contaminant in the original sample?\n\nA. The presence of an acid contaminant would require less acid to reach H from G than to reach G from 0.\nB. The presence of a base contaminant would require less acid to reach G from 0 than to reach F from G.\nC. The presence of a base contaminant would require more acid to reach G from 0 than to reach F from G.\nD. It is impossible to determine.", "Answer (final answer highlighted)": "C-It would be necessary to titrate the strong base and the $CO3^{2-}$ to reach G. However, it is only necessary to titrate the $HCO3^{-}$ to reach H, which means less acid is necessary.", "ImagePath": "Chemistry/31" }, { "Question": "pH versus volume of titrant added\nThe diagram above represents the idealized titration curve for the reaction of pure sodium carbonate, Na2CO3, with a strong acid such as hydrochloric acid, HCl. E and F represent the pH at the endpoints corresponding to the formation of HCO3- and H2CO3, respectively. G and H correspond to the quantity of acid required to reach the endpoints.\nIn addition to water, what are the predominant species in solution at F?\n\nA. $\\ch{Na2CO3}$ and $\\ch{HCl}$\nB. $\\ch{Na+}$, $\\ch{Cl-}$, and $\\ch{H2CO3}$\nC. $\\ch{HCO3-}$ and $\\ch{H+}$\nD.$ \\ch{Na+}$, $\\ch{Cl-}$, $\\ch{H+}$, and $\\ch{CO3^{2-}}$", "Answer (final answer highlighted)": "B: At G the $\\ch{CO3^{2-}}$ is now $\\ch{HCO3-},$ so no $\\ch{CO3^{2-}}$ remains. The $\\ch{Na+}$ did not react, so it is still present as ions. The $\\ch{Cl-}$ is from the HCl and remains as separate ions in solution. After G, the $\\ch{H+}$ from the acid begins to convert $\\ch{HCO3-}$ to form $\\ch{H2CO3}$, which is complete at point F leaving no $\\ch{HCO3-}$ in the solution. Other than water, all species are strong electrolytes and exist as ions in solution. The $\\ch{H2CO3}$ will be decomposing to $\\ch{H2O}$ and $\\ch{CO2(g)}$.", "ImagePath": "Chemistry/32" }, { "Question": "pH versus volume of titrant added\nThe diagram above represents the idealized titration curve for the reaction of pure sodium carbonate, Na2CO3, with a strong acid such as hydrochloric acid, HCl. E and F represent the pH at the endpoints corresponding to the formation of HCO3- and H2CO3, respectively. G and H correspond to the quantity of acid required to reach the endpoints.\nIn addition to water, what are the predominant species in solution at F?\n\nAt what point on the graph for the titration of pure sodium carbonate is the pH =\\ch{ pK_{a2}} for carbonic acid?\n\nA. At point G\nB. Halfway between the start and point G\nC. At point H\nD. Halfway between points G and H", "Answer (final answer highlighted)": "D: The pH will equal the pKa2 when the concentration of $HCO_{3-}$ equals the concentration of H2CO3. This occurs when one-half of the $HCO_{3-}$ has been converted to H2CO3.", "ImagePath": "Chemistry/33" }, { "Question": "What is the reason that the lightest member of Group 15 does not follow the trend of the other members, which show that the boiling point decreases with decreasing atomic mass of the Group 15 element?\nThe graph shows the variation of boiling point with Group number for the hydrogen compounds of the four lightest members of Group 15 on the periodic table (NH3, PH3, AsH3 and SbH3).\n\nA. Ionic bonds\nB. Hybrid orbitals\nC. Resonance structures\nD. Hydrogen bonding", "Answer (final answer highlighted)": "\nD: Hydrogen bonding may occur when hydrogen is attached directly to N, O, or F.", "ImagePath": "Chemistry/34" }, { "Question": "A dimer consists of two closely associated molecules. In the gas phase, acetic acid tends to form dimers as illustrated on the left in the above diagram. Acetyl chloride, on the right in the above diagram, is not very efficient in forming dimers. Why is acetic acid better able to form dimers than acetyl chloride?\n\nA. The molecular mass of acetyl chloride is higher than that of acetic acid making it harder for the acetyl chloride to form dimers.\nB. It is easier to form a covalent bond between acetic acid molecules than between acetyl chloride molecules.\nC. Acetic acid can form strong hydrogen bonds but acetyl chloride can only form weaker dipole-dipole attractions.\nD. Acetic acid is an acidic compound but acetyl chloride is a neutral compound.", "Answer (final answer highlighted)": "C: The two molecules are hydrogen bonded together. Hydrogen bonding is a relatively strong intermolecular force. Acetyl chloride cannot exhibit anything stronger than dipole-dipole forces, which are, in general, weaker than hydrogen bonds.", "ImagePath": "Chemistry/35" }, { "Question": "Two compounds with the formula C2H2Cl2 appear in the above diagram. These two compounds are isomers. The molecules are planar and have the approximate structures shown in the diagram. The boiling point of trans-1, 2-dichloroethene is 47.5\u00b0C and the boiling point of cis-1,2-dichloroethene is 60.3\u00b0C. Which of the following best explains why cis-1,2-dichloroethene has a higher boiling point than its isomer, trans-1, 2-dichloroethene?\n\nA. The higher boiling isomer is more polar than the other isomer.\nB. The higher boiling isomer is better able to form hydrogen bonds than the other isomer.\nC. The higher boiling isomer has a greater molar mass.\nD. The higher boiling isomer has greater London dispersion forces than the other isomer.", "Answer (final answer highlighted)": "A: The higher boiling isomer is more polar than the other isomer because the two very electronegative chlorine atoms are on one side, which leads to their polar bonds working together. When the chlorine atoms are on opposite sides, their polar bonds work against each other.", "ImagePath": "Chemistry/36" }, { "Question": "Use the following information on the bases in the following diagram to answer questions.\nhttps://img.crackap.com/ap/chemistry/a5/Image00543.jpg\n\nAmmonia is only present as a reference. Questions only refer to the other three bases.\nhttps://img.crackap.com/ap/chemistry/a5/Image00544.jpg\n\nAll the bases in the diagram behave as Br\u00f8nsted-Lowry bases in the same way; in each case, they accept a hydrogen ion to the same atom. How is this acceptance of a hydrogen ion accomplished?\n\nA. A hydrogen ion attaches to the lone pair on the nitrogen atom.\nB. The hydroxide ion reacts with the hydrogen ion to form water.\nC. The hydrogen ion forms a hydrogen bond to the base.\nD. The hydrogen ion combines with a hydrogen atom from the base to form H2 gas", "Answer (final answer highlighted)": "A: As in ammonia, all these compounds behave as Br\u00f8nsted-Lowry bases by accepting a hydrogen ion. The reaction involves the hydrogen ion attaching to the lone pair on the nitrogen atoms.", "ImagePath": "Chemistry/37" }, { "Question": "Use the following information on the bases in the following diagram to answer questions.\nhttps://img.crackap.com/ap/chemistry/a5/Image00543.jpg\n\nAmmonia is only present as a reference. Questions only refer to the other three bases.\nhttps://img.crackap.com/ap/chemistry/a5/Image00544.jpg\n\nWhich of the following explains why the pH of a hydroxylamine solution is lower than any of the other solutions?\n\nA. The $-OH$ is capable of donating a hydrogen ion, which will lower the pH.\nB. The presence of carbon makes the bases less stable.\nC. The presence of the very electronegative oxygen inhibits the nitrogen atom from donating its electron pair.\nD. There is insufficient information to explain this observation.", "Answer (final answer highlighted)": "C: These are all bases because the nitrogen atom is capable of reacting with a hydrogen ion by donating its lone pair to the hydrogen ion. The oxygen atom pulls electron density away from the nitrogen atom causing the nitrogen atom to attract the lone pair more strongly making it less able to donate the pair to a hydrogen ion.", "ImagePath": "Chemistry/37" }, { "Question": "Which of the compounds in the above diagram is capable of participating in hydrogen bonding?\n\nA. $C_3H_9N$\nB. $CH_3F$\nC. $C_2H_6O$\nD. $C_4H_11$", "Answer (final answer highlighted)": "D: Hydrogen bonding is possible when hydrogen is attached to N, O, and F. D is the only compound in the diagram where this is true. The simple presence of hydrogen and N, O, or F is insufficient.", "ImagePath": "Chemistry/37" }, { "Question": "Ammonia is the best-known nitrogen-hydrogen compound; however, there are a number of other nitrogen-hydrogen compounds, three of which are in the above diagram. Which of these has the longest average N-N bond length?\n\nA. $N_2H_2$\nB. $N_3H_3$\nC. $N_4H_4$\nD. They are all the same.", "Answer (final answer highlighted)": "C: The higher the average number of bonds between the nitrogen atoms, the shorter the bond is. For diazene there are two bonds, for triazene the average is 1.5 bonds, and for tetrazene the average is 1.33 bonds. The length of the average bond length increases in the order 2 < 1.5 < 1.33.", "ImagePath": "Chemistry/38" }, { "Question": "Use the information on the acids in the following diagram to answer questions.\n\nSample solutions of each of the three acids were titrated with 0.10 M sodium hydroxide, NaOH. Each of the acid solutions had a concentration of 0.10 M. Which of the acid titrations had the highest pH at the endpoint?\n\nA. Formic acid\nB. Benzoic acid\nC. Chloroacetic acid\nD. They all had a pH of 7 at the endpoint.", "Answer (final answer highlighted)": "B: The weakest acid (smallest Ka) will have the highest pH at the endpoint.\n\n", "ImagePath": "Chemistry/39" }, { "Question": "Use the information on the acids in the following diagram to answer questions.\n\nA student prepares three buffer solutions. Each solution is 1.0 M in one of the acids in the table and 1.0 M in its corresponding sodium salt. Which of the solutions has the greatest buffer capacity with respect to added NaOH and why?\n\nA. The benzoic acid buffer because it is the strongest acid.\nB. The chloroacetic acid buffer because it is the strongest acid.\nC. The formic acid buffer because it donate both of its hydrogen atoms.\nD. All are the same.", "Answer (final answer highlighted)": "D: The buffer capacity only depends on the number of moles present. All three solutions have the same number of moles.", "ImagePath": "Chemistry/40" }, { "Question": "Cyclopropane, pictured above, is a relatively unstable compound. As seen in the diagram, the carbon atoms form the corners of an equilateral triangle and each carbon atom has two hydrogen atoms attached to complete an octet of electrons around the carbon atoms. Based upon this structure, why is cyclopropane a relatively unstable compound?\n\nA. Hydrocarbon compounds are relatively unstable in general.\nB. Compounds that have identical atoms bonded to each other are relatively unstable.\nC. The bonds do not match the angles.\nD. There is no resonance to stabilize the compound.", "Answer (final answer highlighted)": "C: A carbon atom with four single bonds should be tetrahedral. Tetrahedral atoms have an ideal bond angle of 109.5\u00b0C. However, the carbon atoms in cyclopropane are at the corners of an equilateral triangle, where the ideal angle is 60\u00b0C. The discrepancy between the two ideal bond angles leads to the relative instability of cyclopropane.", "ImagePath": "Chemistry/41" }, { "Question": "Refer to the following information.\n\n$N_2O_4(g)\\rightleftarrows 2NO_2(g)$\n\n$N_2O_4(g)$ decomposes into $NO_2(g)$ according to the equation above. A pure sample of $N_2O_4(g)$ is placed into a rigid, evacuated, 0.500 L container. The initial pressure of the $N_2O_4(g)$ is 760 atm. The temperature is held constant until the $N_2O_4(g)$ reaches equilibrium with its decomposition products. The figure below shows how the pressure of the system changes while reaching equilibrium. Why does the pressure rise in this experiment?\n\nA. The intermolecular attractions inside the container decrease, so the molecules strike the walls more frequently.\nB. The intermolecular attractions inside the container increase, which increases the force as molecules collide with the walls of the container.\nC. The average kinetic energy increases as the reaction continues.\nD. The number of particles striking the container walls per unit time increases.", "Answer (final answer highlighted)": "D: As $N_2O_4(g)$ reacts, we get twice as many molecules, thus increasing the pressure.", "ImagePath": "Chemistry/42" }, { "Question": "Refer to the following information.\n\n$N_2O_4(g)\\rightleftarrows 2NO_2(g)$\n\n$N_2O_4(g)$ decomposes into $NO_2(g)$ according to the equation above. A pure sample of $N_2O_4(g)$ is placed into a rigid, evacuated, 0.500 L container. The initial pressure of the $N_2O_4(g)$ is 760 atm. The temperature is held constant until the $N_2O_4(g)$ reaches equilibrium with its decomposition products. The figure below shows how the pressure of the system changes while reaching equilibrium. The figure above gives us information about all the following except\n\nA. the activation energy\nB. the reaction rate\nC. the position of equilibrium\nD. the order of reaction", "Answer (final answer highlighted)": "A: The only way we know of to determine the activation energy is to measure reaction rates at different temperatures. However, no temperatures are mentioned.", "ImagePath": "Chemistry/43" }, { "Question": "Refer to the following information.\n\n$N_2O_4(g)\\rightleftarrows 2NO_2(g)$\n\n$N_2O_4(g)$ decomposes into $NO_2(g)$ according to the equation above. A pure sample of $N_2O_4(g)$ is placed into a rigid, evacuated, 0.500 L container. The initial pressure of the $N_2O_4(g)$ is 760 atm. The temperature is held constant until the $N_2O_4(g)$ reaches equilibrium with its decomposition products. The figure below shows how the pressure of the system changes while reaching equilibrium. By how much will the equilibrium pressure increase if this reaction goes to completion?\r\n\r\nA. 760 torr\r\nB. 900 torr\r\nC. 634 torr\r\nD. 886 torr", "Answer (final answer highlighted)": "C: The pressure will increase to 1520 torr, which is 634 torr greater than 886 torr.", "ImagePath": "Chemistry/44" }, { "Question": "Refer to the following information.\n\n$N_2O_4(g)\\rightleftarrows 2NO_2(g)$\n\n$N_2O_4(g)$ decomposes into $NO_2(g)$ according to the equation above. A pure sample of $N_2O_4(g)$ is placed into a rigid, evacuated, 0.500 L container. The initial pressure of the $N_2O_4(g)$ is 760 atm. The temperature is held constant until the $N_2O_4(g)$ reaches equilibrium with its decomposition products. The figure below shows how the pressure of the system changes while reaching equilibrium. What can be said about the equilibrium constant, Kp, for this reaction?\r\n\r\nA. $K_p$ > 1\r\nB. $K_p$< 1\r\nC. $K_p$= 1\r\nD. The data do not allow us to estimate the value of $K_p$.", "Answer (final answer highlighted)": "B: If the pressure rises to 886 torr, which means that 126 \u00d7 2 torr of $NO_2$ is produced and 634 torr of $N_2O_4$ remain. Dividing both by 760 torr gives 0.332 atm $NO_2$ and 0.834 atm $N_2O_4$. Since $K_P = (0.332)^2/(0.834)$, we can see that the result must be less than 1.", "ImagePath": "Chemistry/45" }, { "Question": "Refer to the following information.\n\nThis formation equation for the reaction synthesizing RbBr(s) can be separated into a series of steps. Which of the steps in the table above are endothermic?\r\n\r\nA. \u0394H\u00b0(1) and \u0394H\u00b0(2) only\r\nB. \u0394H\u00b0(1), \u0394H\u00b0(2), and \u0394H\u00b0(3) only\r\nC. \u0394H\u00b0(3) only\r\nD. \u0394H\u00b0(3) and \u0394H\u00b0(4) only", "Answer (final answer highlighted)": "B: All processes that separate molecules or break bonds are endothermic.", "ImagePath": "Chemistry/46" }, { "Question": "Refer to the following information.\n\nThis formation equation for the reaction synthesizing RbBr(s) can be separated into a series of steps. If this reaction goes to completion, producing RbBr from the reactants, and if you use the overall chemical equation to estimate the entropy change for this process, which of the following statements is correct?\r\n\r\nA. The reaction is favorable and driven by the enthalpy change since the entropy decreases in this process.\r\nB. The reaction is unfavorable since the entropy change is a large negative value.\r\nC. The reaction is favorable and driven by both enthalpy and entropy changes.\r\nD. The reaction is unfavorable because of the enthalpy and entropy changes.", "Answer (final answer highlighted)": "A: Using general rules, we have a solid and a liquid combining to make one formula unit of solid. A small change in entropy is expected. The enthalpy is very large compared with the entropy values, especially for binary compounds. So this answer is reasonable.", "ImagePath": "Chemistry/47" }, { "Question": "n-pentane ($C_5H_{12}$ or $CH_3CH_2CH_2CH_2CH_3$) and 2,2-dimethylpropane ($C_5H_{12}$ or $(CH_3)_4C$), shown above as space-filling models, each have the same number of carbon and hydrogen atoms but the atoms are arranged differently. n-pentane boils at 36.1 \u00b0C, and 2,2-dimethylpropane boils at 9.5 \u00b0C. Which statement best explains these data?\r\n\r\nA. The long chains of n-pentane make it more difficult for them to reach the liquid surface and vaporize.\r\nB. The long chains of n-pentane provide more sites for London attractive forces for neighboring molecules to have an effect on each other.\r\nC. The compact structure of the 2,2-dimethylpropane directs the attractive forces internally in the molecule.\r\nD. The bonds in the n-pentane are weaker, allowing small parts of the molecule to vaporize easily.", "Answer (final answer highlighted)": "B: Although London forces tend to be small, molecules that allow many sites for interaction experience stronger attractions", "ImagePath": "Chemistry/48" }, { "Question": "Refer to the following information.\n\nFour different acid solutions of 0.0100 M are prepared, and their pH values are recorded on a laptop computer. One of the solutions contains more than just an acid. At the point designated as \"add,\" all four solutions are diluted with an equal volume of water. The bottom line represents solution 1, and the top line represents solution 4. Which of the four acids is best described as a strong acid?\r\n\r\nA. Solution 1\r\nB. Solution 2\r\nC. Solution 3\r\nD. Solution 4", "Answer (final answer highlighted)": "A: A 0.010 M solution of a strong acid should have a pH = 2.00.", "ImagePath": "Chemistry/49" }, { "Question": "Refer to the following information.\n\nFour different acid solutions of 0.0100 M are prepared, and their pH values are recorded on a laptop computer. One of the solutions contains more than just an acid. At the point designated as \"add,\" all four solutions are diluted with an equal volume of water. The bottom line represents solution 1, and the top line represents solution 4. Which acid(s) will require the most 0.0050 M NaOH to neutralize 25.0 mL of a 0.010 M solution of the acid?\r\n\r\nA. Solution 1\r\nB. Solution 2\r\nC. Solution 3\r\nD. They will all require the same volume of NaOH.", "Answer (final answer highlighted)": "D: All of the acid solutions, 1, 2, and 3, will require the same amount of base to reach the end point.", "ImagePath": "Chemistry/50" }, { "Question": "Refer to the following information.\n\nFour different acid solutions are prepared, and their pH values are determined and tabulated below. Using the data in the table above, which is the weakest acid?\r\n\r\nA. Acid 1\r\nB. Acid 2\r\nC. Acid 3\r\nD. Acid 4", "Answer (final answer highlighted)": "D: The weakest acid has the lowest $[H^+]$ and the highest pH.", "ImagePath": "Chemistry/51" }, { "Question": "Refer to the following information.\n\nFour different acid solutions are prepared, and their pH values are determined and tabulated below. Which of the four acids is best described as a strong acid?\r\n\r\nA. Acid 1\r\nB. Acid 2\r\nC. Acid 3\r\nD. Acid 4", "Answer (final answer highlighted)": "B: A strong acid is completely ionized and the molar concentration is equal to the $[H^+]$.", "ImagePath": "Chemistry/52" }, { "Question": "Refer to the following information.\n\nFour different acid solutions are prepared, and their pH values are determined and tabulated below. Which of the following operations will produce an effective buffer solution?\r\n\r\nA. 50.0 mL of 0.010 M acid 3 mixed with 50.0 mL of 0.010 M acid 2\r\nB. 50.0 mL of 0.010 M acid 2 mixed with 25.0 mL of 0.010 M NaOH\r\nC. 50.0 mL of 0.0050 M acid 4 mixed with 0.25 mL of 0.0050 M NaOH\r\nD. 50.0 mL of 0.0010 M acid 2 mixed with 55.0 mL of 0.0010 M NaOH", "Answer (final answer highlighted)": "B: This is the only way to have a significant concentration of both the conjugate acid and conjugate base.", "ImagePath": "Chemistry/53" }, { "Question": "Refer to the following information.\n\nFour different acid solutions are prepared, and their pH values are determined and tabulated below. Each of the acids were titrated with NaOH to the end point. The end point pH values are shown on the last line of the table. The end point pH values\r\n\r\nA. suggest that acid 3 is strong and all the rest are weak\r\nB. suggest that all the acids are weak\r\nC. suggest that acid 1 is most likely polyprotic\r\nD. suggest serious problems with the pH meter", "Answer (final answer highlighted)": "C: An end point lower than pH 7 is indicative of a polyprotic acid.", "ImagePath": "Chemistry/54" }, { "Question": "The graph above shows the distribution of kinetic energies of a system containing a large number of SO2 molecules at 300 K. Which letter shows the average kinetic energy of this system?\r\n\r\nA. A\r\nB. B\r\nC. C\r\nD. D", "Answer (final answer highlighted)": "C: The average kinetic energy is a little above the maximum for this type of distribution curve.", "ImagePath": "Chemistry/55" }, { "Question": "Three 1-liter flasks are connected to a 3-liter flask by valves. The 3-liter flask is evacuated to start and the entire system is at 585 K. The first flask contains oxygen, the second hydrogen, and the third nitrogen. The pressure of hydrogen is 1.65 atm. The amounts of gas molecules are proportional to their representations in the flasks. If valve 2 is opened first and then the rest of the valves are opened, what will the pressure be after the first valve is opened and after they all are opened? Assume the connections have negligible volume.\n\nValve 2 Opened All Valves Opened\n\nA. 1.0 atm 0.5 atm\nB. 0.41 atm 0.82 atm\nC. 0.81 atm 1.65 atm\nD. 2.0 atm 1.0 atm", "Answer (final answer highlighted)": "B: Opening valve 2 will increase the volume by 4 times, so the pressure will be 1/4 of the starting pressure. The amount of particles is doubled by opening the second two valves, so the pressure doubles.", "ImagePath": "Chemistry/56" }, { "Question": "A mass spectrum of a naturally occurring sample of an element is shown above. What is the element?\r\n\r\nA. Ca\r\nB. Ne\r\nC. K\r\nD. Not enough information is provided.", "Answer (final answer highlighted)": "B: This element is 90 percent of an isotope with a mass of almost 20 and 10 percent of an isotope with a mass close to 22. We calculate 0.90 \u00d7 20 + 0.10 \u00d7 22 = 20.2, which is closest to the average mass of Ne.", "ImagePath": "Chemistry/57" }, { "Question": "Refer to the titration curve below, which is of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.125 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the above graph. Which of the following describes the base that is being titrated?\r\n\r\nA. The base is dibasic since two end points are observed.\r\nB. The concentration of the base is exactly 0.125 M.\r\nC. The concentration of the base is slightly more than 0.125 M.\r\nD. The concentration of the base is slightly less than 0.125 M.", "Answer (final answer highlighted)": "D: The end point is at about 22.5 mL, so (25.0 mL)($M_b$) = (22.5 mL)(0.125 M). Inspection of this equation reveals that the concentration is less than 0.125 M.", "ImagePath": "Chemistry/58" }, { "Question": "Refer to the titration curve below, which is of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.125 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the above graph. Between which two points on the titration curve can the solution be described as a buffer?\n\nA. None, it is impossible for a titration solution to also be a buffer solution.\nB. A to F\nC. A to D\nD. D to F", "Answer (final answer highlighted)": "C: Between these two points, there is a significant amount of both the conjugate acid and the conjugate base.", "ImagePath": "Chemistry/59" }, { "Question": "Refer to the titration curve below, which is of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.125 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the above graph. For the best results with a visual indicator (one that changes color), what will optimize the results?\r\n\r\nA. Add the indicator two drops before the end point.\r\nB. Choose an indicator that has a pK that is close to the end point pH.\r\nC. Choose an indicator that has complementary colors.\r\nD. Choose a polyprotic indicator.", "Answer (final answer highlighted)": "B: Choosing an indicator with the same $pK_a$ as the end point pH assures the sharpest color change and closest agreement of the end point (experimental) with the equivalence point (theoretical or calculated point).", "ImagePath": "Chemistry/60" }, { "Question": "Refer to the titration curve below, which is of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.125 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the above graph. If the student uses a pH indicator that changes color from pH 6 to 8, which statement best characterizes the expected observations?\r\n\r\nA. The observed color change will be distinct, and the calculated molarity of the base will be accurate.\r\nB. The color will change slowly, and the end point volume will be low.\r\nC. The color will change slowly, and the calculated molarity of the base will be low.\r\nD. The observed color change will be distinct, but the calculated molarity of the base will be high.", "Answer (final answer highlighted)": "B: Most of the indicator color change is outside the inflection part of the curve.", "ImagePath": "Chemistry/61" }, { "Question": "Refer to the titration curve below, which is of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.125 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the above graph. Which arrow points to the place on the curve where pH = pKaof the conjugate acid of the base?\r\n\r\nA. A\r\nB. E\r\nC. C\r\nD. F", "Answer (final answer highlighted)": "C: The $pH = pK_a$ when the concentration of the conjugate acid and of the conjugate base are equal. This occurs at point C on the curve. The conjugate acid of the base we are titrating in this case is $HB^+$ in the weak base equilibrium $B + H_2O \u2192 HB^+ + OH^-$.", "ImagePath": "Chemistry/62" }, { "Question": "In the diagram above, which labeled arrow is pointing toward a covalent bond and which is pointing toward a hydrogen bond?\r\n\r\nCovalent Bond Hydrogen Bond\r\n\r\nA. 1 2\r\nB. 2 1\r\nC. 3 4\r\nD. 4 3", "Answer (final answer highlighted)": "D: Covalent bonds are shown as solid lines and hydrogen bonds are shown as dashed lines when aligned with the correct atoms.", "ImagePath": "Chemistry/63" }, { "Question": "Morphine, $C_{17}H_{19}NO_3$ (shown above), has a $K_b = 8.0 \u00d7 10^{-7}$. If a 0.00100 M solution of morphine is prepared, the expected pH will be in which one of the following pH ranges?\r\n\r\nA. 2 to 4\r\nB. 4 to 6\r\nC. 8 to 10\r\nD. 10 to 12", "Answer (final answer highlighted)": "C: The $[OH^-]$ will be the square root of the $K_b$ \u00d7 concentration. We can calculate $(8.0 \u00d7 10^{-7})(0.0010) = 8.0 \u00d7 10^{-10}$, and the square root is approximately $3 \u00d7 10^{-5}$. Our answer is between $10^{-5}$ and $10^{-4}, so the pOH is between 4 and 5. The pH will be between 9 and 10.", "ImagePath": "Chemistry/64" }, { "Question": "The volume of a gas is charted over time, giving the above results. Which of the following options provides a possibel explinatin of what was happening to the gas during each phase of the graph?\n\nA. During phase I, the temperature decreased while the pressure increased. During phase II, the temperature was held constant as the pressure decreased.\nB. During phase I, the temperature increased while the pressure was held constant. During phase II, the temperature and pressure both decreased.\nC. During phase I, the temperature was held constant while the pressure increased. During phase II, the temperature and pressure both decreased.\nD. During phase I, the temperature and pressure both increased. During phase II, the temperature was held constant while the pressure decreased.", "Answer (final answer highlighted)": "B In phase I, an increased temperature means the molecules are moving faster and will spread out more, leading to an increased volume. For the volume to remain constant in phase II, either both pressure and volume have to remain constant, or they both have to increase or decrease together, as they are inversely proportional.", "ImagePath": "Chemistry/65" }, { "Question": "The above experiment was performed several times, and the data was gathered as shown in the figure. What is the rate law for this reaction?\n\nA. rate = k[NO][Br$_2$]$^2$\nB. rate = k[NO]$^2$[Br$_2$]$^2$\nC. rate = k[NO][Br$_2$]\nD. rate = k[NO]$^2$[Br$_2$]", "Answer (final answer highlighted)": "D Between trial 1 and 3, the concentration of NO doubled while the concentration of Br$_2$ held constant, and the rate went up by a factor of four. So, the reaction is second order with respect to NO. Between trial 1 and 2, the concentration of NO was held constant while the concentration of Br2 doubled, and the rate went up by a factor of two. Thus, the reaction is first order with respect to Br$_2$.", "ImagePath": "Chemistry/66" }, { "Question": "Regarding reaction II, to achieve the products present in the above diagram how many moles of each reactant must be present prior to the reaction?\n\nA. 1.0 mol of CH$_4$ and 2.0 mol of H$_2$O\nB. 2.0 mol of CH$_4$ and 2.0 mol of H$_2$O\nC. 2.0 mol of CH$_4$ and 3.0 mol of H$_2$O\nD. 3.0 mol of CH$_4$ and 2.0 mol of H$_2$O", "Answer (final answer highlighted)": "C 2.0 moles of CH$_4$ would react with 2.0 moles of H$_2$O, leaving 1.0 mole left. It would also create 6.0 moles of H$_2$ and 2.0 moles of CO.", "ImagePath": "Chemistry/67" }, { "Question": "Identify the three gases represented on the Maxwell-Boltzmann diagram above. Assume all gases are at the same temperature.\n\nA. I \\( \\mathrm{H_2} \\) II \\( \\mathrm{N_2} \\) III \\( \\mathrm{F_2} \\)\nB. I \\( \\mathrm{H_2} \\) II \\( \\mathrm{F_2} \\) III \\( \\mathrm{N_2} \\)\nC. I \\( \\mathrm{F_2} \\) II \\( \\mathrm{N_2} \\) III \\( \\mathrm{H_2} \\)\nD. I \\( \\mathrm{N_2} \\) II \\( \\mathrm{F_2} \\) III \\( \\mathrm{H_2} \\)", "Answer (final answer highlighted)": "C At identical temperatures, the gases would all have identical amounts of kinetic energy. In order for that to happen, the gas with the lowest mass (H$_2$) would have to have the highest average velocity, and the gas with the highest mass (F$_2$) would have to have the lowest average velocity", "ImagePath": "Chemistry/68" }, { "Question": "The above diagrams shows the decomposition of hydrogen peroxide in a sealed container in the presence of a catalyst. What is the overall order for the reaction? \n\nA. Zero order \nB. First order \nC. Second order \nD. Third order", "Answer (final answer highlighted)": "B In 200 seconds, half of the original sample decayed. In another 200 seconds, half of the remaining sample decayed. This demonstrates a first order reaction", "ImagePath": "Chemistry/69" }, { "Question": "One of the resonance structures for the nitrite ion is shown above. What is the formal charge on each atom? \n\nA. O$_x$ -1; N +2; O$_y$ -1 \nB. O$_x$ +1; N -1; O$_y$ 0 \nC. O$_x$ 0; N 0 ; O$_y$ -1 \nD.O$_x$ -1; N 0 ; O$_y$ 0", "Answer (final answer highlighted)": "D O$_x$ has 6 valence electrons and 7 assigned electrons: 6 - 7 = -1. Both O$_y$ and the N atoms have the same number of valence and assigned electrons, making their formal charges zero.", "ImagePath": "Chemistry/70" }, { "Question": "The following diagram supports which of the following conclusions about the reaction shown below? \n\nA. There is an increase in entropy. \nB. Mass is conserved in all chemical reactions. \nC. The pressure increases after the reaction goes to completion. \nD. The enthalpy value is positive. ", "Answer (final answer highlighted)": "B The amount of matter is equal on both sides of the reaction. None of the other options are supported by the diagram. --------------------- Source Url:https:// /ap/chemistry/question-118-answer-and-explanation.html", "ImagePath": "Chemistry/71" }, { "Question": "The concentrations of the reactants and products in the reaction represented by the above graph are found to be changing very slowly. Which of the following statements best describes the reaction given that the reaction is exergonic? (\u0394G < 0) \n\nA. The reaction is under kinetic control. \nB. The reaction has reached a state of equilibrium. \nC. The reaction is highly exothermic in nature. \nD. The addition of heat will increase the rate of reaction significantly.", "Answer (final answer highlighted)": "A Reactions with high activation energies that do not proceed at a measurable rate are considered to be under kinetic control-that is, their rate of progress is based on kinetics instead of thermodynamics.", "ImagePath": "Chemistry/72" }, { "Question": "What is the equilibrium expression for the reaction \n\nA. \\( K = \\frac{[CO_2]^3}{[O_2]^5} \\) \nB. \\( K = \\frac{[C_3H_8][O_2]^5}{[CO_2]^3[H_2O]^4} \\) \nC. \\( K = \\frac{[C_3H_8]}{[H_2O]^4} \\) \nD. \\( K = \\frac{[O_2]^5}{[CO_2]^3} \\)", "Answer (final answer highlighted)": "A By convention, liquids are not written as part of the equilibrium law. Liquids always have the same number of molecules per liter, which is a constant, combined into the value of the K. The only nonsolid substances in this reaction are O$_2$(g) and CO$_2$(g). In this reaction, CO$_2$ to the third power appears in the numerator because it is a product, and O$_2$ to the fifth power is in the denominator. ", "ImagePath": "Chemistry/73" }, { "Question": "Given the two standard reduction equations and their potentials below, write the thermodynamically favored chemical reaction and its standard cell potential.\n\nA. $\\text{Ag}^+ (\\text{aq}) + \\text{Mg}^{2+} (\\text{aq}) \\rightarrow \\text{Ag}(\\text{s}) + \\text{Mg}(\\text{s}) & -1.57\\ V $\nB. $\\text{Ag}^+ (\\text{aq}) + \\text{Mg}(\\text{s}) \\rightarrow \\text{Ag}(\\text{s}) + \\text{Mg}^{2+} (\\text{aq}) & +3.17\\ V$\nC. $2\\text{Ag}^+ (\\text{aq}) + \\text{Mg}(\\text{s}) \\rightarrow 2\\text{Ag}(\\text{s}) + \\text{Mg}^{2+} (\\text{aq}) & +3.17\\ V$\nD. $2\\text{Ag}^+ (\\text{aq}) + \\text{Mg}(\\text{s}) \\rightarrow 2\\text{Ag}(\\text{s}) + \\text{Mg}^{2+} (\\text{aq}) & +3.97\\ V$", "Answer (final answer highlighted)": "C Only reactions (C) and (D) are balanced. Only reaction (C) simply subtracts -2.37 from +0.80 to get the correct +3.17 V. ", "ImagePath": "Chemistry/74" }, { "Question": "In the diagram above, which labeled arrow is pointing toward a hydrogen bond? \n\nA. 1 \nB. 2 \nC. 3 \nD. 4", "Answer (final answer highlighted)": "C Dashed lines traditionally represent attractions that are NOT covalent bonds. In this case, they represent hydrogen bonds.", "ImagePath": "Chemistry/75" }, { "Question": "The graph above shows the distribution of kinetic energies of a large number of Ne atoms at 500 K. Which letter shows the average kinetic energy of this system? \nA. A \nB. B \nC. C \nD. D", "Answer (final answer highlighted)": "C Slightly to the right of the maximum of the distribution curve is the average kinetic energy. ", "ImagePath": "Chemistry/76" }, { "Question": "Consider the following possible mechanism for the reaction above: \\[ \\text{2SO}_2(g) + \\text{O}_2(g) \\rightarrow \\text{2SO}_3(g) \\] Consider the possible mechanism in the figure for the reaction above. Which of the following statements is true? \n\nA. This mechanism has no free radicals. \nB. \\(\\text{O}_2(g)\\) is an intermediate. \nC. \\(\\text{SO}(g)\\) is a catalyst for this reaction. \nD. The mechanism does not add up to the overall reaction.", "Answer (final answer highlighted)": "A None of the structures has an odd number of electrons, which is necessary for a free radical. ", "ImagePath": "Chemistry/77" }, { "Question": "Three 1-liter flasks are connected to a 3-liter flask by valves. The 3-liter flask is evacuated to start and the entire system is at 298K. The first flask contains helium, the second argon, and the third krypton. The pressure of the argon is 633 torr. The amounts of gas are proportional to their representations in the flasks. If all the valves to the center flask are opened, what will the pressure of the system be? Assume the connections have negligible volume. \n\nA. 633 torr \nB. 316 torr \nC. 1266 torr \nD. 211 torr", "Answer (final answer highlighted)": "B The number of particles adds up to 18, and they are distributed in 6 liters of volume, giving 3 particles per liter. Since 6 particles per liter represents 633 torr, the pressure should be half of that, or 316 torr. ", "ImagePath": "Chemistry/78" }, { "Question": "A portion of a mass spectrum of neon is presented above. Estimate the average mass of naturally occurring atoms of neon, assuming that the height of each line represents the relative amount of each mass. \n\nA. 20.3 \nB. 20.0 \nC. 21.0 \nD. Not enough information is provided", "Answer (final answer highlighted)": "A In this mass spectrum, we see about 90 percent of the atoms with a mass of 20, about 1 percent with a mass of 21, and 10 percent with a mass of 22. Calculate: (0.9)(20) + (0.01)(21) + (0.1)(22) = 18 + 0.2 + 2.2 = 20.4 for the average mass Since each mass was a little less than an integer value, 20.3 is reasonable.", "ImagePath": "Chemistry/79" }, { "Question": "The above graph shows a titration curve of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.075 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the graph. Which arrow points to the end point of this titration? \n\nA. A \nB. E \nC. C \nD. F", "Answer (final answer highlighted)": "B Point E is the inflection point that represents the end point.", "ImagePath": "Chemistry/80" }, { "Question": "The above graph shows a titration curve of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.075 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the graph. Which arrow points to the place on the curve where the pH is equal to 14 - pK$_b$? \n\nA. A \nB. E \nC. C \nD. F", "Answer (final answer highlighted)": "C Point C is the midpoint of the titration. At this point, the pOH = pK$_b$. The pOH = 14 - pH. So 14 - pH = pK$_b$, and this rearranges to the equation shown in the question.", "ImagePath": "Chemistry/81" }, { "Question": "The above graph shows a titration curve of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.075 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the graph. Find the two points on the curve that indicate the region where the solution can be described as a buffer. What is the change in pH from the first point to the second? \n\nA. 0.5 pH unit \nB. 1 pH unit \nC. 2 pH units \nD. 3 pH units.", "Answer (final answer highlighted)": "C Points A and D represent the buffer region. Their pH difference is approximately 2 pH units. ", "ImagePath": "Chemistry/82" }, { "Question": "The above graph shows a titration curve of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.075 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the graph. Which of the following describes the base that is being titrated? \n\nA. The base is dibasic since two end points are observed. \nB. The concentration of the base is 0.075 $M$. \nC. The concentration of the base is slightly more than 0.075 $M$. \nD. The concentration of the base is slightly less than 0.075 $M$.", "Answer (final answer highlighted)": "D The equation is M$_b$(25.0 mL) = (0.075 $M$)(22.5 mL). When solving for M$_b$, we see that 22.5/25.0 is less than 1. So the molarity of the base must be less than 0.075. ", "ImagePath": "Chemistry/83" }, { "Question": "Refer to the figure. The Lewis electron-dot structures for sulfur trioxide and for the sulfite ion are given above. Which statement best describes the geometry of these two substances? \n\nA. The sulfite ion has a triangular pyramid shape, and the sulfur trioxide is a planar triangle. \nB. Both substances are flat, triangular, planar shapes. \nC. Both substances are triangular pyramids. \nD. SO$_3$ is a triangular pyramid, and SO$_3^{2-}$ is a planar triangle. ", "Answer (final answer highlighted)": "A Use the VSEPR theory and the fact that SO$_3$ has three domains (triangular planar) and that SO$_3^{2-}$ has four domains (tetrahedral domain structure and triangular pyramid molecular shape).", "ImagePath": "Chemistry/84" }, { "Question": "Refer to the figure. Which statement below describes the charge, polarity, and resonance characteristics of the sulfite ion and of the sulfur trioxide species shown above? \n\nA. The sulfite ion has two negative charges along with a shape that makes it a dipole. Sulfur trioxide is symmetrical and nonpolar. In addition, as written, both have three resonance structures. \nB. The sulfite ion and sulfur trioxide are both polar with the only difference being that one is an ion and the other is not. \nC. Sulfur trioxide has three resonance structures, and the sulfite ion has no resonance structures. \nD. Sulfite ions have a nonbonding electron pair domain, while sulfur trioxide has all electron domains as bonding domains.", "Answer (final answer highlighted)": "B Both of the statements are true.", "ImagePath": "Chemistry/85" }, { "Question": "Use the arrangement of atoms suggested in the skeleton structure above to construct the Lewis structure for the SO$_3$ molecule. Which of the following statements about this molecule is incorrect?\n\nA. Sulfur trioxide has three resonance structures.\nB. Sulfur trioxide has a planar triangle shape.\nC. Sulfur trioxide is nonpolar.\nD. The S\u2013O bond order is 5/3.\n", "Answer (final answer highlighted)": "D Since the Lewis structure shows three bonding domains and four bonds, three sigma and one pi, the bond order is 4/3, not 5/3.", "ImagePath": "Chemistry/86" }, { "Question": "Use the arrangement of atoms suggested in the skeleton structure above to construct the Lewis structure for the sulfite ion. Be sure to minimize the formal charges. Which of the following statements is incorrect?\n\nA. The sulfite ion has a double bond.\nB. The sulfite ion has a triangular pyramid shape.\nC. The sulfite ion is nonpolar.\nD. The S\u2013O bond order is 4/3.\n", "Answer (final answer highlighted)": "C The sulfite ion has an unsymmetrical triangular pyramid structure and must be polar.", "ImagePath": "Chemistry/87" }, { "Question": "Ethanoic acid (\\ce{HC2H3O2} \\quad \\text{or} \\quad \\ce{CH3CO2H} \\quad \\text{or} \\quad \\ce{CH3COOH}\n) has a much lower vapor pressure than ethanol (\\ce{CH3CH2OH}). What is the most reasonable explanation?\n\nA. The polarizability of two oxygen atoms increases the London forces of attraction in ethanoic acid compared with ethanol.\nB. Hydrogen bonding in ethanoic acid is the strongest attractive force and is mainly responsible for the observed data.\nC. Ethanol has an \u2013OH group and can hydrogen bond; therefore, the London forces must cause the effect.\nD. Both ethanol and ethanoic acid have an \u2013OH, so the difference is the dipole of the second oxygen that increases the attractive forces.\n", "Answer (final answer highlighted)": "B Ethanoic acid molecules strongly hydrogen bond so that most molecules are part of dimers.\n", "ImagePath": "Chemistry/88" }, { "Question": "Vitamin C is oxidized slowly to dehydroascorbic acid by the oxygen in air. It is catalyzed by ions such as \\ce{Cu^2+} and \\ce{Fe^3+}\n. The reaction can be followed by measuring the ultraviolet absorbance at 243 nm.\n\nWhich of the following is the best interpretation of the data given above?\n\nA. The data support a first-order reaction.\nB. The data support a second-order reaction.\nC. The data support a zero-order reaction.\nD. The overall order is 14.\n", "Answer (final answer highlighted)": "A The data show a linear trend for ln A vs. time. This is characteristic of a first-order reaction.", "ImagePath": "Chemistry/89" }, { "Question": "Choose the description of the point on the distribution curve that is the most plausible.\n\nA. Point A represents absolute zero where all motions stops.\nB. Point C is proportional to temperature\nC. Point B is where the transition state occurs.\nD. At point D, the products of the reaction are found. \n", "Answer (final answer highlighted)": "B At point C, which is a little beyond the maximum, the average kinetic energy is directly proportional to temperature.\n", "ImagePath": "Chemistry/89" }, { "Question": "Three 1-liter flasks are connected to a 3-liter flask by valves as shown in the diagram above. The 3-liter flask has the relative number of helium atoms as indicated. At the start, the entire system is at 585K. The first flask contains oxygen; the second contains hydrogen, and the third contains nitrogen. The pressure of hydrogen is 3.00 atm. The number of gas molecules is proportional to their representations in the flasks. If the valves are all opened, what will be the pressure in the system? Assume the connections have negligible volume.\n\nA. 1.0 atm\nB. 2.0 atm\nC. 3.0 atm\nD. 4.0 atm\n", "Answer (final answer highlighted)": "B 6 particles is equivalent to 3 atmospheres. We have 24 particles and 6 liters, or 4 particles per liter. That is 4/6 or 2/3 of the original pressure, or 2.0 atm. \n\n", "ImagePath": "Chemistry/90" }, { "Question": "A mass spectrum of a naturally occurring sample of an element is shown above. What is the element?\n\nA. Cl\nB. S\nC. Ar\nD. There are two peaks, so there must be two compounds.", "Answer (final answer highlighted)": "A Mass 35 is about 75 percent and mass 37 is about 25 percent. Calculate\n\n\\(0.75 \\times 35 + 0.25 \\times 37 = 26.25 + 9.25 = 35.5\\)\n\nThis mass is very close to that of chlorine.", "ImagePath": "Chemistry/91" }, { "Question": "In the diagram above, which labeled arrow is pointing toward a covalent bond and which is pointing toward a hydrogen bond?\n\n\nA. 1 2\nB. 2 1\nC. 3 4\nD. 4 3", "Answer (final answer highlighted)": "D Traditionally, solid lines indicate covalent bonds and dashed lines indicate attractive or repulsive interactions.\n", "ImagePath": "Chemistry/92" }, { "Question": "Space-filling representations of carbon tetrachloride and carbon tetrabromide are shown above. The carbon can be seen in the carbon tetrachloride and is hidden by the bromine in carbon tetrabromide. Which of the following is the most reasonable statement? (Assume that the temperatures of CCl$_4$ and CBr$_4$ are the same in these comparisons.)\n\nA. CCl$_4$ has a higher surface tension compared with CBr$_4$\nB. CCl$_4$has a higher vapor pressure compared with CBr$_4$.\nC. CCl$_4$ has a higher boiling point compared with CBr$_4$.\nD. CCl$_4$ has a higher viscosity compared with CB$_4$.\n", "Answer (final answer highlighted)": "B We can deduce that the attractive forces in CBr$_4$ are stronger than those in CCl$_4$ because the bromine electron cloud is much more polarizable than the chlorine atom's electron cloud. Response (B) is the only one that agrees with the attractive forces.\n", "ImagePath": "Chemistry/93" }, { "Question": "Which of the labeled arrows in the diagram above represents the strongest intermolecular force of the four indicated?\n\nA. Arrow A\nB. Arrow B\nC. Arrow C\nD. Arrow D\n", "Answer (final answer highlighted)": "A This represents an ion-dipole force, which is stronger than a hydrogen bond (B), a dipole-dipole force (C), or a London dispersion force (D).", "ImagePath": "Chemistry/94" }, { "Question": "According to the data in the table above, which of the compounds has the strongest intermolecular forces?\n\nA. Propylamine\nB. Ethyl methyl ether\nC. Trimethyl amine\nD. Ethyl methyl amine", "Answer (final answer highlighted)": "A The compound with the highest boiling point has the strongest intermolecular forces. This is only valid if the molar masses are similar.", "ImagePath": "Chemistry/95" }, { "Question": "Each of the ions in the table form stable oxides (Na$_4$O, CdO, and La$_4$O$_3$). Lanthanum oxide, La$_4$O$_3$, has a melting point significantly higher than that of the other oxides. Which of the following is the best explanation of why this is true?\n\nA. Lanthanum is a lanthanide element and the melting points of these elements are always high.\nB. There is more oxygen in the formula La$_4$O$_3$ than in the other formulas. \nC. Lanthanum had the highest charge; therefore, it has the highest lattice energy.\nD. Alkali metals like sodium and transition metals like cadmium tend to have low melting points.\n", "Answer (final answer highlighted)": "C The melting points of ionic materials depend upon the lattice energy. The higher the lattice energy, the higher the melting point is. Lattice energies depend upon the sizes of the ions and the magnitude of the charge. All three metal ions are approximately the same size; therefore, the size factor is minimal. This leaves the magnitude of the charge, and lanthanum, with the largest charge, should have the highest lattice energy.com/ap/chemistry/question-479-answer-and-explanation.html", "ImagePath": "Chemistry/96" }, { "Question": "The diagram above shows the structure of molecules of CS$_2$ and COS. The boiling point of COS is 223 K, and the boiling point of CS2 is 319 K. Which of the following is the best explanation of why the boiling point of CS$_2$ is higher?\n\nA. The molar mass of CS$_2$ is greater.\nB. COS has weaker covalent bonds than CS$_2$.\nC. Only CS$_2$ can form intermolecular dipole-dipole forces.\nD. COS has stronger intermolecular forces because it is polar and CS$_2$ is not.", "Answer (final answer highlighted)": "A-Stronger intermolecular forces lead to higher boiling points. Even though COS has dipole-dipole forces, which are usually stronger than the London dispersion forces present in CS$_2$, the greater molar mass of CS$_2$ leads to a London dispersion force contribution that is sufficient to compensate for the general trend of dipole-dipole forces being stronger than London dispersion forces. This is why comparisons should only be made between molecules of similar molecular masses.", "ImagePath": "Chemistry/97" }, { "Question": "Which of the labeled arrows in the diagram above represents the strongest intermolecular force?\n\nA. A\nB. B\nC. C\nD. D", "Answer (final answer highlighted)": "B This is a dipole-dipole force, which is stronger than a dipole-induced dipole (A and C) or a London dispersion force (D).", "ImagePath": "Chemistry/98" }, { "Question": "A dimer consists of two closely associated molecules. In the gas phase, acetic acid tends to form dimers as illustrated on the left in the above diagram. Acetyl chloride, on the right in the above diagram, is not very efficient in forming dimers. Why is acetic acid better able to form dimers than acetyl chloride?\n\nA. The molecular mass of acetyl chloride is higher than that of acetic acid making it harder for the acetyl chloride to form dimers.\nB. It is easier to form a covalent bond between acetic acid molecules than between acetyl chloride molecules.\nC. Acetic acid can form strong hydrogen bonds but acetyl chloride can only form weaker dipole-dipole attractions.\nD. Acetic acid is an acidic compound but acetyl chloride is a neutral compound.\n", "Answer (final answer highlighted)": "C The two molecules are hydrogen bonded together. Hydrogen bonding is a relatively strong intermolecular force. Acetyl chloride cannot exhibit anything stronger than dipole-dipole forces, which are, in general, weaker than hydrogen bonds.", "ImagePath": "Chemistry/99" }, { "Question": "Which of the compounds in the above diagram is capable of participating in hydrogen bonding?\n\nA. C$_3$H$_9$ N\nB. CH$_3$F\nC. C$_2$H$_6$O\nD. C$_4$H$_11$", "Answer (final answer highlighted)": "D-Hydrogen bonding is possible when hydrogen is attached to N, O, and F. D is the only compound in the diagram where this is true. The simple presence of hydrogen and N, O, or F is insufficient.", "ImagePath": "Chemistry/100" }, { "Question": "In the diagram above, which labeled arrow is pointing toward a hydrogen bond? \n\nA. 1 \nB. 2 \nC. 3 \nD. 4", "Answer (final answer highlighted)": "C Dashed lines traditionally represent attractions that are NOT covalent bonds. In this case, they represent hydrogen bonds.", "ImagePath": "Chemistry/101" }, { "Question": "The graph above shows the distribution of kinetic energies of a large number of Ne atoms at 500 K. Which letter shows the average kinetic energy of this system? \nA. A \nB. B \nC. C \nD. D", "Answer (final answer highlighted)": "C Slightly to the right of the maximum of the distribution curve is the average kinetic energy. ", "ImagePath": "Chemistry/102" }, { "Question": "The above graph shows a titration curve of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.075 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the graph. Which arrow points to the end point of this titration? \n\nA. A \nB. E \nC. C \nD. F", "Answer (final answer highlighted)": "B Point E is the inflection point that represents the end point.", "ImagePath": "Chemistry/103" }, { "Question": "The above graph shows a titration curve of a weak base titrated with a strong acid. The pH was measured with a pH meter after small volumes of 0.075 M HCl were added to 25.0 mL of a weak base. Data from that experiment are shown in the graph. Which arrow points to the place on the curve where the pH is equal to 14 - pK$_b$? \n\nA. A \nB. E \nC. C \nD. F", "Answer (final answer highlighted)": "C Point C is the midpoint of the titration. At this point, the pOH = pK$_b$. The pOH = 14 - pH. So 14 - pH = pK$_b$, and this rearranges to the equation shown in the question.", "ImagePath": "Chemistry/104" }, { "Question": "The Lewis diagram for nitric acid, $HNO_3$, is above. Which of the following statements is true regarding nitric acid?\nA. $HNO_3$ molecules are planar.\nB. The nitrogen atom carries a negative formal charge.\nC. All N-O bonds are of identical length.\nD. There is a third equivalence resonance structure that is not shown.", "Answer (final answer highlighted)": "A The resonance shown here is for the $N-O$ bonds that do not have hydrogen attached on the other end of the oxygen. This means that two of the $N-O$ bonds are identical (bond order = 1.5), but the third one (from $N-O-H$) is a true single bond. The geometry around the $N$ is trigonal planar, and the geometry around the $O$ in the $N-O-H$ is bent, both of which are planar geometries.", "ImagePath": "Chemistry/105" }, { "Question": "The photoelectron below spectrum is for a neutral fluorine atom. Compared to that spectrum, the spectrum for a fluoride ion would have\nA. one more peak\nB. one less peak\nC. the same number of peaks, but the rightmost peak would be taller\nD. the same number of peaks, but the leftmost peak would be taller", "Answer (final answer highlighted)": "C A fluoride atom is $[He]2s^22p^5$. A fluorine ion would be $[He]2s^22p^6$. The $2p$ peak is the rightmost peak, and in the ion it would contain one more electron and thus be higher than the $2p$ peak from the neutral atom.", "ImagePath": "Chemistry/106" }, { "Question": "A student is attempting to use a distillation apparatus, shown below, to separate a mixture of propanol (boiling point: 97\u00b0C) and propionic acid (boiling point: 141\u00b0C). Which temperature should the apparatus be set at to obtain as pure a distillate of propanol as possible?\nA. 85\u00b0C\nB. 105\u00b0C\nC. 125\u00b0C\nD. 145\u00b0C", "Answer (final answer highlighted)": "B In order to separate out the propanol, it must be boiled, so the temperature must be above the boiling point of propanol. However, the temperature should also be below the boiling point of propionic acid, because if both substances boil, they will not separate effectively. There are two options in the temperature range, and the lower one is better because the propionic acid will have a lower vapor pressure at 105\u00b0C, meaning less of it will evaporate and contaminate the distillate.", "ImagePath": "Chemistry/107" }, { "Question": "Given the half-reactions below, what would the coefficient on the $NO(g)$ be when the full reaction below is balanced?\nA. 1\nB. 2\nC. 3\nD. 4", "Answer (final answer highlighted)": "B To fully balance the reaction, the charge must be balanced. This required multiplying the zinc oxidation half-reaction by two, and the nitrate reduction half-reaction by three. Doing that and combining the reactions yields: $3Zn (s) + 8H^+ (aq) + 2NO_3^- (aq) \\rightarrow 2NO (g) + 4H_2O (l) + 3Zn^{2+} (aq)$", "ImagePath": "Chemistry/108" }, { "Question": "A Lewis diagram of the hydrogen phosphate ion is shown below. Based on this diagram, which of the atoms would have a negative formal charge? \nA. P\nB. Ox\nC. Oy\nD. Oz", "Answer (final answer highlighted)": "D Formal charge is calculated by subtracting the number of assigned electrons on an atom in a Lewis diagram from the number of its valence electrons. When looking at an atom, lone pairs are considered to be two assigned electrons, and any type of bond is considered to be one (so a single bond is one, a double bond would be two, etc). Constructing a formal charge chart for the identified atoms shows that of the identified atoms only $Oz$ would have a negative formal charge. https://img.apstudy.net/ap/chemistry/cr20/0445_Image_0002.jpg", "ImagePath": "Chemistry/109" }, { "Question": "The $K_a$ values for three different weak acids are given below. If the acid is polyprotic, all of the $K_a$ values for that acid are given. If each acid were to be titrated with 0.10 M NaOH, which solution would have the highest pH at the endpoint of the titration when each acid has fully reacted?\nA. Formic\nB. Sulfurous\nC. Citric\nD. All titrations would have identical pHs at the endpoint.", "Answer (final answer highlighted)": "B After all of an acid has reacted during a titration, all that is present in the solutions is the conjugate base of that acid. In a polyprotic titration, the endpoint occurs after all of the protons have been neutralized. In each case, the lower the $K_a$ is for the final dissociation of the weak acid, the higher the $K_b$ will be of its conjugate base (because for any conjugate pair, $K_a \\times K_b = 1.0 \\times 10^{-14}$). A higher $K_b$ means a stronger conjugate base, leading to a higher pH at the endpoint.", "ImagePath": "Chemistry/110" }, { "Question": "A piece of potassium metal is added to a solution of hydrochloric acid, and the metal starts to react. Which of the following is the correct net ionic equation for the reaction that is occurring?\nA. $2H^+(aq) + K^+(aq) + 3e^- \\rightarrow H_2(g) + K(s)$\nB. $2H^+(aq) + 2K^+(aq) + 4e^- \\rightarrow 2K(s) + H_2(g)$\nC. $2H^+(aq) + K(s) \\rightarrow K^+(aq) + H_2(g)$\nD. $2H^+(aq) + 2K(s) \\rightarrow 2K^+(aq) + H_2(g)$", "Answer (final answer highlighted)": "D The $H^+$ ions are being reduced, but the $K (s)$ is being oxidized, so the potassium half-reaction has to be flipped. It also has to be multiplied by two so the electrons will cancel out when the two half reactions are combined.", "ImagePath": "Chemistry/111" }, { "Question": "The Lewis diagram of the bisulfite ion, $HSO^{3-}$, is drawn below. Which of the following descriptions correctly compares the bond lengths of the three sulfur-oxygen bonds found in bisulfite? \nA. All bonds are the same length.\nB. Of the three bonds, there is one longer one and two shorter ones of identical length.\nC. Of the three bonds, there are two longer ones of identical length and one shorter one.\nD. All three bonds are different lengths.", "Answer (final answer highlighted)": "B There is resonance between the two $S-O$ bonds where the $H$ is not attached to the other side of the oxygen atom. These bonds are identical in length, but would be shorter than the true single $S-O$ bond with the oxygen that does have the hydrogen bonded to it.", "ImagePath": "Chemistry/112" }, { "Question": "A sample of hydrogen peroxide, $H_2O_2$, will decompose over time. The graph below charts the concentration of an $H_2O_2$ sample over time. What is the rate law for the overall reaction?\nA. Rate = k\nB. Rate = k[$H_2O_2$]\nC. Rate = k[$H_2O_2$]2\nD. Rate = k[$H_2O$][$O_2$]", "Answer (final answer highlighted)": "B The graph indicates the decomposition reaction has a constant half-life. This means the reaction must be first order.", "ImagePath": "Chemistry/113" }, { "Question": "A semiconductor with a silicon lattice is doped by the addition of another element, symbolized by the letter X in the diagram below. Which of the following statements best describes the possible identity of the element as well as the type of doping that is occurring? \nA. Boron, which has less valence electrons than silicon and creates positive \"holes\" in the lattice\nB. Phosphorus, which has extra valence electrons and creates a mobile negative charge in the lattice\nC. Aluminum, which has metalloid properties that lend to increased conductivity when added to a semiconductor\nD. Carbon, which has an equal number of valence electrons as silicon and strengthens the conducting lattice", "Answer (final answer highlighted)": "A Element X only forms three bonds with the surrounding silicon atoms, meaning it only has three available valence electrons to form bonds. That is consistent with boron, and adding boron into a silicon lattice is called p-doping, which involves creating positive areas for any mobile electrons to be attracted to.", "ImagePath": "Chemistry/114" }, { "Question": "Given the bond enthalpy values in the data table below, determine the enthalpy change for the reaction above it.\nA. -1220 kJ/mol\nB. -400 kJ/mol\nC. 400 kJ/mol\nD. 1220 kJ/mol", "Answer (final answer highlighted)": "A When determining the enthalpy of reaction using bond enthalpies, bonds broken in the reactants are assigned a positive value and bonds formed in the products are assigned a positive value prior to summing them all up. Remember to account for both the number of bonds inside a molecule as well as how many of that molecule there is in the balanced equation when calculating (for instance, there are 4 $H-O$ bonds in 2 $H_2O$ molecules). 4($C-H$) + ($C=C$) + 3($O=O$) - 4($C=O$) - 4($H-O$) = $\\Delta H_{rxn}^{\\circ}$ 4(410) + 720 + 3(500) - 4(800) - 4(470) = -1220 kJ/mol", "ImagePath": "Chemistry/115" }, { "Question": "$[NO]$ (M) \u00a0\u00a0\u00a0\u00a0 $[O_2]$ (M)\nThe reaction below is run with the concentration of both reactants at 0.10 M. Which of the following values for the initial concentration of both reactants would lead to an initial reaction rate which is double that of the first trial?\nA. \u00a0\u00a0\u00a0\u00a0 0.15 \u00a0\u00a0\u00a0\u00a0 0.15\nB. \u00a0\u00a0\u00a0\u00a0 0.20 \u00a0\u00a0\u00a0\u00a0 0.20\nC. \u00a0\u00a0\u00a0\u00a0 0.20 \u00a0\u00a0\u00a0\u00a0 0.050\nD. \u00a0\u00a0\u00a0\u00a0 0.050 \u00a0\u00a0\u00a0\u00a0 0.20", "Answer (final answer highlighted)": "C The reaction is second order with respect to NO. This means doubling the concentration of NO will make the reaction go four times faster. At the same time, given that the reaction is first order with respect to O2, cutting the concentration of O2 in half will halve the speed of the reaction. Combining both factors yield $4 \\times 0.50 = 2$.", "ImagePath": "Chemistry/116" }, { "Question": "Two batteries are constructed via the diagram below. The concentration of the solutions and the mass of the electrodes are identified in the data below the diagram. How would the voltage and the battery life for the two batteries compare?Voltage \u00a0\u00a0\u00a0\u00a0 Battery Life\nA. X 90\u00b0", "Answer (final answer highlighted)": "B Both molecules have four electron groups around the central atom, so their base geometry is tetrahedral, which has bond angles of 109.5\u00b0. However, the $PCl_3$ has a lone pair as well, which exerts a slightly greater repulsive force than a bonded pair, bringing the bond angles in that molecule to slightly less than the ideal 109.5\u00b0.", "ImagePath": "Chemistry/144" }, { "Question": "X \u00a0\u00a0\u00a0\u00a0Y \u00a0\u00a0\u00a0\u00a0Z\nThe formate ion, $HCO_2^-$, is best represented by the Lewis diagram below. Each bond is labeled with a different letter.What is the bond order for each bond?\nA. 1 \u00a0\u00a0\u00a0\u00a01 \u00a0\u00a0\u00a0\u00a02\nB. 2 \u00a0\u00a0\u00a0\u00a02 \u00a0\u00a0\u00a0\u00a01\nC. 1 \u00a0\u00a0\u00a0\u00a01.5 \u00a0\u00a0\u00a0\u00a01.5\nD. 1.33 \u00a0\u00a0\u00a0\u00a01.33 \u00a0\u00a0\u00a0\u00a01.33", "Answer (final answer highlighted)": "C The $H-C$ bond is a single bond with a bond order of one. The $C-O$ bonds display resonance, and the average bond order between them is $(1 + 2)/1 = 1.5$.", "ImagePath": "Chemistry/145" }, { "Question": "Initial pH \u00a0\u00a0\u00a0\u00a0 Equivalence pH \u00a0\u00a0\u00a0\u00a0 Ending pH\nA student titrates some 1.0 M $HCl$ into 20.0 mL of methylamine ($CH_3NH_2$), a weak base which only accepts a single proton. The following titration curve results:The methylamine is replaced by 20.0 mL of sodium hydroxide of an identical concentration. If the sodium hydroxide is titrated with the 1.0 M $HCl$, which of the following options accurately describes the pH levels at various points during the titration when compared to the pH levels at the same point in the $HCl$/methylamine titration?\nA. lower \u00a0\u00a0\u00a0\u00a0same \u00a0\u00a0\u00a0\u00a0higher\nB. higher \u00a0\u00a0\u00a0\u00a0higher \u00a0\u00a0\u00a0\u00a0same\nC. same \u00a0\u00a0\u00a0\u00a0higher \u00a0\u00a0\u00a0\u00a0same\nD. higher \u00a0\u00a0\u00a0\u00a0lower \u00a0\u00a0\u00a0\u00a0lower", "Answer (final answer highlighted)": "B Sodium hydroxide is a strong base, which dissociates completely in solution. Thus, it would initially have a higher pH (be more basic) than any weak base of an identical concentration. At equivalence of a strong acid/strong base titration, water is the only acid or base present, causing the solution to have a neutral pH of 7. Finally, in the post-equivalence region of the graph, the pH is driven by the excess $H^+$ from the $HCl$, and that would not change in the new titration.", "ImagePath": "Chemistry/146" }, { "Question": "The buffer region of this titration is located\nA student titrates some 1.0 M $HCl$ into 20.0 mL of methylamine ($CH_3NH_2$), a weak base which only accepts a single proton. The following titration curve results:\nA. below 3.0 mL\nB. between 3.0 mL and 14.0 mL\nC. between 14.0 mL and 16.0 mL\nD. above 16.0 mL", "Answer (final answer highlighted)": "B A buffer solution is one that resists change in pH due to similar amounts of the base ($CH_3NH_2$) and its conjugate acid ($CH_3NH_3^+$). That occurs after the initial pH change, but prior to the equivalence region. The pH is also stable again starting at 16.5 mL, but that is due to the presence of the excess strong acid, and that does not create a buffer region.", "ImagePath": "Chemistry/147" }, { "Question": "What is the approximate $pK_b$ for methylamine?\nA student titrates some 1.0 M HCl into 20.0 mL of methylamine ($CH_3NH_2$), a weak base which only accepts a single proton. The following titration curve results:\nA. 3.5\nB. 5.5\nC. 10.5\nD. 12.5", "Answer (final answer highlighted)": "A At the half-equivalence point (7.5 mL) of the titration, $pK_b$ of methylamine = $pOH$ of the solution. To determine the $pOH$, you simply have to see what the $pH$ of the solution is at that half-equivalence point and use $pH + pOH = 14$. The $pH$ at the half-equivalence is 10.5. So, 14 - 10.5 = 3.5.", "ImagePath": "Chemistry/148" }, { "Question": "What is the concentration of the methylamine?\nA student titrates some 1.0 M HCl into 20.0 mL of methylamine ($CH_3NH_2$), a weak base which only accepts a single proton. The following titration curve results:\nA. 0.50 M\nB. 0.75 M\nC. 1.0 M\nD. 1.25 M", "Answer (final answer highlighted)": "B There is a 1:1 mole ratio between the $HCl$ and the $CH_3NH_2$, meaning there will be the same number of moles of each present at the equivalence point. The equivalence point is located at 15.0 mL of $HCl$ added. (1.0 M)(0.0150 L) = 0.0150 mol $HCl$ = 0.0150 mol $CH_3NH_2$. Finally, divide that value by the volume of the $CH_3NH_2$, 0.0150 mol $CH_3NH_2$ / 0.020 L = 0.75 M $CH_3NH_2$.", "ImagePath": "Chemistry/149" }, { "Question": "Silver sulfate, $Ag_2SO_4$, has a solubility product constant of $1.0 \\times 10^{-5}$. The below diagram shows the products of a precipitation reaction in which some silver sulfate was formed.Which ion concentrations below would have led the precipitate to form?\nA. $[Ag^+] = 0.01 M$ $[SO_4^{2-}] = 0.01 M$\nB. $[Ag^+] = 0.10 M$ $[SO_4^{2-}] = 0.01 M$\nC. $[Ag^+] = 0.01 M$ $[SO_4^{2-}] = 0.10 M$\nD. This is impossible to determine without knowing the total volume of the solution.", "Answer (final answer highlighted)": "B For a precipitate to form, $Q > K_{sp}$. In this case, $Q = [Ag^+]^2[SO_4^{2-}]$. The concentrations in (B) lead to a $Q$ of $1.0 \\times 10^{-4}$, which is greater than the given $K_{sp}$ of $1.0 \\times 10^{-5}$. The other options lead to a $Q$ value that is equal to or less than $K_{sp}$.", "ImagePath": "Chemistry/150" }, { "Question": "Silver sulfate, $Ag_2SO_4$, has a solubility product constant of $1.0 \\times 10^{-5}$. The below diagram shows the products of a precipitation reaction in which some silver sulfate was formed.If the beaker above were left uncovered for several hours\nA. some of the $Ag_2SO_4$ would dissolve\nB. some of the spectator ions would evaporate into the atmosphere\nC. the solution would become electrically imbalanced\nD. additional $Ag_2SO_4$ would precipitate", "Answer (final answer highlighted)": "D Leaving the container uncovered will cause some of the water molecules to evaporate. This allows some $Ag^+$ and $SO_4^{2-}$ ions to \"fall\" out of solution and combine to create more $Ag_2SO_4$.", "ImagePath": "Chemistry/151" }, { "Question": "Silver sulfate, $Ag_2SO_4$, has a solubility product constant of $1.0 \\times 10^{-5}$. The below diagram shows the products of a precipitation reaction in which some silver sulfate was formed.What is the identity of the excess reactant?\nA. $AgNO_3$\nB. $Ag_2SO_4$\nC. $NaNO_3$\nD. $Na_2SO_4$", "Answer (final answer highlighted)": "A There are no sulfate ions in solution, which means that whatever the sulfate was attached to was the limiting reactant. Thus, silver must have been attached to the excess reactant, which is $AgNO_3$. (Remember, $Ag_2SO_4$ was the product, not a reactant.)", "ImagePath": "Chemistry/152" }, { "Question": "The following curve is obtained during the titration of 30.0 mL of 1.0 M $NH_3$, a weak base, with a strong acid:What ions are present in significant amounts during the first buffer region?\nA. $NH_3$ and $NH_4^+$\nB. $NH_3$ and $H^+$\nC. $NH_4^+$ and $OH^-$\nD. $H_3O^+$ and $NH_3$", "Answer (final answer highlighted)": "A The reaction occurring is $NH_3 + H^+ \\rightleftharpoons NH_4^+$. During the first buffer region, all added hydrogen ions immediately react with $NH_3$ to create $NH_4^+$. $NH_3$ remains in excess until equilibrium is achieved.", "ImagePath": "Chemistry/153" }, { "Question": "The following curve is obtained during the titration of 30.0 mL of 1.0 M NH3, a weak base, with a strong acid:What is the concentration of the acid?\nA. 0.5 M\nB. 1.0 M\nC. 1.5 M\nD. 2.0 M", "Answer (final answer highlighted)": "D At the equivalence point, the moles of acid are equal to the moles of base. Moles base = $(1.0 M)(0.030 L) = 0.030$ mol base = 0.030 moles acid It requires 15.0 mL of acid to reach equivalence, so: https://img.apstudy.net/ap/chemistry/cr20/0307_Image_0004.jpg", "ImagePath": "Chemistry/154" }, { "Question": "Why is the solution acidic at equilibrium?\nThe following curve is obtained during the titration of 30.0 mL of 1.0 M NH3, a weak base, with a strong acid:\nA. The strong acid dissociates fully, leaving excess $[H^+]$ in solution.\nB. The conjugate acid of NH3 is the only ion present at equilibrium.\nC. The water which is being created during the titration acts as an acid.\nD. The acid is diprotic, donating two protons for every unit dissociated.", "Answer (final answer highlighted)": "B The reaction here is $NH_3 + H^+ \\rightleftharpoons NH_4^+$. At equilibrium, the moles of $NH_3$ and $H^+$ would be equal, leaving behind $NH_4^+$ ions, which will then donate ions to water, creating an acidic medium.", "ImagePath": "Chemistry/155" }, { "Question": "The diagram below shows three identical 1.0 L containers filled with the indicated amounts of gas. The stopcocks connecting the containers are originally closed and the gases are all at 25\u00b0C. Assume ideal behavior.The stopcocks are opened. If the tubing connecting the containers has negligible volume, by what percentage will the pressure exerted by the neon gas decrease?\nA. 25%\nB. 33%\nC. 50%\nD. 67%", "Answer (final answer highlighted)": "D $P_1V_1 = P_2V_2$ $P_1(1.0 L) = P_2(3.0 L)$ $P_2/P_1 = 1.0/3.0$ Thus, the pressure of the neon gas is 33% of what it was originally, meaning a decrease of 67%. Note that the same calculation could be used for any of the gases; each gas is expanding to take up three times as much space as it has originally, and thus exerts one-third as much pressure.", "ImagePath": "Chemistry/156" }, { "Question": "The diagram below shows three identical 1.0 L containers filled with the indicated amounts of gas. The stopcocks connecting the containers are originally closed and the gases are all at 25\u00b0C. Assume ideal behavior.Which gas has the strongest IMFs?\nA. He\nB. Ne\nC. NO\nD. All gases have identical IMFs.", "Answer (final answer highlighted)": "D One of the precepts of kinetic molecular theory is that gas molecules exert no forces on each other; thus, in all containers there are no IMFs present.", "ImagePath": "Chemistry/157" }, { "Question": "The diagram below shows three identical 1.0 L containers filled with the indicated amounts of gas. The stopcocks connecting the containers are originally closed and the gases are all at 25\u00b0C. Assume ideal behavior. Which gas exerts the greatest pressure?\nA. He\nB. Ne\nC. NO\nD. All gases exert the same amount of pressure.", "Answer (final answer highlighted)": "A Pressure is directly dependent on the number of moles. In their respective containers, there are 5 moles of He, 2 moles of Ne, and 1 mole of NO. As there are the most moles of He, the He must exert the greatest pressure.", "ImagePath": "Chemistry/158" }, { "Question": "Which structure is more likely to correspond with the actual Lewis diagram for the sulfate ion?\nThere are several different potential Lewis diagrams for the sulfate ion, two of which are below.\nA. Structure A; single bonds are more stable than double bonds\nB. Structure A; it has the most unshared pairs of electrons\nC. Structure B; there are more possible resonance structures\nD. Structure B; fewer atoms have formal charges", "Answer (final answer highlighted)": "D The formal charge tables for each diagram are below (note: for structure B, the double-bonded oxygens are the first two, and the single bonded are the last two). ![image](https://img.apstudy.net/ap/chemistry/cr20/0141_Image_0001.jpg) The total formal charge on each potential structure is -2, which is correct, as that is the charge on a sulfate ion. However, the right-hand structure has fewer atoms with formal charges, making it the more likely structure.", "ImagePath": "Chemistry/159" }, { "Question": "Which of the following statements regarding the structure B is true?\nThere are several different potential Lewis diagrams for the sulfate ion, two of which are below.\nA. The double bonds must be located opposite of each other due to additional electron repulsion.\nB. It is a more polar molecule than the molecule represented by structure A.\nC. The bonds in the molecule are weaker than those in structure A.\nD. All bonds in the molecule are identical to each other.", "Answer (final answer highlighted)": "D In any molecule displaying resonance, all bonds are identical.", "ImagePath": "Chemistry/160" }, { "Question": "What is the S-O bond order in the structure B?\nThere are several different potential Lewis diagrams for the sulfate ion, two of which are below.\nA. 1.0\nB. 1.33\nC. 1.5\nD. 1.67", "Answer (final answer highlighted)": "C Six total bonds divided by four locations gives a bond order of 1.5.", "ImagePath": "Chemistry/161" }, { "Question": "What is the molecular geometry in the structure A?\nThere are several different potential Lewis diagrams for the sulfate ion, two of which are below.\nA. Tetrahedral\nB. Trigonal Planar\nC. Trigonal Pyramidal\nD. Octahedral", "Answer (final answer highlighted)": "A Four charge clouds and no lone pairs means tetrahedral geometry.", "ImagePath": "Chemistry/162" }, { "Question": "Use the PES spectra below to answer questions.How many valence electrons does this atom have?\nA. 2\nB. 3\nC. 4\nD. 5", "Answer (final answer highlighted)": "D Valence electrons are those in the outermost energy level. In this case, that is the third level, which has five valence electrons in it (two in 3s and three in 3p).", "ImagePath": "Chemistry/163" }, { "Question": "An electron from which peak would have the greatest velocity after ejection?\nUse the PES spectra below to answer questions.\nA. The peak at 104 MJ/mol\nB. The peak at 6.84 MJ/mol\nC. The peak at 4.98 MJ/mol\nD. The peak at 1.76 MJ/mol", "Answer (final answer highlighted)": "D The less ionization energy that is required to remove an electron, the more kinetic energy that electron will have after ejection.", "ImagePath": "Chemistry/164" }, { "Question": "How many significant digits are present in the temperature read from the thermometer illustrated to the right?\n\nA.1 \nB.2\nC.3 \nD.4", "Answer (final answer highlighted)": "C The number is 27.5, which have 3 significant digits.", "ImagePath": "Chemistry_extra/1" }, { "Question": "The marks on the following target represent someone who is:\n\nA.accurate, but not precise.\r\nB.precise, but not accurate.\r\nC.both accurate and precise.\r\nD.neither accurate nor precise.\r\n", "Answer (final answer highlighted)": "D They are not centered on the bulls eye and not close to each other", "ImagePath": "Chemistry_extra/2" }, { "Question": "Pictured below is a schematic of the Rutherford experiment. Which scattered \uf061-particle gives the best evidence for the nuclear atom?\n\nA. a\nB. b\nC. c\nD. d", "Answer (final answer highlighted)": "A ", "ImagePath": "Chemistry_extra/3" }, { "Question": "What position on the standing wave shown below corresponds to a crest?\n\nA. a\r\nB. b\r\nC. c\r\nD. d\nE. e", "Answer (final answer highlighted)": "B", "ImagePath": "Chemistry_extra/4" }, { "Question": "The value of l that is related to the following orbital is:\n\nA. 0\nB. 1\nC. 2\nD. 3\nE. 4", "Answer (final answer highlighted)": "B This is a p-orbital, whose value l should be 1.", "ImagePath": "Chemistry_extra/5" }, { "Question": "The titration curves labeled 1 and 2 were obtained by titrating equal volumes of two different acid samples with portions of the same sodium hydroxide solution. What conclusions can be drawn about the relative concentrations and strengths of acids 1 and 2 from these curves?\n\n(A)\tThe concentrations are the same but acid 1 is weaker than acid 2.\r\n(B)\tThe concentrations are the same but acid 1 is stronger than acid 2.\r\n(C)\tAcid 1 is the same strength as acid 2, but it is less concentrated.\r\n(D)\tAcid 1 is the same strength as acid 2, but it is more concentrated. \r\n", "Answer (final answer highlighted)": "A The concentrations are the same because they take the same amount.", "ImagePath": "Chemistry_extra/6" }, { "Question": "According to the above data, what is the half-life of the substance?\n\nA. 1.0 hrs\nB. 2.3 hrs\nC. 3.0 hrs\nD. 8.0 hrs", "Answer (final answer highlighted)": "C", "ImagePath": "Chemistry_extra/7" }, { "Question": "What percent of the original sample remains after 4 hours?\n\nA. 80%\nB. 75%\nC. 60%\nD. 40%", "Answer (final answer highlighted)": "D", "ImagePath": "Chemistry_extra/7" }, { "Question": "The elements I and Te have similar average atomic masses. A sample that was believed to be a mixture of I and Te was run through a mass spectrometer which separates a sample by mass into isotopes, resulting in the data below. All of the following statements are true. Which one would be the best basis for concluding that the sample was pure Te?\n\nA. Te forms ions with a -2 charge, whereas I forms ions with a -1 charge.\nB. Te is more abundant than I in the universe.\nC. I consists of only one naturally occurring isotope with 74 neutrons, whereas Te has more than one isotope\nD. I has a higher first ionization energy than Te does.", "Answer (final answer highlighted)": "C The graph shows different isotopes by mass. Remember that isotopes of an element have a different number of neutrons, giving them a different mass number. If\nIodine only has one isotope with 74 neutrons, it\u2019s mass should be 127 (74 neutrons + 53 protons). There is no peak at 127, so the mixture must not have any iodine.", "ImagePath": "Chemistry_extra/8" }, { "Question": "The diagram below models a change that occurs in matter. Based on what you know about changes in matter, explain why the diagram shows a physical change rather than a chemical change.\r\n\nA. The particles get smaller.\r\nB. The volume of the matter decreases.\r\nC. The composition of the matter stays the same.\r\nD. The particles change into particles of different substances", "Answer (final answer highlighted)": "C In physical changes, the bonds/particles do not change. In this diagram they did not change, they just condensed. This represents gas becoming liquid or solid.", "ImagePath": "Chemistry_extra/9" }, { "Question": "In an experiment, a solid 1 molar sample of Substance A was gradually heated by a source of constant energy for several hours and the temperature was measured periodically. At the end of the heating period, Substance A had been converted to the gas phase. The heating curve produced by this experiment is shown below. During the course of the experiment, there was a period of time when the phase of Substance A was in equilibrium with the liquid phase. At what temperature did this occur?\n\n(A) Between 100 K and 150 K\r\n(B) At 150 K\r\n(C) Between 150 K and 250 K\r\n(D) At 250 K\r\n(E) Between 250 K and 350 K", "Answer (final answer highlighted)": "B The first flat part of the heating curve corresponds to the phase change from solid to liquid. During the phase change, an equilibrium exists between the two phases.", "ImagePath": "Chemistry_extra/10" }, { "Question": "In an experiment, a solid 1 molar sample of Substance A was gradually heated by a source of constant energy for several hours and the temperature was measured periodically. At the end of the heating period, Substance A had been converted to the gas phase. The heating curve produced by this experiment is shown below. Based on the data given in the heating curve,which of the following statements is NOTtrue regarding Substance A?\n\n(A) The boiling point of Substance A is 250 K.\n(B) The freezing point of Substance A is150 K.\n(C) The heat of vaporization of Substance A is greater than the heat of fusion.\n(D) Substance A is a liquid at room temperature.\n(E) The intermolecular forces exhibited by Substan", "Answer (final answer highlighted)": "D Choice (D) is the only choice that's not true. Room temperature is about 298 K. At 298 K,Substance A is in the gas phase, not the liquid phase. As for the other answers, Choices (A)and (B) accurately give the boiling and freezing points. Choice (C) is accurate because the vaporization line is much longer than the fusion line. Heat of vaporization is usually much higher than heat of fusion. Choice (E) is accurate because the boiling and freezing points of substance A are lower than those of water, so Substance A must be held together by weaker intermolecular forces. ", "ImagePath": "Chemistry_extra/10" }, { "Question": "In an experiment, a solid 1 molar sample of Substance A was gradually heated by a source of constant energy for several hours and the temperature was measured periodically. At the end of the heating period, Substance A had been converted to the gas phase. The heating curve produced by this experiment is shown below. During the course of the experiment,Substance A was gradually heated from 100K to 350 K. When the temperature reached 250 K, the energy absorbed by Substance A?\n\n(A} was used to change from liquid to gas phase.\r\n(B) was used to change from gas to liquid phase.\r\n(C) was used to change from solid to liquid phase.\r\n(D) was used to change from liquid to solid phase.\r\n(E) was reduced to zero. ", "Answer (final answer highlighted)": "A At 250 K, Substance A boiled. That means that the temperature remained constant while the energy absorbed was used to break up the forces holding the liquid together and convert the substance to a gas. ", "ImagePath": "Chemistry_extra/10" }, { "Question": "Which of the following is true of the reactions shown in the diagram above?\n\n(A) The reaction is endothermic because the reactants are at a higher energy level than the products.\n(B) The reaction is endothermic because the reactants are at a lower energy level than the products.\n(C) The reaction is exothermic because the reactants are at a higher energy level than the products.\n(D) The reaction is exothermic because the reactants are at a lower energy level than the products.\n(E) The reaction is endothermic because the reactants are at the same energy level as the products.", "Answer (final answer highlighted)": "C In an exothermic reaction, energy is given off as the products are created because the products have less potential energy than the reactants.", "ImagePath": "Chemistry_extra/11" }, { "Question": "Which point on the graph shown above corresponds to an activated complex or transition state?\n\n(A) 1\n(B) 2\n(C) 3\n(D) 4\n(E) 5 ", "Answer (final answer highlighted)": "C Point 3 represents the activated complex, which is the ppint of highest energy. This point is the transition state between the reactants and the products. ", "ImagePath": "Chemistry_extra/12" }, { "Question": "The following titration curve shows the titration of a weak base with a strong acid. Which of the following values most accurately approximates the p$K_b$ of the weak base?\r\n\n(A) 9.8\r\n(B) 8.4\r\n(C) 7\r\n(D) 3.3\r\n(E) 4.2 \r", "Answer (final answer highlighted)": "E The half equivalence point of this titration, is around pH= 9.8. At the half equivalence point, the amount of\r\nbase (which we can call [A-] as we do when talking about acids and pH values) is equal to the neutralized base [HA]. When these two quantities are equal, the H-H equation tells us that the\r\npH = the $pK_a$, which when subtracted from 14 gives the $pK_b$. Therefore, the answer = 4.2.", "ImagePath": "Chemistry_extra/13" }, { "Question": "Given a reaction A+B \u2192C. Based on the following experimental data, what is the rate law for the hypothetical reaction given above?\n\n(A) Rate= $k[A]$\n(B) Rate= $k[A]^2$\n(C) Rate = $k[B]$\n(D) Rate = $k[B]^2$\n(E) Rate = $k[A][B]$\n", "Answer (final answer highlighted)": "C From a comparison of experiments 1 and 2, when [B] is doubled while [A] is held constant, the rate doubles. That means that the reaction is first order with respect to B.From a comparison of experiments 2 and 3, when [A] is doubled while [B] is held constant, the rate doesn't change. That means that the reaction is zero order with respect to A and that A will not appear in the rate law.So the rate law is Rate= k[B]. ", "ImagePath": "Chemistry_extra/14" }, { "Question": "Given a reaction A+B \u2192C. Based on the following experimental data, what is the rate law for the hypothetical reaction given above?\r\n\r\n(A) Rate= $k[A]$\r\n(B) Rate= $k[A]^2$\r\n(C) Rate = $k[B]$\r\n(D) Rate = $k[B]^2$\r\n(E) Rate = $k[A][B]$\r", "Answer (final answer highlighted)": "E From a comparison of experiments 1 and 2, when [B] is doubled while [A] is held constant, the rate doubles. That means that the reaction is first order with respect to B.From a comparison of experiments 2 and 3, when both [A] and [B] are doubled, the rate increases by a factor of 4. We would expect the rate to double based on the change in B; because the rate is in fact multiplied by 4, the doubling of A must also change the rate by a factor of 2, so the action is also first order with respect to A.So the rate law is Rate= k[A][B]. ", "ImagePath": "Chemistry_extra/15" }, { "Question": "Given a reaction A+B \u2192C. Based on the following experimental data, what is the rate law for the hypothetical reaction given above?\n\n(A) Rate= $k[A][B]$\n(B) Rate= $k[A]^2$\n(C) Rate = $k[A][B]^2$\n(D) Rate = $k[B]^2$\n(E) Rate = $k[A]^2[B]^2$\n", "Answer (final answer highlighted)": "C From a comparison of experiments 1 and 2, when [A] is quadrupled while [B] is held constant, the rate quadruples. That means that the reaction is first order with respect to A. From a comparison of experiments 2 and 3, when [B] is doubled while [A] is held constant, the rate quadruples. That means that the reaction is second order with respect to B.So the rate law is Rate = k[A][B]^2.", "ImagePath": "Chemistry_extra/16" }, { "Question": " The formal charge on carbon in the molecule below is.\n\nA) 0 \nB) +1 \nC) -1 \nD) +3 \nE) +2", "Answer (final answer highlighted)": "A", "ImagePath": "Chemistry/165" }, { "Question": "The molecular geometry of the left-most carbon atom in the molecule below is:\n\nA) octahedral\nB) tetrahedral\nC) trigonal planar\nD) T-shaped\nE) trigonal bipyramidal", "Answer (final answer highlighted)": "B", "ImagePath": "Chemistry/166" }, { "Question": "The bond angles marked a, b, and c in the molecule below are about __________, __________, and __________,\nrespectively.\n\nA) 120, 120, 90\nB) 90, 90, 90\nC) 120, 120, 109.5\nD) 109.5, 90, 120\nE) 109.5, 120, 109.5", "Answer (final answer highlighted)": "E", "ImagePath": "Chemistry/167" }, { "Question": "Based on molecular mass and dipole moment of the five compounds in the table below, which should have the\nhighest boiling point?\n\nA) $CH_3OCH_3$\nB) $CH_3CN$\nC) $CH_3CHO$\nD) $CH_3Cl$\nE) $CH_3CH_2CH_3$", "Answer (final answer highlighted)": "B", "ImagePath": "Chemistry/168" }, { "Question": "On the phase diagram above, segment __________ corresponds to the conditions of temperature and pressure under which the solid and the gas of the substance are in equilibrium.\n\nA) CD \nB) AB \nC) AD \nD) BC \nE) AC", "Answer (final answer highlighted)": "E", "ImagePath": "Chemistry/169" }, { "Question": "The phase diagram of a substance is given above. The region that corresponds to the solid phase is __________.\nA) w \nB) x \nC) y \nD) z \nE) x and y", "Answer (final answer highlighted)": "A", "ImagePath": "Chemistry/170" }, { "Question": "Based on the figure above, the boiling point of ethyl alcohol under an external pressure of 0.0724 atm is\n________eC.\n\nA) 60 \nB) 20 \nC) 70 \nD) 80 \nE) 40", "Answer (final answer highlighted)": "B", "ImagePath": "Chemistry/171" }, { "Question": "The graph shown below depicts the relationship between concentration and time for the following chemical\nreaction. The slope of this line is equal to __________.\nA) -k \nB) -1/k \nC) k \nD) ln[A]o \nE) 1/k", "Answer (final answer highlighted)": "A", "ImagePath": "Chemistry/172" }, { "Question": "Which energy difference in the energy profile below corresponds to the activation energy for the forward\nreaction?\n\nA) x \nB) y \nC) x + y \nD) y - x \nE) x - y", "Answer (final answer highlighted)": "A", "ImagePath": "Chemistry/173" }, { "Question": "A 25.0-mL sample of a solution of a monoprotic acid is titrated with a 0.115 M NaOH solution. The titration\ncurve above was obtained. Which of the indicators in the table would be best for this titration?\n\nA) bromocresol purple\nB) bromthymol blue\nC) thymol blue\nD) phenolpthalein\nE) methyl red", "Answer (final answer highlighted)": "B", "ImagePath": "Chemistry/174" }, { "Question": "Consider the following table of $K_{sp}$ values. Which compound listed below has the greatest molar solubility in water?\n\nA) $ZnCO_3$ \nB) $CdCO_3$ \nC) $CaF_2$ \nD) $AgI$ \nE) $Cd(OH)_2$", "Answer (final answer highlighted)": "C", "ImagePath": "Chemistry/175" }, { "Question": "Consider the following table of $K_{sp}$ values. The solubility of manganese hydroxide ($Mn(OH)_2$) is 2.2e-5 M. What is the Ksp of $Mn(OH)_2$?\n\nA) 2.1e-14 \nB) 4.3e-14 \nC) 1.1e-14 \nD) 2.2e-5 \nE) 4.8e-10", "Answer (final answer highlighted)": "B", "ImagePath": "Chemistry/176" }, { "Question": "Consider the following table of $K_{sp}$ values. The molar solubility of __________ is not affected by the pH of the solution.\n\nA) $AlCl_3 $\nB) $Na_3PO_4$\nC) $NaF$ \nD) $KNO_3$\nE) $MnS$", "Answer (final answer highlighted)": "D", "ImagePath": "Chemistry/177" }, { "Question": "Consider the following table of $K_{sp}$ values. In which of the following aqueous solutions would you expect AgCl to have the lowest solubility?\n\nA) 0.020 $AgNO_3$\nB) 0.020 M $BaCl_2$\nC) pure water\nD) 0.015 $NaCl$\nE) 0.020 $KCl$", "Answer (final answer highlighted)": "B", "ImagePath": "Chemistry/178" }, { "Question": "The equilibrium position corresponds to which letter on the graph of G vs f (course of reaction) below?\n\nA) A \nB) B \nC) C \nD) D \nE) E", "Answer (final answer highlighted)": "C", "ImagePath": "Chemistry/179" } ], "Biology": [ { "Question": "Dichlorophenolindophenol (DPIP), an electron acceptor that changes from blue to clear when reduced, can be used to visually determine the rate of photosynthesis. In an experiment, a solution of chloroplasts containing DPIP was divided among 4 tubes. The samples were then exposed to light (1500 lumens) and/or heat (85oC), and light transmittance was measured over time using a spectrophotometer. Higher transmittance is correlated to lighter color. The results of the experiment are provided. Which of the following can be reasonably concluded from the experimental results?\n\nA. The onset of photosynthesis is visible when DPIP is oxidized and changes from clear to blue.\nB. Chloroplasts exposed to heat had the highest rate of photosynthesis.\nC. Photosynthesis is stimulated when chloroplasts are exposed to light only.\nD. The solution in all four tubes was clear at time 0.", "Answer (final answer highlighted)": "C:DPIP acts as a substitute for NADP+ in photosynthesis. During photosynthesis, DPIP is reduced and becomes colorless, which results in an increase in light transmittance. According to the data, an increase in light transmittance over time is found for the tube exposed to light only.", "ImagePath": "Biology/1" }, { "Question": "The figure above shows a model generated from a study of interactions in a Serengeti ecosystem. This figure describes hypothesized relationships between a parasite that causes disease in wildebeest, rinderpest, and other important components of the ecosystem. Thick arrows represent dominant effects, and \u201cgrass\u201d is in a dotted circle because that variable was not directly measured in the study.1. Which of the following can most reasonably be predicted based on this figure?\n\nA. Increasing the amount of rinderpest would decrease the amount of grass. \nB.Increased fire would lead to higher tree and elephant populations. \nC. Increasing the amount of rinderpest could indirectly lower tree numbers.\nD. Increased human populations have a net positive effect on the elephant population.", "Answer (final answer highlighted)": "C: Increased rinderpest prevalence would lower wildebeest populations, increasing the amount of grass (because wildebeests feed on the grass) and providing more material to start and spread fires, thereby decreasing the number of trees. Choice (C) is thus correct. ", "ImagePath": "Biology/2" }, { "Question": "Question below refers to the diagram \n\nWhich of the following chambers or vessels carry deoxygenated blood in the human heart?\n\nA. 4 only\nB. 1 and 2 only\nC. 5 only\nD. 1, 2, and 4 \n", "Answer (final answer highlighted)": "D: Deoxygenated blood from the vena cava enters the right atrium (2), then the right ventricle (1), and then enters the pulmonary arteries (4). The left atrium (5), left ventricle (6), and aorta (3) all carry oxygenated blood. \n", "ImagePath": "Biology/3" }, { "Question": "Which of the following represents the correct pathway taken by a nerve impulse as it travels from the spinal cord to effector cells?\n\nA. 1-2-3-4\nB. 6-5-4-3\nC. 2-3-4-5\nD. 4-5-6-7\n", "Answer (final answer highlighted)": "D: This question tests your ability to trace the neural pathway of a motor (effector) neuron. The nerve conduction will travel from the spinal cord (where interneurons are located) to the muscle\n\n", "ImagePath": "Biology/4" }, { "Question": "The brain of the frog is destroyed. A piece of acid-soaked paper is applied to the frog's skin. Every time the piece of paper is placed on its skin, one leg moves upward. Which of the following conclusions is best supported by the experiment?\n\nA. Reflex actions are not automatic.\nB. Some reflex actions can be inhibited or facilitated.\nC. All behaviors in frogs are primarily reflex responses.\nD. This reflex action bypasses the brain.", "Answer (final answer highlighted)": "D: Because the brain is destroyed, it is not associated with the movement of the leg. \n\n", "ImagePath": "Biology/5" }, { "Question": "A nerve impulse requires the release of neurotransmitters at the axonal bulb of a presynaptic neuron. Which of the following best explains the purpose of neurotransmitters, such as acetylcholine?\n\nA. They speed up the nerve conduction in a neuron.\nB. They open the sodium channels in the axonal membrane.\nC. They excite or inhibit the postsynaptic neuron.\nD. They open the potassium channels in the axonal membrane.", "Answer (final answer highlighted)": "C: Neurotransmitters are released from the axonal bulb of one neuron and diffuse across a synapse to activate a second neuron. The second neuron is called a postsynaptic neuron. A neurotransmitter can either excite or inhibit the postsynaptic neuron. The myelin sheath speeds up the conduction in a neuron, so (A) is wrong. Also eliminate (B) and (D), as both sodium and potassium channels open during an action potential. Neurotransmitters are not involved in actions related to the axon membrane. They do not force potassium ions to move against a concentration gradient", "ImagePath": "Biology/6" }, { "Question": "Which of the following DNA strands would serve as a template for the amino acid sequence shown above?\n\nA. 3\u2032-ATGCGACCAGCACGT-5\u2032\nB. 3\u2032-AUGCCACUAGCACGU-5\u2032\nC. 3\u2032-TACGGTGATCGTGCA-5\u2032\nD. 3\u2032-UACGGUGAUCGUGCA-5\u2032\n", "Answer (final answer highlighted)": "C: The DNA template strand is complementary to the mRNA strand. Using the mRNA strand, work backward to establish the sequence of the DNA strand. Don't forget that DNA strands do not contain uracil, so eliminate (B) and (D).", "ImagePath": "Biology/7" }, { "Question": "If a mutation occurs in which uracil is deleted from the messenger RNA after methionine is translated, which of the following represents the resulting amino acid sequence?\n\nA. Serine\u2013histidine\u2013serine\u2013threonine\nB. Methionine\u2013proline\u2013glutamine\u2013histidine\nC. Methionine\u2013proline\u2013leucine\u2013alanine\u2013arginine\nD. Methionine\u2013proline\u2013alanine\u2013arginine\u2013arginine\n", "Answer (final answer highlighted)": "B Use the amino acid chart to determine the sequence after uracil is deleted. The deletion of uracil creates a frameshift.", "ImagePath": "Biology/8" }, { "Question": "The mRNA above was found to be much smaller than the original mRNA synthesized in the nucleus. This is due to the\n\nA. addition of a poly(A) tail to the mRNA molecule\nB. addition of a cap to the mRNA molecule\nC. excision of exons from the mRNA molecule\nD. excision of introns from the mRNA molecule", "Answer (final answer highlighted)": "D: The mRNA is modified before it leaves the nucleus. It becomes smaller when introns (intervening sequences) are removed. A poly(A) tail and a cap are added to the mRNA and would therefore increase the length of the mRNA, so you can eliminate (A) and (B). Choice (C) is also incorrect, as exons are the coding sequences that are kept by the mRNA.", "https://www.sanfoundry.com/1000-organic-chemistry-questions-answers/": "test 5", "ImagePath": "Biology/9" }, { "Question": "A scientist studies the storage and distribution of oxygen in humans and Weddell seals to examine the physiological adaptations that permit seals to descend to great depths and stay submerged for extended periods. The figure below depicts the oxygen storage in both organisms\n\nCompared with humans, approximately how many liters of oxygen does the Weddell seal store per kilogram of body weight?\n\nA. The same amount of oxygen\nB. Twice the amount of oxygen\nC. Three times the amount of oxygen\nD. Five times the amount of oxygen\n", "Answer (final answer highlighted)": "B: The Weddell seal stores twice as much oxygen as humans. Calculate the liters per kilograms weight for both the seal and man using the information at the bottom of the chart. The Weddell seal stores 0.058 liters/kilograms (25.9 liters/450 kilograms) compared to 0.028 liters/kilograms (1.95 liters/70 kilograms) in humans.", "ImagePath": "Biology/10" }, { "Question": "A scientist studies the storage and distribution of oxygen in humans and Weddell seals to examine the physiological adaptations that permit seals to descend to great depths and stay submerged for extended periods. The figure below depicts the oxygen storage in both organisms\n\n\nDuring a dive, a Weddell seal's blood flow to the abdominal organs is shut off and oxygen-rich blood is diverted to the eyes, brain, and spinal cord. Which of the following is the most likely reason for this adaptation?\n\nA. To increase the number of red blood cells in the nervous system\nB. To increase the amount of oxygen reaching the skeletomuscular system\nC. To increase the amount of oxygen reaching the central nervous system\nD. To increase the oxygen concentration in the lungs\n", "Answer (final answer highlighted)": "C: The most plausible answer is that blood is redirected toward the central nervous system, which permits the seal to navigate for long durations. Choice (A) is incorrect; the seal does not need to increase the number of red blood cells in the nervous system. Choice (B) can also be eliminated, as the seal does not need to increase the amount of oxygen to the skeletal system. Eliminate (D) because the diversion of blood does not increase the concentration of oxygen in the lungs.", "ImagePath": "Biology/11" }, { "Question": "Consider the following enzyme pathway:\n\nAn increase in substance F leads to the inhibition of enzyme 3. All of the following are results of the process EXCEPT\n\nA. an increase in substance X\nB. increased activity of enzyme 6\nC. decreased activity of enzyme 4\nD. increased activity of enzyme 5", "Answer (final answer highlighted)": "D: If substance F leads to the inhibition of enzyme 3, then substances D and E and enzymes 3, 4, and 5 will be affected. The activity of enzyme 5 will be decreased, not increased.", "ImagePath": "Biology/12" }, { "Question": "The graph above shows the oxygen dissociation curves of maternal hemoglobin and fetal hemoglobin. Based on the graph, it can be concluded that\n\nA. fetal hemoglobin surrenders O2 more readily than maternal hemoglobin\nB. the dissociation curve of fetal hemoglobin is to the right of maternal hemoglobin\nC. fetal hemoglobin has a higher affinity for O2 than does maternal hemoglobin\nD. fetal and maternal hemoglobin differ in structure.", "Answer (final answer highlighted)": "C: Based on the graph, fetal hemoglobin has a higher affinity for oxygen than maternal hemoglobin. Fetal hemoglobin does not give up oxygen more readily than maternal hemoglobin, so eliminate (A). You can also get rid of (B), as the dissociation curve of fetal hemoglobin is to the left of the maternal hemoglobin. Finally, eliminate (D) because fetal hemoglobin and maternal hemoglobin are different structurally, but you can't tell this from the graph.", "ImagePath": "Biology/13" }, { "Question": "The graph below shows the growth curve of a bacterial culture.\nWhich of the following represents the carrying capacity of the environment?\n\nA. 2\nB. 3\nC. 4\nD. 5", "Answer (final answer highlighted)": "D\uff1a The carrying capacity is the maximum number of organisms of a given species that can be maintained in a given environment. Once a population reaches its carrying capacity, the number of organisms will fluctuate around it.", "ImagePath": "Biology/14" }, { "Question": "The graph below shows the growth curve of a bacterial culture.\n\nWhich of the following shows the exponential growth curve of the population?\n\nA. 1\nB. 2\nC. 3\nD. 4", "Answer (final answer highlighted)": "D\uff1aDuring the exponential growth phase of a population, the size doubles during each time interval. This part of the graph looks like a parabola.", "ImagePath": "Biology/15" }, { "Question": "The following bar graph shows the relative biomass of four different populations of a particular food pyramid.\nThe largest amount of energy is available to\n\nA. population A\nB. population B\nC. population C\nD. population D", "Answer (final answer highlighted)": "B: The largest amount of energy is available to producers. Population B is most likely composed of producers because they have the largest biomass.", "ImagePath": "Biology/16" }, { "Question": "The following bar graph shows the relative biomass of four different populations of a particular food pyramid.\nWhich of the following would be the most likely result if there was an increase in the number of organisms in population C?\n\nA. The biomass of population D will remain the same.\nB. The biomass of population B will decrease.\nC. The biomass of population C will steadily increase.\nD. The food source available to population C would increase.", "Answer (final answer highlighted)": "B An increase in the number of organisms in population C would most likely lead to a decrease in the biomass of B because population B is the food source for population C. Make a pyramid based on the biomasses given. If population C increases, population B will decrease. Eliminate (A) and (C), as we cannot necessarily predict what will happen to the biomass of populations that are above population C. Choice (D) can also be eliminated because the food source available to population C would most likely decrease, not increase.", "ImagePath": "Biology/17" }, { "Question": "The cell cycle is a series of events in the life of a dividing eukaryotic cell. It consists of four stages: G1, S, G2, and M. The duration of the cell cycle varies from one species to another and from one cell type to another. The G1 phase varies the most. For example, embryonic cells can pass through the G1 phase so quickly that it hardly exists, whereas neurons are arrested in the cell cycle and do not divide.\nDuring which phase do chromosomes replicate?\n\nA. G1\nB. S\nC. G2\nD. M", "Answer (final answer highlighted)": "B: Chromosomes replicate during interphase, the S phase. Choices (A) and (C) are incorrect because during G1 and G2, the cell makes protein and performs other metabolic duties.", "ImagePath": "Biology/18" }, { "Question": "The cell cycle is a series of events in the life of a dividing eukaryotic cell. It consists of four stages: G1, S, G2, and M. The duration of the cell cycle varies from one species to another and from one cell type to another. The G1 phase varies the most. For example, embryonic cells can pass through the G1 phase so quickly that it hardly exists, whereas neurons are arrested in the cell cycle and do not divide.\nIn mammalian cells, the first sign of prophase is the\n\nA. appearance of chromosomes\nB. separation of chromatids\nC. disappearance of the nuclear membrane\nD. replication of chromosomes", "Answer (final answer highlighted)": "A: The first sign of prophase in mammalian cells is the appearance of chromosomes", "ImagePath": "Biology/19" }, { "Question": "The cell cycle is a series of events in the life of a dividing eukaryotic cell. It consists of four stages: G1, S, G2, and M. The duration of the cell cycle varies from one species to another and from one cell type to another. The G1 phase varies the most. For example, embryonic cells can pass through the G1 phase so quickly that it hardly exists, whereas neurons are arrested in the cell cycle and do not divide.\nMitosis occurs in all of the following types of cells EXCEPT\n\nA. epidermal cells\nB. hair cells\nC. red blood cells\nD. pancreatic cells", "Answer (final answer highlighted)": "C: Mitosis occurs in all of the following type of cells except mature red blood cells. Mature red blood cells are short-lived and do not divide.\nSource Url:https:// /ap/biology/question-114-answer-and-explanation.html", "ImagePath": "Biology/20" }, { "Question": "The cell cycle is a series of events in the life of a dividing eukaryotic cell. It consists of four stages: G1, S, G2, and M. The duration of the cell cycle varies from one species to another and from one cell type to another. The G1 phase varies the most. For example, embryonic cells can pass through the G1 phase so quickly that it hardly exists, whereas neurons are arrested in the cell cycle and do not divide.\nSince neurons are destined never to divide again, what conclusion can be made?\n\nA. These cells will go through cell division.\nB. These cells will be permanently arrested in the G1 phase.\nC. These cells will be permanently arrested in the G2 phase.\nD. These cells will quickly enter the S phase.", "Answer (final answer highlighted)": "B Because neurons are not capable of dividing, it is reasonable to conclude that these cells will not complete the G1 phase. This is a reading comprehension question. The passage states that cells that do not divide are arrested at the G1 phase. Choice (A) is incorrect because these cells will not be committed to go through cell division. You can also eliminate (C) and (D), as the cells will not enter the G2 or S phase.", "ImagePath": "Biology/21" }, { "Question": "The following graphs show the permeability of ions during an action potential in a ventricular contractile cardiac fiber. The action potential of cardiac muscle fibers resembles that of skeletal muscles.\n\nBased on the graph, the resting membrane potential of the muscle fibers is closest to\n\nA. -90 mV\nB. -70 mV\nC. 0 mV\nD. +70 mV", "Answer (final answer highlighted)": "A: According to the graph, the resting membrane potential of the muscle fiber is close to -90mV.", "ImagePath": "Biology/22" }, { "Question": "The following graphs show the permeability of ions during an action potential in a ventricular contractile cardiac fiber. The action potential of cardiac muscle fibers resembles that of skeletal muscles.\n\nWhich of the following statements is true concerning the initial phase of depolarization?\n\nA. Voltage-gated K+ channels open in the plasma membrane.\nB. The concentration of Ca2+ ions within the plasma membrane becomes more negative.\nC. The membrane potential stays close to -40 mV.\nD. The permeability of the sarcolemma to Na+ ions increases.", "Answer (final answer highlighted)": "D:Refer to the second graph about the membrane permeability of ions during a muscle contraction. During depolarization, the membrane is permeable to Na+. Choice (A) can be eliminated because the voltage-gated K+ channels do not open until after depolarization. Eliminate (B) because the concentration of Ca2+ does not become more negative. Choice (C) is also incorrect, as the membrane potential changes from -90 mV to +20 mV.", "ImagePath": "Biology/23" }, { "Question": "The following graphs show the permeability of ions during an action potential in a ventricular contractile cardiac fiber. The action potential of cardiac muscle fibers resembles that of skeletal muscles.\nIn cardiac fibers, the duration of an action potential is approximately\n\nA. 0.10 secs\nB. 0.20 secs\nC. 0.25 secs\nD. 0.30 secs\n\n", "Answer (final answer highlighted)": "D: Refer to both graphs in the passage. In cardiac fibers, the duration of an action potential\u2014a neuronal impulse\u2014is approximately 0.3 seconds.", "ImagePath": "Biology/24" }, { "Question": "The following graphs show the permeability of ions during an action potential in a ventricular contractile cardiac fiber. The action potential of cardiac muscle fibers resembles that of skeletal muscles.\nOne major difference between the action potential of cardiac muscle fibers and the action potential of skeletal muscle fibers is that in cardiac muscle fibers\n\nA. the membrane is permeable to Na+, not K+\nB. voltage-gated K+ channels open during depolarization, not repolarization\nC. depolarization is prolonged compared to that in skeletal muscle fibers\nD. the refractory period is shorter than that of skeletal muscle fibers\n\n", "Answer (final answer highlighted)": "C: In cardiac muscle fibers, depolarization is prolonged compared to that in skeletal muscle fibers. Eliminate (A) because the membrane is permeable to both Na+ and K+. Choice (B) can also be eliminated; in cardiac muscle fibers, voltage-gated K+ channels open during repolarization. Finally, (D) is wrong because the refractory period is longer in cardiac muscle fibers compared to skeletal muscle fibers.\n\n", "ImagePath": "Biology/25" }, { "Question": "The data below concerns the general animal body plan of five organisms\nThe two most closely related organisms are\n\nA. sea anemone and hagfish\nB. eel and salamander\nC. hagfish and eel\nD. sea anemone and salamande", "Answer (final answer highlighted)": "B The two most closely related organisms are the two with the most shared derived characteristics.\n\n", "ImagePath": "Biology/26" }, { "Question": "The data below concerns the general animal body plan of five organisms\nThe correct order of evolution for the traits above is\n\nA. jaws \u2013 vertebral column \u2013 walking legs\nB. walking legs \u2013 jaws \u2013 vertebral column\nC. jaws \u2013 walking legs \u2013 vertebral column\nD. vertebral column \u2013 jaws \u2013 walking legs", "Answer (final answer highlighted)": "D: Shared derived characteristics are newly evolved traits that are shared with every group on a phylogenic tree except for one. Vertebral columns are present in every group except for the sea anemone, so it must have evolved first. Walking legs are only found in the salamander, indicating that it most likely evolved most recently.", "ImagePath": "Biology/27" }, { "Question": "The data below concerns the general animal body plan of five organisms\nPre- and post-zygotic barriers exist that prevent two different species from producing viable offspring. All of the following are pre-zygotic barriers EXCEPT\n\nA. anatomical differences preventing copulation\nB. different temporality of mating\nC. sterility of offspring\nD. incompatible mating songs", "Answer (final answer highlighted)": "C: Pre-zygotic barriers to reproduction are those that prevent fertilization, so you can eliminate (A), (B), and (D). Choice (C) is an example of a post-zygotic barrier to reproduction.", "ImagePath": "Biology/28" }, { "Question": "The data below concerns the general animal body plan of five organisms.\nBirds and insects have both adapted wings to travel by flight. The wings of birds and insects are an example of\n\nA. divergent evolution\nB. convergent evolution\nC. speciation\nD. mutation\n", "Answer (final answer highlighted)": "B: Convergent evolution occurs when two organisms that are not closely related independently evolve similar traits, such as the wings of insects and birds. Divergent evolution occurs when two closely related individuals become more different over time and can lead to speciation.", "ImagePath": "Biology/29" }, { "Question": "The following synthetic pathway of a pyrimidine, cytidine 5' triphosphate, CTP, begins with the condensation of two small molecules by the enzyme, aspartate transcarbamylase (ATCase).\nWhich of the following is true when the level of CTP is low in a cell?\n\nA. CTP is converted to ATCase.\nB. The metabolic traffic down the pathway increases.\nC. ATCase is inhibited, which slows down CTP synthesis.\nD. The final product of the pathway is reduced.\n", "Answer (final answer highlighted)": "B: When the level of CTP is low in a cell, the metabolic traffic down the pathway increases. This pathway is controlled by feedback inhibition. The final product of the pathway inhibits the activity of the first enzyme. When the supply of CTP is low, the pathway will continue to produce CTP.", "ImagePath": "Biology/30" }, { "Question": "The following synthetic pathway of a pyrimidine, cytidine 5' triphosphate, CTP, begins with the condensation of two small molecules by the enzyme, aspartate transcarbamylase (ATCase).\nThis enzymatic phenomenon is an example of\n\nA. transcription\nB. feedback inhibition\nC. dehydration synthesis\nD. photosynthesi\n", "Answer (final answer highlighted)": "B: This enzymatic phenomenon is an example of feedback inhibition. Feedback inhibition is the metabolic regulation in which high levels of an enzymatic pathway's final product inhibit the activity of its rate-limiting enzyme. Transcription, (A), is the production of RNA from DNA. Dehydration synthesis, (C), is the formation of a covalent bond by the removal of water. In photosynthesis, (D), radiant energy is converted to chemical energy.", "ImagePath": "Biology/31" }, { "Question": "The following synthetic pathway of a pyrimidine, cytidine 5' triphosphate, CTP, begins with the condensation of two small molecules by the enzyme, aspartate transcarbamylase (ATCase).\nThe biosynthesis of cytidine 5'-triphosphate requires\n\nA. a ribose sugar, a phosphate group, and a nitrogen base\nB. a deoxyribose sugar, a phosphate group, and a nitrogen base\nC. a ribose sugar, phosphate groups, and a nitrogen base\nD. a deoxyribose sugar, phosphate groups, and a nitrogen base\n", "Answer (final answer highlighted)": "C: The biosynthesis of cytidine 5\u2032-triphosphate requires a nitrogenous base, three phosphates, and the sugar ribose. Pyrimidines are a class of nitrogenous bases with a single ring structure. The sugar they contain is ribose, which is shown in the pathway diagram", "ImagePath": "Biology/32" }, { "Question": "Here is a sketch of a molecule of the sex hormone, testosterone, that is derived from cholesterol.\nWhich of the following statements best describes the action of this hormone on cells of the human gonads?\n\nA. The hormone acts as the first messenger when it binds to and activates the G protein-coupled receptor on the surface of cells in the testes. This activates the mobile G protein located inside the cell.\nB. The hormone enters cells in the testes by first binding with a membrane receptor, which causes a channel to open in the membrane, allowing the testosterone to flood into the cell.\nC. The hormone readily passes through the cell membrane and binds to a receptor in the cytoplasm. The hormone and receptor then enter the nucleus and act as a transcription factor that turns on one or more genes.\nD. The hormone binds with cAMP on the surface of the cell. Once attached to cAMP, the hormone enters the cell and initiates a signal transduction pathway.", "Answer (final answer highlighted)": "C: The sex hormone testosterone is lipid soluble (hydrophobic) and dissolves directly through the cell membrane. Choices A and B correctly describe the action of a hydrophilic signal. Cyclic AMP is a secondary messenger found in the cytoplasm, not on the surface of a cell.", "ImagePath": "Biology/33" }, { "Question": "Which of the following statements accurately accounts for the shape of the graph?\n\nA. The rate of photosynthesis stops increasing because chlorophyll molecules begin to decompose due to increased heat, not increased light.\nB. The rate of photosynthesis slows as chlorophyll molecules, which are proteins, denature.\nC. Photosynthesis ceases when protons are no longer released by the photolysis of water.\nD. The rate of photosynthesis increases until the light-harvesting apparatus in the thylakoid membranes become saturated and cannot make use of additional light", "Answer (final answer highlighted)": "D: The graph flattens out but doesn't decrease. Therefore, photosynthesis is still going on. That indicates that choices A, B, and C cannot be correct.\n\n", "ImagePath": "Biology/34" }, { "Question": "Here is a sketch of an animal cell.\n\nWhich of the following statements is correct?\n\nA. Structure A detoxifies poisons in the cell.\nB. Structure B packages proteins for export.\nC. Structure C synthesizes RNA.\nD. Structure D consists of cytoskeleton.", "Answer (final answer highlighted)": "B: Structure B is the Golgi apparatus, which packages and secretes proteins made by the ribosomes in the E.R. The centrioles shown as structure A consist of microtubules. Structure C is a lysosome. Strucure D consists of ribosomes on the E.R.\n", "ImagePath": "Biology/35" }, { "Question": "Chronically high levels of glucocorticoids can result in obesity, muscle weakness, and depression. This looks like several diseases but actually is only one, Cushing syndrome. Excessive activity of either the pituitary or the adrenal gland can cause the disease. To determine which gland has abnormal activity in a particular patient, doctors use the drug dexamethasone, a synthetic glucocorticoid that blocks ACTH (adrenocorticotropic hormone) release.\n\nBased on the graph, which gland is affected in the patient with Cushing syndrome and what is the reasoning behind your answer?\n\nA. The pituitary, because although ACTH is blocked, the pituitary is still sending a signal to the adrenal glands.\nB. The pituitary, because blocking ACTH has no effect on cortisol levels.\nC. The adrenal gland, because the pituitary is prevented from stimulating the adrenal glands, and yet cortisol levels are still high.\nD. The adrenal gland, because the pituitary is sending a signal to the adrenal gland and the adrenal glands have stopped producing cortisol.", "Answer (final answer highlighted)": "C: The patient is still producing too much cortisol even though the pituitary is not sending a signal to the adrenal glands. ACTH, which would normally stimulate the adrenal to release cortisol, is blocked by the dexamethasone. If the adrenals were healthy, they should not be producing anything. Unfortunately, they are. Compare the patient with the normal person.", "ImagePath": "Biology/36" }, { "Question": "Here is the final reaction in the citric acid cycle. It shows the regeneration of oxaloacetate.\n\n\n\nAfter studying the reaction, determine which of the following statements is correct.\n\nA. The enzyme malate dehydrogenase is allosteric.\nB. The reaction is exergonic; the released energy is absorbed by NAD+.\nC. The reaction is a reduction reaction.\nD. NAD+ is oxidized into NADH.", "Answer (final answer highlighted)": "B: Energy is released, and NAD+ binds to hydrogen released by malate.", "ImagePath": "Biology/37" }, { "Question": "Oxygen is carried in the blood by the respiratory pigment hemoglobin, which can combine loosely with four oxygen molecules, forming the molecule oxyhemoglobin. To function properly, hemoglobin must bind to oxygen in the lungs and drop it off at body cells. The more easily the hemoglobin binds to oxygen in the lungs, the more difficult the oxygen is to unload at the body cells. Here is a graph showing two different saturation-dissociation curves for one type of hemoglobin at two different pH levels.\n\n\n\nBased on your knowledge of biology and the information in this graph, which statement about the hemoglobin curves is correct?\n\nA. Hemoglobin B has a greater affinity for oxygen and therefore binds more easily to oxygen in the lungs.\nB. Hemoglobin A is characteristic of a mammal that evolved at sea level where oxygen levels are high.\nC. In an acidic environment, hemoglobin drops off oxygen more easily at body cells.\nD. Hemoglobin A is found in mammals with a higher metabolism.", "Answer (final answer highlighted)": "C: The line to the right shows a lower affinity for oxygen. CO2 dissolved in water produces carbonic acid. What this graph demonstrates is that the blood near respiring cells, which release carbon dioxide, make the surrounding area acidic. This acidic environment causes hemoglobin to release its oxygen to the cells where it is needed.", "ImagePath": "Biology/38" }, { "Question": "2. Animals maintain a minimum metabolic rate for basic functions such as breathing, heart rate, and maintaining body temperature. The minimum metabolic rate for an animal at rest is the basal metabolic rate (BMR). The BMR is affected by many factors, including whether an animal is an ectotherm or endotherm; its age and sex; and size and body mass. Here is a graph that shows the relationship of BMR per kilogram of body mass to body size for a group of mammals.\n\nWhich statement correctly describes the relationship between BMR and body mass?\n\nA. The relationship between BMR and body mass is a direct one. The larger the body mass the higher the BMR is and the greater the breathing rate is.\nB. The relationship between BMR and body mass is a direct one. The larger the body mass the higher the BMR is and the lower the breathing rate is.\nC. The relationship between BMR and body mass is inversely proportional. The larger the body mass, the lower the BMR is and the lower the breathing rate is.", "Answer (final answer highlighted)": "C: The energy to maintain each gram of body mass is inversely related to body size. This graph describes a relationship between X and Y that is inversely proportional. When the relationship is directly proportional the line goes diagonally from the lower left to upper right. Each gram of mouse requires 20 times as many calories as a gram of elephant even though the whole elephant uses more calories than a whole mouse. The higher the metabolic rate, the higher the oxygen and food requirement per unit of body mass.", "ImagePath": "Biology/39" }, { "Question": "Refer to the codon table for the following question.\n\n\n\nHere is a small stretch of mRNA that would be translated at the ribosome:\n\n. . . AUG CUG AAA UCAGGG . . .\n\nSuppose a spontaneous mutation altered the boldface A and changed it to a U.\nWhat effect, if any, would this have on the protein formed?\n\nA. Because of redundancy in the code, there would be no change in the protein formed.\nB. The amino acid sequence formed from this stretch of DNA would be\nMet\u2013Leu\u2013Lys\u2013Ser\u2013Gly.\nC. The polypeptide would not form because translation would stop at UAA.\nD. Translation would continue and a polypeptide would form because AUG codes for start as well as for methionine.\n", "Answer (final answer highlighted)": "C: UAA codes for a stop sequence. Translation would cease at that point in the process.\n\n", "ImagePath": "Biology/40" }, { "Question": "Two ecologists, Peter and Rosemary Grant, spent thirty years observing, tagging, and measuring finches (a type of bird) in the Gal\u00e1pagos Islands. They made their observations on Daphne Major\u2014one of the most desolate of the Gal\u00e1pagos Islands. It is an uninhabited volcanic cone where only low to the ground cacti and shrubs grow. During 1977, there was a severe drought and seeds of all kinds became scarce. The small, soft seeds were quickly eaten by the birds, leaving mainly large, tough seeds that the finches normally ignore. The year after the drought, the Grants discovered that the average width of the finches' beak had increased.\nWhich of the following statements best explains the increase in beak size?\n\nA. Finches with bigger and stronger beaks were able to attack and kill the finches with smaller beaks.\nB. Finches with bigger beaks were larger animals with stronger wings that could fly to other islands and gather a wide variety of seeds.\nC. During the drought, the finches' beaks grew larger to accommodate the need to eat tougher seeds.\nD. Finches with larger beaks were able to eat the tougher seeds and were healthier and reproduced more offspring that inherited the trait for wider beaks.", "Answer (final answer highlighted)": "D: This is classic Darwinian evolutionary theory\u2014the survival of the best adapted.", "ImagePath": "Biology/41" }, { "Question": "Two ecologists, Peter and Rosemary Grant, spent thirty years observing, tagging, and measuring finches (a type of bird) in the Gal\u00e1pagos Islands. They made their observations on Daphne Major\u2014one of the most desolate of the Gal\u00e1pagos Islands. It is an uninhabited volcanic cone where only low to the ground cacti and shrubs grow. During 1977, there was a severe drought and seeds of all kinds became scarce. The small, soft seeds were quickly eaten by the birds, leaving mainly large, tough seeds that the finches normally ignore. The year after the drought, the Grants discovered that the average width of the finches' beak had increased.\nWhich of the following statements best explains the mechanism behind the change in beak size?\n\nA. A new allele appeared in the finch population as a result of a mutation.\nB. A change in the frequency of a gene was due to selective pressure from the environment.\nC. A new trait appeared in the population because of recombination of alleles.\nD. A new trait appeared in the population because of genetic drift.", "Answer (final answer highlighted)": "B: Choices A, C, and D all have the same problem. A new trait may have appeared by a single mutation, by recombination of alleles, or by genetic drift. However, that does not explain how the birds, on average, came to have longer beaks", "ImagePath": "Biology/42" }, { "Question": "Answer the following two questions based on this pedigree for the biochemical disorder known as alkaptonuria. Affected individuals are unable to break down a substance called alkapton, which colors the urine black and stains body tissues. Otherwise, the condition is of no consequence. Males are shown as squares, females as circles. Afflicted individuals are shown in black. If there is a carrier condition, it is not displayed.\nWhich of the following best states the pattern of inheritance shown in the pedigree?\n\nA. The trait is sex-linked dominant.\nB. The trait is sex-linked recessive.\nC. The trait is autosomal dominant.\nD. The trait is autosomal recessive.", "Answer (final answer highlighted)": "D: Look at individuals 1 and 2. Neither has the condition, but they have a daughter with the condition. Sex-linked dominant and autosomal dominant are eliminated because neither parent has the condition. Sex-linked recessive is also eliminated because if the father passed the trait to his daughter, he would have to have the condition. For the daughter to have the condition, she would have had to inherit two affected X chromosomes\u2014one from each parent.", "ImagePath": "Biology/43" }, { "Question": "Answer the following two questions based on this pedigree for the biochemical disorder known as alkaptonuria. Affected individuals are unable to break down a substance called alkapton, which colors the urine black and stains body tissues. Otherwise, the condition is of no consequence. Males are shown as squares, females as circles. Afflicted individuals are shown in black. If there is a carrier condition, it is not displayed.\nWhich of the following statement is supported by the information given in the pedigree?\n\nA. The P generation mother is X-X.\nB. The P generation father is X-Y.\nC. If parents 1 and 2 in row II have another child, the chance that the child would be afflicted with alkaptonuria is 25%.\nD. The genotype of woman 1 is X-X.", "Answer (final answer highlighted)": "C: Since the trait is inherited as autosomal recessive, individuals 1 and 2 are each hybird. The chance that any child of theirs will have the condition is 25%.\n\n", "ImagePath": "Biology/44" }, { "Question": "Four vials were set up to investigate bacterial transformation. Vials 1 and 2 each contained E. coli bacteria that had been made competent and had then been mixed with a plasmid containing the gene for ampicillin (pAMP) resistance. Vials 3 and 4 both contained E. coli that had also been made competent but had not been mixed with a plasmid. Each vial of bacteria was poured onto a nutrient agar plate. Vials 1 and 3 were poured onto plates that contained the antibiotic ampicillin. Vials 2 and 4 were poured onto plates that did not contain ampicillin.\n\nThis figure shows what the nutrient agar plates looked like. The shaded plates represent extensive growth, and the dots represent individual bacterial colonies.\n\nPlates that have only ampicillin-resistant bacteria growing on them include which of the following?\n\nA. Plate 1 only\nB. Plate 2 only\nC. Plate 3 only\nD. Plates 1 and 3 only", "Answer (final answer highlighted)": "A: The few colonies growing on Plate 1 consist of bacteria that have taken up the plasmid and are resistant to ampicillin. Plate 2 consists of both antibiotic-resistant bacteria as well as nonresistant bacteria. There is no antibiotic in the agar on Plate 2 to distinguish the two bacteria.\nSource Url:https:// /ap/biology/question-161-answer-and-explanation.html", "ImagePath": "Biology/45" }, { "Question": "Four vials were set up to investigate bacterial transformation. Vials 1 and 2 each contained E. coli bacteria that had been made competent and had then been mixed with a plasmid containing the gene for ampicillin (pAMP) resistance. Vials 3 and 4 both contained E. coli that had also been made competent but had not been mixed with a plasmid. Each vial of bacteria was poured onto a nutrient agar plate. Vials 1 and 3 were poured onto plates that contained the antibiotic ampicillin. Vials 2 and 4 were poured onto plates that did not contain ampicillin.\n\nThis figure shows what the nutrient agar plates looked like. The shaded plates represent extensive growth, and the dots represent individual bacterial colonies.\n\nWhich of the following statements explains why there was no growth on Plate 3?\n\nA. The heat shock technique to make the E.coli competent killed the bacteria.\nB. Those particular E.coli bacteria were inhibited from growing by the nutrient in the agar.\nC. Those bacteria were not transformed.\nD. The bacteria culture died because they have a short life span.", "Answer (final answer highlighted)": "C: The bacteria on Plate 3 were not transformed. That means they did not uptake a plasmid and were not resistant to antibiotic. There is antibiotic in the agar on that plate, which killed the nontransformed bacteria", "ImagePath": "Biology/46" }, { "Question": "Four vials were set up to investigate bacterial transformation. Vials 1 and 2 each contained E. coli bacteria that had been made competent and had then been mixed with a plasmid containing the gene for ampicillin (pAMP) resistance. Vials 3 and 4 both contained E. coli that had also been made competent but had not been mixed with a plasmid. Each vial of bacteria was poured onto a nutrient agar plate. Vials 1 and 3 were poured onto plates that contained the antibiotic ampicillin. Vials 2 and 4 were poured onto plates that did not contain ampicillin.\n\nThis figure shows what the nutrient agar plates looked like. The shaded plates represent extensive growth, and the dots represent individual bacterial colonies.Which of the following statements best explains why there were fewer colonies on Plate 1 than on Plate 2?\n\nA. The bacteria on Plate 2 did not transform.\nB. There was no antibiotic in the agar in Plate 2 that would have restricted growth of bacteria.\nC. The transformation of bacteria on Plate 2 was more successful.\nD. The bacteria on Plates 1 and 2 were not taken from the same culture.", "Answer (final answer highlighted)": "B: The few colonies growing on Plate 1 consist of bacteria that have taken up the plasmid and are resistant to ampicillin. Plate 2 consists of both antibiotic-resistant bacteria as well as nonresistant bacteria. There is no antibiotic in the agar on Plate 2 to distinguish the two bacteria.", "ImagePath": "Biology/47" }, { "Question": "Four vials were set up to investigate bacterial transformation. Vials 1 and 2 each contained E. coli bacteria that had been made competent and had then been mixed with a plasmid containing the gene for ampicillin (pAMP) resistance. Vials 3 and 4 both contained E. coli that had also been made competent but had not been mixed with a plasmid. Each vial of bacteria was poured onto a nutrient agar plate. Vials 1 and 3 were poured onto plates that contained the antibiotic ampicillin. Vials 2 and 4 were poured onto plates that did not contain ampicillin.\n\nThis figure shows what the nutrient agar plates looked like. The shaded plates represent extensive growth, and the dots represent individual bacterial colonies.\n\nIn a variant of this experiment, the plasmid contained GFP (green fluorescent protein) in addition to ampicillin resistance. Which of the following plates would have the highest percentage of bacteria that would fluoresce?\n\nA. Plate 1 only\nB. Plate 2 only\nC. Plate 3 only\nD. Plate 4 only", "Answer (final answer highlighted)": "A: There would be fluorescent bacteria on both Plates 1 and 2. However, 100% of the bacteria on Plate 1 would fluoresce while only a percentage of the bacteria on Plate 2 would do so", "ImagePath": "Biology/48" }, { "Question": "Here is a sketch of a neuromuscular junction in a patient with an autoimmune disease. Acetylcholine (ACh) is the stimulatory neurotransmitter.\n\n\n\nWhich of the following predicts what will happen in the continued presence of the antibodies?\n\nA. Ca++ ions will flood into the motor neuron ending, increasing the release of more ACh.\nB. The amount of neurotransmitter being released will decrease.\nC. The number of action potentials in the motor neuron will decrease.\nD. Antibodies will destroy the postsynaptic receptors, and the muscle response will diminish.", "Answer (final answer highlighted)": "D: In an autoimmune disease, the immune system mistakenly attacks its own body structures. The antibodies attack the postsynaptic muscle receptors, not the neuron function", "ImagePath": "Biology/49" }, { "Question": "The graph on the left (A) shows an absorption spectrum for chlorophyll a extracted from a plant. The graph on the right (B) shows an action spectrum from a living plant, with wave lengths of light plotted against the rate of photosynthesis as measured by release of oxygen.\n\nWhich statement best explains the difference between the two spectra?\n\nA. Graph A plots the absorption spectrum of a red plant; graph B plots an absorption spectrum for a green plant.\nB. The chlorophyll from Graph A cannot carry out the light-dependent reactions; but the chlorophyll in graph B can.\nC. The data from Graph A characterize several photosynthetic pigments that reflect almost no light; the data from Graph B characterize chlorophyll a, which reflects only green light.\nD. Graph A shows an absorption spectrum for an unusual type of chlorophyll a.\n", "Answer (final answer highlighted)": "B: Graph A shows the absorption spectrum for chlorophyll that was extracted from a living plant. Once separated from the grana and stroma, chlorophyll by itself cannot carry out photosynthesis.\n\n", "ImagePath": "Biology/50" }, { "Question": "Cystic fibrosis is the most common inherited disease in the U.S. Among people of European descent, 4% are carriers of the recessive cystic fibrosis allele. The most common mutation in individuals with cystic fibrosis is a mutation in the CFTR protein that functions in the transport of chloride ions between certain cells and extracellular fluid. These chloride transport channels are defective or absent in the plasma membranes of people with the disorder. The result is abnormally high concentration of extracellular chloride that causes the mucus that coats certain cells to become thicker and stickier than normal. Mucus builds up in the pancreas, lungs, digestive tract, and other organs. This leads to multiple effects, including poor absorption of nutrients from the intestines, chronic bronchitis, and recurrent bacterial infections.Scientific work has been carried out to measure where the relative amounts of CFTR protein are localized in the affected cells\n\nAfter studying the graph, which of the following statements about CFTR protein is correct?\n\nA. Transcription is not occurring.\nB. Translation is not occurring.\nC. CFTR protein does not fold properly after it is synthesized.\nD. CFTR protein is not being packaged in the cytoplasm.\n", "Answer (final answer highlighted)": "D: Ribosomes produce protein for export. Once synthesized, the protein is packaged into vesicles in the Golgi for secretion. The graphs show that the amount of CFTR is high where synthesis occurs in the E.R. and low in the vesicles and Golgi. So the protein was synthesized in the ribosomes but not packaged.\n", "ImagePath": "Biology/51" }, { "Question": "Based on the cladogram, which of the following is NOT true?\n\nA. Only some tetrapods have amnions.\nB. Mammals and amphibians are more closely related than mammals and birds.\nC. Ancestor 2 lived before ancestor 3; and we do know when that was.\nD. Lungfishes and amphibians share a common ancestor.", "Answer (final answer highlighted)": "C: This cladogram does not have a time scale attached to it. All we can say about any clade or lineage is that one evolved earlier or later than another. A cladogram is constructed to show the development of different traits and the lineage of related organisms that evolved with that trait.", "ImagePath": "Biology/52" }, { "Question": "From 1972 to 2004, researchers studying the greater prairie chicken observed that a population collapse mirrored a reduction in fertility as measured by the hatching rate of eggs. Comparison of DNA samples from the Jasper County, Illinois, population with DNA from feathers in a museum collection showed that genetic variation had declined in the studied population. The researchers translocated prairie chickens from Minnesota, Kansas, and Nebraska into the Illinois prairie chicken population in 1992 and found that the hatching rate in Illinois prairie chickens changed. Here is a graph of the data.\n\n\n\nWhich of the following statements most accurately explains what happened to the studied population of prairie chickens after translocation and why?\n\nA. The hatching rate increased because genetic variation declined.\nB. The hatching rate increased because genetic variation increased.\nC. The hatching rate decreased because genetic variation decreased.\nD. The hatching rate decreased because the translocated animals were invasive and grew to dominate the population.", "Answer (final answer highlighted)": "B: Prior to translocation, the chickens had become inbred, diversity had decreased, and fertility had declined.", "ImagePath": "Biology/53" }, { "Question": "In a study of dusty salamanders, Desmognathus ochrophaeus, scientists brought individuals from different populations into the laboratory and tested their ability to mate and produce viable, fertile offspring. Here is the graph of the data.\n\n\n\nThe degree of reproductive isolation is represented by an index ranging from 0 (no isolation) to 2 (complete isolation).\n\nWhich of the following statements best describes the evolutionary history of dusty salamanders?\n\nA. Mutation alone caused the two populations to diverge.\nB. Both mutation and genetic drift cause the two populations to diverge.\nC. Both mutation and genetic drift caused the two populations to become separate species after they were separated by great distance.\nD. Reproductive isolation between the two populations increases as the distance between them increases", "Answer (final answer highlighted)": "D: The question does not reveal anything about mutation or genetic drift. The point here is that in this case, divergence is a function of geographic distance.", "ImagePath": "Biology/54" }, { "Question": "Scientists carried out a series of experiments to study innate immunity in fruit flies. They began with a mutant fly strain in which a pathogen is recognized but the signaling that would normally trigger an innate response is blocked. As a result, the flies did not make any antimicrobial peptides (AMP). The researchers then genetically engineered some of the mutant flies to express significant amounts of a single AMP, either defensin or drosomycin. They then infected the flies with a fungus, Neurospora crassa, by shaking anesthetized flies for 30 seconds in a Petri dish containing a sporulating fungal culture. The 6-day survival rate was monitored and recorded.\n\nHere is a graph displaying some data from the experiment.\n\nKEY:\nA Wild type\nB Mutant + drosomycin\nC Mutant + defensin\nD Mutant\nWhich of the following statements is supported by the data?\n\nA. Each AMP provided minimal immunity against fungal infection.\nB. Both AMPs provided better immunity than did either one alone.\nC. Drosomycin provided immunity against the fungal infection.\nD. There was no control in this experiment.", "Answer (final answer highlighted)": "C: The survival of mutant flies + drosomycin was greater than mutant flies + defensin. Two controls, A and D, were included in this experiment.", "ImagePath": "Biology/55" }, { "Question": "An experiment was carried out with guppies, which are brightly colored, popular, aquarium fish. Three hundred guppies were added to 12 large pools. Cichlids, a voracious predator, were added to 4 of the pools. Killifish that rarely eat guppies were added to 4 other pools. No other fish were added to the last 4 pools. After 16 months, a time period that represents 10 generations for guppies, all the guppies were analyzed for size and coloration. Here are the data.\nWhich of the following statements is supported by the data?\n\nA. Cichlids were an agent of selection, eating the more visible, brightly colored guppies.\nB. Killifish were an agent of selection, eating the more visible, brightly colored guppies.\nC. Guppies, as a group, experienced change in coloration, from brightly colored to dull in order to survive.\nD. Individual guppies experienced a mutation that caused a change in coloration and enabled them to avoid being eaten.", "Answer (final answer highlighted)": "A: Killifish do not eat guppies, but cichlids do. So cichilds were the agent of selection. No organism or population changes in order to survive. If individuals are not adapted, they die. No individual changes during its lifetime. Rather, the frequency of a particular trait in a population may change.", "ImagePath": "Biology/56" }, { "Question": "An experiment was carried out with guppies, which are brightly colored, popular, aquarium fish. Three hundred guppies were added to 12 large pools. Cichlids, a voracious predator, were added to 4 of the pools. Killifish that rarely eat guppies were added to 4 other pools. No other fish were added to the last 4 pools. After 16 months, a time period that represents 10 generations for guppies, all the guppies were analyzed for size and coloration. Here are the data.\nWhich of the following statements best expresses the point of this experiment?\n\nA. Mutations can be brought about by the environment.\nB. Mutations occur randomly.\nC. Agents of selection are not always readily apparent.\nD. Evolution does not always require millions of years", "Answer (final answer highlighted)": "D: The evolution in this population\u2014the change in frequency of the trait for brightly colored spots\u2014occurred rapidly, within 16 months. Evolution does not always require millions of years. The rate of change is a function of the pressure from the environment to change.\n\n", "ImagePath": "Biology/57" }, { "Question": "Here is a sketch of prokaryotic DNA undergoing replication and transcription simultaneously.\nIf 1 is thymine, what is a?\n\nA. Adenine\nB. Thymine\nC. Cytosine\nD. Uracil", "Answer (final answer highlighted)": "B: First orient yourself in the drawing. The process at the top of the sketch is replication; the bottom is transcription. So if 1 is thymine, then its complement, I, is adenine. Therefore, if I is adenine, then its base pair is thymine.", "ImagePath": "Biology/58" }, { "Question": "Here is a sketch of prokaryotic DNA undergoing replication and transcription simultaneously.\nIf 4 is adenine, what is D?\n\nA. Adenine\nB. Thymine\nC. Cytosine\nD. Uracil\n", "Answer (final answer highlighted)": "D: The bottom of the diagram represents transcription. Therefore, if 4 is adenine, then D is its complement in RNA, which is uracil.\n\n", "ImagePath": "Biology/59" }, { "Question": "Intact chloroplasts are isolated from dark-green leaves by low-speed centrifugation and are placed into six tubes containing cold buffer. A blue dye, DPIP, which turns clear when reduced, is also added to all the tubes. Then each tube is exposed to different wavelengths of light. A measurement of the amount of decolorization is made, and the data are plotted on a graph. Although the wavelengths of light vary, the light intensity is the same.\nWhich statement below best describes the results of the experiment?\n\nA. The lower the wavelength of light, the greater the rate of photosynthesis.\nB. The highest wavelengths of light provide the fastest rate of photosynthesis.\nC. The highest rate of photosynthesis results from exposure to two different wavelengths of light.\nD. The greatest reduction in DPIP occurs at 550 nm light intensity.\n\n", "Answer (final answer highlighted)": "C: The greatest reduction (change in color of DPIP) occurs at 650 nm + 700 nm of light. The steeper the decline of the graph, the greater the reduction of DPIP.\n\n", "ImagePath": "Biology/60" }, { "Question": "A group of scientists wished to learn about the energy efficiency of different modes of locomotion. They studied the literature that was based on accurate measurements and produced this graph based on the data they analyzed.\nWhich of the following statement accurately describes what the scientists discovered?\n\nA. An animal with a large body mass expends more energy per kilogram of body mass than a small animal, regardless of the type of locomotion.\nB. Swimming has to overcome drag as well as gravity.\nC. Running is the least energy-efficient means of locomotion.\nD. The best parameter to measure in this type of experiment is CO2 consumption \n\n", "Answer (final answer highlighted)": "C: According to the data, an animal with a small body mass expends more energy per kilogram of body mass regardless of the type of locomotion. Swimming is the most efficient means of locomotion. Swimming does not have to overcome gravity; the swimmer is supported by the water.", "ImagePath": "Biology/62" }, { "Question": "Oxygen is carried in the blood by the respiratory pigment hemoglobin, which can combine loosely with four oxygen molecules to form the molecule oxyhemoglobin. To function properly, hemoglobin must bind to oxygen in the lungs and drop it off at body cells. The more easily the hemoglobin bonds to oxygen in the lungs, the more difficult for the hemoglobin to unload the oxygen at the body cells. Here is a graph showing two different saturation-dissociation curves for one type of hemoglobin at two different pH levels.\n\nBased on your knowledge of biology and the information in this graph, which statement about the hemoglobin curves is correct?\n\nA. Hemoglobin B has a greater affinity for oxygen and will therefore bind more easily to oxygen in the lungs.\nB. Hemoglobin B is characteristic of a mammal that evolved at a high elevation where oxygen is rare.\nC. When CO2 levels in the blood are high, as shown in hemoglobin B, hemoglobin releases oxygen more readily.\nD. Hemoglobin A is the type found in mammals with a higher metabolism. Hemoglobin B is characteristic of mammals.", "Answer (final answer highlighted)": "C: This graph is focused on the strength of the bond between Hb and oxygen at pH 7.2 and pH 7.4. At a lower at pH, which is more acidic, the attachment is weaker. This makes sense because as cells carry out cellular respiration, they release CO2, which makes the blood more acidic. The blood pH changes from normal 7.4 to the more acidic 7.2. At pH 7.2, the Hb can release more of its oxygen where it is needed, at the cells", "ImagePath": "Biology/63" }, { "Question": "The following reaction occurs in the citric acid cycle. Study the reaction as it is shown here.\n\n\n\nWhich of the following statements is correct?\n\nA. This is part of the reaction that produces pyruvate.\nB. The reaction is an example of negative feedback.\nC. The reaction is an oxidation reaction.\nD. The reaction occurs in the cristae membrane.\n", "Answer (final answer highlighted)": "C: Oxidation is the loss of electrons or of hydrogen. You can see that hydrogen has been lost by the succinate to form fumacate. If this is part of the citric acid cycle, then pyruvate is the starting point of this reaction, not the product. The citric acid cycle produces CO2 and ATP. Feedback mechanisms are complex. This is certainly not one. The stem of the question states that this is part of the citric acid cycle, which occurs in the inner matrix of the mitochondria, not the cristae membrane.\n\n", "ImagePath": "Biology/64" }, { "Question": "Identify the phase of meiosis when recombination occurs, and state the reason for your decision.\n\n\n\nA. Picture 1, because sister chromosomes are lined up on the metaphase plate.\nB. Picture 1, because homologous pairs are lined up on the metaphase plate.\nC. Picture 2, because homologues are paired up in synapsis.\nD. Picture 3, because homologous pairs are exchanging genetic material.", "Answer (final answer highlighted)": "C: Recombination occurs when homologous pairs bind together during synapsis and crossing-over occurs. Picture 1 is in metaphase. Synapsis and crossing-over have already occurred. The homologous pairs are about to separate. Picture 2 shows prophase. Synapsis is occurring, and crossing-over can occur at this point. Picture 3 shows sister chromatids lined up on the metaphase plate. There can be no crossing-over because there is only one chromosome.", "ImagePath": "Biology/65" }, { "Question": "Which of the following statements best describes what this cell will accomplish as part of the immune system?\n\n\n\nA. It will secrete a chemical that will form holes in the pathogen.\nB. It will produce antibodies against the antigen it is engulfing.\nC. It will circulate in the bloodstream for a lifetime and will be able to identify the antigen in the future.\nD. It will present pieces of the antigen on its surface membrane.\n", "Answer (final answer highlighted)": "D: A macrophage is an antigen-presenting cells (APC). It will alert the adaptive immune system about a particular invader.", "ImagePath": "Biology/66" }, { "Question": "You carry out an experiment to study transpiration in plants using a two-week-old bean plant. You set up a potometer by cutting the stem of a plant and securing it into clear flexible tubing that has been tightly connected to a calibrated pipette. Water fills the potometer from the plant stem to the tip of the pipette.\n\nYou measure water loss from your potometer at 10-minute intervals and plot your data on the graph as Line B.\nYou then explore what happens if you expose the plant to different conditions. Which of the following statements is correct based on proposed changes to the potometer?\n\nA. Increasing the green wavelengths of light will increase the rate of transpiration and account for Line A on the graph.\nB. Placing a plastic bag over the plant will increase the rate of transpiration and account for Line A.\nC. Placing a fan near the plant will decrease the rate of transpiration and account for Line C.\nD. Painting the upper leaf surface of most of the leaves with clear nail polish will decrease the rate of transpiration and account for Line C.\n", "Answer (final answer highlighted)": "D: Green plants reflect green light; they do not absorb it and cannot use it as an energy source. Placing a plastic bag over the leaves will decrease transpiration, resulting in Line C. Placing a fan near the plant will increase transpiration, causing Line A.", "ImagePath": "Biology/67" }, { "Question": "You carry out an experiment to study transpiration in plants using a two-week-old bean plant. You set up a potometer by cutting the stem of a plant and securing it into clear flexible tubing that has been tightly connected to a calibrated pipette. Water fills the potometer from the plant stem to the tip of the pipette.\n\nYou measure water loss from your potometer at 10-minute intervals and plot your data on the graph as Line B.\nWhich of the following is NOT correct about transpiration in plants?\n\nA. Water moves upward from the roots to the shoots in the xylem by active transport from an area of high osmotic potential to an area of low osmotic potential.\nB. Plants lose water through stomates in their leaves.\nC. The movement of water through a plant is facilitated by the physical and chemical properties of the water itself.\nD. Placing a container of water between the light source and the plant is necessary to prevent the introduction of heat as a second variable in the experiment.", "Answer (final answer highlighted)": "A: Notice the question states NOT. All the other answer choices are correct. Water moves up the plant through the xylem by passive transport because of the physical properties of water. Choice D refers to the use of a heat sink, which is necessary in this experiment to make sure that the temperature does not rise during the experiment. If the temperature did rise, it would constitute another variable in the experiment", "ImagePath": "Biology/68" }, { "Question": "Which of the following statements is supported by the information presented in the graph, which shows a comparison of two regions in Oregon, one deforested and the other undisturbed?\n\n\n\nA. Roots of plants are efficient at absorbing nitrates from the soil.\nB. Variation in the amount of nitrate in stream water is due to periods of intense rain.\nC. Replanting trees after an area has been clear-cut can prevent nitrate runoff into rivers.\nD. The presence of trees in an area causes an increase of nitrates in the soil.", "Answer (final answer highlighted)": "A: After deforestation, the nitrate runoff onto the rivers increased. There is no evidence presented that trees were replanted. Choice D is clearly false\n", "ImagePath": "Biology/69" }, { "Question": "Here is a food web for a habitat that is threatened by developers who will remove three-fourths of the grasses in the area on which the mice and rabbits feed.\n\n\n\nWhich of the following statements describes what will most likely happen to the wildlife in the area?\n\nA. The hawk will begin to eat frogs instead of snakes and mice.\nB. Since three trophic levels are shown in the food web, 75% of the organisms in this food web will die.\nC. Based on the number of trophic levels, about 25% of the mice and rabbits will die.\nD. The hawk population will decrease", "Answer (final answer highlighted)": "D: Even though numbers are mentioned in the question, they are not relevant. There is no way to determine if hawks will begin to eat frogs, which is niche displacement. You can deduce only the obvious.", "ImagePath": "Biology/70" }, { "Question": "Here is a sketch showing cyclic photophosphorylation in the grana of plant cells.\n\n\n\nWhich of the following statements about this process is correct, and what is the reason for it?\n\nA. It is similar to oxidative phosphorylation in cellular respiration because its function is to generate ATP.\nB. It is similar to glycolysis because it involves an electron transport chain.\nC. It is the opposite of cellular respiration because it releases oxygen rather than utilizes it.\nD. It is the opposite of the citric acid cycle because ATP is utilized, not produced.", "Answer (final answer highlighted)": "A: The only thing this process produces is ATP. No NADPH or oxygen is released. The function of this process is to provide ATP for the Calvin cycle, which uses enormous quantities of ATP.", "ImagePath": "Biology/71" }, { "Question": "In the microscopic world of a pond, paramecia are ferocious predators that prey on smaller protists. In a classic experiment, two species of paramecia were grown separately in culture. The species in culture A was P. caudatum. The species in culture B was P. bursaria. Then the two species were combined in one culture dish (culture C).\n\n\n\nWhich of the following is the most likely explanation for the growth pattern of the two populations combined in culture C?\n\nA. P. caudatum is driving P. bursaria to extinction because P. caudatum is the fitter species.\nB. P. caudatum and P. bursaria share a niche.\nC. P.caudatum and P. bursaria occupy different niches.\nD. P. caudatum is feeding on P. bursaria but only to a limited degree", "Answer (final answer highlighted)": "C: Almost by definition, the two species do not share a niche because both populations are surviving. However, the environment has limited resources. In fact, the S-shaped growth curve shown in all three of these graphs is called a logistic growth curve. It is characteristic of some microorganisms under conditions of limited resources.", "ImagePath": "Biology/72" }, { "Question": "Intact chloroplasts are isolated from dark-green leaves by low-speed centrifugation and placed into six tubes containing cold buffer. A blue dye, DPIP, which turns clear when reduced, is also added to all the tubes. The amount of decolorization is a function of how much reduction and, therefore, how much photosynthesis occurs. Each tube is exposed to different wavelengths of light. A measurement of the amount of decolorization is made, and the data are plotted on a graph. Although the wavelengths of light vary, the light intensity in each tube is the same.\n\n\n\nWhich statement below best explains the results of this experiment and the reason for it?\n\nA. The rate of photosynthesis is highest when a tube is exposed to light in the 550 nm range because that wavelength of light contains the greatest amount of energy.\nB. The rate of photosynthesis is highest when exposed to light in the 550 nm range because that wavelength of light contains the least amount of energy.\nC. The rate of photosynthesis is highest when exposed to combined light in the 650 nm and 700 nm ranges because the combination of the two wavelengths of light contains the greatest amount of energy.\nD. The rate of photosynthesis is highest when exposed to combined light in the 650 nm and 700 nm ranges because there are two photosystems in chloroplasts that absorb light in two different wavelengths.", "Answer (final answer highlighted)": "D: The amount of energy in light is inversely proportional to its wavelength. The shorter the wavelength of light, the more energy it contains. The lines on the graph that are closest to the x-axis represent the greatest amount of reduction and, therefore, the greatest amount of photosynthesis. According to the graph, the most reduction or photosynthesis occurs with two wavelengths of light combined. The reason is that in chloroplasts, two photosystems, P700 and P680, absorb light of different wavelengths.", "ImagePath": "Biology/73" }, { "Question": "Today, two distinctly different beak sizes occur in a single population of finch in an isolated region of West Africa. This finch, the black-bellied seedcracker, is considered a delicacy. The oldest residents of the region remember that all black-bellied seedcrackers used to appear identical. The change in population is shown in the graph.\n\n\n\nWhich of the following statements best identifies the change in the population of finches and the most likely reason for it?\n\nA. Convergent evolution; two distinct varieties evolved into one variety because only one type of seed now exists.\nB. Diversifying selection; one population of finch divided into two populations because at least two types of seeds are now available.\nC. Directional selection; one original variety was replaced by another because one food source was replaced by another.\nD. Stabilizing selection; the original population died out, leaving only individuals with either long or short beak size.", "Answer (final answer highlighted)": "B: There used to be one population of black-bellied seedcracker; now there are two. The single population diverged because of a change in food.", "ImagePath": "Biology/74" }, { "Question": "Here is a figure showing the change in one ancestral population of birds over time.\n\n\n\nWhich of the following statements best supports the evidence presented in the picture?\n\nA. Evolution was gradual and regular with small changes over a long period of time.\nB. The environment stayed the same for long periods of time.\nC. These birds evolved from a single species that went extinct.\nD. These birds evolved mainly as a result of genetic drift.", "Answer (final answer highlighted)": "B: The y-axis shows time. The change you see in the birds is sudden. It is not gradual and slow. It occured suddenly. The environment directs evolution. So if a species remains the same for a long time, one can assume that the environment has not changed for all that time. The ancestral species is still alive; it did not go extinct. None of the information leads you to think that evolution occurred because of genetic drift.", "ImagePath": "Biology/75" }, { "Question": "Which of the following statements is correct about the plant cell structure shown?\n\nA. A is the site of ATP synthase.\nB. B is the site where ATP is produced.\nC. C is the structure from which oxygen is released.\nD. D is the site of PGAL formation.", "Answer (final answer highlighted)": "C: This is a chloroplast. The light-dependent reactions, where ATP is synthesized and oxygen is released, occurs in the grana (C). The light-independent reactions, where PGAL is made, occur in the stroma (B). Nothing related to photosynthesis is occurring in A, which is the outer membrane of the chloroplast", "ImagePath": "Biology/76" }, { "Question": "\u03b2-thalassemia is a disease that strikes mainly people of Mediterranean and Asian descent. It involves a flaw in the gene that codes for \u03b2-globin, one of the protein chains that make up hemoglobin (Hb). A trial was conducted. The patient in this trial was typical of individuals with \u03b2-thalassemia. He needed monthly blood transfusions and daily treatments to lower blood iron levels. In 2007, when the patient was 19 years old, scientists removed some of his bone marrow cells and treated them with a modified virus that was engineered to carry a good copy of the \u03b2-globin gene. They infused the repaired cells into the patient. After several months, the scientists assessed the patient. Here is a graph of the results.\n\n\n\nWhich of the following statements is supported by the information provided?\n\nA. The gene therapy trial failed.\nB. The gene therapy trial was a success, but the patient still requires blood transfusions.\nC. Researchers transplanted a gene directly into the patient's red blood cells.\nD. Researchers inserted a gene into a virus vector that carried the normal hemoglobin gene into the patient's cells.", "Answer (final answer highlighted)": "D: This was a very successful treatment. The patient's hemoglobin (Hb) levels are approaching normal levels. There are no sudden and severe drops in Hb levels, and the patient no longer requires transfusions.", "ImagePath": "Biology/77" }, { "Question": "This graph represents three idealized survivorship curves for different populations.\n\n\n\nWhich of the following statements correctly explains the information shown on this graph?\n\nA. Line A describes a population that produces few offspring and requires much parental care.\nB. Line B describes a population like sea stars that exhibit external fertilization.\nC. Line C describes a population that exhibits high survival of the young with high death rates of older individuals in the population.\nD. Line A describes survivorship patterns of insects.", "Answer (final answer highlighted)": "A: Line A describes the survivorship curve for mammals like humans: few offspring, much parental care, and death at old age. Line C is characteristic of external fertilizers, like sea stars, where there is enormous predation of young. Line B is characteristic of a population that is vulnerable throughout its life but is not particularly vulnerable at any one stage more than at any others.", "ImagePath": "Biology/78" }, { "Question": "The agave, or century plant, generally grows in arid climates with unpredictable rainfall and poor soil. The plant exhibits what is commonly called big bang reproduction. An agave grows for years, accumulating nutrients in its tissues until there is an unusually wet year. Then it sends up a large flowering stalk, produces seeds, and dies.\n\n\n\nWhich of the following statements gives the most likely explanation for how the agave plant has evolved this unusual life strategy?\n\nA. This strategy is determined by the plant's genes, which are inherited.\nB. This particular life strategy was selected for by the harsh, desert environment.\nC. This strategy is the result of a series of mutations that occurred because of the great heat in the desert.\nD. This strategy is the result of a series of mutations that occurred because of the great heat in addition to the lack of rain in the desert.", "Answer (final answer highlighted)": "B: Choices C and D have the theory backward. Mutations may provide variety in a population, but they do not occur to provide a variety or a solution to a problem. Mutations occur. If they are advantageous, that new characteristic may increase in frequency in a population. If they are deleterious, that trait may disappear.", "ImagePath": "Biology/79" }, { "Question": "Here are drawings of four amino acids.\n\nMolecule A is serine and has polar side chains. Molecule B is lysine, which is basic and positively charged. Molecule C, glutamate, is acidic and negatively charged. Molecule D is glycine. It has nonpolar side chains.\n\n\n\nWhich of the following statements is correct about these amino acids?\n\nA. Molecule A can readily dissolve through a plasma membrane.\nB. Only Molecules B and C can readily dissolve through a plasma membrane.\nC. Molecules A, B, and C can all readily dissolve through a plasma membrane.\nD. Only Molecule D can readily dissolve through a plasma membrane.\n", "Answer (final answer highlighted)": "D: In general, substances that are polar and/or charged cannot diffuse through a membrane; only nonpolar molecules can.\n", "ImagePath": "Biology/80" }, { "Question": "To which of the following labeled trophic levels would a herbivore most likely be assigned?\n\n\n\nA. A\nB. B\nC. C\nD. D", "Answer (final answer highlighted)": "D: Herbivores tend to be the primary consumers of trophic pyramids, and thus would take up the first level up from the bottom.", "ImagePath": "Biology/81" }, { "Question": "A behavioral endocrinologist captures male individuals of a territorial bird species over the course of a year to measure testosterone (T) levels. In this population, males may play one of two roles: (1) they may stay in their natal group (the group they were born in) and help raise their younger siblings, or (2) they may leave the natal group to establish a new territory. Use this information and the two histograms that follow to answer the following questions.\n\nTestosterone level in this population may be an example of\n\nA. adaptive radiation.\nB. an adaptation.\nC. divergent selection.\nD. development.", "Answer (final answer highlighted)": "B: Testosterone level is an adaptive trait in this population, one that has been molded by natural selection (or possibly sexual selection; we cannot determine this from the question) to aid in reproduction. Adaptive radiation is a process by which many speciation events occur in a newly exploited environment and does not apply here. This is not an example of divergent selection because both breeding and nonbreeding males have low testosterone levels during at least one part of the year; if the two male types always differed in testosterone level, this population could eventually split into two populations. Development and sperm production may be related to testosterone but are not addressed in this experiment.\n\n", "ImagePath": "Biology/82" }, { "Question": "A behavioral endocrinologist captures male individuals of a territorial bird species over the course of a year to measure testosterone (T) levels. In this population, males may play one of two roles: (1) they may stay in their natal group (the group they were born in) and help raise their younger siblings, or (2) they may leave the natal group to establish a new territory. Use this information and the two histograms that follow to answer the following questions.\n\nWhat can you infer about the role of testosterone in reproduction in this species?\n\nA. It is detrimental to breeding.\nB. It aids adult males only.\nC. It ensures that all males reproduce equally.\nD. It aids in breeding.", "Answer (final answer highlighted)": "D: Since testosterone levels are increased only during the breeding season, we can infer that testosterone has some role in breeding. Since reproductive males express higher testosterone levels only during the breeding season, we hypothesize that testosterone is beneficial, as opposed to detrimental, to breeding.", "ImagePath": "Biology/83" }, { "Question": "Which of the following is the best explanation of the results presented in the preceding graph, collected from the same population in a different year?\n\nA. The so-called helper males are actually breeding.\nB. The population has stopped growing.\nC. Females are equally attracted to adult and helper males.\nD. Testosterone level is affected by many processes.", "Answer (final answer highlighted)": "A: Since testosterone seems to be linked with reproduction, we infer from the new data that the \"nonbreeding\" males are actually breeding and therefore have elevated testosterone levels. Females, population growth, and number of offspring produced are not considered in this example. Finally, although testosterone does affect many physiological processes, none of these are discussed or illustrated in this example", "ImagePath": "Biology/84" }, { "Question": "The DNA placed in this electrophoresis gel separates as a result of what characteristic?\n\nA. pH\nB. Charge\nC. Size\nD. Polarity", "Answer (final answer highlighted)": "C: Gel electrophoresis separates DNA on the basis of size. Smaller samples travel a greater distance down the gel compared to larger samples.", "ImagePath": "Biology/85" }, { "Question": "If this gel were used in a court case as DNA evidence taken from the crime scene, which of the following suspects appears to be guilty?\n\nA. Suspect A\nB. Suspect B\nC. Suspect C\nD. Suspect D", "Answer (final answer highlighted)": "B: His DNA fingerprint seems to exactly match that of the evidence DNA sample.", "ImagePath": "Biology/86" }, { "Question": "Which two suspects, while not guilty, could possibly be identical twins?\n\nA. A and B\nB. A and C\nC. B and C\nD. B and D", "Answer (final answer highlighted)": "B: A and C seem to share the exact same restriction fragment cut of their DNA. Perhaps they are messing with our heads and added the DNA from the same individual twice.", "ImagePath": "Biology/87" }, { "Question": "The frequency of genotypes for a given trait are given in the accompanying graph. Answer the following questions using this information:\n\nWhat is the frequency of the recessive homozygote?\n\nA. 15 percent\nB. 19 percent\nC. 25 percent\nD. 40 percent", "Answer (final answer highlighted)": "B: 100 - 45 - 36 = 19 percent.", "ImagePath": "Biology/88" }, { "Question": "The frequency of genotypes for a given trait are given in the accompanying graph. Answer the following questions using this information:\n\nWhat would be the approximate frequency of the heterozygote condition if this population were in Hardy-Weinberg equilibrium?\n\nA. 20 percent\nB. 45 percent\nC. 48 percent\nD. 72 percent", "Answer (final answer highlighted)": "C: 36 percent of the population is AA. Taking the square root of 0.36, we find the frequency of the A allele to be 0.6. This means that the a allele's frequency must be 1 - 0.6, or 0.4. From these numbers, we can calculate the expected Hardy-Weinberg heterozygous frequency is 2pq = 2(A)(a) = 2(0.6)(0.4) = 48.0 or 48 percent.\n\n", "ImagePath": "Biology/89" }, { "Question": "The frequency of genotypes for a given trait are given in the accompanying graph. Answer the following questions using this information:\n\nIs this population in Hardy-Weinberg equilibrium?\n\nA. Yes\nB. No\nC. Cannot tell from the information given\nD. Maybe, if individuals are migrating\n", "Answer (final answer highlighted)": "B: The expected heterozygous probability does not match up with the actual. This population is not in Hardy-Weinberg equilibrium.", "ImagePath": "Biology/90" }, { "Question": "The frequency of genotypes for a given trait are given in the accompanying graph. Answer the following questions using this information:\n\nWhich of the following processes may be occurring in this population, given the allele frequencies?\n\nA. Directional selection\nB. Homozygous advantage\nC. Hybrid vigor\nD. Allopatric speciation", "Answer (final answer highlighted)": "B: The homozygous frequency is higher than expected; one explanation for this is that the homozygotes are being selected for.", "ImagePath": "Biology/91" }, { "Question": "If the pedigree is studying an autosomal recessive condition for which the alleles are A and a, what was the probability that a child produced by parents A and B would be heterozygous?\n\nA. 0.0625\nB. 0.1250\nC. 0.2500\nD. 0.5000", "Answer (final answer highlighted)": "D: The mother (person B) must be heterozygous Aa because she and her husband (aa) have produced children that have the double recessive condition. This means that person B (the mother) must have contributed an a and that the cross is Aa \u00d7aa-and the probability is 1/2.", "ImagePath": "Biology/92" }, { "Question": "Imagine that a couple (C and D) go to a genetic counselor because they are interested in having children. They tell the counselor that they have a family history of a certain disorder and they want to know the probability of their firstborn having this condition. What is the probability of the child having the autosomal recessive condition?\n\nA. 0.0625\nB. 0.1250\nC. 0.2500\nD. 0.3333", "Answer (final answer highlighted)": "D: To answer this question, we must first determine the probability that person D is heterozygous. We know she is not aa because she does not have the condition. Since we know that the father has the condition, we know for certain that his genotype is aa. Both of mother D's parents must be heterozygous since neither of them have the condition, but they have produced a child with the condition. The probability that mother D is heterozygous Aa is 2/3. The probability that a couple with the genotypes Aa \u00d7aa have a double recessive child is 1/2. The probability that these two will have a child with the condition is 1/2 \u00d72/3 = 1/3 = 0.333", "ImagePath": "Biology/93" }, { "Question": "Imagine that a couple (C and D) have a child (E) that has the autosomal recessive condition being traced by the pedigree. What is the probability that their second child (F) will have the autosomal recessive condition?\n\nA. 0.0625\nB. 0.1250\nC. 0.2500\nD. 0.5000", "Answer (final answer highlighted)": "D: If the couple has a child (person E) with the recessive condition, then we know for certain that mother D must be heterozygous. It is definitely an aa \u00d7Aa cross, leaving a 50 percent chance that their child will be aa.\n\n", "ImagePath": "Biology/94" }, { "Question": "The bold line that point C intersects is known as the\n\nA. biotic potential.\nB. carrying capacity.\nC. limiting factor.\nD. maximum attainable population", "Answer (final answer highlighted)": "B", "ImagePath": "Biology/95" }, { "Question": "On the basis of what happens at the end of this chart, what is the most likely explanation for the population decline after point E?\n\nA. The population became too dense and it had to decline.\nB. There was a major environmental shift that made survival impossible for many.\nC. Food became scarce, leading to a major famine.\nD. The population had become too large.", "Answer (final answer highlighted)": "B", "ImagePath": "Biology/96" }, { "Question": "The solutions in the two arms of this U-tube are separated by a membrane that is permeable to water and sodium chloride, but not to sucrose. Side A is filled with a solution of 0.6 M sucrose and 0.2 M sodium chloride (NaCl), and side B is filled with a solution of 0.2 M sucrose and 0.3 M NaCl. Initially, the volume on both sides is the same.\n\nAt the beginning of the experiment,\n\nA. Side A is hypertonic to side B.\nB. Side A is hypotonic to side B.\nC. Side A is isotonic to side B.\nD. Side A is hypotonic to side B with respect to sucrose", "Answer (final answer highlighted)": "A: The total solute potential for side A is 1.0 MPa (remember that for NaCl, i = 2), and the total solute potential for side B is 0.8 MPa. Therefore, side A has a higher concentration of solute (hypertonic).", "ImagePath": "Biology/97" }, { "Question": "The solutions in the two arms of this U-tube are separated by a membrane that is permeable to water and sodium chloride, but not to sucrose. Side A is filled with a solution of 0.6 M sucrose and 0.2 M sodium chloride (NaCl), and side B is filled with a solution of 0.2 M sucrose and 0.3 M NaCl. Initially, the volume on both sides is the same.\n\nIf you examine side A after a couple of days, you will see\n\nA. an increase in the concentration of NaCl and sucrose and an increase in water level.\nB. a decrease in the concentration of NaCl, an increase in water level, and no change in the concentration of sucrose.\nC. no net change.\nD. an increase in the concentration of NaCl and an increase in the water level.", "Answer (final answer highlighted)": "D: Water will move from a hypotonic solution (side B) toward a hypertonic solution (side A). Sodium will diffuse from a region of more sodium (side B) to a region of less sodium (side A).", "ImagePath": "Biology/98" }, { "Question": "If inhibitor 1 is able to bind to the active site and block the attachment of the substrate to the enzyme, this is an example of\n\nA. noncompetitive inhibition.\nB. competitive inhibition.\nC. a cofactor.\nD. a coenzyme.", "Answer (final answer highlighted)": "B: In competitive inhibition, an inhibitor molecule resembling the substrate binds to the active site and physically blocks the substrate from attaching.", "ImagePath": "Biology/99" }, { "Question": "Which of the following is not a change that would affect the efficiency of the enzyme shown above?\n\nA. Change in temperature\nB. Change in pH\nC. Change in salinity\nD. Increase in the concentration of the enzyme", "Answer (final answer highlighted)": "C: The other four are the four main factors that can affect enzyme efficiency.", "ImagePath": "Biology/100" }, { "Question": "Which of the following points on the preceding energy chart represents the activation energy of the reaction involving the enzyme?\n\nA. A\nB. B\nC. C\nD. D", "Answer (final answer highlighted)": "B: The activation energy of a reaction is the amount of energy needed for the reaction to occur. Notice that the activation energy for the enzymatic reaction is much lower than the nonenzymatic reaction.", "ImagePath": "Biology/101" }, { "Question": "What kind of inheritable condition does this pedigree appear to show?\n\nA. Autosomal dominant\nB. Autosomal recessive\nC. Sex-linked dominant\nD. Sex-linked recessive", "Answer (final answer highlighted)": "B: It is not autosomal dominant because in order for the second generation on the left to have those two individuals with the condition, one parent would need to display the condition as well. It is probably not sex-linked because it seems to appear as often in females as in males. Autosomal recessive seems to be the best fit for this disease", "ImagePath": "Biology/102" }, { "Question": "What is the probability that couple C and D will produce a child that has the condition?\n\nA. 0\nB. 0.125\nC. 0.250\nD. 0.333", "Answer (final answer highlighted)": "D: One first needs to determine the probability that person C is heterozygous (Bb). We know that person D is double recessive because she has the condition. We know that the parents for person C must be Bb and Bb because neither of them has the condition, but they produced children with the condition. The probability of person C being heterozygous is 2/3, because a monohybrid cross of his parents (Bb \u00d7 Bb) gives the following Punnett square:\n https://img.crackap.com/ap/biology/a5/Image00211.jpg\n\nSince you know that he doesn't have the condition, he cannot be bb. This leaves just three possible outcomes, two of which are Bb. A cross must then be done between the father (person C) Bb and the mother (person D) bb. The chance of their child being bb is 50 percent or 1/2. This means that the chance of these two having a child with the condition is 2/3 \u00d7 1/2 or 1/3.", "ImagePath": "Biology/103" }, { "Question": "Which of the following conditions could show the same kind of pedigree results?\n\nA. Cri-du-chat syndrome\nB. Turner syndrome\nC. Albinism\nD. Hemophilia", "Answer (final answer highlighted)": "C: Albinism is the only autosomal recessive condition on this list.", "ImagePath": "Biology/104" }, { "Question": "If child E does in fact have the condition, what is the probability that child F will also have it?\n\nA. 0\nB. .250\nC. .500\nD. .750", "Answer (final answer highlighted)": "C: It is 1/2, because finding out that one of their children has the condition lets us know that the father (person C) is definitely Bb. This changes the probability of 2/3 to 1, meaning that the probability of the two having another child with this condition is simply the result of the Punnett square of Bb \u00d7bb, or 1/2.", "ImagePath": "Biology/105" }, { "Question": "An experiment involving fruit flies produced the following results:\n\nVestigial wings are wild type, crumpled wings are mutant.\n\nGray body is dominant, black body is mutant.\n\nFrom the data presented above, one can conclude that these genes are\n\nA. sex-linked.\nB. epistatic.\nC. holandric.\nD. linked.", "Answer (final answer highlighted)": "D: When you see a ratio like the one in this problem-7:7:1:1 (approximately)-the genes are probably linked. The reason the crumpled, gray, and vestigial black flies exist at all is because crossover must have occurred.\n\n", "ImagePath": "Biology/106" }, { "Question": "An experiment involving fruit flies produced the following results:\n\nVestigial wings are wild type, crumpled wings are mutant.\n\nGray body is dominant, black body is mutant.\n\nWhat is the crossover frequency of these genes?\n\nA. 10 percent\nB. 20 percent\nC. 30 percent\nD. 35 percent", "Answer (final answer highlighted)": "A: To determine the crossover frequency in a problem like this, simply add up the total number of crossovers (75 + 45 = 120) and divide that sum by the total number of offspring (120 + 555 + 525 = 1200). This results in 120/1200 or 10 percent.\n", "ImagePath": "Biology/107" }, { "Question": "An experiment involving fruit flies produced the following results:\n\nVestigial wings are wild type, crumpled wings are mutant.\n\nGray body is dominant, black body is mutant.\n\nHow many map units apart would these genes be on a linkage map?\n\nA. 5 map units\nB. 10 map units\nC. 20 map units\nD. 30 map units", "Answer (final answer highlighted)": "B: One map unit is equal to a 1 percent recombination frequency", "ImagePath": "Biology/108" }, { "Question": "A population of rodents is studied over the course of 100 generations to examine changes in dental enamel thickness. Species that are adapted to eat food resources that require high levels of processing have thicker enamel than do those that eat softer, more easily processed foods. Answer the following questions using this information and the curves that follow\nHow is average enamel thickness changing in this population?\n\nA. There is no real change.\nB. The color and size are changing.\nC. It is increasing.\nD. It is decreasing.", "Answer (final answer highlighted)": "C: The average enamel thickness started at 10, increased to 12, and then increased to 15. It is therefore increasing overall.", "ImagePath": "Biology/109" }, { "Question": "A population of rodents is studied over the course of 100 generations to examine changes in dental enamel thickness. Species that are adapted to eat food resources that require high levels of processing have thicker enamel than do those that eat softer, more easily processed foods. Answer the following questions using this information and the curves that follow\nYou randomly pick one data point from all three sets of data (all three generations), and the individual\u2019s enamel thickness score is 15. Which of the following can be inferred?\n\nA. The individual comes from generation 1.\nB. The individual comes from generation 50.\nC. The individual comes from generation 100.\nD. The individual could be from any of these generations.", "Answer (final answer highlighted)": "D: The average enamel thickness does not describe the range of possible values; an individual with a thickness of 15 could reasonably come from any of the three generations (if we took into account probability, we could say that the individual most likely came from the 100th generation because this population has the highest frequency of individuals with this thickness; however, the question does not ask for probabilities).", "ImagePath": "Biology/110" }, { "Question": "A population of rodents is studied over the course of 100 generations to examine changes in dental enamel thickness. Species that are adapted to eat food resources that require high levels of processing have thicker enamel than do those that eat softer, more easily processed foods. Answer the following questions using this information and the curves that follow.\nWhat inference can you make about this species\u2019 diet?\n\nA. Its food resources are getting softer and easier to process.\nB. Its food resources are getting harder and more difficult to process.\nC. The population is growing.\nD. The population is shrinking.", "Answer (final answer highlighted)": "B: Because thicker enamel in this species indicates foods that are more difficult to process, the answer is B. Answer E is incorrect because our model has no predictive power; if the food resources change, the enamel thickness may as well, to either a thicker or thinner average (enamel thickness could also stay the same).", "ImagePath": "Biology/111" }, { "Question": "A student sets up a lab experiment to study the behavior of slugs. She sets up a large tray filled with soil that measures 1 square meter and has four sets of conditions, one in each quadrant:\n\nShe places 20 slugs in the tray, 5 in each quadrant. Use this information to answer the following questions:\nWhat is this lab setup called?.\n\nA. A gel sheet\nB. A choice chamber\nC. A potometer\nD. An incubation chambe", "Answer (final answer highlighted)": "B: Experimental setups where individuals are given a choice as to where to move are called \"choice chambers.\"", "ImagePath": "Biology/112" }, { "Question": "A student sets up a lab experiment to study the behavior of slugs. She sets up a large tray filled with soil that measures 1 square meter and has four sets of conditions, one in each quadrant:\n\nShe places 20 slugs in the tray, 5 in each quadrant. Use this information to answer the following questions:\nAfter 5 minutes, there are 5 slugs in each quadrant. Which of the following is not a viable explanation for this finding?\n\nA. The slugs haven\u2019t had time to move yet.\nB. The slugs have no preference for temperature or salinity conditions.\nC. The slugs can\u2019t move from one area of the tray to another.\nD. The slugs do not like to live in high-temperature areas.", "Answer (final answer highlighted)": "D: All the answers except D are possible, and are important things to consider when setting up an experiment. For example, it is important to allow your study animals enough time to move and/or get used to their new surroundings and conditions before drawing conclusions about their behavior. D is not a good answer because half of the slugs started in a high-temperature area and haven't moved.", "ImagePath": "Biology/113" }, { "Question": "A student sets up a lab experiment to study the behavior of slugs. She sets up a large tray filled with soil that measures 1 square meter and has four sets of conditions, one in each quadrant:\n\nShe places 20 slugs in the tray, 5 in each quadrant. Use this information to answer the following questions:\nAfter 20 minutes, 20 slugs are in the high-temperature, low-salinity quadrant. What kind of animal behavior has this experiment displayed?\n\nA. Kinesis\nB. Taxis\nC. Survival\nD. Feeding", "Answer (final answer highlighted)": "A: Kinesis is the movement of animals in response to current conditions; animals tend to move until they find a favorable environment, at which point their movement slows.", "ImagePath": "Biology/114" }, { "Question": "In the following cladogram, a common ancestor (*) and species derived from it are illustrated. How many species have four or more common ancestors with Iguanodon?\nA. 1\nB. 2\nC. 4\nD. 6\n", "Answer (final answer highlighted)": "D Iguanodon had one common ancestor with Hypsilophodon before Hypsilophodon diverged. Iguanodon had two with Tenontosaurus because one came from where Tenontosaurus diverged and they both share the common ancestor with Hypsilophodon. By that logic, Iguanodon has three common ancestors with Zalmoxes, four with Dryosaurus, and five with Camptosaurus. It will also share those five common ancestors with the other species on the tree, because everything above Camptosaurus still shares those original five. The higher levels also share the ancestor that existed when Iguanodon diverged. Either way, six species share at least four common ancestors with Iguanodon. Remember, don\u00e2\u0080\u0099t count Iguanodon itself.", "ImagePath": "Biology/115" }, { "Question": "Which of the following are true statements according to the figure?\nI. r-strategists are unlikely to die young.\nII. The death rate for a c-strategist is constant.\nThe following graph demonstrates 3 different strategies for survival.III. Humans are an example of a k-strategist.\nA. I only\nB. II only\nC. II and III\nD. I, II, and III\n", "Answer (final answer highlighted)": "C Most r-strategists die early in their lifetime, (A), but most k-strategists live long lives and then die when old. Humans are an example of k-strategists. The c-strategist survivorship line declines evenly, meaning that they are just as likely to die when old as they are when young, (C).", "ImagePath": "Biology/116" }, { "Question": "Questions below refer to the following synthetic pathway of nRNA pyrimidine, cytidine 5' triphosphate, CTP. This pathway begins with the condensation of two small molecules by the enzyme aspartate transcarbamylase (ATCase).This enzymatic phenomenon is an example of\nA. transcription\nB. feedback inhibition\nC. dehydration synthesis\nD. photosynthesis\n", "Answer (final answer highlighted)": "B This enzymatic phenomenon is an example of feedback inhibition. Feedback inhibition is the metabolic regulation in which high levels of an enzymatic pathway\u00e2\u0080\u0099s final product inhibit the activity of its rate-limiting enzyme. Transcription, (A), is the production of RNA from DNA. Dehydration synthesis, (C), is the formation of a covalent bond by the removal of water. In photosynthesis, (D), radiant energy is converted to chemical energy.", "ImagePath": "Biology/117" }, { "Question": "During labor, pressure on the cervix and oxytocin form a positive feedback loop as shown below.Which of the following other pathways also demonstrate positive feedback?\nA. Glycolysis leads to the production of ATP. ATP, in turn, turns off the enzyme phosphofructokinase, which catalyzes a key phosphorylation step in glycolysis.\nB. The anterior pituitary gland in the brain releases adrenocorticotropic hormone (ACTH). ACTH then causes the adrenal cortex to release glucocorticoids. Glucocorticoids then prevent the pituitary from releasing more ACTH.\nC. Luteinizing hormone triggers ovulation and the formation of the corpus luteum, which is a hormone-producing structure formed during ovulation. The corpus luteum secretes progesterone, which inhibits LH. The drop in LH causes the degradation of the corpus luteum.\nD. When a tissue is injured, it releases chemicals that activate platelets. Activated platelets themselves then release chemicals that activate more platelets. These activated platelets then release chemicals to activate more platelets.\n", "Answer (final answer highlighted)": "D Positive feedback occurs when a process creates an end product whose production stimulates the process to create even more of the end product. In (D), the platelets lead to more platelet creation. Choices (A), (B), and (C) illustrate negative feedback.", "ImagePath": "Biology/118" }, { "Question": "The following diagram demonstrates the ecological succession that occurs in an environment over time as it is colonized by different species.Why does it take 75 years for a beech-maple to occur in the figure above?\nA. Beech seeds have a very long period of dormancy prior to germination.\nB. It takes an average of 75 years for conifer trees to become extinct.\nC. Agriculture was the predominant industry, and hardwood trees were removed.\nD. Maple trees grow better in a pine forest than they do in a grassland.\n", "Answer (final answer highlighted)": "D Few species can grow in barren areas, but once they are colonized with plants, then more species can grow and live there. It takes a long time for the beech and maple trees to grow because first species need to change the environment, allowing other species to colonize. The environment was not hospitable until it was a pine forest, which took a long time to reach as well.", "ImagePath": "Biology/119" }, { "Question": "Embryogenesis is a carefully timed and well-organized process. As a single-celled zygote divides and grows into hundreds and thousands of cells, a process called differentiation occurs wherein certain areas of the embryo become specialized to become different types of tissue. As differentiation continues, the level of specificity increases, and the cell potency decreases until highly specialized unique tissues and organs develop. The figure below shows 12 stages of development of human embryos.A totipotent embryonic cell has the most cell potency. Which of the following is most likely to be totipotent?\nA. 8-cell zygote\nB. Inner cell mass\nC. Mesoderm\nD. Digestive tract\n", "Answer (final answer highlighted)": "A Potency is the potential to become many things. The most potent cells are the least differentiated or the least specialized. The more specialized they become, the more they lose their potency. The 8-cell zygote is the least specialized and has the most potency.", "ImagePath": "Biology/120" }, { "Question": "Embryogenesis is a carefully timed and well-organized process. As a single-celled zygote divides and grows into hundreds and thousands of cells, a process called differentiation occurs wherein certain areas of the embryo become specialized to become different types of tissue. As differentiation continues, the level of specificity increases, and the cell potency decreases until highly specialized unique tissues and organs develop. The figure below shows 12 stages of development of human embryos.The inner cell mass is what eventually forms the embryo. During development, the embryo differentiates into various types of cell layers. Which of the following is NOT one of them?\nA. Mesoderm\nB. Hypoblast\nC. Blastomere\nD. Endoderm\n", "Answer (final answer highlighted)": "C The blastomere is shown prior to the inner cell mass; therefore, it cannot be a differentiation of the inner cell mass. The hypoblast comes from the inner cell mass, and the endoderm and mesoderm also come from it.", "ImagePath": "Biology/121" }, { "Question": "Diabetes mellitus is a disease characterized by an inability of the cells to properly produce (type I) or respond (type II) to insulin, a hormone produced by the pancreas in response to high levels of blood glucose. Without insulin, glucose accumulates in the blood. In situations of low blood glucose, another pancreatic enzyme, glucagon, is released, which triggers the process of gluconeogenesis, shown on the right side of the pathway below. The stimulators, activators, or inhibitors of each step are shown with + or - signs.Which of the following situations likely stimulates gluconeogenesis?\nA. High levels of insulin\nB. High levels of F-2,6-BP\nC. High levels of glucagon\nD. High levels of ADP\n", "Answer (final answer highlighted)": "C Gluconeogenesis is the formation of glucose. If the body had high insulin, then it would already have lots of glucose, so (A) is eliminated, but if the body had high glucagon, it would need glucose, (C). High ADP would inhibit gluconeogenesis as shown in the figure, (D). High F-2,6-BP would also inhibit gluconeogenesis, (B).", "ImagePath": "Biology/122" }, { "Question": "Diabetes mellitus is a disease characterized by an inability of the cells to properly produce (type I) or respond (type II) to insulin, a hormone produced by the pancreas in response to high levels of blood glucose. Without insulin, glucose accumulates in the blood. In situations of low blood glucose, another pancreatic enzyme, glucagon, is released, which triggers the process of gluconeogenesis, shown on the right side of the pathway below. The stimulators, activators, or inhibitors of each step are shown with + or - signs.Patients with type I diabetes often require insulin injections. Which of the following situations would most require an insulin injection?\nA. After eating a stalk of celery\nB. After eating a cookie\nC. After skipping breakfast\nD. After drinking a lot of water\n", "Answer (final answer highlighted)": "B Insulin is needed when blood glucose gets too high. Eating a cookie would increase blood sugar more than eating celery, fasting, or drinking water.", "ImagePath": "Biology/123" }, { "Question": "Diabetes mellitus is a disease characterized by an inability of the cells to properly produce (type I) or respond (type II) to insulin, a hormone produced by the pancreas in response to high levels of blood glucose. Without insulin, glucose accumulates in the blood. In situations of low blood glucose, another pancreatic enzyme, glucagon, is released, which triggers the process of gluconeogenesis, shown on the right side of the pathway below. The stimulators, activators, or inhibitors of each step are shown with + or - signs.Which of the following conditions would lead to increased production of fructose 1,6-bisphosphate?\nA. High ATP and high citrate\nB. High AMP and high citrate\nC. High AMP and high F-2,6-BP\nD. High ATP and high F-2,6-BP\n", "Answer (final answer highlighted)": "C ATP inhibits its production since it inhibits phosphofructokinase. This eliminates (A) and (D). Citrate stimulates turning fructose 1,6-bisphosphate into fructose 6-phosphate, which eliminates (B). Choice (C) includes two things that stimulate phosphofructokinase and lead to production of fructose 1,6-bisphosphate.", "ImagePath": "Biology/124" }, { "Question": "A population of goldfish in a large, isolated pond were studied in 1958 and again in 2008. The fishes' pigment level varied from pale white-orange fish to dark brown-orange fish. The color of each of the fish was recorded in the figure below.Which addition to the pond did NOT likely contribute to the change between 1958 and 2008?\nA. A poisonous fish with a medium orange pigment\nB. Runoff from fields that makes the water dark and murky\nC. A light-orange water grass that grows in the pond\nD. Predatory birds that can easily see medium-orange pigment\n", "Answer (final answer highlighted)": "A From 1958 to 2008, the graph shifted away from medium-orange and moved toward the extremes (light and dark). Choice (A) would make fewer orange fish be eaten, which would promote more medium-orange fish. Choices (B) and (C) would cause fewer light and dark fish to be eaten, respectively. This would promote the light and dark fish. Choice (D) would cause the medium-orange fish to be eaten more often and thus promote the light and dark extremes shown in 2008.", "ImagePath": "Biology/125" }, { "Question": "A population of goldfish in a large, isolated pond were studied in 1958 and again in 2008. The fishes' pigment level varied from pale white-orange fish to dark brown-orange fish. The color of each of the fish was recorded in the figure below.Which of the following theories is supported by the evidence?\nA. The pigment trait in fish demonstrates incomplete dominance.\nB. The pigment trait in fish demonstrates classical dominance.\nC. The pigment trait in fish demonstrates codominance.\nD. None of the above\n", "Answer (final answer highlighted)": "D These graphs of phenotype tell us nothing about the mode of inheritance.", "ImagePath": "Biology/126" }, { "Question": "A population of goldfish in a large, isolated pond were studied in 1958 and again in 2008. The fishes' pigment level varied from pale white-orange fish to dark brown-orange fish. The color of each of the fish was recorded in the figure below.Which of the following best describes the fish population in the year 1958?\nA. All medium-orange in color\nB. Mostly medium-orange fish with some nearly white and some nearly brown\nC. Mostly white fish and brown fish with a few orange fish\nD. Equal numbers of orange fish, white fish, and brown fish\n", "Answer (final answer highlighted)": "B The peak in 1958 is in the middle, corresponding to medium-orange fish. However, there are also some fish on each extreme (light or dark).", "ImagePath": "Biology/127" }, { "Question": "A group of Daphnia, small crustaceans known as water fleas, was placed in one of three culture jars of different sizes to determine their reproductive rate. There were 100 females in the jar. The graph below shows the average number of offspring produced per female each day in each jar of pond water.The data in the figure above would best support which conclusion?\nA. If you decreased the number of females, the container would have to remain constant.\nB. The number of offspring produced scales proportionally with the container's size.\nC. The number of offspring produced increases with time.\nD. Daphnia prefer high-density conditions to have the most efficient reproductive rate.\n", "Answer (final answer highlighted)": "B The passage does not say that the container would stay the same; in fact, that was the independent variable. Decreasing the number of females would not mean that the container could not be changed for a new experiment. The graph shows that both samples have a reproduction rate decrease after 10\u00e2\u0080\u009320 days, so not (C). The highest density condition (same number of Daphnia but lower volume) shows no reproductive activity after trauma (so not (D)). Choice (B) is the correct answer because as the container size increased, the number of offspring increased.", "ImagePath": "Biology/128" }, { "Question": "Scientists used embryology, morphology, paleontology, and molecular biology to create the phylogenetic tree below.Which of the sources of evolutionary evidence would be the most reliable of those listed?\nA. Embryology\nB. Morphology\nC. Paleontology\nD. Molecular biology\n", "Answer (final answer highlighted)": "D Because molecular biology demonstrates where the actual mutations occurred (rather than just what phenotype is observed), it is the most reliable; it allows you to detect changes that are not phenotypically observable.", "ImagePath": "Biology/129" }, { "Question": "Scientists used embryology, morphology, paleontology, and molecular biology to create the phylogenetic tree below.Which of the following is the least closely related according to the phylogenetic tree?\nA. B. physalus and B. brydei\nB. B. boreales and B. brydei\nC. B. musculus and B. brydei\nD. B. musculus and Eschrichtius robustus\n", "Answer (final answer highlighted)": "C Relatedness is shown on a phylogenetic tree by how far back you have to go to reach the common ancestor of the two species (shown by a branch node). Since the recent species are on the right, traveling to the left goes back in time. Because you have to go to the oldest common ancestor to connect B. musculus and B. brydei, they are the least closely related. Even though they are near each other on the tree, clades can rotate around a node so this does not matter.", "ImagePath": "Biology/130" }, { "Question": "The rainfall and biomass of several trophic levels in an ecosystem were measured over several years. The results are shown in the graph below.If it rained 120 inches, what would you project the primary consumer biomass to be?\nA. 150-200\nB. 60\nC. 45\nD. 20\n", "Answer (final answer highlighted)": "A The biomass seems to correlate fairly well with the rainfall. Therefore, a rainfall higher than any recorded would give a biomass higher than any recorded. The axis on the right shows the biomass. With a rainfall of 120, the biomass should be greater than 150.", "ImagePath": "Biology/131" }, { "Question": "The rainfall and biomass of several trophic levels in an ecosystem were measured over several years. The results are shown in the graph below.Which of the following concepts is best demonstrated by this experiment?\nA. Populations with higher genetic variation can withstand droughts better.\nB. Meteorological impacts will affect the evolution of populations.\nC. Environmental changes can affect all the levels of the ecosystem.\nD. Unoccupied biological niches are dangerous because they attract invasive species.\n", "Answer (final answer highlighted)": "C The graph does show a drought, but it says nothing about genetic variation. It is true that the rainfall could affect evolution of the population, but the graph doesn\u00e2\u0080\u0099t address evolution. It shows only the decrease in biomass. Choice (C) is the best answer since it addresses how the environmental effects ripple through the levels of the ecosystem. Invasive species do not need an unoccupied niche, and that is not shown in the graph.", "ImagePath": "Biology/132" }, { "Question": "An experiment was performed to assess the growth of two species of plants when they were grown in different pHs, given different volumes of water, and watered at different times of day over 6 weeks. Two plants were grown of each species and the average heights (in cm) are shown in the table.Which of the following would most improve the statistical significance of the results?\nA. Let the plants grow for a longer period of time.\nB. Add more conditions to test, such as amount of light and amount of soil.\nC. Test the same plants with more pHs and more volumes and times of day.\nD. Increase the number of plants in each group.\n", "Answer (final answer highlighted)": "D Choices (A), (B), and (C) would all give interesting information about the experiment, but the only one that would make the results more statistically significant is to increase the number of plants in each group. Two plants is not enough to be sure about the results of the experiment.", "ImagePath": "Biology/133" }, { "Question": "An experiment was performed to assess the growth of two species of plants when they were grown in different pHs, given different volumes of water, and watered at different times of day over 6 weeks. Two plants were grown of each species and the average heights (in cm) are shown in the table.Which pH and volume were likely used for the watering time experiment?\nA. pH 4 and 40 mL\nB. pH 7 and 40 mL\nC. pH 4 and 80 mL\nD. pH 7 and 80 mL\n", "Answer (final answer highlighted)": "D The plants in the watering time experiment seemed to be around 60 and 20 cm in height. This corresponds to a pH of 7 rather than 4 and a watering volume of 80 mL rather than 40 mL.", "ImagePath": "Biology/134" }, { "Question": "An experiment was performed to assess the growth of two species of plants when they were grown in different pHs, given different volumes of water, and watered at different times of day over 6 weeks. Two plants were grown of each species and the average heights (in cm) are shown in the table.What are the preferred growth conditions for Species B?\nA. pH 7, 40 mL, any time of day\nB. pH 10, 40 mL, 7:00 A.M.\nC. pH 7, 80 mL, any time of day\nD. pH 10, 80 mL, 12:00 P.M.\n", "Answer (final answer highlighted)": "A The top growth conditions for Species B are pH 7, 40 mL, and any time of day. In those conditions, the Species B plants grew the tallest.", "ImagePath": "Biology/135" }, { "Question": "An experiment was performed to assess the growth of two species of plants when they were grown in different pHs, given different volumes of water, and watered at different times of day over 6 weeks. Two plants were grown of each species and the average heights (in cm) are shown in the table.For which conditions do the species have different preferences?\nA. pH\nB. Volume\nC. Volume and watering time\nD. pH and volume and watering time\n", "Answer (final answer highlighted)": "B The two species differ in their preference for water volume. Species A prefers 80 mL, and Species B prefers 40 mL. The different watering times do not seem to play a role in growth as there is no obvious pattern and all of the times had similar growth. Both plants prefer pH 7.", "ImagePath": "Biology/136" }, { "Question": "Pumping blood through the human heart must be carefully organized for maximal efficiency and to prevent backflow. In the figure below, the blood enters the heart through the vena cava (1), passes through the right atrium and right ventricle and then goes through the pulmonary artery toward the lungs. After the lungs, the blood returns through the pulmonary vein and then passes into the left atrium and the left ventricle before leaving the heart via the aorta.Blood is pumped via heart contractions triggered by action potentials spreading through the heart muscle. If there is a sudden increase in blood in chamber 3, which chamber of the heart received an increased number of action potentials?\nA. Left atrium\nB. Left ventricle\nC. Right atrium\nD. Right ventricle\n", "Answer (final answer highlighted)": "C The action potentials cause the heart to contract. If chamber 3 is full of more blood, then that would indicate that the preceding chamber, chamber 2 (right atrium), had suddenly contracted a larger amount.", "ImagePath": "Biology/137" }, { "Question": "Pumping blood through the human heart must be carefully organized for maximal efficiency and to prevent backflow. In the figure below, the blood enters the heart through the vena cava (1), passes through the right atrium and right ventricle and then goes through the pulmonary artery toward the lungs. After the lungs, the blood returns through the pulmonary vein and then passes into the left atrium and the left ventricle before leaving the heart via the aorta.Which of the following chambers or vessels carry deoxygenated blood in the human heart?\nA. 1 only\nB. 2 and 3\nC. 1, 2, 3, 4\nD. 4 and 5\n", "Answer (final answer highlighted)": "C Deoxygenated blood flows through all chambers before going to the lungs. This means the correct answer is chambers 1, 2, 3, and 4.", "ImagePath": "Biology/138" }, { "Question": "Note: + indicates a feature present in an organism.\nQuestions below refer to the data below concerning the general animal body plan of four organisms.The two most closely related organisms are\nA. sea anemone and hagfish\nB. eel and salamander\nC. hagfish and eel\nD. sea anemone and salamander\n", "Answer (final answer highlighted)": "B The two most closely related organisms are the two with the most shared derived characteristics.", "ImagePath": "Biology/139" }, { "Question": "Questions below refer to the following figures which show 5 species of insects that were discovered on a previously unknown island and were named as shown in the table. Proteomic analysis was performed on a highly conserved protein in the insects and the number of amino acid differences was calculated and included in the table below. The scientists used this data to create the phylogenetic tree shown below with positions labeled I, II, III, and IV as well as O, P, Q, R, and S.Which 2 species would you expect to have the most shared derived characters?\nA. Snippeiq and Sqellert\nB. Gerdellen and Sqellert\nC. Snorflak and Gerdellen\nD. Snorflak and Fixxels\n", "Answer (final answer highlighted)": "D Snorflak and Fixxels, (D), would have the most shared derived characters because they have the fewest amino acid differences. Snippeiq and Sqellert would be expected to have the least since they are so different, which rules out (A). Sqellert and Gerdellen, (B), were close with only 4 differences but still not as low as Snorflak and Fixxels. Snorflak and Gerdellen, (C), must be an intermediate with 9 differences observed in the table.", "ImagePath": "Biology/140" }, { "Question": "Questions below refer to the following figures which show 5 species of insects that were discovered on a previously unknown island and were named as shown in the table. Proteomic analysis was performed on a highly conserved protein in the insects and the number of amino acid differences was calculated and included in the table below. The scientists used this data to create the phylogenetic tree shown below with positions labeled I, II, III, and IV as well as O, P, Q, R, and S.Which species is the out-group?\nA. Snippeiq\nB. Fixxels\nC. Snorflak\nD. Sqellert\n", "Answer (final answer highlighted)": "A Snippeiq, (A), is the out-group because it is the least related to the other species. The table shows that Snippeiq has the most differences from all of the other species.", "ImagePath": "Biology/141" }, { "Question": "Questions below refer to the following figures which show 5 species of insects that were discovered on a previously unknown island and were named as shown in the table. Proteomic analysis was performed on a highly conserved protein in the insects and the number of amino acid differences was calculated and included in the table below. The scientists used this data to create the phylogenetic tree shown below with positions labeled I, II, III, and IV as well as O, P, Q, R, and S.Which location contains the oldest common ancestor?\nA. Position I\nB. Position II\nC. Position III\nD. Position IV\n", "Answer (final answer highlighted)": "C Position III, (C), contains the oldest common ancestor because it is the node for all the current species designated by the lettered positions.", "ImagePath": "Biology/142" }, { "Question": "Questions below refer to the following figures which show 5 species of insects that were discovered on a previously unknown island and were named as shown in the table. Proteomic analysis was performed on a highly conserved protein in the insects and the number of amino acid differences was calculated and included in the table below. The scientists used this data to create the phylogenetic tree shown below with positions labeled I, II, III, and IV as well as O, P, Q, R, and S.Based on the data, which is the LEAST possible location for Gerdellen to be placed?\nA. Position O\nB. Position P\nC. Position R\nD. Position S\n", "Answer (final answer highlighted)": "D Since Snippeiq has the most differences with the other organisms it must be at position S. This means that Gerdellen cannot be there, which makes (D) the best answer. (Position Q or R is the best position for Gerdellen, though positions O and P could possibly be correct as well.)", "ImagePath": "Biology/143" }, { "Question": "The cell cycle is a series of events in the life of a dividing eukaryotic cell. It consists of four stages: G1, S, G2, and M. The duration of the cell cycle varies from one species to another and from one cell type to another. The G1 phase varies the most. For example, embryonic cells can pass through the G1 phase so quickly that it hardly exists, whereas neurons are arrested in the cell cycle and do not divide.Since neurons are destined never to divide again, what conclusion can be made?\nA. These cells will go through cell division.\nB. These cells will be permanently arrested in the G0 phase.\nC. These cells will be permanently arrested in the M phase.\nD. These cells will quickly enter the S phase.\n", "Answer (final answer highlighted)": "B Because neurons are not capable of dividing, it is reasonable to conclude that these cells will stay in the G1 phase (specifically in an extension of G1 called G0) phase. This is a reading comprehension question. The passage states that cells that do not divide are arrested at the G1 phase. Choice (A) is incorrect because these cells will not be committed to go through cell division. You can also eliminate (C) and (D), as the cells will not enter the M or S phase.", "ImagePath": "Biology/144" }, { "Question": "The cell cycle is a series of events in the life of a dividing eukaryotic cell. It consists of four stages: G1, S, G2, and M. The duration of the cell cycle varies from one species to another and from one cell type to another. The G1 phase varies the most. For example, embryonic cells can pass through the G1 phase so quickly that it hardly exists, whereas neurons are arrested in the cell cycle and do not divide.If the cell cycle fails to progress, which of the following is NOT a possible explanation?\nA. There are inadequate phosphate groups available for the cyclin dependent kinase.\nB. A tumor suppressor protein has signaled for apoptosis.\nC. A cyclin is unable to release from its cyclin dependent kinase.\nD. An inhibitor of a cyclin gene has been highly expressed.\n", "Answer (final answer highlighted)": "C To induce cell cycle progression, an inactive CDK (cyclin-dependent kinase) binds a regulatory cyclin. Once together, the complex is activated, can affect many proteins in the cell, and causes the cell cycle to continue. To do this, the CDK transfers phosphate groups onto other molecules. If there are inadequate phosphate groups, CDK would not function properly and the cell cycle would not progress, which rules out (A). Tumor suppressor proteins inhibit cell cycle progression and can trigger apoptosis, which rules out (B). To inhibit cell cycle progression, CDKs and cyclins are kept separate. Together, they promote the cell cycle. If a cyclin is unable to release from its cyclin dependent kinase, the cell cycle would be promoted, not stopped, making (C) correct. Choice (D) could\u00e2\u0080\u0099ve been eliminated because an inhibitor of a cyclin gene would prevent expression of the cyclin gene. With lower levels of the cyclin protein, cell cycle progression would be inhibited.", "ImagePath": "Biology/145" }, { "Question": "Questions below refer to the following bar graph, which shows the relative biomass of four different populations of a particular food pyramid.Which of the following would be the most likely result if there was an increase in the number of organisms in population C?\nA. The biomass of population D will remain the same.\nB. The biomass of population B will decrease.\nC. The biomass of population A will steadily decrease.\nD. The food source available to population C would increase.\n", "Answer (final answer highlighted)": "B An increase in the number of organisms in population C would most likely lead to a decrease in the biomass of B because population B is the food source for population C. Make a pyramid based on the biomasses given. If population C increases, population B will decrease. Eliminate (A) and (C), as you cannot necessarily predict what will happen to the biomass of populations that are above population C. Choice (D) can also be eliminated because the food source available to population C would most likely decrease, not increase.", "ImagePath": "Biology/146" }, { "Question": "It is difficult to determine exactly how life began. Answer the following questions as if the following data had been collected billions of years ago.Photosynthesis likely began ________ billion years ago when the first ________ appeared.\nA. 4.5; autotrophs\nB. 3.2; autotrophs\nC. 3.5; heterotrophs\nD. 3.2; heterotrophs\n", "Answer (final answer highlighted)": "B The sign that photosynthesis began was when oxygen appeared. Oxygen was absent at 3.25 billion years and present at 3 billion years so photosynthesis must have begun between those times; eliminate (A) and (C). Autotrophs, not heterotrophs, perform photosynthesis. Heterotrophs rely on eating other things for their energy.", "ImagePath": "Biology/147" }, { "Question": "It is difficult to determine exactly how life began. Answer the following questions as if the following data had been collected billions of years ago.When is the earliest that functional ribosomes could have been found?\nA. Between 4 billion and 3.5 billion years ago\nB. Between 3.5 billion and 3.25 billion years ago\nC. Between 3.25 billion and 3 billion years ago\nD. Between 3 billion years ago and the present\n", "Answer (final answer highlighted)": "B Functional ribosomes would not likely be found before the proteins they make. Therefore, this would be between 3.5 and 3.25 billion years ago.", "ImagePath": "Biology/148" }, { "Question": "It is difficult to determine exactly how life began. Answer the following questions as if the following data had been collected billions of years ago.Which best describes the origin of life according to the data?\nA. Life required an environment with atmospheric oxygen and any type of nucleic acids.\nB. Life required an environment with atmospheric carbon dioxide, but not atmospheric oxygen.\nC. Life required an environment with self-replicating nucleic acids that can take on many shapes.\nD. Life required an environment with nucleic acids and proteins, but not atmospheric oxygen.\n", "Answer (final answer highlighted)": "C The origin of life refers to the period when the first life began. Life is shown to be present 3.5 billion years ago when no atmospheric oxygen was present yet, so (A) can be eliminated. Also, there was no life at 4 billion years despite having CO2 and no O2; therefore, something else must be required, and (B) can be eliminated. There were no proteins when the first life arose, so (D) is incorrect. Choice (C) states that self-replicating nucleic acids were necessary, which is why life could only occur when RNA appeared.", "ImagePath": "Biology/149" }, { "Question": "Which process is demonstrated in the figure below?\nA. Krebs cycle\nB. Photosynthesis\nC. Glycolysis\nD. Fermentation\n", "Answer (final answer highlighted)": "B Photosynthesis requires light, carbon dioxide, and water and produces oxygen and glucose.", "ImagePath": "Biology/150" }, { "Question": "The following are important pieces of replication and transcription machinery:What might have occurred to produce the following situation?\nA. Stalled DNA replication\nB. Initiation of transcription\nC. Repression of transcription\nD. Crossing-over in meiosis\n", "Answer (final answer highlighted)": "C The RNA polymerase is not bound, but there is a bound repressor. The transcription must be repressed.", "ImagePath": "Biology/151" }, { "Question": "The graph below shows two growth curves for bacterial cultures, A and B.What could explain the difference between culture A and culture B?\nA. Culture B started with more bacteria than culture A.\nB. Culture A was grown with a competitive inhibitor.\nC. Culture B was not measured as often.\nD. Culture A has not yet exhausted its space and resources.\n", "Answer (final answer highlighted)": "D The growth of curve A is exponential, meaning that the bacteria are replicated as fast as possible without any restrictions. It looks like the populations started at the same level, and an inhibitor would not cause high growth as shown in culture A. Not being measured as often would not cause a graph like the one shown for culture B.", "ImagePath": "Biology/152" }, { "Question": "The graph below shows two growth curves for bacterial cultures, A and B.Which of the following represents the carrying capacity for culture B?\nA. 10\nB. 50\nC. 100,000\nD. 1,000,000\n", "Answer (final answer highlighted)": "C The carrying capacity is the maximum number of organisms of a given species that can be maintained in a given environment. Once a population reaches its carrying capacity, the number of organisms will fluctuate around it.", "ImagePath": "Biology/153" }, { "Question": "The Loop of Henle is a structure within each of the million nephrons within a kidney. As shown in the figure, the two sides have different permeabilities, and there is differential movement across each membrane. The Loop acts as a counter-current multiplier that makes the medulla of the kidney very osmotic. The longer the loop, the higher and more powerful the osmolarity gradient that is created. The gradient is required for the reclamation of water from the urine collecting duct. On the right side of the figure is the urine collecting duct. If the body needs to retain water, anti-diuretic hormone makes this region permeable to water via the introduction of aquaporins, and the osmotic pull of the medulla reclaims the water, out of the collecting duct, which makes the urine more concentrated.What type of transport is occurring when water flows out of the descending tubule?\nA. Simple diffusion\nB. Facilitated diffusion\nC. Active transport\nD. Secondary active transport\n", "Answer (final answer highlighted)": "B When water flows out of the tubule, it is moving by simple osmosis. However, because it is a polar molecule, it must pass through an aquaporin channel, which is facilitated diffusion.", "ImagePath": "Biology/154" }, { "Question": "The Loop of Henle is a structure within each of the million nephrons within a kidney. As shown in the figure, the two sides have different permeabilities, and there is differential movement across each membrane. The Loop acts as a counter-current multiplier that makes the medulla of the kidney very osmotic. The longer the loop, the higher and more powerful the osmolarity gradient that is created. The gradient is required for the reclamation of water from the urine collecting duct. On the right side of the figure is the urine collecting duct. If the body needs to retain water, anti-diuretic hormone makes this region permeable to water via the introduction of aquaporins, and the osmotic pull of the medulla reclaims the water, out of the collecting duct, which makes the urine more concentrated.Which of the following statements correctly describes the state of things near the top of the descending limb?\nA. The fluid within the descending limb is hypotonic to fluid in the space surrounding the tubule.\nB. The blood within the vasa recta is hypotonic to the filtrate within the descending limb.\nC. The fluid in the area surrounding the tubule is hypertonic to the blood in the vasa recta.\nD. The water in the area surrounding the tubule has a higher water potential than the water in the descending tubule.\n", "Answer (final answer highlighted)": "A The figure shows that water leaves the descending limb and flows by osmotic pressure into the surrounding space and then into the vasa recta. This means that each of those places is more hypertonic than the previous. The most hypotonic is the descending tubule. (This is why the water leaves.)", "ImagePath": "Biology/155" }, { "Question": "The affinity of hemoglobin for oxygen is reduced by many factors, including low pH and high CO2. The graph below shows the different dissociation curves that maternal (normal) hemoglobin and fetal hemoglobin have.How much pO2 would it take in an extremely CO2-rich environment to saturate hemoglobin 90 percent?\nA. 15\nB. 30\nC. 45\nD. 60\n", "Answer (final answer highlighted)": "D The CO2-rich environment would decrease the affinity of hemoglobin for oxygen, so the curve should shift toward the right. The regular curve seems to hit 90% saturation around 45\u00e2\u0080\u009350 pO2, so the CO2-rich curve would take more oxygen to get there.", "ImagePath": "Biology/156" }, { "Question": "The affinity of hemoglobin for oxygen is reduced by many factors, including low pH and high CO2. The graph below shows the different dissociation curves that maternal (normal) hemoglobin and fetal hemoglobin have.Hemoglobin's affinity for O2\nA. decreases as blood pH decreases\nB. increases as H+ concentration increases\nC. increases as blood pH decreases\nD. decreases as OH- concentration increases\n", "Answer (final answer highlighted)": "A Hemoglobin\u00e2\u0080\u0099s affinity for O2 decreases as the concentration of H+ increases (or the pH decreases) and as the concentration of OH\u00e2\u0080\u0093 increases (or the pH increases). As the pH decreases, the affinity for oxygen will decrease, and as the pH increases, the affinity for oxygen will increase.", "ImagePath": "Biology/157" }, { "Question": "The affinity of hemoglobin for oxygen is reduced by many factors, including low pH and high CO2. The graph below shows the different dissociation curves that maternal (normal) hemoglobin and fetal hemoglobin have.Which of the following processes would likely shift the normal dissociation curve to the right?\nA. Photosynthesis\nB. Respiration\nC. Fermentation\nD. Mitosis\n", "Answer (final answer highlighted)": "C The passage says that high CO2 and low pH lead to reduced affinity. A right shift curve would represent a reduced affinity. Photosynthesis consumes CO2, so this would not increase the CO2. Mitosis and respiration are not related. Fermentation is done in cells that are doing anaerobic cell respiration, so CO2 should be released, possibly along with lactic acid, which would lower pH.", "ImagePath": "Biology/158" }, { "Question": "If a competitive inhibitor is bound to enzyme 1, which of the following would be decreased?\nI. Protein A\nII. Protein C\nConsider the following pathway of reactions catalyzed by enzymes (shown in numbers):III. Protein X\nA. I only\nB. II only\nC. II and III\nD. I, II, and III\n", "Answer (final answer highlighted)": "C If enzyme 1 were inhibited, then everything that comes after that in the pathway would be reduced. Substance A would not be reduced, but both C and X would. Choice (C) is correct.", "ImagePath": "Biology/159" }, { "Question": "Consider the following pathway of reactions catalyzed by enzymes (shown in numbers):An increase in substance F leads to the inhibition of enzyme 3. All of the following are direct or indirect results of the process EXCEPT\nA. an increase in substance X\nB. increased activity of enzyme 6\nC. decreased activity of enzyme 4\nD. increased activity of enzyme 5\n", "Answer (final answer highlighted)": "D If substance F leads to the inhibition of enzyme 3, then substances D and E and enzymes 3, 4, and 5 will be affected. The activity of enzyme 5 will be decreased, not increased.", "ImagePath": "Biology/160" }, { "Question": "Consider the following pathway of reactions catalyzed by enzymes (shown in numbers):Which of the following situations represents feedback inhibition?\nA. Protein D activating enzyme 4\nB. Protein B stimulating enzyme 1\nC. Protein 7 inhibiting enzyme C\nD. Protein X inhibiting enzyme 2\n", "Answer (final answer highlighted)": "D Feedback inhibition occurs when something created by a process then inhibits that process. Choices (A) and (B) involve stimulations, so they can be eliminated. Choice (C) doesn\u00e2\u0080\u0099t make sense because it says that \"C\" is an enzyme and the passage says that the enzymes are the numbers shown between the steps.", "ImagePath": "Biology/161" }, { "Question": "G-protein coupled receptors (GPCRs) are a common type of protein receptor containing seven transmembrane segments and bearing intracellular and extracellular portions. The structure of a typical GPCR and its associated partners is shown below. GPCRs are coupled to G-proteins consisting of three subunits (\u00ce\u00b1, \u00ce\u00b2, and \u00ce\u00b3) that bind the nucleotides GTP or GDP on the intracellular side of the GPCR. The presence or absence of a ligand on the extracellular side of the GPCR determines whether GDP or GTP will bind to the intracellular G-protein. Extracellular ligand binding initiates GDP being exchanged for GTP and the separation of the G-protein. One subunit will travel to join with a secondary partner and will initiate a cascade of signaling effects within the cell. In the example shown below, the secondary partner is adenylyl cyclase and the signaling is cAMP upregulation.What does a GPCR's capability of making a ligand-induced conformational change allow?\nA. Binding of the ligand to the phospholipid head groups within the membrane\nB. Communication between the outside of the cell and the inside of the cell\nC. A solid attachment to the intermembrane region of the cell membrane\nD. Intracellular binding of the GDP-associated G-protein complex\n", "Answer (final answer highlighted)": "B The conformational change allows a message to be passed from the outside of the cell to the inside. The conformational change is a sign that the ligand is bound. The ligand does not bind to the membrane, so (A) is incorrect. The ligand triggers binding of the GTP-protein, so (D) is incorrect. A conformational change would not make an attachment more solid, which rules out (C).", "ImagePath": "Biology/162" }, { "Question": "G-protein coupled receptors (GPCRs) are a common type of protein receptor containing seven transmembrane segments and bearing intracellular and extracellular portions. The structure of a typical GPCR and its associated partners is shown below. GPCRs are coupled to G-proteins consisting of three subunits (\u00ce\u00b1, \u00ce\u00b2, and \u00ce\u00b3) that bind the nucleotides GTP or GDP on the intracellular side of the GPCR. The presence or absence of a ligand on the extracellular side of the GPCR determines whether GDP or GTP will bind to the intracellular G-protein. Extracellular ligand binding initiates GDP being exchanged for GTP and the separation of the G-protein. One subunit will travel to join with a secondary partner and will initiate a cascade of signaling effects within the cell. In the example shown below, the secondary partner is adenylyl cyclase and the signaling is cAMP upregulation.Which of the following situations is most similar to extracellular binding to a GPCR?\nA. A police officer pulling over a speeding car on the expressway\nB. A celebrity chef visiting the kitchen of another restaurant\nC. A driver giving their order to a person through a drive-up window\nD. A taxi driver picking up a group of passengers\n", "Answer (final answer highlighted)": "C The G-protein coupled receptor (GPCR) allows a message to be transmitted inside the cell without the ligand actually entering the cell. This is most like a drive-through window where the order is communicated to someone inside a restaurant, but the patron does not actually enter the building.", "ImagePath": "Biology/163" }, { "Question": "G-protein coupled receptors (GPCRs) are a common type of protein receptor containing seven transmembrane segments and bearing intracellular and extracellular portions. The structure of a typical GPCR and its associated partners is shown below. GPCRs are coupled to G-proteins consisting of three subunits (\u00ce\u00b1, \u00ce\u00b2, and \u00ce\u00b3) that bind the nucleotides GTP or GDP on the intracellular side of the GPCR. The presence or absence of a ligand on the extracellular side of the GPCR determines whether GDP or GTP will bind to the intracellular G-protein. Extracellular ligand binding initiates GDP being exchanged for GTP and the separation of the G-protein. One subunit will travel to join with a secondary partner and will initiate a cascade of signaling effects within the cell. In the example shown below, the secondary partner is adenylyl cyclase and the signaling is cAMP upregulation.Based on Figure 1, which of the following is the first step in the activation of cAMP-dPK?\nA. The exchange of GTP for GDP\nB. The binding of epinephrine\nC. The separation of \u00ce\u00b1-GTP\nD. Phosphorylation of intracellular enzymes\n", "Answer (final answer highlighted)": "B According to the figure, the first step in the activation pathway was the binding of epinephrine, the external ligand.", "ImagePath": "Biology/164" }, { "Question": "G-protein coupled receptors (GPCRs) are a common type of protein receptor containing seven transmembrane segments and bearing intracellular and extracellular portions. The structure of a typical GPCR and its associated partners is shown below. GPCRs are coupled to G-proteins consisting of three subunits (\u00ce\u00b1, \u00ce\u00b2, and \u00ce\u00b3) that bind the nucleotides GTP or GDP on the intracellular side of the GPCR. The presence or absence of a ligand on the extracellular side of the GPCR determines whether GDP or GTP will bind to the intracellular G-protein. Extracellular ligand binding initiates GDP being exchanged for GTP and the separation of the G-protein. One subunit will travel to join with a secondary partner and will initiate a cascade of signaling effects within the cell. In the example shown below, the secondary partner is adenylyl cyclase and the signaling is cAMP upregulation.A setup like a GPCR is unnecessary in which of the following situations?\nA. The signaling event is very specific.\nB. The ligand is a hormone traveling in the bloodstream.\nC. The effector molecules are located inside the cytoplasm.\nD. The ligand is a small nonpolar molecule.\n", "Answer (final answer highlighted)": "D G-protein coupled receptors (GPCRs) are necessary to bring a signal from outside the cell to inside the cell. If the ligand is a small nonpolar molecule, then it can go through the membrane without trouble and does not need an extracellular receptor.", "ImagePath": "Biology/165" }, { "Question": "Which of the following could NOT be represented by Figure 1?\nA. A monomer used to build a protein\nB. A nucleotide\nC. A reactant used to synthesize nucleic acids\nD. A chemical used to relay genetic information\n", "Answer (final answer highlighted)": "A Figure 1 is adenine, which is a nucleotide. Nucleotides are the monomers of nucleic acids, so the image represents (B) and (C). According to the information in the passage, nucleic acids relay genetic information, so (A) is the only answer that incorrectly describes the figure.", "ImagePath": "Biology/166" }, { "Question": "According to Figure 1, within the protein ARKKKK60491, which of the following locations contain polypeptide N-termini?\nI. Position A\nII. Position B\nThe enzymatic catalysis of a reaction essential in the production of dog saliva is mediated by the protein ARKKKK60491. ARKKKK60491 is a homodimer, with each subunit being 337 amino acids. Figure 1, below, indicates a modular structure of the homodimer. Three positions are indicated on the model. Position A is the active site. Position B is a region known to have a large number of nonpolar residues. Position C is known to have a large number of charged residues.III. Position C\nA. I only\nB. I and II\nC. II and III\nD. I and III\n", "Answer (final answer highlighted)": "C The protein is known to be a homodimer, so it must have two polypeptides in it. Each polypeptide has one N-terminus, so this dimer protein would have two. They would not occur at the active site, so Position A should not be in the answer.", "ImagePath": "Biology/167" }, { "Question": "The enzymatic catalysis of a reaction essential in the production of dog saliva is mediated by the protein ARKKKK60491. ARKKKK60491 is a homodimer, with each subunit being 337 amino acids. Figure 1, below, indicates a modular structure of the homodimer. Three positions are indicated on the model. Position A is the active site. Position B is a region known to have a large number of nonpolar residues. Position C is known to have a large number of charged residues.Which of the following statements best predicts the effect on the protein's structure if the subunits of the homodimer fail to attach?\nA. The primary structure will change because the order of amino acids will differ.\nB. The secondary structure will differ because hydrogen bonds will occur in different locations and the protein will fold into a different shape.\nC. The tertiary structure will be destroyed because the side chain interactions will not occur and the protein will not fold into a 3-dimensional shape.\nD. The quaternary structure will be destroyed because the different amino acid chains will not join together.\n", "Answer (final answer highlighted)": "D A homodimer is formed when more than one polypeptide subunit come together. This is defined as a quaternary structure, (D).", "ImagePath": "Biology/168" }, { "Question": "The enzymatic catalysis of a reaction essential in the production of dog saliva is mediated by the protein ARKKKK60491. ARKKKK60491 is a homodimer, with each subunit being 337 amino acids. Figure 1, below, indicates a modular structure of the homodimer. Three positions are indicated on the model. Position A is the active site. Position B is a region known to have a large number of nonpolar residues. Position C is known to have a large number of charged residues.Which of the following is Position B most likely to assist the protein with?\nA. Stabilization of the substrate into the transition state during catalysis\nB. Transportation of catalyzed cargo from the nucleus to the mitochondria\nC. Creation of a homodimer through catalysis of homodimerization\nD. Attachment to the membrane by embedding into the phospholipid bilayer\n", "Answer (final answer highlighted)": "D Position B has nonpolar residues and is not the active site, since Position A is the active site. Therefore, (A) is not correct since the substrate does not bind at Position B. It doesn\u00e2\u0080\u0099t look like it is where the homodimer is, so (C) is incorrect. There is no information to indicate (B). Nonpolar residues are known to be helpful for inserting into the lipid bilayer, which makes (D) a strong answer.", "ImagePath": "Biology/169" }, { "Question": "The enzymatic catalysis of a reaction essential in the production of dog saliva is mediated by the protein ARKKKK60491. ARKKKK60491 is a homodimer, with each subunit being 337 amino acids. Figure 1, below, indicates a modular structure of the homodimer. Three positions are indicated on the model. Position A is the active site. Position B is a region known to have a large number of nonpolar residues. Position C is known to have a large number of charged residues.A mutation is discovered in the gene for ARKKKK60491 that converts positively charged lysine residue into negatively charged glutamic acid residue. This single change directly impacts the location where the substrate to ARKKKK60491 attaches during catalysis. Which position is likely affected by this change?\nA. Position A\nB. Position B\nC. Position C\nD. None of the positions will be affected.\n", "Answer (final answer highlighted)": "A The question states that the change affects the place where the substrate binds, which is defined as the active site. Position A is identified as the active site.", "ImagePath": "Biology/170" }, { "Question": "A certain gene has been identified on chromosome 2 in a species of butterfly. The mRNA transcript has been found to be 1578 base pairs in length. A portion of the transcript is shown below. The area shown in grey is part of a known ribosome binding site.Where on the strand shown in Figure 1 is a transcription factor likely to bind?\nA. Bases 0 to 15\nB. Bases 20 to 25\nC. Bases -20 to -15\nD. None of the above\n", "Answer (final answer highlighted)": "D A transcription factor binds to DNA before RNA is created during transcription. Since this is already a map of an RNA transcript, transcription has already happened and no transcription factors will bind at any location.", "ImagePath": "Biology/171" }, { "Question": "A certain gene has been identified on chromosome 2 in a species of butterfly. The mRNA transcript has been found to be 1578 base pairs in length. A portion of the transcript is shown below. The area shown in grey is part of a known ribosome binding site.RNA polymerase transcribes DNA into mRNA by matching base pairs of nucleotides. Which of the following would be the segment of DNA on the coding strand corresponding to bases 0-6 in Figure 1?\nA. 5' AAUGCA 3'\nB. 5' TTACGT 3'\nC. 3' AATGCA 5'\nD. 3' TTUGCT 5'\n", "Answer (final answer highlighted)": "B The coding strand is the strand that is identical to the mRNA transcript, except that the mRNA has the nucleotide uracil in place of the nucleotide thymine. It is the partner strand to the coding strand and used as a template during transcription. Therefore, the answer should match the transcript shown in the image with \"U\u00e2\u0080\u0099s\" in place of any \"T\u00e2\u0080\u0099s.\"", "ImagePath": "Biology/172" }, { "Question": "A certain gene has been identified on chromosome 2 in a species of butterfly. The mRNA transcript has been found to be 1578 base pairs in length. A portion of the transcript is shown below. The area shown in grey is part of a known ribosome binding site.A transcript was identified in the nucleus that is similar to this transcript. How is it likely different from the mRNA transcript?\nA. The nuclear transcript likely contained introns.\nB. The nuclear transcript likely contained exons.\nC. The nuclear transcript likely contained a poly-A tail.\nD. The nuclear transcript likely contained a 3' GTP-Cap.\n", "Answer (final answer highlighted)": "A Before the transcripts are completed and leave the nucleus, they undergo certain modifications including the removal of introns and the addition of a 5\u00e2\u0080\u0099 GTP cap and a 3\u00e2\u0080\u0099 poly-A tail. The transcript in the nucleus would not have undergone these modifications yet, so it would contain introns.", "ImagePath": "Biology/173" }, { "Question": "A certain gene has been identified on chromosome 2 in a species of butterfly. The mRNA transcript has been found to be 1578 base pairs in length. A portion of the transcript is shown below. The area shown in grey is part of a known ribosome binding site.If bases 0-15 were deleted, what would be the likely consequence?\nA. No transcription would be allowed to occur.\nB. No translation would be allowed to occur.\nC. Neither transcription nor translation would occur.\nD. No consequence would occur as these bases are non-coding.\n", "Answer (final answer highlighted)": "B The bases at the 5\u00e2\u0080\u0099 side of the transcript are in the untranslated region because this is generally the site for ribosome binding. Without this region, the ribosome couldn\u00e2\u0080\u0099t bind, and there would be no translation.", "ImagePath": "Biology/174" }, { "Question": "Which of the following populations does NOT demonstrate exponential growth?\nI. Cougar\nII. Chipmunk\nIn a heavily populated suburb, two cougars were once spotted roaming in a small field. Local wildlife experts, though not surprised, warned the public to be aware of their surroundings and to keep small pets protected. A group of local junior high school students were curious about the population of cougars in the area since no one they asked had ever seen one in the area. With the help of local wildlife enthusiasts and carefully placed motion-activated wildlife cameras, the group of students recorded sightings of animals in a local forest preserve for their entire four years of high school. The results are shown below.III. Deer\nA. I only\nB. I and II\nC. I and III\nD. I and II and III\n", "Answer (final answer highlighted)": "D None of the populations demonstrate exponential growth because they each have a carrying capacity that sets a limit on their growth. Only populations growing as fast as they can reproduce at a maximal amount will grow at an exponential rate.", "ImagePath": "Biology/175" }, { "Question": "In a heavily populated suburb, two cougars were once spotted roaming in a small field. Local wildlife experts, though not surprised, warned the public to be aware of their surroundings and to keep small pets protected. A group of local junior high school students were curious about the population of cougars in the area since no one they asked had ever seen one in the area. With the help of local wildlife enthusiasts and carefully placed motion-activated wildlife cameras, the group of students recorded sightings of animals in a local forest preserve for their entire four years of high school. The results are shown below.It has been shown that the population size of chipmunks is directly tied to the number of acorns dropped. This can be scientifically summarized by which of the following statements?\nA. Acorn number is a density-dependent population factor and affects the carrying capacity of the chipmunk population.\nB. Acorn number is a density-dependent population factor and does not affect the carrying capacity of the chipmunk population.\nC. Acorn number is a density-independent population factor and affects the carrying capacity of the chipmunk population.\nD. Acorn number is a density-independent population factor and does not affect the carrying capacity of the chipmunk population.\n", "Answer (final answer highlighted)": "A If the chipmunk is dependent on the acorns, then the acorns affect the carrying capacity. Since the quantity of acorns would affect a large population differently than a small population, this makes it a density-dependent factor.", "ImagePath": "Biology/176" }, { "Question": "In a heavily populated suburb, two cougars were once spotted roaming in a small field. Local wildlife experts, though not surprised, warned the public to be aware of their surroundings and to keep small pets protected. A group of local junior high school students were curious about the population of cougars in the area since no one they asked had ever seen one in the area. With the help of local wildlife enthusiasts and carefully placed motion-activated wildlife cameras, the group of students recorded sightings of animals in a local forest preserve for their entire four years of high school. The results are shown below.Which change will cause fewer skunks to be sighted in the future?\nA. An increase in the number of cougars\nB. An increase in the number of raccoons\nC. An increase in the number of deer\nD. It is impossible to make this determination.\n", "Answer (final answer highlighted)": "D There is no information about what species is a predator of skunks, and the population seems to be stable over time, so this is impossible to determine. Even though the skunks and raccoons are both stable, there is no indication that they are related to each other.", "ImagePath": "Biology/177" }, { "Question": "In a heavily populated suburb, two cougars were once spotted roaming in a small field. Local wildlife experts, though not surprised, warned the public to be aware of their surroundings and to keep small pets protected. A group of local junior high school students were curious about the population of cougars in the area since no one they asked had ever seen one in the area. With the help of local wildlife enthusiasts and carefully placed motion-activated wildlife cameras, the group of students recorded sightings of animals in a local forest preserve for their entire four years of high school. The results are shown below.Although the data is limited, which of the following populations is the most likely to be a primary food source for the cougars?\nA. Skunk\nB. Deer\nC. Raccoon\nD. Chipmunk\n", "Answer (final answer highlighted)": "B The cougar population is shown to be decreasing over time. One possible explanation for the decline may be due to a disappearing food source, so the food source should also show a decrease over time. The only animal that also shows a decreasing population is deer.", "ImagePath": "Biology/178" }, { "Question": "In a heavily populated suburb, two cougars were once spotted roaming in a small field. Local wildlife experts, though not surprised, warned the public to be aware of their surroundings and to keep small pets protected. A group of local junior high school students were curious about the population of cougars in the area since no one they asked had ever seen one in the area. With the help of local wildlife enthusiasts and carefully placed motion-activated wildlife cameras, the group of students recorded sightings of animals in a local forest preserve for their entire four years of high school. The results are shown below.Raccoons eat a diet rich in berries. Which statement is the most likely to describe the berry population?\nA. A hard frost eliminated nearly all of the berries in 2007, but 2008 was a milder winter.\nB. A virus was introduced in 2006 that eliminated a fly using the berry bushes as a niche habitat.\nC. Cougars destroyed much of the berry habitat in 2005.\nD. The berry population remained steady, with a slight decrease due to lower rainfall in 2008.\n", "Answer (final answer highlighted)": "D The raccoon population seems steady, with a slight dip in 2008. If raccoons rely on berries as a primary food source, then it is likely that the berry population would have also remained stable.", "ImagePath": "Biology/179" }, { "Question": "A chain of three small islands was found to be the home to a small species of mouse. The angle of jaw opening was found to vary significantly. The average size angle of the maximal jaw opening found in mice at 10 locations on the three small islands is shown in Figure 1, below.Which of the following statements best supports that the jaw angle on Island B changed via punctuated equilibrium?\nA. Fossil evidence has shown that over time the jaw angle on Island B slowly increased.\nB. Fossil evidence has shown that the jaw angle of the mice on Island B increased very quickly.\nC. Fossil evidence has shown that over time the jaw angle on Island B slowly decreased.\nD. Fossil evidence has shown that the jaw angle of the mice on Island B fluctuates over time.\n", "Answer (final answer highlighted)": "B Punctuated equilibrium is defined as an isolated episode of rapid development of a population. A slow change, described in (A) and (C), or a fluctuation, described in (D), do not suggest a quick change.", "ImagePath": "Biology/180" }, { "Question": "A chain of three small islands was found to be the home to a small species of mouse. The angle of jaw opening was found to vary significantly. The average size angle of the maximal jaw opening found in mice at 10 locations on the three small islands is shown in Figure 1, below.Skeletons have been found that indicate that mice with jaw angles less than 30 degrees were once found on Island B. Which explanation best accounts for this?\nA. A small jaw angle hinders the survival of mice on Island B.\nB. A large jaw angle hinders the survival of mice on Island A.\nC. A small jaw angle encourages the survival of mice on Island C.\nD. A large jaw angle encourages the survival of mice on Island A.\n", "Answer (final answer highlighted)": "A Since the jaw angle on island B is now large, the smaller jaw angle must have disappeared. The small jaw angle is likely selected against, and only mice with large jaws survive on Island B. The survival on the other islands is not directly relevant.", "ImagePath": "Biology/181" }, { "Question": "A chain of three small islands was found to be the home to a small species of mouse. The angle of jaw opening was found to vary significantly. The average size angle of the maximal jaw opening found in mice at 10 locations on the three small islands is shown in Figure 1, below.If the mice from Island A and the mice from Island B were placed together, what would likely happen?\nA. The mice would mate, but it is impossible to predict jaw angle.\nB. The mice would mate, and the jaw angle would be approximately 27\u00c2\u00b0.\nC. The mice would mate, and the jaw angle would be either 21\u00c2\u00b0 or 32\u00c2\u00b0.\nD. The mice would not be capable of mating.\n", "Answer (final answer highlighted)": "A It says in the passage that the mice are the same species. This means they should be able to mate with each other. As we do not know anything about the genetics and inheritance of jaw angle, it is not possible to predict how the jaw angle would be affected.", "ImagePath": "Biology/182" }, { "Question": "A chain of three small islands was found to be the home to a small species of mouse. The angle of jaw opening was found to vary significantly. The average size angle of the maximal jaw opening found in mice at 10 locations on the three small islands is shown in Figure 1, below.Which of the following might account for the variations in maximal jaw angle?\nA. Different wind speeds on each island\nB. Different heights of trees on each island\nC. Different sizes of seeds on each island\nD. Differences in altitude on each island\n", "Answer (final answer highlighted)": "C The wind speed, tree height, and altitude do not tie directly into the function of the jaw and the size of the opening. Only the size of seeds that the mice eat would directly relate to the mouth size.", "ImagePath": "Biology/183" }, { "Question": "A gene responsible for production of hair pigment in dogs is called Fursilla (frsl). A map of the Fursilla locus is shown in Figure 1, below. When expressed, it results in darkly pigmented dog fur. When unexpressed, the hair is devoid of pigmentation and appears pure white. Expression of Fursilla (frsl) depends on the binding/lack of binding of several proteins: Nefur (NEFR), Lesfur (LSFR), and Dirkfur (DRKFR). Figure 2 shows the relative levels of frsl transcript as measured via RT-qPCR when each protein is overexpressed or unexpressed in the cell.How would the overexpression of BLD affect the transcript levels of Fursilla?\nA. Fursilla transcript levels would increase.\nB. Fursilla transcript levels would decrease.\nC. Fursilla transcript levels would be unaffected.\nD. Fursilla transcript would completely disappear.\n", "Answer (final answer highlighted)": "A DRKFR is a transcriptional inhibitor, and it significantly decreases Fursilla transcript levels when overexpressed. If BLD binds to the transcriptional inhibitor, DRKFR, then it would reduce inhibition and increase the transcript levels of Fursilla.", "ImagePath": "Biology/184" }, { "Question": "A gene responsible for production of hair pigment in dogs is called Fursilla (frsl). A map of the Fursilla locus is shown in Figure 1, below. When expressed, it results in darkly pigmented dog fur. When unexpressed, the hair is devoid of pigmentation and appears pure white. Expression of Fursilla (frsl) depends on the binding/lack of binding of several proteins: Nefur (NEFR), Lesfur (LSFR), and Dirkfur (DRKFR). Figure 2 shows the relative levels of frsl transcript as measured via RT-qPCR when each protein is overexpressed or unexpressed in the cell.An additional protein, Baldidog (BLD), was identified and found to interact with the DRKFR protein. Based on this information, which of the following best describes why these proteins are able to bind together?\nA. Complementary nucleotides sequences\nB. Amino acid pockets with complementary conformations\nC. Opposing regions rich in cytosines and thymines\nD. Hydrophobic lipids and hydrophobic molecules\n", "Answer (final answer highlighted)": "B Two proteins fitting together would not occur from similarities in their nucleotide sequences, which is referenced in (A) and (C). As proteins, they should not be formed from lipids, so (D) is incorrect. Proteins are formed from amino acids, and complementary conformations would allow them to bind together.", "ImagePath": "Biology/185" }, { "Question": "A gene responsible for production of hair pigment in dogs is called Fursilla (frsl). A map of the Fursilla locus is shown in Figure 1, below. When expressed, it results in darkly pigmented dog fur. When unexpressed, the hair is devoid of pigmentation and appears pure white. Expression of Fursilla (frsl) depends on the binding/lack of binding of several proteins: Nefur (NEFR), Lesfur (LSFR), and Dirkfur (DRKFR). Figure 2 shows the relative levels of frsl transcript as measured via RT-qPCR when each protein is overexpressed or unexpressed in the cell.Based on the data, which of the following most likely describes how the binding of proteins affects the production of Fursilla transcript?\nA. Because Fursilla transcript levels change when certain proteins are overexpressed or unexpressed in the cell, Fursilla must interfere with the other proteins.\nB. Because Fursilla transcript levels stay the same whether NEFR is overexpressed or unexpressed, NEFR must bind inhibit the production of Fursilla transcript.\nC. Because Fursilla transcript levels decrease when LSFR is unexpressed in the cell, LSFR must compete for the binding site or RNA polymerase.\nD. Because Fursilla transcript levels increase when DRKFR is unexpressed in the cell, DRKFR must compete for the binding site of RNA polymerase.\n", "Answer (final answer highlighted)": "D If something competes with the polymerase, then it is likely an inhibitor and high amounts of it would decrease transcription. DRKFR is the only protein that significantly decreases Fursilla transcript levels when overexpressed.", "ImagePath": "Biology/186" }, { "Question": "A gene responsible for production of hair pigment in dogs is called Fursilla (frsl). A map of the Fursilla locus is shown in Figure 1, below. When expressed, it results in darkly pigmented dog fur. When unexpressed, the hair is devoid of pigmentation and appears pure white. Expression of Fursilla (frsl) depends on the binding/lack of binding of several proteins: Nefur (NEFR), Lesfur (LSFR), and Dirkfur (DRKFR). Figure 2 shows the relative levels of frsl transcript as measured via RT-qPCR when each protein is overexpressed or unexpressed in the cell.Which of the following would likely produce a dog with the darkest fur?\nA. High levels of LSFR and high levels of DRKFR\nB. High levels of LSFR and low levels of DRKFR\nC. Low levels of LSFR and high levels of DRKFR\nD. Low levels of LSFR and low levels of DRKFR\n", "Answer (final answer highlighted)": "B Dark fur would be caused by high expression of fursilla. The triggers for that high expression would be an underexpression of DRKFR and high expression of LSFR.", "ImagePath": "Biology/187" }, { "Question": "A gene responsible for production of hair pigment in dogs is called Fursilla (frsl). A map of the Fursilla locus is shown in Figure 1, below. When expressed, it results in darkly pigmented dog fur. When unexpressed, the hair is devoid of pigmentation and appears pure white. Expression of Fursilla (frsl) depends on the binding/lack of binding of several proteins: Nefur (NEFR), Lesfur (LSFR), and Dirkfur (DRKFR). Figure 2 shows the relative levels of frsl transcript as measured via RT-qPCR when each protein is overexpressed or unexpressed in the cell.Scientists identified a mutant allele of the Fursilla gene caused by a deletion of bases 1231-1295 on chromosome 8. What is the likely effect of this mutation?\nA. No transcription and no translation of Fursilla will occur.\nB. Transcription will not occur, but translation will be unaffected.\nC. Transcription of Fursilla will occur, but no translation will occur.\nD. Both transcription and translation of Fursilla will be unaffected.\n", "Answer (final answer highlighted)": "A The location appears to be upstream of the transcription start site. This is the promoter region and is likely important for polymerase binding and initiation of transcription. Without it, there would be no transcription and subsequently there could not be any translation.", "ImagePath": "Biology/188" }, { "Question": "Figure 1 shows a cell at the onset of meiosis (just prior to initiation of prophase I) and the resulting 4 gametes achieved at the end of meiosis. Select the statement that is likely true.\nA. Meiosis occurred as it should.\nB. There was a nondisjunction event in Meiosis I.\nC. There was a nondisjunction event in Meiosis II.\nD. Two Barr bodies were produced instead of four gametes.\n", "Answer (final answer highlighted)": "B If meiosis occurred as it should, there should be 4 haploid gametes, each with one long and one short chromosome. None of the gametes look correct. There was a nondisjunction at Meiosis I, and the two long homologous chromosomes failed to separate. This caused two gametes to get no copies of the long chromosome and two gametes to get two copies. If the nondisjunction was in Meiosis II, then two of the gametes would look normal and two of the gametes would have incorrect amounts of chromosomes. Barr bodies are small and unviable, but they still have the correct number of chromosomes in them.", "ImagePath": "Biology/189" }, { "Question": "The active site of the enzyme Ritzolinine (RZN45) contains three positively charged lysine residues. When ascorbic acid is present, binding of JB-76, the substrate of RZN45, decreases. The reaction rate is affected by the presence of ascorbic acid as shown in the figure below. It is thought that a daily supplement of Vitamin C might aid those suffering from Ritzolierre's Disease, which is caused by elevated levels of RZN45.If Figure 1 were to include additional data for higher concentrations of JB-76, how would the reaction rate change?\nA. The reaction rate would be lower than any reaction rate shown in Figure 1.\nB. The reaction rate would be higher than any reaction rate shown in Figure 1.\nC. The reaction rate would be equal to the highest reaction rate shown in Figure 1.\nD. The reaction rate would increase gradually for each concentration of JB-76 added.\n", "Answer (final answer highlighted)": "C As shown in the graph, the amount of substrate has reached a saturation point and adding additional substrate will not increase the rate further. The reaction rate will remain at the same high level.", "ImagePath": "Biology/190" }, { "Question": "A patient with Ritzolierre's Disease would likely benefit from which of the following:\nI. Injections of RZN45\nII. Injections of JB-76\nThe active site of the enzyme Ritzolinine (RZN45) contains three positively charged lysine residues. When ascorbic acid is present, binding of JB-76, the substrate of RZN45, decreases. The reaction rate is affected by the presence of ascorbic acid as shown in the figure below. It is thought that a daily supplement of Vitamin C might aid those suffering from Ritzolierre's Disease, which is caused by elevated levels of RZN45.III. Injections of ascorbic acid\nA. I only\nB. II only\nC. III only\nD. II and III\n", "Answer (final answer highlighted)": "C Ritzolierre\u00e2\u0080\u0099s Disease is caused by elevated enzyme levels. Only option III would decrease the enzyme activity levels. Options I and II would raise the levels and make the disease worse.", "ImagePath": "Biology/191" }, { "Question": "The active site of the enzyme Ritzolinine (RZN45) contains three positively charged lysine residues. When ascorbic acid is present, binding of JB-76, the substrate of RZN45, decreases. The reaction rate is affected by the presence of ascorbic acid as shown in the figure below. It is thought that a daily supplement of Vitamin C might aid those suffering from Ritzolierre's Disease, which is caused by elevated levels of RZN45.Which is the best explanation for the differing effects on reaction rate caused by ascorbic acid at low and high concentrations of JB-76?\nA. At high concentrations of JB-76, there are fewer free active sites for the ascorbic acid to bind to.\nB. At low concentrations of JB-76, there are fewer free allosteric sites for the RZN45 to bind to.\nC. At high concentrations of JB-76, there are more free allosteric sites for the ascorbic acid to bind to.\nD. At low concentrations of JB-76, there are more free active sites for the RZN45 to bind to.\n", "Answer (final answer highlighted)": "A The graph shows that at low/medium levels of substrate the reaction rate is low in the presence of ascorbic acid and then at high levels of substrate the reaction rate is high, even with ascorbic acid present. This is because with lots of substrate, the ascorbic acid does not stand a chance at finding a free active site to bind to because the superfluous amount of substrate is likely to be bound at most of the sites.", "ImagePath": "Biology/192" }, { "Question": "The active site of the enzyme Ritzolinine (RZN45) contains three positively charged lysine residues. When ascorbic acid is present, binding of JB-76, the substrate of RZN45, decreases. The reaction rate is affected by the presence of ascorbic acid as shown in the figure below. It is thought that a daily supplement of Vitamin C might aid those suffering from Ritzolierre's Disease, which is caused by elevated levels of RZN45.Which of the following is likely true?\nA. RZN45 and JB-76 have similarly charged amino acids at their active sites.\nB. Ritzolinine is stabilized in the presence of Vitamin C.\nC. Ascorbic acid and JB-76 each have a pocket of negatively charged amino acids.\nD. JB-76 and ascorbic acid have an identical number of amino acids.\n", "Answer (final answer highlighted)": "C RZN45 is the enzyme and it binds to JB-76. Ascorbic acid (vitamin C) is an inhibitor of this reaction and binding to JB-76 is reduced, which suggests the inhibitor binds to the same place as the substrate. The graph confirms that the inhibition is competitive since it shows a decreased reaction rate when ascorbic acid is present. Choice (A) is not true because similarly charged amino acids would repel each other and RZN45 and JB-76 bind to each other. There is nothing to suggest that (B) is correct. Choice (C) would make sense since both ascorbic acid and JB-76 bind to the same place, so they probably have similar structures. Choice (D) could be true, but it is unlikely. Even things that are the same shape do not necessarily have the same number of amino acids. Proteins are often hundreds of amino acids long, so having the exact same number is like a needle in a haystack.", "ImagePath": "Biology/193" }, { "Question": "A proponent of the vegan diet writes a blog post that claims that the vegan diet is the only way to \"reduce your carbon footprint, with respect to food, because it cuts your carbon footprint in half\" and shows the graph above. Which of the following directly supports this claim?\nA. According to the 10% rule, only 10% of energy is passed from producers to consumers, so when humans consume animals, the energy harvested is greatly reduced.\nB. Livestock produce methane emissions and consume large amounts of plants every year.\nC. Deforestation for grazing livestock contributes to the loss of plants for carbon sequestration.\nD. Beef and lamb livestock\u00e2\u0080\u0094not chicken, fish, or pork\u00e2\u0080\u0094has the most dramatic impact on carbon footprint.\n", "Answer (final answer highlighted)": "D If (D) is a correct statement, then simply cutting out beef and lamb from your diet can dramatically decrease your carbon footprint-even if you do not decide to eat vegan. Choices (A), (B), and (C) are all true statements with respect to reducing the carbon footprint of food.", "ImagePath": "Biology/194" }, { "Question": "Viruses are obligate intracellular parasites, requiring their host cells for replication. Consequently, viruses generally attempt to reproduce as efficiently and quickly as possible in a host. Below is a graph depicting the initial growth pattern of a bacteriophage within a population of E. coli. This reproductive strategy is most similar to which of the following?\nA. An r-strategist, because it aims to produce a large abundance of offspring to ensure survival\nB. A k-strategist, because it aims to produce a large abundance of offspring to ensure survival\nC. An r-strategist, because it is best suited to thrive in stable environments and over a long life span\nD. A k-strategist, because it is best suited to thrive in stable environments and over a long life span\n", "Answer (final answer highlighted)": "A Viruses would display reproductive strategies most similar to r-strategists because they aim to reproduce as fast as possible and create as many progeny as possible in order to increase their odds of transmission to other hosts.", "ImagePath": "Biology/195" }, { "Question": "During the Industrial Revolution, a major change was observed in many insect species due to the mass production and deposition of ash and soot around cities and factories. One of the most famous instances was within the spotted moth population. An ecological survey was performed in which the number of spotted moths and longtail moths were counted in 8 different urban settings over a square kilometer in 1802. A repeat experiment was performed 100 years later in 1902.How would the results of this study have been different if factories produced white or light gray ash and soot rather than black?\nA. There would be no change to the results of the experiment.\nB. There would have been added selection pressure for more white-bodied spotted moths and against black-bodied spotted moths.\nC. There would have been added selection pressure for more black-bodied spotted moths and against white-bodied spotted moths.\nD. There would have been an increase in the frequency of both black-bodied and white-bodied spotted moths.\n", "Answer (final answer highlighted)": "B If the color of ash or soot produced by the Industrial Revolution were white or light gray, this would likely reverse the trend observed, applying additional selection against the black moths.", "ImagePath": "Biology/196" }, { "Question": "During the Industrial Revolution, a major change was observed in many insect species due to the mass production and deposition of ash and soot around cities and factories. One of the most famous instances was within the spotted moth population. An ecological survey was performed in which the number of spotted moths and longtail moths were counted in 8 different urban settings over a square kilometer in 1802. A repeat experiment was performed 100 years later in 1902.Why was the population of longtail moths also surveyed in this study?\nA. Variations in the environment were expected to alter the population of longtail moths.\nB. Longtail moths were included as a control because they were not expected to change appreciably due to changes associated with the Industrial Revolution.\nC. The peppered moth did not have a long enough tail to visualize.\nD. Longtail moths were poisoned by the coal dust and suffered drastic population loss.\n", "Answer (final answer highlighted)": "B Longtail moths were included in the experiment as a control to compare the effects that are not associated with color.", "ImagePath": "Biology/197" }, { "Question": "During the Industrial Revolution, a major change was observed in many insect species due to the mass production and deposition of ash and soot around cities and factories. One of the most famous instances was within the spotted moth population. An ecological survey was performed in which the number of spotted moths and longtail moths were counted in 8 different urban settings over a square kilometer in 1802. A repeat experiment was performed 100 years later in 1902.Which of the following statements best explains the data?\nA. As time passed from 1802 to 1902, the frequency of white-bodied pepper moths increased and black-bodied pepper moths decreased.\nB. As time passed from 1802 to 1902, the frequency of white-bodied pepper moths decreased and black-bodied pepper moths increased.\nC. As time passed from 1802 to 1902, the frequency of white-bodied pepper moths and black-bodied pepper moths both increased.\nD. As time passed from 1802 to 1902, the frequency of white-bodied pepper moths and black-bodied pepper moths both decreased.\n", "Answer (final answer highlighted)": "B Based on the data, the number of white-bodied pepper moths decreased between 1802 and 1902, and the number of black-bodied pepper moths increased during the same period.", "ImagePath": "Biology/198" }, { "Question": "During the Industrial Revolution, a major change was observed in many insect species due to the mass production and deposition of ash and soot around cities and factories. One of the most famous instances was within the spotted moth population. An ecological survey was performed in which the number of spotted moths and longtail moths were counted in 8 different urban settings over a square kilometer in 1802. A repeat experiment was performed 100 years later in 1902.What type of selection is represented by the results of this study?\nA. Stabilizing selection\nB. Directional selection\nC. Disruptive selection\nD. Divergent selection\n", "Answer (final answer highlighted)": "B The data provided show a transition toward one extreme (black) and away from another (white). This is an example of directional selection.", "ImagePath": "Biology/199" }, { "Question": "An experiment is performed to evaluate the amount of DNA present during a complete cell cycle. All of the cells were synced prior to the start of the experiment. During the experiment, a fluorescent chemical was applied to cells, which would fluoresce only when bound to DNA. The results of the experiment are shown above. Differences in cell appearance by microscopy or changes in detected DNA were determined to be phases of the cell cycle and are labeled with the letters A-D.During which of the labeled phases of the experiment would the cell undergo anaphase?\nA. Phase A\nB. Phase B\nC. Phase C\nD. Phase D\n", "Answer (final answer highlighted)": "D Anaphase represents the cell division stage of the cell cycle and would be the phase that occurs right before the amount of genetic material should decrease. Phase D is the phase right before the genetic material would drop, so (D) is the correct answer.", "ImagePath": "Biology/200" }, { "Question": "An experiment is performed to evaluate the amount of DNA present during a complete cell cycle. All of the cells were synced prior to the start of the experiment. During the experiment, a fluorescent chemical was applied to cells, which would fluoresce only when bound to DNA. The results of the experiment are shown above. Differences in cell appearance by microscopy or changes in detected DNA were determined to be phases of the cell cycle and are labeled with the letters A-D.Approximately how long does S phase take to occur in these cells?\nA. 15 min\nB. 20 min\nC. 30 min\nD. 40 min\n", "Answer (final answer highlighted)": "C The synthesis, or S phase, of the cell cycle represents the step in which the genetic material is duplicated. The only phase labeled in the experiment that represents an increase is phase B. Based on the time scale on the x-axis, this phase lasts approximately 30 minutes.", "ImagePath": "Biology/201" }, { "Question": "A scientist is testing new chemicals designed to stop the cell cycle at various stages of mitosis. Upon applying one of the chemicals, she notices that all of the cells appear as shown below. Which of the following best explains how the chemical is likely acting on the cells?\nA. The chemical has arrested the cells in prophase and has prevented attachment of the spindle fibers to the kinetochore.\nB. The chemical has arrested the cells in metaphase and has prevented dissociation of the spindle fibers from the centromere.\nC. The chemical has arrested the cells in metaphase and is preventing the shortening of the spindle fibers.\nD. The chemical has arrested the cells in anaphase and is preventing the formation of a cleavage furrow.\n", "Answer (final answer highlighted)": "C During anaphase, the chromatids are separated by shortening of the spindle fibers. Chemically blocking the shortening of these fibers would arrest the cell in metaphase. The cells are arrested in metaphase as indicated by the alignment of the chromosomes in the center of the cell and their attachment to spindle fibers, eliminating (A) and (D). The chromosomes still seem to be attached to the fibers, so there doesn't appear to be dissociation of the fibers, eliminating (B).", "ImagePath": "Biology/202" }, { "Question": " \nGlycolysis (shown below) is a critical metabolic pathway that is utilized by nearly all forms of life. The process of glycolysis occurs in the cytoplasm of the cell and converts 1 molecule of glucose into 2 molecules of pyruvic acid.Which of the following most accurately describes the net reaction of glycolysis?\nA. It is an endergonic process because it results in a net increase in energy.\nB. It is an exergonic process because it results in a net increase in energy.\nC. It is an endergonic process because it results in a net decrease in energy.\nD. It is an exergonic process because it results in a net decrease in energy.\n", "Answer (final answer highlighted)": "B Glycolysis results in the production of ATP (energy), so it is considered an exergonic process.", "ImagePath": "Biology/203" }, { "Question": " \nGlycolysis (shown below) is a critical metabolic pathway that is utilized by nearly all forms of life. The process of glycolysis occurs in the cytoplasm of the cell and converts 1 molecule of glucose into 2 molecules of pyruvic acid.Glycolysis does not require oxygen to occur in cells. However, under anaerobic conditions, glycolysis normally requires fermentation pathways to occur to continue to produce ATP. Which best describes why glycolysis is dependent on fermentation under anaerobic conditions?\nA. Glycolysis requires fermentation to produce more glucose as a substrate.\nB. Glycolysis requires fermentation to synthesize lactic acid and restore NADH to NAD+.\nC. Glycolysis requires fermentation to generate ATP molecules to complete the early steps of the pathway.\nD. Glycolysis requires fermentation to generate pyruvate for a later step in the pathway.\n", "Answer (final answer highlighted)": "B In fermentation, pyruvic acid is converted into either ethanol or lactic acid. During this process, NADH is recycled into NAD+.", "ImagePath": "Biology/204" }, { "Question": " \nGlycolysis (shown below) is a critical metabolic pathway that is utilized by nearly all forms of life. The process of glycolysis occurs in the cytoplasm of the cell and converts 1 molecule of glucose into 2 molecules of pyruvic acid.How many net ATP would be generated directly from glycolysis from the breakdown of 2 glucose molecules?\nA. 2\nB. 4\nC. 8\nD. 12\n", "Answer (final answer highlighted)": "B Based on the pathway provided, consumption of one glucose and two ATP results in production of four ATP. In other words, each glucose results in a net gain of two ATP. Therefore, two glucose molecules would result in a net gain of four ATP.", "ImagePath": "Biology/205" }, { "Question": "Binding of Inhibitor Y as shown below inhibits a key catalytic enzyme by inducing a structural conformation change. Which of the following accurately describes the role of Inhibitor Y?\nA. Inhibitor Y competes with substrates for binding in the active site and functions as a competitive inhibitor.\nB. Inhibitor Y binds allosterically and functions as a competitive inhibitor.\nC. Inhibitor Y competes with substrates for binding in the active site and functions as a noncompetitive inhibitor.\nD. Inhibitor Y binds allosterically and functions as a noncompetitive inhibitor.\n", "Answer (final answer highlighted)": "D Inhibitor Y is binding at a site outside the active site and is inducing a conformational change in the enzyme structure. By binding outside the active site, it must be an allosteric inhibitor, eliminating (A) and (C). Because the inhibitor is binding outside the active site, it is not competing with the substrate for binding, so it is considered a noncompetitive inhibitor.", "ImagePath": "Biology/206" }, { "Question": "The mitochondrion is a critical organelle structure involved in cellular respiration. Below is a simple schematic of the structure of a mitochondrion. Which of the structural components labeled below in the mitochondrion is the primary location of the Krebs cycle?\nA. Inner membrane\nB. Matrix\nC. Intermembrane space\nD. Outer membrane\n", "Answer (final answer highlighted)": "B The Krebs cycle occurs primarily in the matrix of the mitochondria. The inner membrane and the intermembrane space-(A) and (C), respectively-are used in oxidative phosphorylation.", "ImagePath": "Biology/207" }, { "Question": "Vibrio cholerae (shown below) are highly pathogenic bacteria that are associated with severe gastrointestinal illness and are the causative agent of cholera. In extreme cases, antibiotics are prescribed that target bacterial structures that are absent in animal cells. Which of the following structures is most likely targeted by antibiotic treatment?\nA. Cytoplasm\nB. Plasma membrane\nC. Ribosomes\nD. Cell wall\n", "Answer (final answer highlighted)": "D The cell wall is a structure that is present in bacteria but absent in animal cells. Consequently, this structure is targeted by several leading classes of antibiotics and would be an effective target of therapeutics against V. cholerae. Cytoplasm, plasma membrane, and ribosomes-(A), (B), and (C), respectively-are all structures that are present in animal cells.", "ImagePath": "Biology/208" }, { "Question": "After one day of exposure, the mixture in the flask had turned pink in color, and later analysis showed that at least 10% of the carbon had been transformed into simple and complex organic compounds including at least 11 different amino acids and some basic sugars. No nucleic acids were detected in the mixture.\nIn 1953, Stanley Miller and Harold Urey performed an experiment at the University of Chicago to test the hypothesis that the conditions of the early Earth would have favored the formation of larger, more complex organic molecules from basic precursors. The experiment, shown in Figure 1, consisted of sealing basic organic chemicals (representing the atmosphere of the primitive Earth) in a flask, which was exposed to electric sparks (to simulate lightning) and water vapor.A scientist believes that the Miller-Urey experiment failed to yield the remaining amino acids and the nucleic acids because of the absence of critical chemical substrates that would have existed on the primordial Earth due to volcanism. Which of the following basic compounds, which are associated with volcanism, would NOT need to be added in a follow-up Miller-Urey experiment?\nA. H2S (gas)\nB. SiO2 (silica)\nC. SO2\nD. H3PO4 (phosphoric acid)\n", "Answer (final answer highlighted)": "B Silica is a mineral form of glass, is not a common component of life-forms, and is largely chemically inert. Since oxygen is already present in several compounds included in the experiment, the addition of this compound does not provide any additional elements or chemical substrates, which would permit generation of additional amino acids or synthesis of nucleic acids. The addition of sulfur compounds and phosphorus is necessary to generate some amino acids and all nucleic acids, which eliminates (A), (C), and (D).", "ImagePath": "Biology/209" }, { "Question": "After one day of exposure, the mixture in the flask had turned pink in color, and later analysis showed that at least 10% of the carbon had been transformed into simple and complex organic compounds including at least 11 different amino acids and some basic sugars. No nucleic acids were detected in the mixture.\nIn 1953, Stanley Miller and Harold Urey performed an experiment at the University of Chicago to test the hypothesis that the conditions of the early Earth would have favored the formation of larger, more complex organic molecules from basic precursors. The experiment, shown in Figure 1, consisted of sealing basic organic chemicals (representing the atmosphere of the primitive Earth) in a flask, which was exposed to electric sparks (to simulate lightning) and water vapor.Some amino acids, such as cysteine and methionine, could not be formed in this experiment. Which of the following best explains why these molecules could not be detected?\nA. The chemical reactions necessary to create amino acids such as cysteine and methionine require more energy than the simulated lightning provided in the experiment.\nB. The chemical reactions necessary to create amino acids such as cysteine and methionine require enzymes for catalysis to occur, which were not included in the experiment.\nC. Sulfur-based compounds were not included in the experiment.\nD. Nitrogen-based compounds were not included in the experiment.\n", "Answer (final answer highlighted)": "C The amino acids cysteine and methionine contain the element sulfur (as indicated by the S in the amino acid structure shown). However, no sulfur-based compounds were included in the Miller-Urey experiment, so it was impossible to form these two amino acids under the conditions of the experiment.", "ImagePath": "Biology/210" }, { "Question": "After one day of exposure, the mixture in the flask had turned pink in color, and later analysis showed that at least 10% of the carbon had been transformed into simple and complex organic compounds including at least 11 different amino acids and some basic sugars. No nucleic acids were detected in the mixture.\nIn 1953, Stanley Miller and Harold Urey performed an experiment at the University of Chicago to test the hypothesis that the conditions of the early Earth would have favored the formation of larger, more complex organic molecules from basic precursors. The experiment, shown in Figure 1, consisted of sealing basic organic chemicals (representing the atmosphere of the primitive Earth) in a flask, which was exposed to electric sparks (to simulate lightning) and water vapor.Which of the following contradicts the hypothesis of the experiment that life may have arisen from the formation of complex molecules in the conditions of the primitive Earth?\nA. Complex carbon-based compounds were generated after only one day of exposure to simulated primitive Earth conditions.\nB. Nucleic acid compounds such as DNA and RNA were not detected in the mixture during the experiment.\nC. Over half of known amino acids involved in life were detected in the mixture during the experiment.\nD. Basic sugar molecules were generated and detected in the mixture during the experiment.\n", "Answer (final answer highlighted)": "B The hypothesis that life may have arisen from formation of complex molecules from the primordial \"soup\" of Earth is not supported by the absence of nucleic acids. All life is DNA-based, yet no nucleic acid molecules were detected. The presence of carbon molecules, amino acids, and sugars, which are common compounds and compose life, supports the hypothesis, so eliminate (A), (C), and (D). Choice (B) is correct.", "ImagePath": "Biology/211" }, { "Question": "Amino acids are the basic molecular units which compose proteins. All life on the planet forms proteins by forming chains of amino acids. Which component of Figure 1 will vary from amino acid to amino acid?\nA. Label A\nB. Label B\nC. Label C\nD. Label D\n", "Answer (final answer highlighted)": "C All amino acids share a carboxylic acid group, COOH, labeled (B), and an amino-group, NH2, labeled (D). They also share a hydrogen atom bound to the central carbon, (A). Differences in amino acids are defined by variations in the fourth position called the R-group, labeled (C).", "ImagePath": "Biology/212" } ], "Physics": [ { "Question": "At which position in the above circuit will the charge passing that position in one second be largest?\n\nA. A\nB. B\nC. C\nD. D", "Answer (final answer highlighted)": "A: Kirchoff's junction rule, a statement of conservation of electric charge in a circuit, says that current entering a junction equals current leaving a junction. Current is charge flowing per second. The charge passing point A in one second must be equal to the sum of the charge passing B, C, and D in one second; A must have the greatest charge flow per second.", "Notes": "2", "ImagePath": "Physics/1" }, { "Question": "In the laboratory, a 0.5-kg cart collides with a fixed wall, as shown in the preceding diagram. The collision is recorded with a video camera that takes 20 frames per second. A student analyzes the video, placing a dot at the center of mass of the cart in each frame. The analysis is shown above.\n\nAbout how fast was the cart moving before the collision?\n\nA. 0.25 m/s\nB. 4.0 m/s\nC. 0.20 m/s\nD. 5.0 m/s", "Answer (final answer highlighted)": "B: The dots divide the 1-meter distance into five parts. In the time between dots, the cart travels 1/5 of a meter, or 0.2 m. The time between dots is 1/20 of a second, or 0.05 s. At constant speed, the speed is given by distance/time: 0.20 m/0.05 s = 4 m/s.", "Notes": "4", "ImagePath": "Physics/2" }, { "Question": "In the laboratory, a 0.5-kg cart collides with a fixed wall, as shown in the preceding diagram. The collision is recorded with a video camera that takes 20 frames per second. A student analyzes the video, placing a dot at the center of mass of the cart in each frame. The analysis is shown above.\n\nWhich of the following best estimates the change in the cart\u2019s momentum during the collision?\n\nA. 27 N\u00b7s\nB. 13 N\u00b7s\nC. 1.3 N\u00b7s\nD. 2.7 N\u00b7s", "Answer (final answer highlighted)": "D: Initially, the cart's mass is 0.5 kg and speed is 4 m/s, so the cart's momentum is mv = 2 N\u00b7s. In the collision, the cart loses that 2 N\u00b7s in order to stop briefly and then gains more momentum in order to speed up again. So the momentum change must be more than 2 N\u00b7s. How much more? After collision, the cart is moving slower than 4 m/s because the dots are closer together, so the cart's momentum is less than 2 N\u00b7s. The cart's momentum change is (2 N\u00b7s) + (something less than 2 N\u00b7s); the only possible answer is 2.7 N\u00b7s.", "Notes": "5", "ImagePath": "Physics/3" }, { "Question": "In the laboratory, a 60-Hz generator is connected to a string that is fixed at both ends. A standing wave is produced, as shown in the preceding figure. In order to measure the wavelength of this wave, a student should use a meterstick to measure from positions\n\nA. B to C\nB. B to D\nC. D to E\nD. A to F", "Answer (final answer highlighted)": "D: On a standing wave, the wavelength is measured from node-to-node-to-node (i.e., across two \"humps\").", "Notes": "6", "ImagePath": "Physics/4" }, { "Question": "Four identical lead balls with large mass are connected by rigid but very light rods in the square configuration shown in the preceding figure. The balls are rotated about the three labeled axes. Which of the following correctly ranks the rotational inertia I of the balls about each axis?\n\nA. $I_B > I_A = I_C$\nB. $I_A > I_C = I_B$\nC. $I_C > I_A > I_B$\nD. $I_C > I_A = I_B$", "Answer (final answer highlighted)": "D: The rotational inertia of a point mass is $MR^2$, where $R$ is the distance from the mass to the axis of rotation. Pretend the side of the square is of length 2 m, and that each mass is 1 kg. For axis A, each mass has rotational inertia $(1 kg) (1 m)^2 = 1 kg\u00b7m^2$. With four masses total, that's $4 kg\u00b7m^2$. For axis B, each mass is $\\sqrt 2$ m from the axis (the diagonal of the square is $2\\sqrt 2$ m, each mass is half a diagonal from the axis). Each mass has $(1 kg)(\\sqrt 2 m)^2 = 2 kg\u00b7m^2$. Two masses make a total of $4 kg\u00b7m^2$. And for axis C, the masses are each 2 m from the axis, so they each have $(1 kg) \u00d7 (2 m)^2 = 4 kg\u00b7m^2$. With two masses, that's a total of $8 kg\u00b7m^2$. So this would be ranked axis C, followed by equal axes A and B.", "Notes": "7", "ImagePath": "Physics/5" }, { "Question": "In the laboratory, a 3-kg cart experiences a varying net force. This net force is measured as a function of time, and the data collected are displayed in the graph above. What is the change in the cart\u2019s momentum during the interval t = 0 to t = 2 s?\n\nA. 5 N\u00b7s\nB. 10 N\u00b7s\nC. 15 N\u00b7s\nD. 30 N\u00b7s", "Answer (final answer highlighted)": "A: Change in momentum is also known as impulse and is equal to force times time interval. On this graph, the multiplication of the axes means to take the area under the graph. Each segment of the data looks like it represents a straight line, making a big triangle. The area of a triangle is \u00bd(base)(height). That's \u00bd(5 N)(2 s) = 5 N\u00b7s.", "Notes": "10", "ImagePath": "Physics/6" }, { "Question": "A block is attached to a vertical spring. The block is pulled down a distance A from equilibrium, as shown above, and released from rest. The block moves upward; the highest position above equilibrium reached by the mass is less than A, as shown. When the mass returns downward, how far below the equilibrium position will it reach?\n\nA. Greater than the distance A below equilibrium\nB. Less than the distance A below equilibrium\nC. Equal to the distance A below equilibrium\nD. No distance\u2014the block will fall only to the equilibrium position.", "Answer (final answer highlighted)": "B: If friction and air resistance are negligible, a mass on a spring oscillates about the equilibrium position, reaching the same maximum distance above and below. In this case, since the mass doesn't get all the way to position A at the top, mechanical energy was lost (to friction or air resistance or some nonconservative force). Thus, without some external energy input, the mass won't reach its maximum position at the bottom, either-at the bottom it will have no kinetic energy, so all the energy will be potential, and we've already established that some total mechanical energy was lost.", "Notes": "1", "ImagePath": "Physics/7" }, { "Question": "Two charged Styrofoam balls are brought a distance d from each other, as shown. The force on Ball B is 2 \u03bcN to the right. When the distance between the balls is changed, the force on Ball B is 8 \u03bcN to the right.\n\nWhich of the following can indicate the sign of the charges of balls A and B?\n\nBall A Ball B\n\nA. positive nagative\nB. neutral positive\nC. negative negative\nD. positive neutral", "Answer (final answer highlighted)": "C: If Ball B is forced to the right by Ball A, then Ball A must be forced to the left by Ball B-that's Newton's third law. These balls repel-only like-signed charges repel.", "Notes": "2", "ImagePath": "Physics/8" }, { "Question": "Two charged Styrofoam balls are brought a distance d from each other, as shown. The force on Ball B is 2 \u03bcN to the right. When the distance between the balls is changed, the force on Ball B is 8 \u03bcN to the right.\n\nWhen the force on Ball B is 8 \u03bcN, what is the distance between the centers of the two balls?\n\nA. $d/4$\nB. $d/2$\nC. $d/16$\nD. $d/\\sqrt 2$", "Answer (final answer highlighted)": "B: Coulomb's law gives the force of one charge on another, $k\\frac{Q_1Q_2}{r^2}$. We haven't changed the charges $Q$; it's the force of A on B that's quadrupled. Since the force $F$ has increased, the distance between charges $r$ has decreased. Since the force has quadrupled, and since the r in the denominator is square, the distance has been cut in half $(1/2)^2 = 1/4$; and making the denominator four times smaller makes the whole fraction four times bigger.", "Notes": "3", "ImagePath": "Physics/9" }, { "Question": "A disk of radius 1 m and rotational inertia I = 0.5 kg.m2 is free to rotate, but initially at rest. A blob of putty with mass 0.1 kg is traveling toward the disk with a speed of 10 m/s, as shown in the preceding figure. The putty collides with the outermost portion of the disk and sticks to the disk. What is the angular momentum of the combined disk-putty system after the collision?\n\nA. $5 kg\u00b7m^2/s$\nB. $1 kg\u00b7m^2/s$\nC. $0.5 kg\u00b7m^2/s$\nD. $0 kg\u00b7m^2/s$", "Answer (final answer highlighted)": "B: In a collision, momentum-including angular momentum-is conserved. The question might as well be asking, \"What is the angular momentum of the two objects before the collision?\" And since the disk is at rest initially, the question is asking the even easier question, \"What is the angular momentum of the putty before collision?\" The axis of rotation is the center of the disk. The putty is a point mass; the angular momentum of a point mass is mvr with r the distance of closest approach to the axis. That's $(0.1 kg)(10 m/s)(1 m) = 1 kg\u00b7m^2/s$.", "Notes": "4", "ImagePath": "Physics/10" }, { "Question": "What is the current in the 4 \u2126 resistor in the circuit in the preceding illustration?\n\nA. 1.5 A\nB. 2.0 A\nC. 3.0 A\nD. 6.0 A", "Answer (final answer highlighted)": "A: First simplify the 4 \u2126 and 12 \u2126 parallel combination to a 3 \u2126 equivalent resistance. In series with the other 3 \u2126 resistance, that gives a total resistance for the circuit of 6 \u2126. By Ohm's law used on the whole circuit, 12 V = I(6 \u2126). The total current in the circuit is thus 2 A. This current must split between the two parallel resistors. The only possible answer, then, is 1.5 \u2126-the current in the 4 \u2126 resistor must be less than the total current.", "Notes": "6", "ImagePath": "Physics/11" }, { "Question": "Two sounds are played in the laboratory. A microphone is connected to an oscilloscope, which displays the traces shown above for each sound. On these traces, the horizontal axis is time; the vertical axis is related to the distance the microphone\u2019s diaphragm is displaced from its resting position. The scales are identical for each diagram. Which of the following is correct about the sounds that produce the traces above?\n\nA. Sound 1 is louder, and sound 2 is higher pitched.\nB. Sound 2 is louder, and sound 2 is higher pitched.\nC. Sound 1 is louder, and sound 1 is higher pitched.\nD. Sound 2 is louder, and sound 1 is higher pitched.", "Answer (final answer highlighted)": "C: The amplitude of a sound is related to the loudness. Sound 1 has higher amplitude, so it is louder. The pitch of a sound is related to the frequency. Since the horizontal axis is time, the peak-to-peak distance corresponds to a period, which is the inverse of the frequency. Sound 1 has a smaller period, so it has a larger frequency and a larger pitch.", "Notes": "7", "ImagePath": "Physics/12" }, { "Question": "In an experiment, a marble rolls to the right at speed v, as shown in the top diagram. The marble rolls under a canopy, where it is heard to collide with marbles that were not initially moving. Such a collision is known to be elastic. After the collision, two equal-mass marbles are observed leaving the canopy with velocity vectors directed as shown. Which of the following statements justifies why the experimenter believes that a third marble was involved in the collision under the canopy?\n\nA. Before collision, the only marble momentum was directed to the right. After the collision, the combined momentum of the two visible marbles is still to the right. Another marble must have a leftward momentum component to conserve momentum.\nB. Before collision, the only marble momentum was directed to the right. After the collision, the combined momentum of the two visible marbles has a downward component; another marble must have an upward momentum component to conserve momentum.\nC. Before collision, the only marble kinetic energy was directed to the right. After the collision, the combined kinetic energy of the two visible marbles is still to the right. Another marble must have a leftward kinetic energy component to conserve kinetic energy.\nD. Before collision, the only marble kinetic energy was directed to the right. After the collision, the combined kinetic energy of the two visible marbles has a downward component; another marble must have an upward kinetic energy component to conserve kinetic energy.", "Answer (final answer highlighted)": "B: Choices C and D are wrong because kinetic energy doesn't have a direction. Choice A is wrong because momentum conservation does not require a leftward momentum component-since the initial momentum was all to the right, the final momentum should be to the right. It's the vertical momentum that's the problem. Since the vertical momentum was zero to start with, any vertical momentum after collision must cancel out.", "Notes": "9", "ImagePath": "Physics/13" }, { "Question": "In the laboratory, two carts on a track collide in the arrangement shown in the preceding figure. Before the collision, the 2-kg cart travels through photogate 1, which measures its speed; the 0.25-kg cart is initially at rest. After the collision, the carts bounce off one another. Photogate 2 measures the speed of each cart as it passes.\n\nA student is concerned about his experimental results. When he adds the momentum of both carts after collision, he gets a value greater than the momentum of the 2-kg cart before collision. Which of the following is a reasonable explanation for the discrepancy?\n\nA. The track might have been slanted such that the carts were moving downhill.\nB. Human error might have been involved in reading the photogates.\nC. Friction might not have been negligible.\nD. The collision might not have been elastic.", "Answer (final answer highlighted)": "A: Choice B is ridiculous-scientists should never refer generically to \"human error.\" Significant friction should reduce, not increase, the speed (and thus the momentum) measured by Photogate 2. The elasticity of a collision refers to kinetic energy conservation, not momentum conservation-even inelastic collisions must conserve momentum. If the track is slanted downhill to the right, then the carts speed up; conservation of momentum won't be valid between Photogates 1 and 2 because the downhill component of the gravitational force is a force external to the two-cart system.", "Notes": "10", "ImagePath": "Physics/14" }, { "Question": "Three wagons each have the same total mass (including that of the wheels) and four wheels, but the wheels are differently styled. The structure, mass, and radius of each wagon\u2019s wheels are shown in the preceding chart. In order to accelerate each wagon from rest to a speed of 10 m/s, which wagon requires the greatest energy input?\n\nA. Wagon A\nB. Wagon B\nC. Wagon C\nD. All require the same energy input", "Answer (final answer highlighted)": "B: The energy input must be enough to change the translational kinetic energy of the cart and to change the rotational kinetic energy of the wheels. Since all carts have the same mass and change speed by the same amount, they all require the same energy input to change the translational KE. Whichever wheels have the largest rotational inertia will require the largest energy input to get to the same speed. Calculating, wagon B has the largest rotational inertia of 0.004 $kg\u00b7m^2$.", "Notes": "1", "ImagePath": "Physics/15" }, { "Question": "A 10-kg wagon moves horizontally at an initial speed of 5 m/s. A 30-N force is applied to the wagon by pulling the rigid handle, which is angled 60\u00b0 above the horizontal. The wagon continues to move horizontally for another 20 m. A negligible amount of work is converted into thermal energy. By how much has the wagon\u2019s kinetic energy increased over the 20 m?\n\nA. 300 J\nB. 600 J\nC. 125 J\nD. 63 J", "Answer (final answer highlighted)": "A: The work-energy theorem says that the work done by a nonconservative force is equal to the change in potential energy plus the change in kinetic energy. Since the wagon is on a horizontal surface, the potential energy change is zero; the work done by the 30-N pulling force is the change in the wagon's KE. Work is force times parallel displacement, so we don't use 30 N in this formula, we use the component of the 30-N force parallel to the 20-m displacement. That's (30 N)(cos 60)(20 m) = 300 N.", "Notes": "3", "ImagePath": "Physics/16" }, { "Question": "Four identical resistors are connected to a battery in the configuration shown in the preceding figure.\n\nWhich of the following ranks the current I through each resistor?\n\nA. $I_1 = I_4 > I_2 > I_3$\nB. $I_1 = I_4 > I_2 = I_3$\nC. $I_1 = I_2 = I_3 = I_4$\nD. $I_1 > I_2 = I_3 > I_4$", "Answer (final answer highlighted)": "B: Current can only travel through a wire. At the junction after Resistor 1, the current splits; the current comes back together after resistors 2 and 3. Thus, resistors 1 and 4 have the same current that's equal to the total coming from the battery. Since resistors 2 and 3 are identical, they split the current evenly.", "Notes": "5", "ImagePath": "Physics/17" }, { "Question": "A force probe is used to stretch a spring by 20 cm. The graph of the force as a function of distance shown in the preceding figure is produced and used to determine the amount of work done in stretching the spring 20 cm. The experimenter reports the result as 3,000 N\u00b7cm. Which of the following is a reasonable estimate of the experimental uncertainty on this measurement?\n\nA. 3,000 \u00b1 3 N.cm\nB. 3,000 \u00b1 30 N.cm\nC. 3,000 \u00b1 300 N.cm\nD. 3,000 \u00b1 3,000 N.cm", "Answer (final answer highlighted)": "C: The work done by the spring is the area under a force-distance graph because work = force times distance. Using the best-fit line drawn as the top of a triangle, the area is (1/2) \u00d7 (300 N)(20 cm) = 3,000 N.cm.* Now, put your ruler along the data points. Try to draw another line that's still a reasonable best fit, but is a bit shallower. Where does that line intersect the 20-cm position? It intersects at a point probably not much below 280 N, maybe even 290 N. The smallest possible work done, given this data, would be area = (1/2)(280 N)(20 cm) = 2,800 N.cm, which is 200 N.cm short of the 3,000 N.cm original estimate. That's closest to Choice C. If you've done a lot of in-class lab work, you might have noticed that your data often look about as scattered as shown in the graph; and that anything you calculate is never much closer to a known value or to your classmates' calculations than 5 or 10 percent. Here, Choice B works out to an uncertainty of 1 percent; Choice D is 100 percent. So C is the reasonable choice.", "Notes": "7", "ImagePath": "Physics/18" }, { "Question": "In the laboratory, a long platform of negligible mass is free to rotate on a fulcrum. A force probe is placed a fixed distance x from the fulcrum, supporting the platform. An object of fixed mass is placed a variable distance d from the fulcrum. For each position d, the force probe is read. It is desired to determine the mass of the object from a graph of data. Which of the following can determine the object\u2019s mass?\n\nA. Plot the reading in the force probe times x on the vertical axis; plot the gravitational field times d on the horizontal axis. The mass is the slope of the line.\nB. Plot the reading in the force probe on the vertical axis; plot the distance d on the horizontal axis. The mass is the area under the graph.\nC. Plot the reading in the force probe on the vertical axis; plot the distance d multiplied by the distance x on the horizontal axis. The mass is the y-intercept of the graph.\nD. Plot the reading in the force probe times d on the vertical axis; plot the distance x on the horizontal axis. The mass is the slope of the line divided by the gravitational field.", "Answer (final answer highlighted)": "A: Since the platform itself is of negligible mass, only two torques act on the platform: counterclockwise by the force of the force probe ($F_P$), and clockwise by the downward force of the object (mg). Torque is force times distance from a fulcrum, so set these torques equal: $F_P(x) = mg(d)$. Solving for the mass, we get $\\frac{F_P x}{gd}$. Plot the numerator on the vertical, the denominator on the horizontal, and the slope is the mass m.", "Notes": "9", "ImagePath": "Physics/19" }, { "Question": "A rigid rod is pivoted at its right end. Three forces of identical magnitude but different directions are applied at the positions 1, 2, and 3 as shown. Which of the following correctly ranks the torques $\u03c4_1$, $\u03c4_2$, and $\u03c4_3$ provided by the forces $F_1$, $F_2$, and $F_3$?\n\nA. $\u03c4_1 > \u03c4_2 > \u03c4_3$\nB. $\u03c4_3 > \u03c4_2 > \u03c4_1$\nC. $\u03c4_2 > \u03c4_1 > \u03c4_3$\nD. $\u03c4_2 > \u03c4_1 = \u03c4_3$", "Answer (final answer highlighted)": "A: Torque is force times distance from a fulcrum; but that force must be perpendicular to the rod, so in this case the force used in the equation will be the vertical component, which includes a sin 45\u00b0 term for $F_1$ and $F_3$. The sine of 45\u00b0 is 0.7; call the length of the rod L, so $F_2$ is a distance L/2 from the pivot, and $F3$ is about L/4 from the pivot. So $\u03c4_1 = 0.7FL$. $\u03c4_2 = 0.5FL$. $\u03c4_3 = (0.7\u00b70.25)FL$.", "Notes": "2", "ImagePath": "Physics/20" }, { "Question": "The preceding diagram represents a photograph of three transverse waves, each of which is moving to the right in the same material as the others. Which of the following ranks the waves by their amplitudes?\n\nA. A = B > C\nB. B > C > A\nC. A > C > B\nD. A = B = C", "Answer (final answer highlighted)": "A: The amplitude is measured from the midpoint to the peak or trough of a wave. Waves A and B are each two \"bars\" above the midpoint, while C is only one bar above the midpoint.", "Notes": "4", "ImagePath": "Physics/21" }, { "Question": "Question below refers to the following information:\n\nBlock B is at rest on a smooth tabletop. It is attached to a long spring, which in turn is anchored to the wall. Identical block A slides toward and collides with block B. Consider two collisions, each of which occupies a duration of about 0.10 s:\n\nCollision I: Block A bounces back off of block B.\n\nCollision II: Block A sticks to block B.\n\nIn which collision, if either, is the period and frequency of the ensuing oscillations after the collision larger?\n\nA. Period and frequency are the same in both.\nB. Period is greater in collision II, and frequency is greater in collision I.\nC. Period and frequency are both greater in collision I.\nD. Period and frequency are both greater in collision II.", "Answer (final answer highlighted)": "B: The period of a mass-on-a-spring oscillator is $T=2\\pi\\sqrt{\\frac{m}{k}}$. The important part here is that the mass term is in the numerator-a larger mass means a larger period. More mass oscillates on the spring in collision II, so collision II has a greater period. Frequency is the inverse of the period, so the period is smaller in collision II.", "Notes": "1", "ImagePath": "Physics/22" }, { "Question": "Three equal-mass objects (A, B, and C) are each initially at rest horizontally on a pivot, as shown in the figure. Object A is a 40 cm long, uniform rod, pivoted 10 cm from its left edge. Object B consists of two heavy blocks connected by a very light rod. It is also 40 cm long and pivoted 10 cm from its left edge. Object C consists of two heavy blocks connected by a very light rod that is 50 cm long and pivoted 20 cm from its left edge. Which of the following correctly ranks the objects\u2019 angular acceleration about the pivot point when they are released?\n\nA. A = B > C\nB. A > B = C\nC. A < B < C\nD. A > B > C", "Answer (final answer highlighted)": "D: Angular acceleration is net torque divided by rotational inertia, $\\alpha=\\frac{\\tau_{net}}{I}$. Imagine each object has total mass of 2 kg. Begin by comparing objects A and B: To find the net torque on object A, assume the entire 20 N weight is concentrated at the dot representing the rod's center of mass. That's located 10 cm from the pivot, giving a net torque of 200 N\u00b7cm. For object B, consider the torques provided by each block separately. The right block provides a torque of (10 N)(30 cm) = 300 N\u00b7cm clockwise; the left block provides a torque of (10 N)(10 cm) = 100 N\u00b7cm counterclockwise. That makes the net torque 200 N\u00b7cm, the same as for object A. But object B has more rotational inertia, since its 2 kg of mass are concentrated farther away from the pivot than object A's mass. So the denominator of the angular acceleration equation is bigger for object B with the same numerator, which means A > B.", "Notes": "3", "ImagePath": "Physics/23" }, { "Question": "An object of mass m is attached to an object of mass 3m by a rigid bar of negligible mass and length L. Initially, the smaller object is at rest directly above the larger object, as shown in the figure. How much work is necessary to flip the object 180\u00b0, such that the larger mass is at rest directly above the smaller mass?\n\nA. 2\u03c0mgL\nB. 4mgL\nC. 4\u03c0mgL\nD. 2mgL", "Answer (final answer highlighted)": "D: Consider the system consisting of the objects and Earth, with the location of the 3m mass being the zero of gravitational energy. The initial gravitational energy of the system is mgL. After the rotation, the final gravitational energy of the system is 3mgL. That extra gravitational energy of 2mgL came from the work done on the system, meaning choice D. If you want instead to think of work on the objects as force times distance, remember that the force of Earth on the objects acts straight down, not along a circle. So the distance term to use here is just L, not \u03c0L.", "Notes": "5", "ImagePath": "Physics/24" }, { "Question": "A person pulls on a string, causing a block to move to the left at a constant speed. The free body diagram shows the four forces acting on the block: the tension ($T$) in the string, the normal force ($F_n$), the weight ($W$), and the friction force ($F_f$). The coefficient of friction between the block and the table is 0.30.\n\nWhich is the Newton\u2019s third law force pair to $T$?\n\nA. The force of the block on the string\nB. The force of the block on the table\nC. The force of the table on the block\nD. The force of friction on the block", "Answer (final answer highlighted)": "A: The tension is the force of the string acting on the block. Newton's third law says that since the string pulls on the block, the block pulls equally on the string. (The answer is NOT for force of friction: Newton's third law force pairs can never act on the same object.)", "Notes": "1", "ImagePath": "Physics/25" }, { "Question": "A person pulls on a string, causing a block to move to the left at a constant speed. The free body diagram shows the four forces acting on the block: the tension ($T$) in the string, the normal force ($F_n$), the weight ($W$), and the friction force ($F_f$). The coefficient of friction between the block and the table is 0.30.\r\n\r\nWhich of the following correctly ranks the four forces shown?\r\n\r\nA. $T > F_f > W = F_n$\r\nB. $W = F_n > T = F_f$\r\nC. $W = F_n > T > F_f$\r\nD. $W = F_n = T = F_f$", "Answer (final answer highlighted)": "B: Since the block has no acceleration, left forces equal right forces, and up forces equal down forces. The equation for a force of friction is $F_f = \u03bcF_n$. Since the coefficient of friction \u03bc is less than 1, the friction force must be less than the normal force.", "Notes": "2", "ImagePath": "Physics/26" }, { "Question": "Question below refers to the circuit shown in the figure, which includes a 9 V battery and three resistors.\n\nWhich of the following ranks the resistors by the charge that flows through each in a given time interval?\n\nA. 300 \u03a9 > 100 \u03a9 = 50 \u03a9\nB. 50 \u03a9 > 100 \u03a9 > 300 \u03a9\nC. 300 \u03a9 > 100 \u03a9 > 50 \u03a9\nD. 50 \u03a9 = 100 \u03a9 > 300 \u03a9", "Answer (final answer highlighted)": "D: \"Charge that flows through each in a given time interval\" is a complicated way of saying \"current.\" Current through series resistors must always be the same through each, so the 50 \u03a9 resistor and the 100 \u03a9 resistor should rank equally. Then simplify the circuit to two parallel branches. The left branch has an equivalent resistance of 150 \u03a9 and the right branch of 300 \u03a9. With the same voltage across each branch, the larger current goes through the path with smaller resistance by Ohm's law.", "Notes": "4", "ImagePath": "Physics/27" }, { "Question": "Question below refers to the circuit shown in the figure, which includes a 9 V battery and three resistors.\r\n\r\nWhat is the voltage across the 50 \u03a9 resistor?\r\n\r\nA. 9.0 V\r\nB. 6.0 V\r\nC. 3.0 V\r\nD. 1.0 V", "Answer (final answer highlighted)": "C: Consider just the two series resistors, which have an equivalent resistance of 150 \u03a9 and are connected to the 9 V battery. The current through that branch of the circuit is $\\frac{9V}{150\\Omega}=0.06$. Now consider just the 50 \u03a9 resistor. The voltage across it is (0.06 A)(50 \u03a9) = 3 V. As a sanity check, we know that for two resistors in series (which take the same current), V = IR says that the smaller resistor takes less voltage; 3 V across the 50 \u03a9 resistor leaves 6 V across the 100 \u03a9 resistor.", "Notes": "5", "ImagePath": "Physics/28" }, { "Question": "A cart attached to a spring initially moves in the x direction at a speed of 0.40 m/s. The spring is neither stretched nor compressed at the cart\u2019s initial position (x = 0.5 m). The figure shows a graph of the magnitude of the net force experienced by the cart as a function of x, with two areas under the graph labeled. Is it possible to analyze the graph to determine the change in the cart\u2019s kinetic energy as it moves from its initial position to x = 1.5 m?\r\n\r\nA. No, the cart\u2019s mass must be known.\r\nB. Yes, subtract area 2 from area 1.\r\nC. Yes, add area 2 to area 1.\r\nD. Yes, determine area 1.", "Answer (final answer highlighted)": "D: The work done by the net force is the area under the graph. Since the cart only moved from position x = 0.5 m to x = 1.5 m, area 1 is the work done by the net force. By the work-energy theorem, work done by the net force is the change in an object's kinetic energy. (Yes, the mass must be known to determine the values of the initial and final kinetic energy; however, the question asks only for the change in kinetic energy.)", "Notes": "7", "ImagePath": "Physics/29" }, { "Question": "Question below refers to the following information: A bicycle wheel of known rotational inertia is mounted so that it rotates clockwise around a vertical axis, as shown in the first figure. Attached to the wheel\u2019s edge is a rocket engine, which applies a clockwise torque \u03c4 on the wheel for a duration of 0.10 s as it burns. A plot of the angular position \u03b8 of the wheel as a function of time t is shown in the graph.\r\n\r\nIn addition to the wheel\u2019s rotational inertia and the duration of time the engine burns, which of the following information from the graph would allow determination of the net torque the rocket exerts on the wheel?\r\n\r\nA. The area under the graph between t = 0 s and t = 3 s\r\nB. The change in the graph\u2019s slope before and after t = 2 s\r\nC. The vertical axis reading of the graph at t = 3 s\r\nD. The vertical axis reading of the graph at t = 2 s", "Answer (final answer highlighted)": "B: Newton's second law for rotation says $\\tau_{net} = I\\alpha$, where \u03b1 is the angular acceleration, or change in the wheel's angular velocity per time. To find the wheel's angular velocity, look at the slope of the angular position versus time graph. The slope changes after the torque is applied; so the change in the slope is the change in the angular velocity, which (when divided by the 0.10 s duration of the rocket firing) gives the angular acceleration.", "Notes": "1", "ImagePath": "Physics/30" }, { "Question": "Question below refer to the following information:\r\n\r\nTwo metal balls of equal mass (100 g) are separated by a distance (d). In state 1, shown in the figure, the left ball has a charge of +20 \u00b5C, while the right ball has a charge of \u201320 \u00b5C. In state 2, both balls have an identical charge of \u201340 \u00b5C.\r\n\r\nWhich of the following statements about the magnitudes of the electrostatic and gravitational forces between the two balls is correct? \n A. The electrostatic force is greater in state 2 than in state 1. The electrostatic force is greater than the gravitational force in state 1, but the gravitational force is greater than the electrostatic force in state 2. \n B. The electrostatic force is greater in state 1 than in state 2. The electrostatic force is greater than the gravitational force in state 1, but the gravitational force is greater than the electrostatic force in state 2. \n C. The electrostatic force is greater in state 2 than in state 1. The electrostatic force is greater than the gravitational force in both states. \n D. The electrostatic force is greater in state 1 than in state 2. The electrostatic force is greater than the gravitational force in both states.", "Answer (final answer highlighted)": "C: The magnitude of the electrostatic force depends on the product of the charges, regardless of sign. In state 2, the charges are both bigger than in state 1, giving a bigger electrostatic force in state 2. Without even doing the calculation, you can recognize that since Newton's gravitational constant G is orders of magnitude less than the coulomb's law constant k, the electrostatic force will be much greater than the gravitational force between two objects in virtually any laboratory situation. The only time these forces become comparable is when objects the size of planets exert gravitational forces.", "Notes": "4", "ImagePath": "Physics/31" }, { "Question": "Two metal balls of equal mass (100 g) are separated by a distance (d). In state 1, shown in the figure, the left ball has a charge of +20 \u00b5C, while the right ball has a charge of \u201320 \u00b5C. In state 2, both balls have an identical charge of \u201340 \u00b5C.\r\n\r\nAn experimenter claims that he took the balls from state 1 to state 2 without causing them to contact anything other than each other. Which of the following statements provides correct evidence for the reasonability of this claim?\r\n\r\nA. The claim is not reasonable, because there was more net charge in the two-ball system in state 2 than in state 1.\r\nB. The claim is not reasonable, because there was identical charge on each ball in state 2.\r\nC. The claim is reasonable, because in both states, each ball carried the same magnitude of charge as the other.\r\nD. The claim is reasonable, because the positive charge in state 1 could have been canceled out by the available negative charge.", "Answer (final answer highlighted)": "A: Charge is conserved, meaning that while negative charge can neutralize positive charge, the net charge of a system cannot change. The net charge of state 1 is zero; thus, the net charge of state 2 must also be zero, regardless of whether the balls touched or not. State 2 has a net charge of \u201380 \u00b5C, not zero; thus, the claim is not reasonable due to this violation of charge conservation.", "Notes": "5", "ImagePath": "Physics/32" }, { "Question": "When a 0.20 kg block hangs at rest vertically from a spring of force constant 4 N/m, the spring stretches 0.50 m from its unstretched position, as shown in the figure. Subsequently, the block is stretched an additional 0.10 m and released such that it undergoes simple harmonic motion. What is the maximum kinetic energy of the block in its harmonic motion?\n\nA. 0.50 J\nB. 0.02 J\nC. 0.72 J\nD. 0.20 J", "Answer (final answer highlighted)": "B: You can look at this two ways. The hard way is to consider the spring energy gained and the gravitational energy lost in stretching the spring the additional 0.10 m separately. The block-earth system loses $mgh = (0.20 kg)(10 N/kg)(0.10 m) = 0.20 J$ of gravitational energy; but the block-spring system gains $0.5kx_2^2 \u2013 0.5kx_1^2 = {0.5(4 N/m)(0.60 m)^2 \u2013 0.5(4 N/m)(0.50 m)^2} = 0.22 J$ of spring energy. Thus, the net work done on the block in pulling it the additional 0.10 m is 0.02 J. That's what is converted into the block's maximum kinetic energy. You can also look at it the easy way. With a vertical spring, consider the block-earth-spring system as a whole. Define the hanging equilibrium as the zero of the whole system's potential energy; then the potential energy of the whole system can be written as $0.5kx^2$, where x is the distance from this hanging equilibrium position. That's $0.5(4 N/m)(0.10 m)^2 = 0.02 J$.", "Notes": "7", "ImagePath": "Physics/33" }, { "Question": "Question below refers to the following information:\r\n\r\nA student pushes cart A toward a stationary cart B, causing a collision. The velocity of cart A as a function of time is measured by a sonic motion detector, with the resulting graph shown in the figure.\r\n\r\nAt which labeled time did the collision begin to occur?\r\n\r\nA. A\r\nB. B\r\nC. C\r\nD. D", "Answer (final answer highlighted)": "C: The graph represents the speed of cart A, the one that's initially moving. So right before the collision, the vertical axis of the graph must be nonzero. Right after the collision, the vertical axis must quickly either decrease or perhaps become negative if the cart changed directions. That's what happens in the tenth of a second or so after the time labeled C.", "Notes": "8", "ImagePath": "Physics/34" }, { "Question": "Question below refers to the following information:\n\nA student pushes cart A toward a stationary cart B, causing a collision. The velocity of cart A as a function of time is measured by a sonic motion detector, with the resulting graph shown in the figure.\n\nWhat additional measurements, in combination with the information provided in the graph, could be used to verify that momentum was conserved in this collision?\n\nA. The mass of each cart and cart B\u2019s speed after the collision\nB. The force of cart A on cart B, and cart B\u2019s speed after the collision\nC. The mass of each cart only\nD. The force of cart A on cart B only", "Answer (final answer highlighted)": "A: Conservation of momentum requires that the total momentum of the two-cart system be the same before and after the collision. You already know cart A's speed and direction of motion before and after the collision by looking at the vertical axis of the graph; so the mass of cart A will give us cart A's momentum before and after the collision. You know cart B has no momentum before the collision. But you need both cart B's mass AND its velocity after the collision to finish the momentum conservation calculation.\r\n", "Notes": "9", "ImagePath": "Physics/35" }, { "Question": "The circuits shown in the figure contain the same three resistors connected in different configurations. Which of the following correctly explains which configuration (if either) produces the larger current coming from the battery?\r\n\r\nA. Circuit 1; the larger resistor is closer to the battery.\r\nB. Circuit 2; the equivalent resistance of the three resistors is smaller than in circuit 1.\r\nC. Neither; the batteries are both the same.\r\nD. Neither; the individual resistors are the same in each circuit, even if they are in a different order.", "Answer (final answer highlighted)": "B: The equivalent resistance of the parallel resistors in circuit 1 is 12 k\u03a9; adding that to the 100 k\u03a9 resistor gives a total resistance in circuit 1 of 112 k\u03a9. Circuit 2's parallel combination has an equivalent resistance of 23 k\u03a9, giving a total resistance in that circuit of 43 k\u03a9. By V = IR applied to both circuits in their entirety with the same total voltage, the circuit with smaller total resistance will produce the larger current. That's circuit 2.", "Notes": "1", "ImagePath": "Physics/36" }, { "Question": "In an experiment, a cart is placed on a flat, negligible-friction track. A light string passes over a nearly ideal pulley. An object with a weight of 2.0 N hangs from the string. The system is released, and the sonic motion detector reads the cart\u2019s acceleration. Can this setup be used to determine the cart\u2019s inertial mass?\r\n\r\nA. Yes, by dividing 2.0 N by the acceleration, and then subtracting 0.2 kg.\r\nB. No, because only the cart\u2019s gravitational mass could be determined.\r\nC. Yes, by dividing 2.0 N by the acceleration.\r\nD. No, because the string will have different tensions on either side of the pulley.", "Answer (final answer highlighted)": "A: The net force on the cart-object system is 2.0 N. Dividing 2.0 N by the acceleration gives the mass of the entire cart-object system, not just the mass of the cart; so subtract the 0.2 kg mass of the object from the whole system mass to get the cart mass. This is actually inertial mass, because it uses the equation $F_{net} = ma$; Newton's second law defines inertial mass as resistance to acceleration.", "Notes": "3", "ImagePath": "Physics/37" }, { "Question": "The diagram shown here represents the particles in a longitudinal standing wave. Which of the following is an approximate measure of the standing wave\u2019s maximum amplitude?\r\n\r\nA. Half the distance from 1 to 4\r\nB. The distance from 2 to 3\r\nC. The distance from 1 to 4\r\nD. Half the distance from 2 to 3", "Answer (final answer highlighted)": "D: Positions 1 and 4 show minimum particle displacement, so these are the nodes. The maximum amplitude occurs at the antinode, which is somewhere near the positions labeled 2 and 3. The particles are moving left and right in this longitudinal wave. The amplitude is twice the peak-to-peak displacement; since the particle displacement near the antinode is about the distance from 2 to 3, the amplitude is half that.", "Notes": "5", "ImagePath": "Physics/38" }, { "Question": "Question below refers to the following information:\r\n\r\nA small ball of mass m moving to the right at speed $v$ collides with a stationary rod, as shown in the figure. After the collision, the ball rebounds to the left with speed $v_1$, while the rod\u2019s center of mass moves to the left at speed $v_2$. The rod also rotates counterclockwise.\r\n\r\nWhich of the following equations determines the rod\u2019s change in angular momentum about its center of mass during the collision?\r\n\r\nA. I\u03c9 where I is the rod\u2019s rotational inertia about its center of mass, and \u03c9 is its angular speed after collision.\r\nB. $Iv_2/r$, where I is the rod\u2019s rotational inertia about its center of mass, and r is half the length of the rod.\r\nC. $mv_1d$, where d is the distance between the line of the ball\u2019s motion and the rod\u2019s center of mass.\r\nD. $mv_1r$, where r is half the length of the rod.", "Answer (final answer highlighted)": "A: The rod starts from rest, so its final angular momentum is the same as its change in angular momentum. Although the equation \u03c9 = v/r is valid for a point object moving in a circle, it does not apply to a rotating rod; thus, choice B is wrong. Choice C gives the final angular momentum of the ball, which is not the same as the angular momentum change of the rod because the ball does NOT start from rest.", "Notes": "6", "ImagePath": "Physics/39" }, { "Question": "Question below refers to the following information:\n\nA small ball of mass m moving to the right at speed $v$ collides with a stationary rod, as shown in the figure. After the collision, the ball rebounds to the left with speed $v_1$, while the rod\u2019s center of mass moves to the left at speed $v_2$. The rod also rotates counterclockwise.\n\nIs angular momentum about the rod\u2019s center of mass conserved in this collision?\n\nA. No, the ball always moves in a straight line and thus does not have angular momentum.\nB. No, nothing is spinning clockwise after the collision to cancel the rod\u2019s spin.\nC. Yes, the only torques acting are the ball on the rod and the rod on the ball.\nD. Yes, the rebounding ball means the collision was elastic.", "Answer (final answer highlighted)": "C: Choice C states the fundamental condition for angular momentum conservation, which is correct here. The ball does have angular momentum about the rod's center of mass before and after the collision, because its line of motion does not go through the rod's center of mass. Whether or not the collision is elastic has to do with conservation of mechanical energy, not angular or linear momentum.", "Notes": "7", "ImagePath": "Physics/40" }, { "Question": "Question below refers to the following information:\n\nA model rocket with a mass of 100 g is launched straight up. Eight seconds after launch, when it is moving upward at 110 m/s, the force of the engine drops as shown in the force-time graph.\n\nWhich of the following is the best estimate of the impulse applied by the engine to the rocket after the t = 8 s mark?\n\nA. 100 N\u00b7s\nB. 20 N\u00b7s\nC. 5 N\u00b7s\nD. 50 N\u00b7s", "Answer (final answer highlighted)": "C: Impulse is the area under a force-time graph. From t = 8 s to t = 10 s, the area is an approximate rectangle of 2 N times 2 s, giving 4 N\u00b7s. Add an approximate triangle from t = 10 s to t = 11 s, which has the area \u00bd(2 N)(1 s) = 1 N\u00b7s. That gives a total of 5 N\u00b7s.", "Notes": "8", "ImagePath": "Physics/41" }, { "Question": "Question below refers to the following information:\r\n\r\nA model rocket with a mass of 100 g is launched straight up. Eight seconds after launch, when it is moving upward at 110 m/s, the force of the engine drops as shown in the force-time graph.\r\n\r\nWhich of the following describes the motion of the rocket between t = 8 s and t = 10 s?\r\n\r\nA. The rocket moves upward and slows down.\r\nB. The rocket moves downward and speeds up.\r\nC. The rocket moves upward at a constant speed.\r\nD. The rocket moves upward and speeds up.", "Answer (final answer highlighted)": "D: The force of the engine on the rocket during this time is 2 N upward. The weight of the rocket is 1 N (that is, 0.1 kg times the gravitational field of 10 N/kg). So the net force is still upward during this time. Since the rocket was already moving upward, it will continue to move upward and speed up.", "Notes": "9", "ImagePath": "Physics/42" }, { "Question": "The velocity-time graph shown here represents the motion of a 500 g cart that initially moved to the right along a track. It collided with a wall at approximately time (t) = 1.0 s. Which of the following is the best estimate of the impulse experienced by the cart in this collision?\r\n\r\nA. 3.6 N\u00b7s\r\nB. 0.5 N\u00b7s\r\nC. 0.2 N\u00b7s\r\nD. 1.8 N\u00b7s", "Answer (final answer highlighted)": "D: Impulse is change in momentum. The initial momentum was something like (0.5 kg)(1.6 m/s) = 0.8 N\u00b7s to the right. The cart came to rest, changing its momentum by 0.8 N\u00b7s, then sped back up, again changing momentum by (0.5 kg)(2 m/s) = 1.0 N\u00b7s. Thus, the total momentum change is about 1.8 N\u00b7s.", "Notes": "10", "ImagePath": "Physics/43" }, { "Question": "If a ball is rolling down an inclined plane without slipping, which force is responsible for causing its rotation?\r\n\r\nA. Normal force\r\nB. Gravity\r\nC. Kinetic friction\r\nD. Static friction", "Answer (final answer highlighted)": "D: As a ball rolls down an inclined plane, the three forces act on the ball, as shown in the diagram below. https://img.crackap.com/ap/physics-1/cr20/Prin_9780525568292_xp_all_r1_Page_036_Image_0001.jpg In order for a force to cause an object to rotate, the force must be located off-center, and must not point directly at or away from the object's center of mass. An object's weight always acts at its center of mass, so (B) is wrong. The normal force does act at the edge of the ball, but it points directly out of the ramp, which is straight at the center of the ball. Choice (A) is wrong. Friction acts where the ball meets the inclined plane, and it points parallel to the surface, which is tangent to the ball's surface. So friction is what causes rotation. What kind of friction do we have? The phrase \"without slipping\" tells us that even though the ball as a whole is moving, the spot on the ball that touches the ramp is at rest with respect to the ramp. That means we have static friction, (D).", "Notes": "1", "ImagePath": "Physics/44" }, { "Question": "The graph above shows the velocity of an object as a function of time. What is the net displacement of the object over the time shown?\r\n\r\nA. -23 m\r\nB. -9 m\r\nC. 9 m\r\nD. 23 m", "Answer (final answer highlighted)": "B: In a velocity-versus-time (also referred to as a v-versus-t) graph, the displacement of an object is the area between the curve and the horizontal axis; area below the t-axis counts as negative. In this case, the area can be broken into multiple rectangles and triangles.\n\nhttps://img.crackap.com/ap/physics-1/cr20/Prin_9780525568292_xp_all_r1_Page_036_Image_0002.jpg\n\nIn order of the number labels, each shape has an area of 6, 1, 4, and 12, respectively. The last two, however, are below the t-axis, so their area represents negative displacement. Therefore, the net displacement is 6 m + 1 m - 4 m - 12 m = -9 m. As a check, it looks like most of the area is below the t-axis, so the answer should be negative.", "Notes": "2", "ImagePath": "Physics/45" }, { "Question": "An object is resting on a platform that rotates at a constant speed. At first, it is a distance of half the platform's radius from the center. If the object is moved to the edge of the platform, what happens to the centripetal force that it experiences? Assume the platform continues rotating at the same speed.\r\n\r\nA. Increases by a factor of 4\r\nB. Increases by a factor of 2\r\nC. Decreases by a factor of 2\r\nD. Decreases by a factor of 4", "Answer (final answer highlighted)": "B: The formula for centripetal force is $F_c = mv^2/r$, which initially seems to indicate the force is inversely proportional to the radius. However, in the case of circular motion, an object's linear speed is v = \u03a9r. Substituting this value into the equation gives $F_c = m(\u03a9r)^2/r = m\u03a9^2r$. So it turns out that the force is directly proportional to r, which means doubling the radius will double the force on the object.", "Notes": "3", "ImagePath": "Physics/46" }, { "Question": "A car of mass 1000 kg is traveling at a speed of 5 m/s. The driver applies the breaks, generating a constant friction force, and skids for a distance of 20 m before coming to a complete stop. Given this information, what is the coefficient of friction between the car's tires and the ground?\r\n\r\nA. 0.25\r\nB. 0.2\r\nC. 0.125\r\nD. 0.0625", "Answer (final answer highlighted)": "D: First, you know $F_f = \\mu F_N = \\mu (mg)$. Second, you know that $W = \u0394K\u0395 = KE_f - KE_0 = -KE_0$ (since $KE_f = 0$ in this case) = $-0.5 mv_0^2$. Plugging in numbers, you get $W = -\\frac{1}{2}(1000 kg)(5 m/s)^2 = -12,500 J$. You also know that W = Fdcos\u03b8 = [\u00b5(mg)]dcos\u03b8. Solving for \u03bc, you get \u03bc = W/[(mg)dcos\u03b8]. Plugging in the numbers then gives $\u03bc = -12,500 J/[(1000 kg)(10 m/s^2)(20 m)(cos180\u00b0)] = 0.0625$.", "Notes": "4", "ImagePath": "Physics/47" }, { "Question": "A spring-block system is oscillating without friction on a horizontal surface. If a second block of equal mass were placed on top of the original block at a time when the spring is at maximum compression, which of the following quantities would NOT be affected? Assume that the top block stays on the bottom block.\r\n\r\nA. Frequency\r\nB. Maximum speed\r\nC. Amplitude\r\nD. All of the above quantities would be affected.", "Answer (final answer highlighted)": "C: The frequency of a spring-block system is $f=\\frac{1}{2\\pi}\\sqrt{\\frac{k}{m}}$ , so it would be affected by the change in mass. Furthermore, when a spring is at maximum compression or extension, all of its energy is potential energy, which is given by $U = \\frac{1}{2}kx^2$. In adding this block, none of the relevant values are changed, so the spring will still extend to the same length, which means the amplitude is unchanged. Finally, maximum speed will be limited by the maximum K of the system (which will be unchanged since the maximum U was unchanged). $K = \\frac{1}{2}mv^2$, so the increased mass would have to be balanced by a decrease in speed to leave the K unaltered.\nIf you want a physical, rather than mathematical, explanation, think about the acceleration of the pair of blocks. The spring exerts the same force as before, but we effectively raised the block's mass. Thus, the acceleration is less than before. Since the distance from the starting point (maximum compression) to equilibrium is unchanged, the blocks will pick up less speed than the single block did before. Thus, maximum speed decreases.", "Notes": "5", "ImagePath": "Physics/48" }, { "Question": "A certain theme park ride involves people standing against the walls of a cylindrical room that rotates at a rapid pace, making them stick to the walls without needing support from the ground. Once the ride achieves its maximum speed, the floor drops out from under the riders, but the circular motion holds them in place. Which of the following factors could make this ride dangerous for some riders but not others?\r\n\r\nA. The mass of the individuals\r\nB. The coefficient of friction of their clothing in contact with the walls\r\nC. Both of the above\r\nD. None of the above", "Answer (final answer highlighted)": "B: The diagram below shows the forces involved.\n\nhttps://img.crackap.com/ap/physics-1/cr20/Prin_9780525568292_xp_all_r1_Page_037_Image_0002.jpg\n\nIn this case, the person will remain suspended in the air as long as $F_f = F_g$. Furthermore, because this is an example of uniform circular motion, you know $F_N = F_C = mv^2/r$. So you can rewrite the first equation as $\\mu (mv^2/r) = mg. Thus, the coefficient of friction is an important factor, but the mass of the person is not since it exists on both sides of the equation and will cancel out.", "Notes": "6", "ImagePath": "Physics/49" }, { "Question": "As a pendulum swings back and forth, it is affected by two forces: gravity and tension in the string. Splitting gravity into component vectors, as shown above, produces mg sin\u03b8 (the restoring force) and mg cos\u03b8. Which of the following correctly describes the relationship between the magnitudes of tension in the string and mg cos\u03b8?\r\n\r\nA. Tension > mg cos\u03b8\r\nB. Tension = mg cos\u03b8\r\nC. Tension < mg cos\u03b8\r\nD. The relationship depends on the position of the ball.", "Answer (final answer highlighted)": "D: Whenever the ball is in motion, it will be experiencing circular motion, which means there must be a centripetal force. Centripetal force is a net force toward the center, so that means tension must be the greater force whenever the ball is moving. However, the ball is not always moving. At the two extreme edges of its motion, the ball is motionless for an instant as it changes directions. At those times, the net centripetal force is zero, meaning the two given forces are equal.", "Notes": "8", "ImagePath": "Physics/50" }, { "Question": "In order to ensure that no current will pass through the cross path (bold in the image above), what must the resistance of $R$ be in terms of $R_1$, $R_2$, and $R_3$ ?\r\n\r\nA. $R=\\frac{R_1+R_3}{R_2}$\r\nB. $R=\\frac{R_2}{R_1+R_3}$\r\nC. $R=\\frac{R_1R_3}{R_2}$\r\nD. $R=\\frac{R_2}{R_1R_3}$", "Answer (final answer highlighted)": "C: In a circuit with multiple paths, the current through each path is inversely proportional to the resistance of that path. If no current passes through the indicated segment of wire, then the ratio (current in top path)/(current in bottom path) is the same before the cross bar as it is after the cross bar. Thus, $\\frac{R_1}{R_2}=\\frac{R}{R_3}$, which means $R =\\frac{R_1R_3}{R_2}$.", "Notes": "9", "ImagePath": "Physics/51" }, { "Question": "If the surface of the incline is frictionless, how long will the block take to reach the bottom if it was released from rest at the top? \n \n \n A. 0.5 s \n B. 1.0 s \n C. 1.4 s \n D. 2.0 s", "Answer (final answer highlighted)": "D: The acceleration of the block is $a = g \\sin \\theta$, where $\\theta$ is the incline angle, and the distance it must travel\u2014the length of the incline\u2014is $h/\\sin \\theta = h/\\sin 30^\\circ = 2h$.\n\nUsing the equation $s = \\frac{1}{2} a t^2$, we find that\n\n\\[ t = \\sqrt{\\frac{2s}{a}} = \\sqrt{\\frac{2(2h)}{g \\sin \\theta}} = \\sqrt{\\frac{4(5 m)}{(10 m/s^2) \\sin 30^\\circ}} = 2 s \\]\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/52" }, { "Question": "If the surface of the incline is frictionless, with what speed will the block reach the bottom if it was released from rest at the top? \n \n \n A. 8 m/s \n B. 10 m/s \n C. 14 m/s \n D. 18 m/s", "Answer (final answer highlighted)": "B: The easiest way to answer this question is to use Conservation of Energy:\n\n$mgh = \\frac{1}{2}mv^2$ implies $v = \\sqrt{2gh} = \\sqrt{2(10 m/s^2)(5 m)} = 10 m/s$\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/53" }, { "Question": "If the coefficient of friction between the block and the incline is 0.4, how much work is done by the normal force on the block as it slides down the full length of the incline? \n \n \n A. 0 J \n B. 2.0 J \n C. 4.0 J \n D. 4.9 J", "Answer (final answer highlighted)": "A: Since the normal force is perpendicular to the object's displacement, it does no work.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/54" }, { "Question": "The graph above shows a wave. What quantity of the wave does the indicated segment represent? \n \n \n A. Frequency \n B. Wavelength \n C. Period \n D. Cannot be determined", "Answer (final answer highlighted)": "C: Based only on the curve itself, the segment could be either wavelength or period, but the x-axis is labeled as time, which means the segment must be the period.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/55" }, { "Question": "In the figure above, the coefficient of sliding friction between the small block and the tabletop is 0.2. If the pulley is frictionless and massless, what will be the acceleration of the blocks once they are released from rest? \n \n \n A. 0.5g \n B. 0.6g \n C. 0.7g \n D. 0.8g", "Answer (final answer highlighted)": "C: The net force on the two-block system is $3mg - F_f$, where $F_f$ is the magnitude of the frictional force acting on the small block. Since $F_f = \\mu mg$, we find that\n\n\\[ a = \\frac{F_{\\text{net}}}{\\text{total mass}} = \\frac{3mg - 0.2mg}{m + 3m} = \\frac{2.8mg}{4m} = 0.7g \\]", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/56" }, { "Question": "The graphs above show the changes in speed for two different blocks. The left graph shows the speed over time of Block 1, which has a mass of m1, and the right graph shows the speed of Block 2, which has a mass of 2m1. While speeding up, they both had to overcome some frictional force, f. Which of the two blocks had more power provided to it? \n \n \n A. Block 1 \n B. Block 2 \n C. They had equal power provided. \n D. It depends on the ratio of m/f.", "Answer (final answer highlighted)": "A: Both objects started at rest, so finding their final kinetic energies will give the changes in kinetic energy for each block.\n\n\\[ K_1 = \\frac{1}{2} m_1 v_1^2 \\]\n\\[ K_1 = \\frac{1}{2} m_1 (10 \\text{ m/s})^2 \\]\n\\[ K_1 = 50 m_1 \\text{ J} \\]\n\n\\[ K_2 = \\frac{1}{2} m_2 v_2^2 \\]\n\\[ K_2 = \\frac{1}{2} (2 m_1)(5 \\text{ m/s})^2 \\]\n\\[ K_2 = 25 m_1 \\text{ J} \\]\n\nThe Work-Energy Theorem tells us that change in kinetic energy is equal to work, so Block 1 had more work done to it. Because both blocks were affected for the same time period, that means Block 1 also had more power provided.\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/57" }, { "Question": "The figure above shows a plane diagram. The figure shows four point charges arranged at the corners of a square with point B as its center. A positive charge would experience no net force if it were placed at which of the three points shown in the figure? \n \n \n A. A only \n B. B only \n C. C only \n D. A, B, or C", "Answer (final answer highlighted)": "B: A point charge placed at point A, B, or C would experience no net force only if the electric field at the point were zero. Let's label the four charges 1, 2, 3, and 4, starting at the upper right and counting counterclockwise. The diagram below shows the identical electric field vectors at points A, B, and C due to the four charges. Only at point B do the four electric field vectors cancel each other to give a sum of zero, so only at point B would a charge feel zero net force.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/58" }, { "Question": "If the rod in the figure above is uniform and has mass m, what is the tension in the supporting string? The rod is free to rotate about point P. \n \n \n A. $ \\frac{1}{2} mg \\sin \\theta $\n B. $ mg \\sin \\theta $\n C. $ \\frac{1}{2} mg \\cos \\theta $\n D. $ \\frac{1}{2} mg $", "Answer (final answer highlighted)": "D: With respect to the point at which the rod is attached to the vertical wall, the tension in the string exerts a counterclockwise (CCW) torque, and the gravitational force\u2014which acts at the rod's center of mass\u2014exerts a clockwise (CW) torque. If the rod is in equilibrium, these torques must balance. Letting \\( L \\) denote the length of the rod, this gives\n\n\\[ T_{\\text{CCW}} = T_{\\text{CW}} \\]\n\\[ F_T L \\sin \\theta = \\left( \\frac{1}{2} L \\right) (mg) \\sin \\theta \\]\n\\[ F_T = \\frac{1}{2} mg \\]\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/59" }, { "Question": "In the diagram above, a positive charge and negative charge are placed at y = -2 and y = 3, respectively. If the negative charge has a greater magnitude, then the only place of 0 net electric field would be \n \n \n A. Along the positive x-axis \n B. Along the negative x-axis \n C. Along the positive y-axis \n D. Along the negative y-axis", "Answer (final answer highlighted)": "D: Remember that the electric field for any given particle will point toward a negative charge and away from a positive charge. Anywhere between the two charges here (regardless of x-coordinate) would have an electric field that pointed up. The negative charge would pull it up, and the positive one would push it up. This eliminates (A) and (B). Finally, the negative charge is greater magnitude. Therefore, the fields could only be in balance somewhere closer to the positive charge. This eliminates (C)", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/60" }, { "Question": "A simple pendulum executes simple harmonic motion as it swings through small angles of oscillation. If \u00ce\u00b8max denotes the amplitude of the oscillations, which of the following statements is true? \n \n \n A. When $\\theta$ = 0, the tangential acceleration is 0. \n B. When $\\theta$ = $\\theta_{max}$ , the tangential acceleration is 0. \n C. When $\\theta$ = 0, the speed is 0. \n D. When $\\theta$ = 0, the restoring force is maximized.", "Answer (final answer highlighted)": "A: At the instant a simple harmonic oscillator passes through equilibrium, the restoring force is zero. Therefore, the tangential acceleration of the pendulum is also zero.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/61" }, { "Question": "In the graph above, the instantaneous velocity at 9 seconds is closest to \n \n \n A. 4/9 m/s \n B. -4/9 m/s \n C. 11/4 m/s \n D. -11/4 m/s", "Answer (final answer highlighted)": "D: The slope of the tangent line gives the instantaneous velocity. You could also use Process of Elimination. Recognize the answer must be negative, so you can eliminate (A) and (C). The point in question is (9, 4). Dividing the y-coordinate by the x-coordinate is not the same as the obtaining the slope and is there to distract you.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/62" }, { "Question": "Two charges are placed as shown at the vertices of an equilateral triangle. What is the direction of the electric field at point P? \n \n \n A. a \n B. b \n C. c \n D. d", "Answer (final answer highlighted)": "D: The two electric fields vectors are shown. The resultant can be determined as shown below. https://img.crackap.com/ap/physics-1/cr2017/00143.jpg ", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/63" }, { "Question": "If a charge of +q is placed at point P, the electric field at point P would \n \n \n A. increase by 1/3\n B. increase by 1/2 \n C. decrease by 1/3 \n D. remain the same", "Answer (final answer highlighted)": "D: Charges do not create an electric field at the location of the charge itself. Therefore, the electric field at point p is not changed by the addition of a charge at point p.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/64" }, { "Question": "A tube with one end closed and one end open resonates for a wave with wavelength \u00ce\u00bba as shown. The next shorter wavelength at which resonance will occur is \u00ce\u00bbb. The ratio of these two wavelengths \u00ce\u00bba/\u00ce\u00bbb is \n \n \n A. 1/4\n B. 1/3\n C. 3/5\n D. 5/3", "Answer (final answer highlighted)": "D: Resonance occurs at \\(\\lambda = \\frac{4L}{n}\\) for odd integers. This means at \\(4L\\), \\(\\frac{4L}{3}\\), \\(\\frac{4L}{5}\\), ...\n\nWe are shown a picture where a wave is in a tube of length \\(L\\). This means \\(\\lambda_a = \\frac{4L}{3}\\). The next shorter wavelength is \\(\\lambda_b = \\frac{4L}{5}\\). The ratio of these is \\(\\frac{\\lambda_a}{\\lambda_b}\\) or \\(\\frac{5}{3}\\).\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/65" }, { "Question": "If R1 were to burn out, the current coming out from the battery would \n \n \n A. increase \n B. decrease \n C. stay the same \n D. there is no current, because the circuit is now incomplete", "Answer (final answer highlighted)": "B: If R1 were to burn out, the total resistance in the circuit would increase. Because I = V/R this increase in resistance would decrease the current.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/66" }, { "Question": "A Wheatstone bridge (diagram above) is a configuration of resistors and a sensitive current meter, called a galvanometer, that is used to determine the resistance of an unknown resistor. In the Wheatstone bridge shown here, find the value of Rx such that the current through galvanometer G is zero. \n \n \n A. $25 \\Omega$\n B. $15 \\Omega$\n C. $10 \\Omega$\n D. $2.5 \\Omega$", "Answer (final answer highlighted)": "D: The question specifies that the current through G must be 0. Recall that in parallel circuits current will distribute itself in a manner inversely proportional to the resistance in each path. Looking at the left-hand side of the configuration, we see that the resistance on the top is half the resistance of the bottom. That means the current will distribute itself with 2/3 along the top path and 1/3 along the bottom path. For no current to pass through G, this same distribution must also be true on the right-hand side, otherwise some current would pass through G to correct any changes to the relative resistances. The 5 \u03a9 resistor must have the same proportional resistance to the unknown resistor that the 20 \u03a9 resistor has to the 10 \u03a9 resistor. Therefore, the unknown must be 2.5 \u03a9.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/67" }, { "Question": "In the figure above, four charges are arranged. If the magnitudes of all the charges q are all the same and the distance R between them is as shown above, what is the magnitude of the net force on the bottom right charge in terms of q, R, and k (where )? \n \n \n A. $ k \\left( \\frac{q^2}{2r^2} \\right) (1 + \\sqrt{2}) $\n B. $ k \\left( \\frac{q^2}{r^2} \\right) (1 + \\sqrt{2}) $\n C. $ k \\left( \\frac{q^2}{2r'^2} \\right) $\n D. $ k \\left( \\frac{q^2}{r'^2} \\right) $", "Answer (final answer highlighted)": "A: Although we do not care about the direction of our net vector in the end, we do have to take orientation into account to find our magnitude. Numbering our charges from the top left and going clockwise as 1, 2, 3, and 4. Drawing out our different forces on the bottom right charge (charge 3), we get: https://img.crackap.com/ap/physics-1/cr2017/00138.jpg Now solve each of these force vectors\n\n\\[ F_{4 \\text{ on } 3} = \\frac{kq^2}{r^2} \\]\n\\[ F_{2 \\text{ on } 3} = \\frac{kq^2}{r^2} \\]\n\nThese two are the simpler force vectors to solve. In order to solve the charge 1's force on charge 3 our distance first needs to be solved. Because they are ordered in a square using a diagonal creates a 45\u00b0-45\u00b0-90\u00b0 triangle. The distance in this case is \\( r\\sqrt{2} \\). So,\n\n\\[ F_{1 \\text{ on } 3} = \\frac{kq^2}{(r\\sqrt{2})^2} = \\frac{kq^2}{2r^2} \\]\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/68" }, { "Question": "Which of the following correctly ranks the change in kinetic energy for each segment from least to greatest? \n \n \n A. BC, EF, DE, CD, AB \n B. AB, CD, DE, EF, BC \n C. BC, EF, DE, CD, AB \n D. CD, DE, EF, BC, AB", "Answer (final answer highlighted)": "D: Mass is not changing, so we only need to consider the changes in velocity. For each segment in order, the change in velocity is +7 m/s, 0 m/s, \u20134 m/s, \u20133 m/s, and \u20132 m/s. The question does not specify magnitude only, so all negatives will come before the others.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/69" }, { "Question": "During which segment is the magnitude of average acceleration greatest? \n \n \n A. AB \n B. BC \n C. CD \n D. DE", "Answer (final answer highlighted)": "C: Acceleration is the change in velocity divided by the change in time. We found the changes in velocity for each segment in the previous question, and the times for each segment are, in order, 3 s, 2 s, 1 s, 3 s, and 2 s. Divide the results in the previous question by these values, and the highest result (ignoring sign because the problem specifies magnitude only) is for segment CD.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/70" }, { "Question": "What is the total distance traveled by the object? \n \n \n A. 32 m \n B. 34 m \n C. 36 m \n D. 38 m", "Answer (final answer highlighted)": "C: In a velocity vs. time graph, displacement is the area beneath the curve. If the question had asked for displacement, then anything beneath the x-axis would be added as a negative displacement. However, distance cannot be negative, so there is no distinction between positive and negative velocity for this question.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/71" }, { "Question": "Consider the above configuration of masses attached via a massless rope and pulley over a frictionless inclined plane. What is the acceleration of the masses? \n \n \n A. (m1- m2) g/(m1+ m2) \n B. (m1- m2sin\u00ce\u00b8) g/(m1+ m2) \n C. (m1- m2cos\u00ce\u00b8) g/(m1+ m2) \n D. g", "Answer (final answer highlighted)": "B: By Process of Elimination, we know we need a sine in the equation for the downward pull of the second mass down the incline of the plane, so the answer is (B).", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/72" }, { "Question": "In the figure above, two blocks of mass 3m and 2m are attached together. The plane is frictionless and the pulley is frictionless and massless. The inclined portion of the plane creates an angle \u00ce\u00b8 with the horizontal floor. What is the acceleration of the block 2m if both blocks are released from rest (gravity = g)? \n \n \n A. $ 2mg $\n B. $ \\frac{2}{5} g \\sin \\theta $\n C. $ \\frac{2}{3} g \\sin \\theta $\n D. $ \\frac{3}{5} g \\sin \\theta $", "Answer (final answer highlighted)": "B: Because all the masses are attached and moving as a single unit, the acceleration of any block in the system is the same as that of any other. The net force on the blocks is \\( F_{\\text{net}} = (2M)g \\sin \\theta \\). Therefore,\n\n\\[ F_{\\text{net}} = ma \\rightarrow (5M)a = (2M)g \\sin \\theta = \\left(\\frac{2}{5}\\right) g \\sin \\theta \\]\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/73" }, { "Question": "The diagram above shows a top view of an object of mass m on a circular platform of mass 2m that is rotating counterclockwise. Assume the platform rotates without friction. Which of the following best describes an action by the object that will increase the angular speed of the entire system? \n \n \n A. The object moves toward the center of the platform, increasing the total angular momentum of the system. \n B. The object moves toward the center of the platform, decreasing the rotational inertia of the system. \n C. The object moves away from the center of the platform, increasing the total angular momentum of the system. \n D. The object moves away from the center of the platform, decreasing the rotational inertia of the system.", "Answer (final answer highlighted)": "B: The only true statement in regards to rotational motion is (B). A mass that has greater inertia is harder to rotate. The further away the mass is from the axis of rotation, the greater the rotational inertia will be. So, when the object moves toward the center of rotation, rotational inertia is\ndecreased.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/74" }, { "Question": "A moon has an elliptical orbit about the planet as shown above. At point A, the moon has speed vA and is at a distance rA from the planet. At point B, the moon has a speed of vB. Which of the following correctly explains the method for determining the distance of the moon from the planet at point B in the given quantities? \n \n \n A. Conservation of angular momentum, because the gravitational force exerted by the moon on the planet is the same as that exerted by the planet on the moon \n B. Conservation of angular momentum, because the gravitational force exerted on the moon is always directed toward the planet \n C. Conservation of energy, because the gravitational force exerted on the moon is always directed toward the planet \n D. Conservation of energy, because the gravitational force exerted by the moon on the planet is the same as that exerted by the planet on the moon", "Answer (final answer highlighted)": "A: By Newton's Third Law, the gravitational force exerted by the planet on the moon will equal the gravitational force exerted by the moon on the planet (eliminate (B) and (C)). Between Conservation of Angular Momentum and Conservation of Energy, the correct one to use to help us find distance is Conservation of Angular Momentum. Conservation of Energy will help us find the speed of the moon. Conservation of Angular Momentum will help us find the distance of the moon from the planet.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/75" }, { "Question": "In the diagram above, a mass m starting at point A is projected with the same initial horizontal velocity v0 along each of the three tracks shown here (with negligible friction) sufficient in each case to allow the mass to reach the end of the track at point B. (Path 1 is directed up, path 2 is directed horizontal, and path 3 is directed down.) The masses remain in contact with the tracks throughout their motions. The displacement A to B is the same in each case, and the total path length of path 1 and 3 are equal. If t1,t2, and t3 are the total travel times between A and B for paths 1, 2, and 3, respectively, what is the relation among these times? \n \n A. t3 < t2 < t1 \n B. t2 < t3 < t1 \n C. t2 < t1 = t3 \n D. t2 = t3 < t1", "Answer (final answer highlighted)": "A: All the masses begin with the same speed v0. For Path 1, the object must climb up which would decrease its speed, then come back down to reach its same initial speed. During this time, the speed is always below the initial speed. For Path 2, the object maintains the same initial speed the whole time. For Path 3, the object speeds up as it goes down the path and then slows down back to its initial speed when it climbs. During this time, the speed is always above the initial speed. If we compare the average speed, v3> v2> v1, hence t3< t2< t1.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/76" }, { "Question": "The graph above shows the velocities of two objects undergoing a head-on collision. Given that Object 1 has 4 times the mass of Object 2, which type of collision is it? \n \n \n A. Perfectly elastic \n B. Perfectly inelastic \n C. Inelastic \n D. Cannot be determined", "Answer (final answer highlighted)": "A: First, perfectly inelastic can be immediately eliminated because the objects have different velocities after the collision. Next, recall that a collision is perfectly elastic if kinetic energy is conserved.\n\n\\[ K_0 = K_f \\]\n\\[ \\frac{1}{2} m_{1,0} v_{1,0}^2 + \\frac{1}{2} m_{2,0} v_{2,0}^2 = \\frac{1}{2} m_{1,f} v_{1,f}^2 + \\frac{1}{2} m_{2,f} v_{2,f}^2 \\]\n\\[ \\frac{1}{2} m_1 (6 \\text{ m/s})^2 + \\frac{1}{2} (4 m_1)(1 \\text{ m/s})^2 = 20 m_1 \\text{ J} = 20 m_1 \\text{ J} \\]\n\nBecause kinetic energy was conserved, the collision must be perfectly elastic.\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/77" }, { "Question": "Determine the total power dissipated through the circuit shown above in terms of v, R1, R2, and R3. \n \n \n A. $ \\frac{V^2}{R_1 + R_2 + R_3} $\n B. $ \\frac{R_1 + R_2 + R_3}{V^2} $\n C. $ \\frac{R_1 (R_2 + R_3)}{V^2 (R_1 + R_2 + R_3)} $\n D. $ \\frac{V^2 (R_1 + R_2 + R_3)}{R_1 (R_2 + R_3)} $", "Answer (final answer highlighted)": "D: First, we will need to replace all the resistors with an equivalent resistor.\n\n\\[ R_2 \\text{ and } R_3 \\text{ are in series, so } R_{2 \\text{ and } 3} = R_2 + R_3. \\]\n\n\\[ R_1 \\text{ and } R_{2 \\text{ and } 3} \\text{ are in parallel, so } \\frac{1}{R_{\\text{eq}}} = \\frac{1}{R_1} + \\frac{1}{R_{2} + R_{3}} \\text{ or } R_{\\text{eq}} = \\frac{R_1 (R_2 + R_3)}{R_1 + R_2 + R_3}. \\]\n\nSecond, we need to calculate the current coming out of the battery,\n\n\\[ I_{\\text{total}} = \\frac{V}{R_{\\text{eq}}} = \\frac{V}{\\frac{R_1 (R_2 + R_3)}{R_1 + R_2 + R_3}}. \\]\n\nFinally, we calculate the power,\n\n\\[ P = IV = \\left( \\frac{V^2 (R_1 + R_2 + R_3)}{R_1 (R_2 + R_3)} \\right). \\]\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/78" }, { "Question": "If v = 100 V, R1 = 50 \u00ce\u00a9, R2 = 80 \u00ce\u00a9 and R3 = 120 \u00ce\u00a9, determine the voltage across R3. \n \n \n A. 100 V \n B. 60 V \n C. 40 V \n D. 20 V", "Answer (final answer highlighted)": "B: Because R1 and R2 and R3 are in parallel, the voltage across each matches the battery of 100 V. Using what we solved from problem 39 and our knowledge that current splits off in parallel, to calculate the current going into R2 and R3 we use\n\nI = V/R = V/R2 and 3 = V/(R2 + R3) = (100 V)/(80 \u03a9 + 120 \u03a9) = (100 V)/(200 \u03a9) = 0.5 A\n\nNow that we know the current going into this branch of the parallel circuit, we know that R2 and R3 are in series, and in series the current remains the same. So the current going across R3 is 0.5 A. Using this we can calculate the voltage going across R3,\n\nV3 = I3R3 = (0.5 A)(120 \u03a9) = 60 V", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/79" }, { "Question": "Question below refers to the following information:A rigid rod of length L and mass M sits at rest on an air table with negligible friction. A small blob of putty with a mass of m moves to the right on the same table, as shown in overhead view in the figure. The putty hits and sticks to the rod, a distance of 2L/3 from the top end.How will the rod-putty system move after the collision? \n \n \n A. The system will have no translational motion, but it will rotate about the rod\u2019s center of mass. \n B. The system will move to the right and rotate about the rod-putty system\u2019s center of mass. \n C. The system will move to the right and rotate about the rod\u2019s center of mass. \n D. The system will have no translational motion, but it will rotate about the rod-putty system\u2019s center of mass.", "Answer (final answer highlighted)": "B: Conservation of linear momentum requires that the center of mass of the system continue to move to the right after the collision. The rotation will be about the combined rod-putty center of mass. To understand that, imagine if the putty were really heavy. Then after the collision, the rod would seem to rotate about the putty, because the center of mass of the rod-putty system would be essentially at the putty's location. In this case, you don't know whether the putty or the rod is more massive, but you do know that when the two objects stick together, they will rotate about wherever their combined center of mass is located.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/80" }, { "Question": "Question below refers to the following information:A rigid rod of length L and mass M sits at rest on an air table with negligible friction. A small blob of putty with a mass of m moves to the right on the same table, as shown in overhead view in the figure. The putty hits and sticks to the rod, a distance of 2L/3 from the top end.What quantities, if any, must be conserved in this collision? \n \n \n A. Linear momentum only \n B. Neither linear nor angular momentum \n C. Angular momentum only \n D. Linear and angular momentum", "Answer (final answer highlighted)": "D: No unbalanced forces act here other than the putty on the rod and the rod on the putty. (The weight of these objects is canceled by the normal force.) Thus, linear momentum is conserved. No torques act on the rod-putty system except those due to each other; thus, angular momentum is conserved. It's essentially a fact of physics that in a collision between two objects, both linear and angular momentum must be conserved.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/81" }, { "Question": "Bob and Tom hold a rod with a length of 8 m and weight of 500 N. Initially, Bob and Tom each hold the rod 2 m from the its ends, as shown in the figure. Next, Tom moves slowly toward the right edge of the rod, maintaining his hold. As Tom moves to the right, what happens to the torque about the rod\u2019s midpoint exerted by each person? \n \n \n A. Bob\u2019s torque decreases, and Tom\u2019s torque increases. \n B. Bob\u2019s torque increases, and Tom\u2019s torque decreases. \n C. Both Bob\u2019s and Tom\u2019s torque increases. \n D. Both Bob\u2019s and Tom\u2019s torque decreases.", "Answer (final answer highlighted)": "C: The net torque on the rod must be zero, because the rod doesn't rotate. Therefore, whatever happens to Bob's torque must also happen to Tom's torque-these torques must cancel each other out. That eliminates choices A and B. The forces provided by Bob and Tom must add up to 500 N, the weight of the rod. Try doing two quick calculations: In the original case, Bob and Tom must each bear 250 N of weight and are each 2 m from the midpoint, for 500 N\u00b7m of torque each. Now put Tom farther from the midpoint-say, 3 m away. For the torques to balance, Fbob(2 m) = Ftom(3 m). The only way to satisfy this equation and get both forces to add up to 500 N is to use 300 N for Fbob and 200 N for Ftom. Now, the torque provided by each is (300 N)(2 m) = 600 N\u00b7m. ", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/82" }, { "Question": "An object of mass m hangs from two ropes at unequal angles, as shown in the figure. Which of the following makes correct comparisons between the horizontal and vertical components of the tension in each rope? \n \n \n A. Horizontal tension is equal in both ropes, but vertical tension is greater in rope A. \n B. Both horizontal and vertical tension are equal in both ropes \n C. Horizontal tension is greater in rope B, but vertical tension is equal in both ropes. \n D. Both horizontal and vertical tension are greater in rope B", "Answer (final answer highlighted)": "A: The object is in equilibrium, so left forces equal right forces. Thus, the horizontal tensions must be the same in each rope. Rope A pulls at a steeper angle than rope B, but with the same amount of horizontal force as rope B. To get to that steeper angle, the vertical component of the tension in rope A must be larger than in rope B.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/83" }, { "Question": "Question below refers to the following information:Block B is at rest on a smooth tabletop. It is attached to a long spring, which in turn is anchored to the wall. Identical block A slides toward and collides with block \n \n \n B. Consider two collisions, each of which occupies a duration of about 0.10 s:Collision I: Block A bounces back off of block B.Collision II: Block A sticks to block B.In which collision, if either, does block B move faster immediately after the collision? \n A. In collision I, because block A experiences a larger change in momentum, and conservation of momentum requires that block B does as well. \n B. In collision I, because block A experiences a larger change in kinetic energy, and conservation of energy requires that block B does as well. \n C. In neither collision, because conservation of momentum requires that both blocks must have the same momentum as each other in each collision. \n D. In neither collision, because conservation of momentum requires that both blocks must change their momentum by the same amount in each collision.", "Answer (final answer highlighted)": "A: There's no indication that energy must be conserved in collision 1. However, momentum is always conserved in a collision. When block A bounces, its momentum has to change to zero and then change even more to go back the other way. Since block A changes momentum by more in collision I, block B must as well because conservation means that any momentum change by block A must be picked up by block B. Choices C and D are wrong because, among other things, they use conservation of momentum to draw conclusions about two separate collisions; momentum conservation means that total momentum remains the same before and after a single collision, not in all possible collisions.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/84" }, { "Question": "If two people pull with a force of 1000 N each on opposite ends of a rope and neither person moves, what is the magnitude of tension in the rope? \n \n\n A. 0 N \n B. 500 N \n C. 1000 N \n D. 2000 N", "Answer (final answer highlighted)": "C: Just focus on one end of the rope. Nothing is moving, so the net force must be 0. If a person pulls with a force of 1000 N and nothing moves, then the resulting tension must also be 1000 N. Additionally, tension is a constant magnitude throughout a string. The direction of the tension can change (as in the case of a pulley system), but the magnitude will remain the same.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/85" }, { "Question": "Two identical blocks are stacked on top of each other and placed on a table. To overcome the force of static friction, a force of 10 N is required. If the blocks were placed side by side and pushed as shown in the figure above, how much force would be required to move them? \n \n\n A. $\\frac{10 \\sqrt{2}}{2 \\mathrm{~N}}$\n B. 10 N \n C. $10 \\sqrt{2} \\mathrm{~N}$\n D. 20 N", "Answer (final answer highlighted)": "B: The force of static friction will be $F_f=\\mu F_N=\\mu(m g)$. Changing the arrangement of the blocks does not change any of these three quantities, so the force will remain the same. Thus, $10 \\mathrm{~N}$ will again be required to move them.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/86" }, { "Question": "A block of known mass M is connected to a horizontal spring that is sliding along a flat, frictionless surface. There is an additional block of known mass m resting on top of the first block. Which of the following quantities would NOT be needed to determine whether the top block will slide off the bottom block? \n \n\n A. The maximum coefficient of static friction between the blocks \n B. The amplitude of the system's motion \n C. The spring constant \n D. The average speed of the blocks", "Answer (final answer highlighted)": "D: It's easiest to consider both blocks as one system, calculate the maximum acceleration of the pair of blocks caused by the spring (which occurs at maximum displacement from equilibrium), and determine whether friction between the two block is strong enough to give the top block the necessary acceleration to keep up with the bottom block. Applying Newton's Second Law to the system of blocks, $F_{\\text {spring }}=$ (combined mass) ${ }^* a$ $\\rightarrow k A=(M+m) a$. In order for the top block to accelerate at this rate, static friction must be strong enough that $F_{\\mathrm{sf}}=m a \\rightarrow \\mu \\mathrm{s} F \\mathrm{~N}=m a$. You don't need to do any math to see that $\\mu \\mathrm{s}$ (coefficient of static friction), $A$ (amplitude), and $k$ (spring constant) appear, but average speed doesn't.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/87" }, { "Question": "Question below refers to the below circuit diagram.If switch S1 is connected to point A but switch S2 is left unconnected, what is the current through the 1-\u03a9 resistor? \n \n\n A. 0 A \n B. 2 A \n C. 3 A \n D. 72/11 A", "Answer (final answer highlighted)": "B: With $S_1$ closed but $S_2$ open, only the left-hand loop is connected. The resistors are in series, so the equivalent resistance is $R_{\\text {eq }}=2 \\Omega+1 \\Omega+3 \\Omega=6 \\Omega$. The current through the circuits including the $1 \\Omega$ resistor is $I_{\\text {left }}=$ $\\frac{V_{\\text {left }}}{R_{\\text {eq }}}=\\frac{12 \\mathrm{~V}}{6 \\Omega}=2 \\mathrm{~A}$.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/88" }, { "Question": "Question below refers to the below circuit diagram.If switch S2 is connected to point B but switch S1 is left unconnected, what is the current through the 1-\u03a9 resistor? \n \n\n A. 0 A \n B. 2 A \n C. 3 A \n D. 288/19 A", "Answer (final answer highlighted)": "C: With $S_1$ open but $S_2$ closed, only the right-hand loop is connected. Again, the resistors are in series so the equivalent resistances is $R_{\\text {eq }}=4 \\Omega+1 \\Omega+3 \\Omega=8 \\Omega$. The current through the circuit including the $1 \\Omega$, I_{\\text{right}} = \\frac{V_{\\text{right}}}{R_{\\text{eq}}} = \\frac{24\\ V}{8\\ \\Omega} = 3\\ A.\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/89" }, { "Question": "Question below refers to the below circuit diagram.If both switches S1 and S2 are left in the unconnected positions, what is the current through the 1-\u03a9 resistor? \n \n\n A. 0 A \n B. 1 A \n C. 5 A \n D. 36 A", "Answer (final answer highlighted)": "A: If neither switch is connected, then no loop can be made, which means no current will flow.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/90" }, { "Question": "In real projectile motion, an object experiences three forces: gravity, drag, and lift. These are depicted in the picture above. Given this information, how does lift affect the speed of a projectile? \n \n\n A. Increases \n B. Decreases \n C. Varies \n D. It has no effect.", "Answer (final answer highlighted)": "D: Because the lift force is perpendicular to the velocity of the object, lift can have no effect on the magnitude of velocity. The magnitude of velocity is also known as speed, so (D) is correct.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/91" }, { "Question": "The picture above shows a tube open at one end. A standing wave is represented by the dotted curves. If this wave has frequency f, what is the frequency of the next harmonic that can be formed in this tube? \n \n\n A. 1/2 f\n B. 2f \n C. 3f \n D. The above wave shows the highest possible harmonic frequency for this system.", "Answer (final answer highlighted)": "C: Remember that in a system with one closed end and one open end, there will be a node at one end and an antinode at the other. From the drawing, you can see that the tube is the length of 1/4 wavelength of this standing wave. That means that this wave is the fundamental standing wave, also called the first harmonic. As you'll learn on this page, the next harmonic is the third harmonic, and it has 3 times the frequency of the first harmonic.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/92" }, { "Question": "Which of the following correctly describes an electron moving from point A to point B in the situation above? Assume the two regions of charge are identical in magnitude and only different in sign. \n \n\n A. The electron moves with increasing speed and gains electric potential energy. \n B. The electron moves with increasing speed and loses electric potential energy. \n C. The electron moves with decreasing speed and gains electric potential energy. \n D. The electron moves with decreasing speed and loses electric potential energy.", "Answer (final answer highlighted)": "B: An electron is repelled from negative charge and attracted to positive charge, so there are two electric forces on it, both pointing to the right. Thus, as it moves from A to B, the electron's speed increases. This eliminates (C) and (D). As for potential energy: one way to think about it is to realize that an increase in speed implies an increase in kinetic energy. Where does this energy come from? It comes from the potential energy of the system, which decreases by an equal amount.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/93" }, { "Question": "What is the equivalent resistance of the electric circuit in the picture above? \n \n\n A. 0.46 \u03a9 \n B. 1.2 \u03a9 \n C. 4.5 \u03a9 \n D. 14.5 \u03a9", "Answer (final answer highlighted)": "D: Remember that parallel resistors require you to use the reciprocal sum, while series resistors simply add. For example, the first set of parallel resistors would be combined by doing $\\frac{1}{R}=\\frac{1}{1.5}+\\frac{1}{3}=1$, which means $R=1 \\Omega$. For the second set of parallel resistors, you would get $\\frac{1}{R}=\\frac{1}{2}+\\frac{1}{6}=\\frac{4}{6}$, which means $R=1.5 \\Omega$. Adding those two values to the lone series resistor gives $R_{\\text {Total }}=2+1+1.5=4.5 \\Omega$.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/94" }, { "Question": "Escape velocity is defined as the minimum speed at which an object must be launched to \"break free\" from a massive body's gravitational pull. Which of the following principles could be used to derive this speed for a given planet?\n\nA. Conservation of Linear Momentum\nB. Newton's Third Law\nC. Conservation of Angular Momentum\nD. Conservation of Energy", "Answer (final answer highlighted)": "D: If an object leaves a planet at exactly escape velocity, its speed will approach zero as its distance from the planet approaches infinity. Zero speed implies zero KE, and infinite separation implies zero Ug if our reference separation is infinity. Thus, the total mechanical energy of an object traveling at escape velocity is 0 J. That's why conservation of energy is the relevant concept.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/95" }, { "Question": "An ambulance is driving toward you. As it approaches, which of the following correctly describes the changes in the sound of the siren's pitch and intensity? \n \n\n A. Increasing pitch, increasing intensity \n B. Increasing pitch, decreasing intensity \n C. Decreasing pitch, increasing intensity \n D. Decreasing pitch, decreasing intensity", "Answer (final answer highlighted)": "A: The intensity of a wave is proportional to $1 / r^2$, so it will increase as the ambulance approaches. This eliminates (B) and (D). The change in pitch will be determined by the Doppler effect. Pitch is simply another term for frequency, and the Doppler effect says that if the source of a wave and the object detecting the wave are growing closer, then the frequency will increase. Thus, $(\\mathrm{A})$ is correct.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/96" }, { "Question": "The graph above depicts a medium's instantaneous displacement from equilibrium, caused by a wave, as a function of distance from the source. If the wave has a speed of 600 m/s, which of the following is the best approximation of the wave's frequency? \n \n\n A. 50 Hz \n B. 100 Hz \n C. 200 Hz \n D. Cannot be determined without additional information", "Answer (final answer highlighted)": "B: The distance from one crest to another is the wavelength. In this case, that distance is 6 m. Furthermore, you know that v = f\u03bb for any wave. Solving for f gives f = v/\u03bb. Plugging in the known values gives f = (600)/(6) = 100 Hz.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/97" }, { "Question": "Both of the above strings have their ends locked in place. The two strings have the same linear density, but the first string, S1, is twice as long as the second string, S2. If sound waves are going to be sent through both, what is the correct ratio of the fundamental frequency of S1 to the fundamental frequency of S2? \n \n\n A. 2:1 \n B. $\\sqrt{2}: 1$\n C. $1: \\sqrt{2}$\n D. 1:2", "Answer (final answer highlighted)": "D: A wave passing along a string with both ends held in place will have a fundamental frequency of f = v/(2l), where v is the speed of the wave and l is the length of the string. Thus, fundamental frequency is inversely proportional to the length of the string, so the first string, which is twice as long as the second, will have a fundamental frequency that is half of the second string's. Expressed as a ratio, that is 1:2.", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/98" }, { "Question": "A pendulum with a ball of mass m hanging from a string of length l is set in motion on Earth, and the system is found to have a frequency of f. If the length of the string were doubled, the hanging mass tripled, and the system moved to the moon, what would be the new frequency?NOTE: Acceleration due to gravity of the Moon is approximately of Earth's. \n \n\n A. $\\frac{1}{12} f$\n B. $\\sqrt{\\frac{1}{12}} f$\n C. $\\sqrt{12} f$\n D. 12f", "Answer (final answer highlighted)": "B: The frequency of a pendulum is \\( f = \\frac{1}{2\\pi} \\sqrt{\\frac{g}{l}} \\). Therefore, the change in mass would have no effect on the system, and the others would change the equation to \\( f = \\frac{1}{2\\pi} \\sqrt{\\frac{g}{2l}} \\). Thus, the original frequency \\( f \\) will become \\( \\frac{1}{\\sqrt{12}} f \\).\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/99" }, { "Question": "A block of mass M is at rest on a table. It is connected by a string and pulley system to a block of mass m hanging off the edge of the table. Assume the hanging mass is heavy enough to make the resting block move. Knowing the acceleration of the system and the mass of each block is sufficient to calculate all of the following quantities EXCEPT which one? \n \n\n A. Net force on each block \n B. Tension in the string \n C. Coefficient of kinetic friction between the table and the block of mass M \n D. The speed of the block of mass M when it reaches the edge of the table", "Answer (final answer highlighted)": "D: The net force on each block can be found by using Newton's Second Law, \\( F_{\\text{Net}} = ma \\). The tension in the string can be found by focusing on the hanging mass. You know the net force on it will be \\( F_{\\text{Net}} = ma = F_g - T = (mg) - T \\), which means \\( T = (mg) - (ma) \\). Finally, the coefficient of kinetic friction can be found by looking at the top block. For that block, the net force in the horizontal direction will be the same as the overall net force since the two vertical forces (normal and gravity) will cancel out. Thus, you get \\( F_{\\text{Net}} = ma = T - F_f = T - \\mu F_N = T - \\mu mg \\). The only value in the answers you cannot calculate is the speed of the block when it reaches the edge. In order to compute this value, you would need to know how far from the edge the block is when it begins moving.\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/100" }, { "Question": "A block of mass m is connected by a string which runs over a frictionless pulley to a heavier block of mass M. The smaller block rests on an inclined plane of angle \u03b8, and the larger block hangs over the edge, as shown above. In order to prevent the blocks from moving, the coefficient of static friction must be \n \n\n A. $\\frac{mgsin\\theta}{Mg-mg\\cos\\theta}$\n B. $\\frac{Mg-mgsin\\theta}{Mg\\cos\\theta}$\n C. $\\frac{Mg-mgsin\\theta}{mg\\cos\\theta}$\n D. $\\frac{Mg-mg\\cos\\theta}{mg\\sin\\theta}$", "Answer (final answer highlighted)": "C: If nothing is moving, then you know that the net force will be 0. Looking first at the forces perpendicular to the plane, you get \\( F_N = F_g \\cos\\theta = mg\\cos\\theta \\). Next, using Newton's Second Law and defining 'up the ramp' as positive, you can say \\( F_{\\text{Net}} = T - F_g \\sin\\theta - F_f = 0 \\). Solving for tension and plugging in all the variables gives you \\( T = mgsin\\theta + \\mu mg\\cos\\theta \\).\n\nNext, looking at the hanging block, you can again use Newton's Second Law to determine that \\( F_{\\text{Net}} = F_g - T = Mg - (mgsin\\theta + \\mu mg\\cos\\theta) = 0 \\). Thus, solving for \\(\\mu\\) gives you \\(\\mu = \\frac{Mg - mgsin\\theta}{mg\\cos\\theta}\\).\n", "Contributor": "\ud83c\udf4a", "ImagePath": "Physics/101" }, { "Question": "A comet orbits the Sun in a periodic elliptical orbit as shown below:A comet orbits the Sun in a periodic elliptical orbit as shown below:\nA comet orbits the Sun in a periodic elliptical orbit as shown below:What happens to the gravitational potential energy and the kinetic energy, respectively, of the comet-Sun system as the comet moves from point A to point B?\nA comet orbits the Sun in a periodic elliptical orbit as shown below:Ug \u00a0\u00a0\u00a0\u00a0 K\nA. Increases \u00a0\u00a0\u00a0\u00a0 Increases\nB. Decreases \u00a0\u00a0\u00a0\u00a0 Decreases\nC. Increases \u00a0\u00a0\u00a0\u00a0 Decreases\nD. Decreases \u00a0\u00a0\u00a0\u00a0 Increases\n", "Answer (final answer highlighted)": "(D) As the comet moves toward the Sun, the gravitational potential energy, https://img.apstudy.net/ap/physics-1/a500/Ans_466.jpg decreases (becomes more negative) as the radial distance r, from the Sun decreases. Since there is no net force on the comet-Sun system, its mechanical energy must remain constant. Thus, with the gravitational potential energy decreasing, the kinetic energy must increase.", "ImagePath": "Physics/102" }, { "Question": "A comet orbits the Sun in a periodic elliptical orbit as shown below:A comet orbits the Sun in a periodic elliptical orbit as shown below:\nA comet orbits the Sun in a periodic elliptical orbit as shown below:As the comet moves from point A to point B, what happens to the comet's angular momentum about the Sun?\nA. Increases linearly\nB. Increases proportionally to the square of the distance from the Sun\nC. Decreases\nD. Stays constant\n", "Answer (final answer highlighted)": "(D) The gravitational force from the Sun is the only force acting on the comet. Since this force is pointed directly at the Sun, it will not have a lever arm to apply a net torque to the comet system about the Sun. With zero net torque on the comet, its angular momentum must stay constant for angular momentum to be conserved.", "ImagePath": "Physics/103" }, { "Question": "\nFour identical rods shown above experience the forces as shown. Rank the magnitude of the torques about the pivot point on the left end of the rod.\nA. III > I = IV > II\nB. II > IV > III > I\nC. I = III = IV > II\nD. III > II > I > IV\n", "Answer (final answer highlighted)": "(C) Torque is calculated by https://img.apstudy.net/ap/physics-1/a500/Ans_461_1.jpg Assuming the rod length L, the individual torques are calculated as follows: https://img.apstudy.net/ap/physics-1/a500/Ans_461_2.jpg The rank is as follows: https://img.apstudy.net/ap/physics-1/a500/Ans_461_3.jpg", "ImagePath": "Physics/104" }, { "Question": "The diagram below shows a top-view of a rod that is free to rotate about its center and is initially rotating with a positive counter-clockwise angular velocity. Two forces are applied to the rod that are steady in magnitude and will continue to act perpendicular to the rod, even after it rotates.The diagram below shows a top-view of a rod that is free to rotate about its center and is initially rotating with a positive counter-clockwise angular velocity. Two forces are applied to the rod that are steady in magnitude and will continue to act perpendicular to the rod, even after it rotates.\nThe diagram below shows a top-view of a rod that is free to rotate about its center and is initially rotating with a positive counter-clockwise angular velocity. Two forces are applied to the rod that are steady in magnitude and will continue to act perpendicular to the rod, even after it rotates.What value of the unknown downward force will result in a constant angular velocity of the rod?\nA. F\nB. F/2\nC. 2F\nD. 4F\n", "Answer (final answer highlighted)": "(C) In order for angular velocity to be constant, there must be zero net torque on the rod: https://img.apstudy.net/ap/physics-1/a500/Ans_452.jpg", "ImagePath": "Physics/105" }, { "Question": "\nThe figure above shows four identically shaped disks, each with a fixed axis of rotation at their centers. Disk IV has twice the rotational inertia of disks I, II, and III. The disks are subjected to a variety of forces as shown. Rank the magnitude of the angular acceleration of the disks.\nA. III > II = IV > I\nB. I = II = III = IV\nC. II = IV > I = III\nD. II > I = III = IV\n", "Answer (final answer highlighted)": "(D) Angular acceleration is the ratio of net torque to rotational inertia: https://img.apstudy.net/ap/physics-1/a500/Ans_446_1.jpg . Assume the forces act at a distance R from the axis of rotation. https://img.apstudy.net/ap/physics-1/a500/Ans_446_2.jpg https://img.apstudy.net/ap/physics-1/a500/Ans_446_3.jpg", "ImagePath": "Physics/106" }, { "Question": "Questions below are based on the following figure of a mass-spring system. Assume the mass is pulled back to position +A and released, and it slides back and forth without friction.At what position does the mass have the greatest acceleration?\nA. -A\nB. -A/2\nC. 0\nD. +A/2\n", "Answer (final answer highlighted)": "(A) At position -A and +A, the compression/extension of the spring is the greatest distance from equilibrium, giving the largest magnitude of force. This force at position -A is to the right (the positive direction) and yields the largest positive net force. Thus, acceleration, the ratio of net force to mass, is at a maximum at this position.", "ImagePath": "Physics/107" }, { "Question": "Questions below are based on the following figure of a mass-spring system. Assume the mass is pulled back to position +A and released, and it slides back and forth without friction.When the mass reaches position 0, what can be said about its speed?\nA. It is at its minimum.\nB. It is at its maximum.\nC. It is zero.\nD. It is decreasing.\n", "Answer (final answer highlighted)": "(B) As the mass passes through equilibrium, it has accelerated to its maximum speed.", "ImagePath": "Physics/108" }, { "Question": "\nIn the physics lab, a hooked mass is hung from a string as shown above. A photogate is set up at the bottom of the swing that provides a signal to the computer when and infrared beam (represented by the dashed line on the diagram) is blocked or unblocked by the hooked mass. How can the photogate signal be used to measure the oscillation period of the swing of the hooked mass?\nA. Divide the diameter of the hooked mass by the elapsed time between when the beam is blocked and subsequently unblocked.\nB. Measure the elapsed time between when the beam is blocked and subsequently unblocked.\nC. Measure the elapsed time between when the beam is blocked and subsequently blocked again.\nD. Double the elapsed time between when the beam is blocked and subsequently blocked again.\n", "Answer (final answer highlighted)": "(D) The period of a pendulum is defined as the time for one complete back and forth swing. When the hooked mass gets to the bottom of the swing, the clock will start when the beam gets blocked. If the clock is turned off the next time the bob blocks the beam, it has only swung through half the swing. Thus, the period may be calculated by doubling the elapsed time between when the beam is blocked and subsequently blocked again.", "ImagePath": "Physics/109" }, { "Question": "\nA spring-mass system hangs on a ring stand that rests on top of a cabinet as shown in the diagram above. The cabinet houses the air compressor for a physics lab. The compressor shakes the ring stand 0.2 cm up and down at a rate of 6 vibrations per second. Which of the following is a true statement?\nA. The maximum vibration amplitude of the spring-mass system is 0.2 cm.\nB. The spring-mass system will only vibrate for very high values of the spring constant.\nC. The spring-mass system may vibrate with an amplitude considerably greater than 0.2 cm.\nD. The spring-mass system will vibrate wildly if it has a natural frequency of 12 vibrations per second.\n", "Answer (final answer highlighted)": "(C) Resonance is a dramatic growth in vibration amplitude that occurs when a system is forced to vibrate at its natural frequency. The natural frequency of a spring-mass system depends on its mass and the spring constant. If the natural frequency of the spring mass system is 6 Hz, then it will resonate with amplitudes considerably greater than 0.2 cm.", "ImagePath": "Physics/110" }, { "Question": "\nThe graph shows the displacement versus time for an object. Which equation best describes its displacement in meters?\nA. \u00ce\u0094x = 20 cos(0.5t)\nB. \u00ce\u0094x = 10 cos(2t)\nC. \u00ce\u0094x = 10 cos(\u00cf\u0080t)\nD. \u00ce\u0094x = 20 sin(\u00cf\u0080t)\n", "Answer (final answer highlighted)": "(C) The general equation for this oscillation is \u00ce\u0094x = A cos(2\u00cf\u0080f t), where A is the amplitude and f is the frequency of vibration. According to the graph, a complete cycle occurs every 2 s which is a frequency of 0.5 cycles per second. The graph also shows an amplitude of vibration of 10 m. This gives the following equation: \u00ce\u0094x = 10 cos(\u00cf\u0080t).", "ImagePath": "Physics/111" }, { "Question": "\nAn isolated, stationary sphere of mass 4m explodes into three fragments as shown in the figure above. The fragment with mass 2m moves vertically upward with a speed V and the fragment with mass m moves to the left with speed 2V. What is the magnitude and direction of the momentum of the third fragment?\nMagnitude of momentum \u00a0\u00a0\u00a0\u00a0 Direction\nA. 2mV \u00a0\u00a0\u00a0\u00a0 \u00e2\u0086\u0096\nB. \u00e2\u0088\u009a2(mV) \u00a0\u00a0\u00a0\u00a0 \u00e2\u0086\u0098\nC. 2\u00e2\u0088\u009a2(mV) \u00a0\u00a0\u00a0\u00a0 \u00e2\u0086\u0098\nD. 0 \u00a0\u00a0\u00a0\u00a0 None\n", "Answer (final answer highlighted)": "(C) Because there is no net force on the sphere during the explosion, the momentum must be conserved for the system. Since the system has no momentum before the explosion, the total momentum after the explosion must be zero. The following figure may be used to visualize the postexplosion momenta: https://img.apstudy.net/ap/physics-1/a500/Answer_360.jpg The arrow up and to the left represents the combined momenta of the first two fragments. To obtain zero net momentum, the third fragment must have an equal momentum down and to the right. Its value may be obtained from the Pythagorean theorem as follows: https://img.apstudy.net/ap/physics-1/a500/Ans_028.jpg", "ImagePath": "Physics/112" }, { "Question": "\nAs shown in the diagram above, a block of mass m and speed vo has an elastic collision with a second block of unknown mass that is originally at rest. The first block bounces back in the opposite direction at half its original speed. Is it possible to find the unknown mass and the final velocity of the second block in terms of the given quantities?\nA. No. Momentum conservation may be applied to this collision, but there are too many unknowns to find a solution.\nB. Yes. Momentum is conserved as well as mechanical energy. Both principles may be used together to solve this problem.\nC. Yes. Momentum conservation alone is sufficient to determine the unknown mass and velocity.\nD. Yes. Energy conservation alone is sufficient to determine the unknown mass and velocity.\n", "Answer (final answer highlighted)": "(B) Because this is an elastic collision, the kinetic energy in the two-body system before the collision must be equal to the kinetic energy in the two-body system after the collision. This provides the first equation with two unknowns. Momentum conservation may also be used to develop a second equation with the same two unknowns. Two equations are sufficient to solve a problem with two unknowns.", "ImagePath": "Physics/113" }, { "Question": "\nA 4-kg lab cart is moving to the right at a velocity of +5 m/s and has a head-on collision with a 2-kg lab cart moving at an unknown initial velocity. After a perfectly inelastic collision, the system moves to the right with a velocity of +2 m/s. Determine the velocity of the 2-kg cart before the collision.\nA. +4 m/s\nB. -4 m/s\nC. +8 m/s\nD. -8 m/s\n", "Answer (final answer highlighted)": "(B) Momentum is conserved as follows: https://img.apstudy.net/ap/physics-1/a500/An0_265.jpg", "ImagePath": "Physics/114" }, { "Question": "A 50.0-g ball moving to the left strikes a wall and bounces back to the right. Slow-motion video analysis produces the following horizontal position versus time graph.A 50.0-g ball moving to the left strikes a wall and bounces back to the right. Slow-motion video analysis produces the following horizontal position versus time graph.\nA 50.0-g ball moving to the left strikes a wall and bounces back to the right. Slow-motion video analysis produces the following horizontal position versus time graph.The video camera used in the experiment has a frame rate of 30 pictures per second. In the video, the ball makes contact with the floor for three frames. What is the magnitude and direction of the average force that the ball exerts on the wall?\nA. 7.2 N to the right\nB. 4.5 N to the right\nC. 4.5 N to the left\nD. 7.2 N to the left\n", "Answer (final answer highlighted)": "(C) With 30 frames per second, a picture is taken each thirtieth of a second. Three frames will be 3/30 of a second, or 0.1 second. To find the average force, solve the momentum-impulse theorem for force as follows: https://img.apstudy.net/ap/physics-1/a500/Ans_338.jpg . This is the force of the floor on the wall, which is in the positive direction (to the right). According to Newton's third law, the force of the ball on the wall is equal in magnitude and opposite in direction, or -4.5 N (to the left).", "ImagePath": "Physics/115" }, { "Question": "A 50.0-g ball moving to the left strikes a wall and bounces back to the right. Slow-motion video analysis produces the following horizontal position versus time graph.A 50.0-g ball moving to the left strikes a wall and bounces back to the right. Slow-motion video analysis produces the following horizontal position versus time graph.\nA 50.0-g ball moving to the left strikes a wall and bounces back to the right. Slow-motion video analysis produces the following horizontal position versus time graph.Determine the momentum change of the bouncing ball.\nA. +0.05 kg \u00c3\u0097 m/s\nB. +0.45 kg \u00c3\u0097 m/s\nC. -0.45 kg \u00c3\u0097 m/s\nD. -0.05 kg \u00c3\u0097 m/s\n", "Answer (final answer highlighted)": "(B) First the initial and final velocities are determined from the slope of the graph: https://img.apstudy.net/ap/physics-1/a500/A_09.jpg Next, calculate the momentum change: https://img.apstudy.net/ap/physics-1/a500/Ans_337.jpg", "ImagePath": "Physics/116" }, { "Question": "\nThe graph above of momentum versus time depicts the motion of a box being pushed across a horizontal floor with negligible friction. Which of the following statements describes the force upon the box?\nA. The force on the box is constant.\nB. The force on the box is decreasing.\nC. The force on the box is increasing.\nD. More information is needed to describe the force on the box.\n", "Answer (final answer highlighted)": "(C) The slope of a momentum-time graph is force. Another way of looking at this is with the momentum-impulse theorem: The change in momentum divided by the time interval is the average force exerted on an object: https://img.apstudy.net/ap/physics-1/a500/An_04.jpg . Notice that the momentum is changing more and more rapidly as time elapses (i.e., the slope gets greater), which means the force is increasing.", "ImagePath": "Physics/117" }, { "Question": "\nA 500-kg spaceship in deep space is holding a 50-kg space probe, and the pair is initially drifting to the right at 20 m/s as shown in the first diagram above. If the spaceship fires the probe to the left at 40 m/s, what is the new speed of the spaceship?\nA. 9 m/s\nB. 13 m/s\nC. 18 m/s\nD. 26 m/s\n", "Answer (final answer highlighted)": "(D) Because there is no net force on the spacecraft/probe system, momentum is conserved: https://img.apstudy.net/ap/physics-1/a500/An000_7.jpg", "ImagePath": "Physics/118" }, { "Question": "\nA 1-kg block of dry ice moving at 6 m/s collides and sticks to a 2-kg block of dry ice initially at rest. The combination slides off a 20-m tall cliff as shown in the diagram above. What is the horizontal distance from the base of the cliff to the landing location of the block combination?\nA. 1 m\nB. 2 m\nC. 4 m\nD. 5 m\n", "Answer (final answer highlighted)": "(B) Since there is no net force on the system during the collision, momentum conservation may be used to find the postcollision speed: https://img.apstudy.net/ap/physics-1/a500/BKN_17.jpg Next, the vertical free-fall time is found for the projectile: https://img.apstudy.net/ap/physics-1/a500/A_324.jpg During the 1-second free-fall time, the projectile moves at a constant horizontal speed with no horizontal acceleration: https://img.apstudy.net/ap/physics-1/a500/A_324A.jpg", "ImagePath": "Physics/119" }, { "Question": "An 1,800-kg truck moving north at 15 m/s has a head-on collision with a 900-kg car moving south at 22 m/s. During the collision, compare the magnitudes of the following quantities for the car versus the truck during the collision. \nAn 1,800-kg truck moving north at 15 m/s has a head-on collision with a 900-kg car moving south at 22 m/s. During the collision, compare the magnitudes of the following quantities for the car versus the truck during the collision.Force \u00a0\u00a0\u00a0\u00a0 Acceleration \u00a0\u00a0\u00a0\u00a0 Momentum change\nA. Same \u00a0\u00a0\u00a0\u00a0 Same \u00a0\u00a0\u00a0\u00a0 Same\nB. Same \u00a0\u00a0\u00a0\u00a0 Different \u00a0\u00a0\u00a0\u00a0 Same\nC. Different \u00a0\u00a0\u00a0\u00a0 Same \u00a0\u00a0\u00a0\u00a0 Different\nD. Different \u00a0\u00a0\u00a0\u00a0 Different \u00a0\u00a0\u00a0\u00a0 Different\n", "Answer (final answer highlighted)": "(B) Newton's third law states that the magnitudes of the forces are the same during a collision, regardless of the mass or speeds of the objects involved. With the same forces and different masses, the net force to mass ratio will be different, so the accelerations will be different according to Newton's second law. With the same forces and the same time of contact, the magnitude of the impulse will be the same for both vehicles, and impulse is equal to the momentum change according to the impulse-momentum theorem.", "ImagePath": "Physics/120" }, { "Question": "\nThe graph above depicts how the momentum of a box pushed across the floor changes with time. Which of the following statements describes the force on the box?\nA. The force on the box is a constant 0.5 N.\nB. The force on the box is a constant 1 N.\nC. The force on the box is a constant 2 N.\nD. The force on the box is 2 N and increasing.\n", "Answer (final answer highlighted)": "(C) Newton defined momentum as the time rate of change of force, so the slope of a momentum-time graph is force. Another way of looking at this is using the momentum-impulse theorem: The change in momentum divided by the time interval is the average force exerted on an object: https://img.apstudy.net/ap/physics-1/a500/A_306.jpg", "ImagePath": "Physics/121" }, { "Question": "\nA person pulls a 25-kg block of dry ice (initially at rest) with a changing force as shown in the diagram and graph above. The block moves a distance of 6.0 m along a frictionless table in 3.2 s of time. Determine the power output of the person.\nA. 56 W\nB. 75 W\nC. 90 W\nD. 180 W\n", "Answer (final answer highlighted)": "(A) Power is the time rate at which the person works on the system. The person does work to give the block kinetic energy, and this work can be found by finding the average force times the displacement (or the area bounded by the force-displacement graph). https://img.apstudy.net/ap/physics-1/a500/f0265-02.jpg", "ImagePath": "Physics/122" }, { "Question": "\nIn its initial state, the 75-kg wrecking ball shown in the diagram above is released from rest at a distance of 3.5 m off the ground. After swinging back and forth multiple times, it's captured in its final state swinging up at a speed of 5.0 m/s at the instant it is 2.0 m off the ground. Determine the total work done by dissipative forces (such as air drag and pivot friction) on the pendulum system between its initial and final states.\nA. 0 J\nB. -190 J\nC. -560 J\nD. -1,700 J\n", "Answer (final answer highlighted)": "(B) The total work done on the system by dissipative forces is the change in mechanical energy of the system. https://img.apstudy.net/ap/physics-1/a500/f0264-01.jpg", "ImagePath": "Physics/123" }, { "Question": "\nA tall sailing ship (m = 1.43 \u00c3\u0097 104 kg) is initially at rest. A steady wind blows at the 60\u00c2\u00b0 angle shown in the diagram and moves the ship forward a distance of 850 m. The ship's final speed is 9.0 m/s. Assuming that water resistance is negligible, what is the force of the wind on the boat?\nA. 200 N\nB. 390 N\nC. 680 N\nD. 790 N\n", "Answer (final answer highlighted)": "(D) The work done by the wind equals the change in kinetic energy of the boat: https://img.apstudy.net/ap/physics-1/a500/BK_17.jpg The total force of the wind, F, is found as follows: https://img.apstudy.net/ap/physics-1/a500/BK_18.jpg", "ImagePath": "Physics/124" }, { "Question": "A 5-kg box slides 10 m diagonally down a frictionless ramp inclined at 45\u00c2\u00b0. At the bottom of the ramp, it slides on a rough horizontal concrete floor with a coefficient of friction of 0.6.A 5-kg box slides 10 m diagonally down a frictionless ramp inclined at 45\u00c2\u00b0. At the bottom of the ramp, it slides on a rough horizontal concrete floor with a coefficient of friction of 0.6.\nA 5-kg box slides 10 m diagonally down a frictionless ramp inclined at 45\u00c2\u00b0. At the bottom of the ramp, it slides on a rough horizontal concrete floor with a coefficient of friction of 0.6.How far does the box travel on the concrete before coming to a complete stop?\nA. 6 m\nB. 8 m\nC. 10 m\nD. 12 m\n", "Answer (final answer highlighted)": "(D) The force of friction works against the motion of the box to bring it to a stop. First calculate the force of friction, and then use the work-energy theorem to find the distance the box travels: https://img.apstudy.net/ap/physics-1/a500/A_242.jpg https://img.apstudy.net/ap/physics-1/a500/A_242a.jpg", "ImagePath": "Physics/125" }, { "Question": "A 5-kg box slides 10 m diagonally down a frictionless ramp inclined at 45\u00c2\u00b0. At the bottom of the ramp, it slides on a rough horizontal concrete floor with a coefficient of friction of 0.6.A 5-kg box slides 10 m diagonally down a frictionless ramp inclined at 45\u00c2\u00b0. At the bottom of the ramp, it slides on a rough horizontal concrete floor with a coefficient of friction of 0.6.\nA 5-kg box slides 10 m diagonally down a frictionless ramp inclined at 45\u00c2\u00b0. At the bottom of the ramp, it slides on a rough horizontal concrete floor with a coefficient of friction of 0.6.What is the speed of the box as it reaches the bottom of the ramp?\nA. 6 m/s\nB. 10 m/s\nC. 12 m/s\nD. 14 m/s\n", "Answer (final answer highlighted)": "(C) Use conservation of energy to find the velocity of the box: https://img.apstudy.net/ap/physics-1/a500/A_223.jpg https://img.apstudy.net/ap/physics-1/a500/A_241A.jpg", "ImagePath": "Physics/126" }, { "Question": "\nA spacecraft in deep space is isolated from its surroundings and is initially moving with the velocity v shown in the diagram above. It has thrusters on a swivel that fire such that the spacecraft experiences three possible forces that act at fixed angles relative to the velocity vector of the spacecraft. With each of the forces separately with a steady magnitude, what initially happens to the kinetic energy K, of the spacecraft?\nF1 \u00a0\u00a0\u00a0\u00a0 F2 \u00a0\u00a0\u00a0\u00a0 F3\nA. K decreases \u00a0\u00a0\u00a0\u00a0 K constant \u00a0\u00a0\u00a0\u00a0 K increases\nB. K increases \u00a0\u00a0\u00a0\u00a0 K increases \u00a0\u00a0\u00a0\u00a0 K increases\nC. K decreases \u00a0\u00a0\u00a0\u00a0 K constant \u00a0\u00a0\u00a0\u00a0 K decreases\nD. K increases \u00a0\u00a0\u00a0\u00a0 K decreases \u00a0\u00a0\u00a0\u00a0 K decreases\n", "Answer (final answer highlighted)": "(A) When F1 is applied, a vertical component of the force acts opposite the velocity vector and slows the spacecraft down, but the horizontal component only changes its direction because it's perpendicular to the velocity. As the spacecraft's speed slows, K decreases. When F2 is applied, it only changes the spacecraft's direction because it remains perpendicular to the velocity vector, thus K will not change. When F3 is applied, the vertical component of force acts as a net force in the same direction of the velocity vector and speeds the spacecraft up, but the horizontal component only changes its direction because it's perpendicular to the velocity. As the spacecraft speeds up, K increases.", "ImagePath": "Physics/127" }, { "Question": "An experiment was conducted with a hoop spring attached to a force probe, both of which were mounted to a low friction dynamics cart. The compression of a hoop spring may be modeled as a Hookean spring. The system was placed on a horizontal track with a motion encoder to measure the displacement of the cart. The following graph shows the experimental force vs. displacement for a black hoop (steeper line) and a white hoop, each tested separately. The white hoop/probe/cart mass is 0.500 kg and the black hoop/probe/cart mass is 1.000 kg.An experiment was conducted with a hoop spring attached to a force probe, both of which were mounted to a low friction dynamics cart. The compression of a hoop spring may be modeled as a Hookean spring. The system was placed on a horizontal track with a motion encoder to measure the displacement of the cart. The following graph shows the experimental force vs. displacement for a black hoop (steeper line) and a white hoop, each tested separately. The white hoop/probe/cart mass is 0.500 kg and the black hoop/probe/cart mass is 1.000 kg.\nAn experiment was conducted with a hoop spring attached to a force probe, both of which were mounted to a low friction dynamics cart. The compression of a hoop spring may be modeled as a Hookean spring. The system was placed on a horizontal track with a motion encoder to measure the displacement of the cart. The following graph shows the experimental force vs. displacement for a black hoop (steeper line) and a white hoop, each tested separately. The white hoop/probe/cart mass is 0.500 kg and the black hoop/probe/cart mass is 1.000 kg.How far must the white cart's hoop be compressed against the wall for it to leave at the same speed as the black-hoop cart moved in the previous question?\nA. 5.0 cm\nB. 5.7 cm\nC. 6.2 cm\nD. 8.1 cm\n", "Answer (final answer highlighted)": "(B) The final speed of the black-hoop cart was found in the previous solution: https://img.apstudy.net/ap/physics-1/a500/A_239.jpg To have the same speed as the black-hoop cart, the white-hoop cart needs a kinetic energy of: https://img.apstudy.net/ap/physics-1/a500/A_239A.jpg", "ImagePath": "Physics/128" }, { "Question": "An experiment was conducted with a hoop spring attached to a force probe, both of which were mounted to a low friction dynamics cart. The compression of a hoop spring may be modeled as a Hookean spring. The system was placed on a horizontal track with a motion encoder to measure the displacement of the cart. The following graph shows the experimental force vs. displacement for a black hoop (steeper line) and a white hoop, each tested separately. The white hoop/probe/cart mass is 0.500 kg and the black hoop/probe/cart mass is 1.000 kg.An experiment was conducted with a hoop spring attached to a force probe, both of which were mounted to a low friction dynamics cart. The compression of a hoop spring may be modeled as a Hookean spring. The system was placed on a horizontal track with a motion encoder to measure the displacement of the cart. The following graph shows the experimental force vs. displacement for a black hoop (steeper line) and a white hoop, each tested separately. The white hoop/probe/cart mass is 0.500 kg and the black hoop/probe/cart mass is 1.000 kg.\nAn experiment was conducted with a hoop spring attached to a force probe, both of which were mounted to a low friction dynamics cart. The compression of a hoop spring may be modeled as a Hookean spring. The system was placed on a horizontal track with a motion encoder to measure the displacement of the cart. The following graph shows the experimental force vs. displacement for a black hoop (steeper line) and a white hoop, each tested separately. The white hoop/probe/cart mass is 0.500 kg and the black hoop/probe/cart mass is 1.000 kg.If the cart with the black hoop is pushed against a wall and compresses the spring 5.0 cm, how fast will it be released?\nA. 0.22 m/s\nB. 0.44 m/s\nC. 0.53 m/s\nD. 0.55 m/s\n", "Answer (final answer highlighted)": "(B) The elastic energy stored in the spring transfers to kinetic energy. https://img.apstudy.net/ap/physics-1/a500/BK_15.jpg", "ImagePath": "Physics/129" }, { "Question": "\nThe four blocks shown in the figure above are released from the same height. Blocks B, C, and D are each released from rest, and block A is initially moving horizontally with a speed v. Blocks A and C each have a mass of 1 kg and blocks B and D are each 2 kg. Assuming air drag and incline friction are negligible, rank the speed of each block as it reaches the ground.\nA. vA = vB > vC >vD\nB. vA > vB = vC = vD\nC. vA = vB = vC = vD\nD. vB = vD > vA > vC\n", "Answer (final answer highlighted)": "(B) Because all four objects start at the same height relative to the ground, they all begin with the same gravitational energy. With negligible surface friction and air drag, all of that gravitational energy transfers to kinetic energy as they arrive at the ground level. Since objects B, C, and D all start at rest, the analysis looks like this: https://img.apstudy.net/ap/physics-1/a500/A_236.jpg Therefore, objects B, C, and D all arrive at the ground with the same speed (albeit at different times). In contrast, object A already has kinetic energy when it's released, so its analysis differs as follows: https://img.apstudy.net/ap/physics-1/a500/A_14.jpg Thus, object A arrives at a greater speed. The final ranking is as follows: https://img.apstudy.net/ap/physics-1/a500/A_236A.jpg", "ImagePath": "Physics/130" }, { "Question": "\nA 3.0-kg object, initially moving to the right with a velocity of +4.0 m/s, experiences a positive net force that decreases linearly throughout the displacement as shown on the graph above. What is the kinetic energy of the object at the instant the net force is zero?\nA. 24 J\nB. 51 J\nC. 99 J\nD. 174 J\n", "Answer (final answer highlighted)": "(C) Work is defined as the area bounded by the net force-displacement graph: https://img.apstudy.net/ap/physics-1/a500/A_232.jpg", "ImagePath": "Physics/131" }, { "Question": "A roller coaster is initially moving to the right as it approaches point A in the figure below. Assume that air drag and friction are negligible.A roller coaster is initially moving to the right as it approaches point A in the figure below. Assume that air drag and friction are negligible.\nA roller coaster is initially moving to the right as it approaches point A in the figure below. Assume that air drag and friction are negligible.At which point is the total mechanical energy of the coaster-Earth system the greatest?\nA. Location A\nB. Location D\nC. Location E\nD. It is the same at all points.\n", "Answer (final answer highlighted)": "(D) The total mechanical energy is the sum of the kinetic energy and gravitational potential energy. It is the same at all points because there is no change in internal energy of the system (air drag and track friction are negligible).", "ImagePath": "Physics/132" }, { "Question": "A roller coaster is initially moving to the right as it approaches point A in the figure below. Assume that air drag and friction are negligible.A roller coaster is initially moving to the right as it approaches point A in the figure below. Assume that air drag and friction are negligible.\nA roller coaster is initially moving to the right as it approaches point A in the figure below. Assume that air drag and friction are negligible.At which location will the roller-coaster car move at the greatest speed?\nA. Location E\nB. Location B\nC. Location C\nD. Location D\n", "Answer (final answer highlighted)": "(A) The car will move the fastest at the point with the most kinetic energy, which is the lowest point, E, where most of the gravitational energy in the car-Earth system has transferred to the kinetic energy.", "ImagePath": "Physics/133" }, { "Question": "A roller coaster is initially moving to the right as it approaches point A in the figure below. Assume that air drag and friction are negligible.A roller coaster is initially moving to the right as it approaches point A in the figure below. Assume that air drag and friction are negligible.\nA roller coaster is initially moving to the right as it approaches point A in the figure below. Assume that air drag and friction are negligible.At which locations will a roller-coaster car have the same gravitational potential energy?\nA. Locations A and E\nB. Locations B and C\nC. Locations C and D\nD. Locations A and C\n", "Answer (final answer highlighted)": "(D) Points A and C are at the same height from the ground and thus have the same gravitational potential energy: Ug = mg\u00ce\u0094y.", "ImagePath": "Physics/134" }, { "Question": "The mass, turn radius, and speed of each car in the table below are shown relative to car A. Which of the following best ranks the centripetal force on the cars?The mass, turn radius, and speed of each car in the table below are shown relative to car A. Which of the following best ranks the centripetal force on the cars?\nA. D > A = B > C\nB. D > C = B > A\nC. D = A = B > C\nD. D = B > A > C\n", "Answer (final answer highlighted)": "(D) Centripetal force is the net force on the car toward the center of the circle and is calculated as follows: https://img.apstudy.net/ap/physics-1/a500/A_207.jpg Thus, D = B > A > C.", "ImagePath": "Physics/135" }, { "Question": "\nThe graph above depicts the tangential velocities of several circular space stations with different radii. All the stations are spinning. Which of the following statements is true?\nA. The centripetal accelerations of the 3 shorter radii space stations are greater than 10 m/s2; those of the larger ones are less than 10 m/s2.\nB. The centripetal accelerations of the 3 shorter radii space stations are greater than 5 m/s2; those of the larger ones are less than 5 m/s2.\nC. The centripetal accelerations of all the stations are all nearly 5 m/s2.\nD. The centripetal accelerations of all the stations are all nearly 10 m/s2.\n", "Answer (final answer highlighted)": "(D) Pick any two points on the graph and calculate the centripetal acceleration. Square the velocity, and divide it by the radius. You will find that all of them have approximately the same centripetal acceleration, i.e., 10 m/s2.", "ImagePath": "Physics/136" }, { "Question": "\nThe driver of a race car takes a turn on a horizontal track and is moving southeast at a particular instant as shown in the diagram above. If the car is gaining speed, which of the following is a possible direction of acceleration of the car at the instant shown in the diagram?\nA. Southwest toward the center of the turn\nB. Southeast in the direction of motion\nC. South on the diagram\nD. Northeast away from the center of the turn\n", "Answer (final answer highlighted)": "(C) Since the car is gaining speed, there is a southeast component of acceleration tangent to the curved path. But also, because the car is turning, there is a southwest component of acceleration toward the center of the turn (the centripetal acceleration). These two components sum as vectors to yield a resultant vector that is in the southerly direction. (Note: Depending on the magnitudes of the components, the resultant vector may have a slight easterly or westerly component, but the dominant direction will be south.)", "ImagePath": "Physics/137" }, { "Question": "\nA car is moving over the top of a hill at a constant speed. Which of the following may be said about the vertical forces on the car in this scenario?\nA. The normal force of the road is greater than the gravitational force from the Earth.\nB. The normal force of the road is less than the gravitational force from the Earth.\nC. The normal force of the road equals the gravitational force from the Earth.\nD. The centrifugal force equals the gravitational force from the Earth.\n", "Answer (final answer highlighted)": "(B) Since the car is moving in a vertical circle, it must accelerate toward the center of the circle (centripetal acceleration). Since the center of the circle is downward relative to the car, the acceleration, and consequently the net force, is downward. This implies that the downward gravitational force from the Earth is greater than the upward normal force from the road.", "ImagePath": "Physics/138" }, { "Question": "\nAn empty 150-kg roller coaster cart is approaching a 6.0-meter-tall circular-shaped loop-the-loop as shown in the figure above. In order to complete the loop, determine the minimum speed of the cart when it is upside-down at the top of the loop.\nA. 5.5 m/s\nB. 7.7 m/s\nC. 10 m/s\nD. 12 m/s\n", "Answer (final answer highlighted)": "(A) The minimum speed condition occurs when the cart loses contact with the track (normal force is zero) and the gravitational force solely provides the required centripetal force: https://img.apstudy.net/ap/physics-1/a500/Ans-N_054.jpg", "ImagePath": "Physics/139" }, { "Question": "\nA rope accelerates a 20.0-kg block up a 30\u00c2\u00b0 ramp at a rate of 2.0 m/s/s. The kinetic friction coefficient between the block and the ramp is 0.18. Determine the value of the tension in the rope.\nA. 71 N\nB. 130 N\nC. 170 N\nD. 180 N\n", "Answer (final answer highlighted)": "(C) The first free-body diagram below shows the forces on the object. The second diagram divides the weight vector into its components. Since the block is not accelerating perpendicular to the incline, the normal force will balance the cosine component of the weight. https://img.apstudy.net/ap/physics-1/a500/An0_060.jpg Newton's second law may be used to determine the tension as follows: https://img.apstudy.net/ap/physics-1/a500/f0221-01.jpg", "ImagePath": "Physics/140" }, { "Question": "\nA force sensor interfaced with a computer pulls horizontally on a 2.0-kg box that is initially at rest on a horizontal surface. The box then breaks free and slides along the surface. The graph above shows how the measured force varies with time. Determine the value for the coefficient of static friction.\nA. 0.3\nB. 0.4\nC. 0.5\nD. 0.6\n", "Answer (final answer highlighted)": "(B) The static friction coefficient may be found as the ratio of the maximum static friction force and the normal force. Since the box is on a horizontal surface and is not accelerating vertically, the normal force balances the weight, mg. During the region of the graph where the force increases from zero to the maximum, the box hasn't broken free; the force sensor measures the static friction because the box is in a state of constant velocity. According to the graph, the static friction force increases from zero to a maximum value of 8 N. The coefficient of static friction is calculated as follows: https://img.apstudy.net/ap/physics-1/a500/An0_059.jpg", "ImagePath": "Physics/141" }, { "Question": "\nThe sign in the elevator above is suspended by two cables. If the elevator is moving upward at a constant speed, select two of the following statements that are true.\nA. The upward normal force on the sign is greater than the individual tensions in each rope.\nB. The vertical component of the tension in rope #1 is greater than the downward weight of the sign.\nC. The vertical component of the tension in rope #1 balances the downward weight of the sign.\nD. The horizontal component of the tension in rope #1 balances the tension in rope #2.\n", "Answer (final answer highlighted)": "(C, D) Since the sign is moving upward at a constant velocity (zero acceleration), there must be no net force on the sign; therefore, the forces on each axis must be balanced. There is no normal force on the sign.", "ImagePath": "Physics/142" }, { "Question": "\nA rope applies 35 N force as shown in the figure above. As a result, the box accelerates to the left along the surface. In addition to the gravitational force, which two of the following forces act on the box?\nA. The downward force of the box on the table\nB. The frictional force of the surface on the box\nC. The upward force of the table on the box\nD. The force of motion to the left on the box\n", "Answer (final answer highlighted)": "(B, C) A free-body diagram would show an upward normal force, a downward gravitational force, a tension force up and to the left at a 30\u00c2\u00b0 angle, a frictional force to the right parallel to the surface, and possibly an air drag force to the right that is probably negligible. \"Motion\" is not a force, and the force of the block on the table is a valid force but does not act on the system of interest (which is the box).", "ImagePath": "Physics/143" }, { "Question": "\nThe graph above depicts the velocity of a skydiver over time during a vertical fall through the air. Which of the following statements is true about the magnitude of the net force on the skydiver?\nA. It increases until the acceleration reaches its maximum and the velocity becomes constant.\nB. It decreases until the acceleration reaches zero and the velocity becomes constant.\nC. It has a value of zero throughout the skydiver's free fall.\nD. It increases until the acceleration reaches zero and the velocity becomes constant.\n", "Answer (final answer highlighted)": "(B) The forces acting upon the skydiver are the downward gravitational force and upward air resistance force (drag). Initially, the net force is high (gravity > air resistance), the skydiver accelerates, and the velocity increases rapidly. Over time, the air resistance increases with speed, so the net force and acceleration decrease. At some point in time the skydiver reaches terminal velocity where there is no net force (gravity = air resistance), acceleration is zero, and the skydiver's velocity is constant.", "ImagePath": "Physics/144" }, { "Question": "\nAn object's position with time is depicted in this graph. At which time range will there be nearly no net force acting on the object?\nA. 0.5 to 1.0 s\nB. 1.0 to 1.5 s\nC. 1.8 to 2.2 s\nD. 2.5 to 3.5 s\n", "Answer (final answer highlighted)": "(C) A curve on the position versus clock reading graph indicates a changing slope, which is a changing velocity. The straight section between 1.8 and 2.2 s indicates a constant velocity. Newton's first law states that objects will maintain constant velocity as long as there's zero net force acting on it.", "ImagePath": "Physics/145" }, { "Question": "\nA box of unknown mass (m) slides down a plane inclined at an angle (\u00ce\u00b8) as shown in the diagram above. The plane has a coefficient of friction (\u00ce\u00bc). Which of the following expressions represents the rate of acceleration (a) of the box?\nA. a = g(sin\u00ce\u00b8 - \u00ce\u00bcg cos\u00ce\u00b8)/m\nB. a = g(cos\u00ce\u00b8 - \u00ce\u00bcg sin\u00ce\u00b8)/m\nC. a = g(cos\u00ce\u00b8 - \u00ce\u00bcsin\u00ce\u00b8)\nD. a = g(sin\u00ce\u00b8 - \u00ce\u00bccos\u00ce\u00b8)\n", "Answer (final answer highlighted)": "(D) Remember that the force of gravity (mg) must be resolved into x and y components, and that the force of friction (Ff) is related to the normal force (FN) by Ff = \u00ce\u00bcFN. The box does not move above or into the plane, so the forces in the y direction must be balanced. Apply Newton's second law to both the x and y directions to come up with an expression for acceleration: https://img.apstudy.net/ap/physics-1/a500/Ans-N_039.jpg", "ImagePath": "Physics/146" }, { "Question": "\nThe four blocks shown in the figure above are released from the same height above the ground. Blocks B, C, and D are each released from rest, and block A is initially moving horizontally with a speed v. The mass of blocks A and C is 1 kg and the mass of blocks B and D is 2 kg. Assuming air drag and surface friction are negligible, rank the time it takes each block to reach the ground.\nA. tA = tC < tB = tD\nB. tA < tB < tC < tD\nC. tA = tB = tC = tD\nD. tA = tB < tC < tD\n", "Answer (final answer highlighted)": "(D) Blocks A and B are both free falling, and free-fall acceleration is independent of mass; therefore, they will hit the ground at the same time. The mass of blocks C and D will not affect their acceleration for the same reason that mass does not affect free-fall acceleration: the mass cancels out of the ratio of net force to mass in Newton's second law. Blocks C and D only have a component of gravitational force accelerating them along the incline, so they have less net force acting on them compared to blocks A and B and they must travel along the whole length of the incline, as compared with the direct path of block B. Thus blocks C and D will take more time to reach the ground. Because block C has a greater component of gravitational force than D and a shorter path to travel, its time of travel will be less than D.", "ImagePath": "Physics/147" }, { "Question": "\nAn airplane uses a cable to tow a large banner advertisement as shown in the figure above. When the airplane cruises at a constant horizontal velocity through the air, which of the following correctly compares forces?\nA. The tension force in the cable equals the gravitational force on the banner.\nB. The forward force on the airplane equals the air drag force on the airplane and banner.\nC. The y-component of cable tension equals the aerodynamic lift force on the airplane.\nD. The x-component of cable tension is greater than the air drag force on the banner.\n", "Answer (final answer highlighted)": "(B) A system that cruises at a constant velocity has no acceleration. As a consequence, Newton's second law predicts that the system will have no net force. Applying this to the horizontal forces on the airplane/banner system, the forward force on the airplane must equal the combined forces of air drag on the airplane and banner.", "ImagePath": "Physics/148" }, { "Question": "Problems below refer to the system of two boxes connected by a rope as shown below on the floor of an elevator. A force F is applied to the 6-kg box.Assuming negligible friction between the blocks and the elevator floor, determine the value of the tension in the rope between the boxes if F = 24 N.\nA. 2 N\nB. 6 N\nC. 8 N\nD. 20 N\n", "Answer (final answer highlighted)": "(B) Use Newton's second law to calculate the acceleration of the entire 8-kg system: https://img.apstudy.net/ap/physics-1/a500/Ans-N_038.jpg Next, apply Newton's second law to the 6-kg subsystem: https://img.apstudy.net/ap/physics-1/a500/A_05.jpg Newton's second law may also be applied to the 2-kg subsystem, and the same value of tension will be found.", "ImagePath": "Physics/149" }, { "Question": "Problems below refer to the system of two boxes connected by a rope as shown below on the floor of an elevator. A force F is applied to the 6-kg box.Which of the following pair of forces ALWAYS have the same magnitude, regardless of the state of motion of the system?\nA. The force of the rope pulling the 6-kg block to the right and the force of the 6-kg block pulling the rope to the left\nB. The force F to the left and the force of the rope pulling the 6-kg box to the right\nC. The normal force of the floor on the 6-kg block and the gravitational force on the 6-kg box\nD. The force F to the left and the force of the rope on the 2-kg box to the left\n", "Answer (final answer highlighted)": "(A) The force of the rope pulling the 6-kg block to the right and the force of the 6-kg block pulling the rope to the left form a Newton's third law pair. These forces will always be equal in magnitude and opposite in direction. The other force pairs may or may not be congruent, depending on the state of motion of the system and the presence or absence of friction. The normal force and the gravitational force on the 6-kg box will only be congruent if the vertical acceleration of the elevator system is zero.", "ImagePath": "Physics/150" }, { "Question": "\nOnly two forces act on a 0.1-kg object. This graph depicts the magnitudes and directions of those two forces. What is the acceleration of the object at the 2-second clock reading?\nA. 0 m/s2\nB. 0.2 m/s2\nC. 1 m/s2\nD. 2 m/s2\n", "Answer (final answer highlighted)": "(D) The object accelerates only when the forces acting upon it are unbalanced. The net force on the object at t = 2 s is 1.2 N - 1.0 N = 0.2 N. The acceleration is the net force divided by the mass, or (0.2 N/0.1 kg) = 2 m/s2.", "ImagePath": "Physics/151" }, { "Question": "\nThe acceleration of a 5-kg object through 4 seconds of elapsed time is shown in the graph above. What is the net force on the object at the 1-second clock reading?\nA. -10 N\nB. -5 N\nC. -2.5 N\nD. 5 N\n", "Answer (final answer highlighted)": "(A) From the graph, the acceleration at t = 1 s is - 2 m/s2. The object's mass is 5 kg. So, the net force can be calculated from Newton's second law: https://img.apstudy.net/ap/physics-1/a500/Ans-N_031.jpg", "ImagePath": "Physics/152" }, { "Question": "\nA boy is pushing a 50-kg crate across horizontal, frictionless rollers. The velocity is changing with time as shown in the graph above. What is the magnitude of the force that the boy applies to the crate?\nA. 5 N\nB. 10 N\nC. 15 N\nD. 25 N\n", "Answer (final answer highlighted)": "(D) The acceleration is the slope of a velocity-time graph. In this case, the slope of the graph yields an acceleration of 0.5 m/s2. The mass of the crate is 50 kg. From Newton's second law, calculate the force applied: https://img.apstudy.net/ap/physics-1/a500/f0214-01.jpg", "ImagePath": "Physics/153" }, { "Question": "\nThis position-time graph is typical of which type of motion?\nA. Motion of an object with an increasing net force acting on it\nB. Motion of an object with constant positive net force acting on it\nC. Motion of an object with no net force acting on it\nD. Motion of an object with negative net force acting on it\n", "Answer (final answer highlighted)": "(C) The position in the graph is increasing linearly in the positive direction. It is consistent with motion with a constant positive velocity. The constant velocity means that acceleration is zero. According to Newton's second law, when acceleration is zero, there is no net force acting upon it.", "ImagePath": "Physics/154" }, { "Question": "Questions below refer to the 80-kg astronaut and her 40-kg daughter who are floating in deep space shown in the diagram below.Determine the magnitude of the mother's acceleration during her 160 N push on the daughter.\nA. 0 m/s2\nB. 0.5 m/s2\nC. 1 m/s2\nD. 2 m/s2\n", "Answer (final answer highlighted)": "(D) In deep space, there is no gravitational force from a planet and the gravitational attraction between the bodies is negligible. Thus, the only force during the push is the 160-N force of the daughter pushing the mother to the left. Using Newton's second law, https://img.apstudy.net/ap/physics-1/a500/Ans-N_029.jpg to the left.", "ImagePath": "Physics/155" }, { "Question": "Questions below refer to the 80-kg astronaut and her 40-kg daughter who are floating in deep space shown in the diagram below.If the mother pushes her daughter to the right with a force of 160 N, with what magnitude of force does the daughter push her mother?\nA. 0 N\nB. 80 N\nC. 160 N\nD. 640 N\n", "Answer (final answer highlighted)": "(C) This problem refers to a single pushing interaction between the mother and the daughter. The mother's push on the daughter forms a Newton's third law pair with the daughter's push on the mother, and thus forms an N3L pair that must be equal in magnitude and opposite in direction.", "ImagePath": "Physics/156" }, { "Question": "\nA box is pulled along a surface by a rope. The acceleration-time graph of an object's motion is shown in the figure above. At what time will the forces acting on the box be balanced?\nA. 0 s\nB. 1 s\nC. 2 s\nD. 3 s\n", "Answer (final answer highlighted)": "(C) According to Newton's second law, the forces acting upon an object are balanced when the acceleration is zero. As shown in the graph, this occurs at 2 s.", "ImagePath": "Physics/157" }, { "Question": "\nThe velocity versus time graph above compares the motion of object A with object B. Which of the following statements is true?\nA. Both objects have the same acceleration at the 3-second clock reading.\nB. Object B is changing directions near the 2-second clock reading.\nC. Object A is slowing down while object B is speeding up throughout the 4-second trip.\nD. The displacement of object B is greater than that of object A during the 4-second trip.\n", "Answer (final answer highlighted)": "(B) Both objects demonstrate uniform acceleration throughout the trip as demonstrated by the constant slopes, but since the slopes are different in both sign and magnitude, the value of their accelerations are different. The sign (\u00c2\u00b1) of the velocity determines the direction of motion. Object A is slowing down while moving in the positive direction because its positive velocity is decreasing. Object B starts with negative velocity (negative direction) and slows down for 2 seconds, then it speeds up in the positive direction.", "ImagePath": "Physics/158" }, { "Question": "\nThe graph above shows position vs. time for an object. Which of the following best describes the motion of the object?\nA. Gaining speed with a positive acceleration\nB. Gaining speed with a negative acceleration\nC. Losing speed with a positive acceleration\nD. Losing speed with a negative acceleration\n", "Answer (final answer highlighted)": "(B) Velocity is the slope of the position versus time graph. Because the graph starts out with a zero slope, the velocity is initially zero. As the slope gets more negative, the velocity gets more negative. Since speed is the absolute value of velocity, that means the speed is increasing. Acceleration is the slope of the velocity graph, and since the velocity is decreasing from zero to a negative value, the acceleration is negative.", "ImagePath": "Physics/159" }, { "Question": "\nThe graph above shows the position of an object versus clock reading. Which of the following best describes the motion of the object during the 6 seconds of elapsed time?\nA. The object speeds up for the first 2 seconds and slows down during the final 4 seconds.\nB. The object travels a distance of 6 meters during the 6 seconds of elapsed time.\nC. The object slows down and then speeds up with a total displacement of -6 meters.\nD. The object's acceleration starts out negative and transitions to positive acceleration at the 2-second clock reading.\n", "Answer (final answer highlighted)": "(C) Since the slope of the X versus t graph starts positive and goes to zero in the first 2 seconds, the object is slowing down. Then the slope increases negatively, indicating that the object is gaining speed in the negative direction. The total displacement is \u00ce\u0094X = Xf - Xi = 0 - 6m = -6m. (Note: Option D is incorrect because acceleration is defined as the slope of the velocity versus clock reading graph. This slope remains negative even after the 2-second clock reading, as the velocity transitions from zero to more negative values.)", "ImagePath": "Physics/160" }, { "Question": "\nThe velocity-time graph of an object's motion is shown in this graph. At 10 s, what is the object's displacement relative to its position at t = 0?\nA. 3 m\nB. 6 m\nC. 0 m\nD. -6 m\n", "Answer (final answer highlighted)": "(A) To find the displacement, integrate the area under the curve to the t axis. This involves adding the areas of two trapezoids, one in the 0-6 s time interval and the other in the 6-10 s time interval. https://img.apstudy.net/ap/physics-1/a500/Ans-N_022.jpg", "ImagePath": "Physics/161" }, { "Question": "\nRank the average velocities of the car in regions A, B, C, and E of the graph above.\nA. B > A = C > E\nB. B = A > C = E\nC. B > A = C = E\nD. A > B > C = E\n", "Answer (final answer highlighted)": "(A) The average velocity of region A is (0 + 30 m/s)/2 = +15 m/s. Region B is (30 m/s + 30 m/s)/2 = +30 m/s. Region C is (30 m/s + 0 m/s)/2 = +15 m/s. Region E is (0 m/s + -30 m/s)/2 = -15 m/s.", "ImagePath": "Physics/162" }, { "Question": "\nWhich of the following are true about the motion of the carts in the graph above?\nA. At the 7-second clock reading, cart 1 is moving with the same speed as cart 2.\nB. Cart 1 moves at a constant speed in the negative direction.\nC. Cart 1 moves in the negative direction over the entire 8-second trip.\nD. At the 8-second clock reading, cart 1 was moving faster than cart 2.\n", "Answer (final answer highlighted)": "(A, D) Option A is correct because speed is the absolute value of velocity, and both carts were moving at 4 m/s. Option D is also correct because, at the 8-second clock reading, Cart 1 was moving at 6 m/s and cart 2 was moving at 4 m/s. Option C is tempting but incorrect because it had positive velocity for the first half of the trip, indicating that it was moving in the positive direction.", "ImagePath": "Physics/163" }, { "Question": "\nWhich of the following best describes the motion of the car in regions C, D, and E of the velocity versus time graph above?\nA. It is slowing down until it reverses direction and speeds back up again.\nB. It moves at a constant velocity in the negative direction.\nC. It accelerates at a constant, nonzero acceleration except at point C when its acceleration is zero.\nD. Its position changes at a constant rate.\n", "Answer (final answer highlighted)": "(A) At the beginning of region C, the velocity gradually decreases to zero, indicating its speed is decreasing. At point D, the velocity has reached zero (resting instantaneously). At the beginning of region E, the negative velocity indicates that the direction is now negative, and the increasing magnitude of the velocity indicates it is speeding up.", "ImagePath": "Physics/164" }, { "Question": "\nAn object's position versus time is depicted in the graph above. Based on the graph, at which time points will the object's velocity be closest to zero?\nA. 0 s and 2 s\nB. 0 s and 4 s\nC. 1 s and 2 s\nD. 1 s and 3 s\n", "Answer (final answer highlighted)": "(D) When a position-time graph is horizontal, the velocity of the object is zero. The velocity at any instant in time is the slope of the line tangent to any point on the position-time graph. For this graph, that occurs at 1 s and 3 s.", "ImagePath": "Physics/165" }, { "Question": "The four different projectiles are fired from the surface of the Earth with negligible air drag. The following data table compares the four projectiles:Rank the vertical acceleration of the four projectiles.\nA. a1 = a2 > a3 > a4\nB. a4 < a2 < a3 < a4\nC. a1 = a2 = a3 = a4\nD. The masses must be known in order to rank the accelerations.\n", "Answer (final answer highlighted)": "(C) The masses are all free falling since there is negligible air drag. Free-fall acceleration is independent of mass, so they have the same vertical acceleration.", "ImagePath": "Physics/166" }, { "Question": "The following diagrams show possible scenarios of a dynamics cart going through 2 photogates:Photogate #1 measures a 0.02-second elapsed time for the cart's vertical rod (diameter = 1.2 cm) to block the infrared beam and then unblock the same beam. Photogate #2 works in the same manner and measures a 0.06-second elapsed time for the rod to pass through the beam. Based on this data and the fact that the photogates are 20 cm apart, describe the motion of the cart and calculate the magnitude of its acceleration.\nA. Speeding up with |a| = 0.5 m/s/s\nB. Slowing down with |a| = 0.5 m/s/s\nC. Speeding up with |a| = 0.8 m/s/s\nD. Slowing down with |a| = 0.8 m/s/s\n", "Answer (final answer highlighted)": "(D) https://img.apstudy.net/ap/physics-1/a500/Ans-N_006.jpg https://img.apstudy.net/ap/physics-1/a500/Asw_02.jpg", "ImagePath": "Physics/167" }, { "Question": "\nThe position-time graphs of four different objects are shown in these graphs. If the positive direction is forward, then which object is moving backward at a constant velocity?\nA. Object A\nB. Object B\nC. Object C\nD. Object D\n", "Answer (final answer highlighted)": "(D) If the positive direction is forward, then an object that is moving backward at a constant velocity would have a position vs. time graph that is linear with a negative slope.", "ImagePath": "Physics/168" }, { "Question": "\nThis graph above depicts the motion of an object on a coordinate system for 10 s. During which time interval is the object moving at a constant positive velocity?\nA. 0-2 s\nB. 3-4 s\nC. 4-6 s\nD. 6-7 s\n", "Answer (final answer highlighted)": "(A) The slope of a position-time graph is velocity. In the time interval from 0-2 seconds the slope is positive and constant, so the velocity is positive and constant in that same interval.", "ImagePath": "Physics/169" }, { "Question": "\nThe position-time graph shown above is typical of which type of motion?\nA. Motion with a constant negative velocity\nB. Motion with zero velocity\nC. Motion with a constant positive acceleration\nD. Motion with zero acceleration\n", "Answer (final answer highlighted)": "(D) The position in the graph is increasing linearly in the positive direction. This is consistent with motion with a constant positive velocity and, hence, zero acceleration.", "ImagePath": "Physics/170" }, { "Question": "\nFor the diverging lens shown above, which principle rays are correctly drawn? Select two answers.\nA. 1\nB. 2\nC. 3\nD. 4\n", "Answer (final answer highlighted)": "A, D For a diverging lens, the \"focus\" is on the far side of the lens. So (1) shows a light ray traveling into the focus and then bending parallel to the optic axis. (4) shows a light ray traveling parallel to the optic axis, and it leaves on a line connecting the other focal point.", "ImagePath": "Physics/171" }, { "Question": "\nThe circuit shown above is set up. The switch is closed and a long time passes. What conditions on the two resistors result in the greatest amount of energy stored in the capacitor?\nA. The energy stored in the capacitor will be greatest if R1 > R2.\nB. The energy stored in the capacitor will be greatest if R1 = R2.\nC. The energy stored in the capacitor will be greatest if R1 < R2.\nD. The energy will be the same regardless of the resistor values.\n", "Answer (final answer highlighted)": "D The energy stored in a capacitor depends on the voltage across the capacitor when it is fully charged. The capacitor will have the same voltage as the battery when fully charged regardless of the resistances of either resistor.", "ImagePath": "Physics/172" }, { "Question": "\nAn experiment is conducted to determine the critical angle for light going from glass into air, as shown above. A linear plot is made with a vertical axis of sin (\u00ce\u00b81) and a horizontal axis of sin (\u00ce\u00b82). How is the critical angle determined from the graph?\nA. The critical angle can be found from the slope of the line.\nB. The critical angle can be found from the y-intercept of the line.\nC. The critical angle can be found from the horizontal axis value which corresponds to the maximum vertical value.\nD. The critical angle can be found from the vertical axis value which corresponds to the maximum horizontal value.\n", "Answer (final answer highlighted)": "C The critical angle occurs at the angle for \u00ce\u00b82 when the value of sin(\u00ce\u00b81) = 1, which is the maximum value that sin (\u00ce\u00b8) can obtain.", "ImagePath": "Physics/173" }, { "Question": "\nThree cylinders of the same metal act as resistors arranged in series, as shown above. Which of the following correctly ranks the voltage drops across the three resistors?\nA. V1 = V2 = V3\nB. V3 > V1 > V2\nC. V2 > V3 > V1\nD. V1 > V3 > V2\n", "Answer (final answer highlighted)": "C The resistance of a wire is directly proportional to the length of the wire and inversely proportional to the cross-sectional area. 1 must have the least resistance and 2 must have the most resistance. Because the resistors are in series, they have the same current through them. Ohm's Law states that the greatest voltage drop is across the greatest resistance value.", "ImagePath": "Physics/174" }, { "Question": "\nCharges are distributed as shown above. At point A is a charge of +3Q. At B is a charge of +1Q. At C is a charge of -1Q. What is the direction of the force on a proton located at point P?\nA. Up and to the left\nB. Down and to the left\nC. Up and to the right\nD. Down and to the right\n", "Answer (final answer highlighted)": "C From the charge at point A, the field will be up and to the right. From B, the field will be up and to the left. The right component of A will be stronger than the leftward component of B. From the charge at C, the field will point down and to the right. The upward field lines from either A or B will be greater than the downward field lines from C.", "ImagePath": "Physics/175" }, { "Question": "\nA current-carrying wire and coordinate system is shown above. Initially, the wire carries a current I toward the top of the page. The amount of current is steadily decreased until it is 0 A, then steadily increased until it reaches a value of I in the downward direction. This change in current takes time t. The magnetic field versus time at the observation point P from t = 0 until t is graphed. Which statement is true concerning the graph if +z is above the horizontal axis and -z is below the horizontal axis?\nA. The graph has a constant slope.\nB. The graph is piecewise linear with a negative slope for the first half and a positive slope for the second half.\nC. The graph is piecewise linear with a positive slope for the first half and a negative slope for the second half.\nD. The graph is a curve showing an inverse relationship.\n", "Answer (final answer highlighted)": "B As the current decreases, the magnetic field observed at P will decrease in magnitude. When the current reaches 0, the observed field will be 0. As the current increases, the field magnitude will again increase.", "ImagePath": "Physics/176" }, { "Question": "Radiothorium-228 decays into Radon-220 through two alpha decays, as shown below.Radiothorium-228 decays into Radon-220 through two alpha decays, as shown below.\nRadiothorium-228 decays into Radon-220 through two alpha decays, as shown below.Which equation correctly describes the energy released during this process?\nA. (mTh - mRn)c2\nB. (mTh + 2mHe - mRn)c2\nC. (mTh - 2mHe - mRn)c2\nD. (mRn + 2mHe - mTh)c2\n", "Answer (final answer highlighted)": "D Rest-mass energy of a particle is given by E = mc2. The released energy is given by the mass that remains after the decay less the mass that existed before the decay.", "ImagePath": "Physics/177" }, { "Question": "\nThe wave function of a quantum object vs. position is graphed above. Which of the following correctly ranks the probabilities of observing the particle at the listed positions?\nA. P(x = 0.5 m) > P(x = 2.25 m) > P(x = 1.75 m)\nB. P(x = 0.5 m) > P(x = 1.75 m) > P(x = 1.25 m)\nC. P(x = 3.0 m) > P(x = 1.75 m) > P(x = 2.0 m)\nD. P(x = 3.5 m) > P(x = 3.0 m) > P(x = 1.75 m)\n", "Answer (final answer highlighted)": "B The square of the wave function of a quantum object can be interpreted as the likelihood of an observation occurring at the stated position.", "ImagePath": "Physics/178" }, { "Question": "\nAn experiment is conducted to determine the power output from a circuit as various voltages are supplied to the circuit. The circuit is set up so that it draws a constant current. What is the value of the current in the circuit that produced the graph above?\nA. 0.00 A\nB. 0.25 A\nC. 1.0 A\nD. 6.0 A\n", "Answer (final answer highlighted)": "B Power dissipated in a circuit is directly proportional to the product of the current and voltage. The slope of the line of a power vs. voltage graph gives the current.", "ImagePath": "Physics/179" }, { "Question": "\nA positive charge of 2Q and a negative charge of 4Q are arranged at positions as shown above. What is the correct ranking of the electric potential at points along the x-axis?\nA. V(x = 4 m) = V(x = 2 m) > V(x = 1 m)\nB. V(x = 4 m) > V(x = 1 m) > V(x = 2 m)\nC. V(x = 1 m) > V(x = 2 m) > V(x = 4 m)\nD. V(x = 4 m) > V(x = 2 m) > V(x = 1 m)\n", "Answer (final answer highlighted)": "C In the presence of a positive and a negative point charge, the electric potential will be higher at locations closer to the positive charge and farther from the negative charge.", "ImagePath": "Physics/180" }, { "Question": "\nAn insulating rod separates two conducting spheres as shown above. Point A is midway between the spheres. Point B lies on the axis of the rod. Which of the following arrangements of charges would result in a net torque on the rod?\nA. Charge both spheres negatively and place a positive charge at point A.\nB. Charge one sphere negatively and the other positively and place a positive charge at point A.\nC. Charge both spheres negatively and place a positive charge at point B.\nD. Charge one sphere negatively and the other positively and place a positive charge at point B.\n", "Answer (final answer highlighted)": "B By the process of elimination, placing charges at B will result in the lever arm being parallel to the force and will not cause torque, eliminating (C) and (D). The sign of the charges on the two spheres must be different to have a net torque.", "ImagePath": "Physics/181" }, { "Question": "\nThe tube shown above carries water. At some point, the tube splits, as shown above. Three points within the tube are labeled A, B, and C. The greatest diameter is at A and the smallest diameter is at B. How do the pressures in the pipes compare at the three points?\nA. PA > PC > PB\nB. PA = PB = PC\nC. PB = PC > PA\nD. PB > PC > PA\n", "Answer (final answer highlighted)": "D Pressure is highest when speed is slowest. At the widest point in the tube, position A, the speed will be lowest. Because B is narrower than C, the speed at B will be greater than at C, making the pressure highest at point B.", "ImagePath": "Physics/182" }, { "Question": "\nA ray of light enters the pair of tanks as shown above. The light rays in the water and glass tank are shown at the left, with the light exiting the pair of tanks at a point Y. The light ray in the air tank is identical to the ray in the water tank, entering at the same height and same angle. Both sets of tanks use the same glass. How will the ray exiting the second glass tank compare to height Y?\nA. The ray will not exit the second tank due to total internal reflection.\nB. The exiting ray will be closer to the top of the tank than Y.\nC. The exiting ray will be at the same height as Y.\nD. The exiting ray will be farther from the top of the tank than Y.\n", "Answer (final answer highlighted)": "B The index of refraction of air is less than the index of refraction of water. According to Snell's Law, n1sin(\u00ce\u00b81) = n2sin(\u00ce\u00b82), a smaller n1 results in a smaller \u00ce\u00b82. The ray in the glass will be at an angle closer to the normal than the ray in glass from the water/glass apparatus.", "ImagePath": "Physics/183" }, { "Question": "\nThree neutral conducting spheres sit on insulating bases. The spheres are separated by a very large distance. The sphere in the center is given a positive charge. The spheres are brought close together, as shown above, but not allowed to come into contact with one another. Which is the correct description of the net charge on each sphere?\nA. All three spheres are positively charged.\nB. The center sphere is positively charged and the two outer spheres are negatively charged.\nC. The center sphere is positively charged and the other two are neutral.\nD. All three spheres are neutral.\n", "Answer (final answer highlighted)": "C The spheres do not touch, so there cannot be any charging by contact. While the outside sphere will have non-symmetric charge distributions, each will still have a net charge of 0 C.", "ImagePath": "Physics/184" }, { "Question": "\nThe instrument in an aircraft to measure airspeed is known as the pitot tube, shown in the figure above. The opening facing the incoming air (with the small aperture) is the part meant to capture the air at rest. The opening perpendicular to the flow of air (with the large aperture) is meant to capture air at speed. If h = 1 m and the fluid within the manometer is water, what is the airspeed? Take the density of air to be \u00cf\u0081air = 1.2 kg/m3.\nA. 27 m/s\nB. 68 m/s\nC. 95 m/s\nD. 128 m/s\n", "Answer (final answer highlighted)": "D First, use Bernoulli's Equation. Call the point with the air at rest B and the point with the speeding air A. You have vB = 0 and yA = vB, so the equation reduces to The pressure difference, PB = PA arises from the fluid depth \u00cf\u0081fgh. Solving for va and using the given values", "ImagePath": "Physics/185" }, { "Question": "\nA beam of light goes from water to air. Depending on the actual angle that the light strikes the surface, which of the following rays are possible outcomes?\nA. A only\nB. B only\nC. A or D\nD. C or D\n", "Answer (final answer highlighted)": "D Water has a higher index of refraction than air, so if light refracts through the water the light will bend away from the normal-so C is possible. Another possibility is D, total internal reflection when the angle in water is greater than the critical angle.", "ImagePath": "Physics/186" }, { "Question": "\nA tube with two T branches that has an open end is inserted in a liquid. However, the section of the tube above part B is hidden from view. The hidden section may be wider or narrower. Air is blown through the tube and the water levels rise as shown. You can conclude which of the following?\nA. The picture as drawn is impossible-A and B must be at equal heights.\nB. The tube is narrower and the air speed is greater above section B.\nC. The tube is narrower and the air speed is less above section B.\nD. The tube is wider and the air speed is greater above section B.\n", "Answer (final answer highlighted)": "B Because the fluid is higher in column B, the air speed must be greater above column B. This must be due to a narrower tube.", "ImagePath": "Physics/187" }, { "Question": "\nIn the figure above, a ray of light hits an object and travels parallel to the principal axis as shown by the dotted line. Which line shows the correct continuation of the ray after it hits the concave lens?\nA. a\nB. b\nC. c\nD. d\n", "Answer (final answer highlighted)": "A The rules for ray-tracing diagrams state that a line parallel to the principle axis bends away from the focal point as shown.", "ImagePath": "Physics/188" }, { "Question": "\nA machine shoots a proton, a neutron, or an electron into a magnetic field at various locations. The paths of two particles are shown above. Assume they are far enough apart so that they do not intersect and the magnetic field is going out of the page, as shown. What can you say about the paths that represent each particle?\nA. a is the proton and b is the electron.\nB. b is the proton and a is the electron.\nC. Either may be a neutron.\nD. You cannot make any conclusions without knowing the velocities.\n", "Answer (final answer highlighted)": "A Path a follows the right-hand rule so must be positively charged. Path b is opposite the right-hand rule so must be negatively charged. Neutrons would follow a straight line path, so it is impossible for either a or b to be a neutron.", "ImagePath": "Physics/189" }, { "Question": "\nWhich statement correctly characterizes the work done by the gas during the ABCDA cycle shown in the above P-V diagram?\nA. There is no work done by the gas because the system both starts and concludes in state A.\nB. There is no work done because the work done during the transition from A\u00e2\u0086\u0092B cancels out the work done in transition from C\u00e2\u0086\u0092D.\nC. The work done by the gas is positive because the work done during the transition from A\u00e2\u0086\u0092B is greater than the work done in transition from C\u00e2\u0086\u0092D.\nD. The work done by the gas is positive because the work done during the transition from B\u00e2\u0086\u0092C is greater than the work done in transition from D\u00e2\u0086\u0092A.\n", "Answer (final answer highlighted)": "C Work is done when there is a change in volume. At constant pressure, the equation W = -P\u00ce\u0094V tells you that when P is higher (as it is at path A\u00e2\u0086\u0092B), a greater amount of negative work is done on the gas than at lower P. Thus, the work done by the gas during the entire cycle is positive, and the constant volume paths have no influence on the amount of work.", "ImagePath": "Physics/190" }, { "Question": "\nA neutral conducting sphere is hung from a thin insulating string. A positively charged object is brought to point P. The two objects are not allowed to touch. What is true about the string when the positively charged object is present at point P?\nA. The tension is the same as before the object was present at point P.\nB. The tension is greater than when the object was not at point P, and the string stretches to the left of its original orientation.\nC. The tension is greater than when the object was not at point P, and the string stretches to the right of its original orientation.\nD. The tension is less than when the object was not at point P, and the string stretches to the left of its original orientation.\n", "Answer (final answer highlighted)": "C Negative charges will be drawn to the right side of the sphere, causing a force on the sphere to the right. The vertical tension will still have to balance with gravity, but there will also be a component of tension to the right.", "ImagePath": "Physics/191" }, { "Question": "\nPoints P and Q lie between the plates of a fully charged parallel plate capacitor as shown above. The lower plate is negatively charged and the upper plate is positively charged. How do the magnitudes of the electric fields at points P and Q compare?\nA. The field is 0 N/C at both points.\nB. The field is the same at both points, but not 0 N/C.\nC. EP > EQ\nD. EQ > EP\n", "Answer (final answer highlighted)": "B Between the plates of a parallel plate capacitor, the field will be constant and non-zero.", "ImagePath": "Physics/192" }, { "Question": "\nA pipe with a diameter of D splits into two smaller, identical pipes with diameter d. If the speed of the water in the small pipes is v, what is the speed of the water in the large pipe?\nA. dv/D\nB. 2dv/D\nC. d2v/D2\nD. 2d2v/D2\n", "Answer (final answer highlighted)": "D The continuity equation, A1v1 = A2v2 applies here as A1v1 = 2A2v2 where position 1 is in the large pipe. Solving for > https://img.apstudy.net/ap/physics-2/br20/Page_031_Image_0001.jpg .", "ImagePath": "Physics/193" }, { "Question": "What's the missing particle in the following nuclear reaction?What's the missing particle in the following nuclear reaction?\nA. Proton\nB. Neutron\nC. Electron\nD. Positron\n", "Answer (final answer highlighted)": "B In order to balance the mass number (the superscripts), you must have 2 + 63 = 64 + A, so A = 1. In order to balance the charge (the subscripts), you need 1 + 29 = 30 + Z, so Z = 0. A particle with a mass number of 1 and no charge is a neutron, https://img.apstudy.net/ap/physics-2/br20/Page_328_Image_0001.jpg .", "ImagePath": "Physics/194" }, { "Question": "A partial energy-level diagram for an atom is shown below. What photon energies could this atom emit if it begins in the n = 3 state?A partial energy-level diagram for an atom is shown below. What photon energies could this atom emit if it begins in the n = 3 state?\nA partial energy-level diagram for an atom is shown below. What photon energies could this atom emit if it begins in the n = 3 state? \nA. 5 eV only\nB. 3 eV or 7 eV only\nC. 2 eV, 3 eV, or 7 eV\nD. 3 eV, 4 eV, or 7 eV\n", "Answer (final answer highlighted)": "D If the atom begins in the n = 3 state, it could lose energy by making any of the following transitions: 3 \u00e2\u0086\u0092 2, 3 \u00e2\u0086\u0092 1, or 3 \u00e2\u0086\u0092 2 \u00e2\u0086\u0092 1. The 3 \u00e2\u0086\u0092 2 transition would result in the emission of -5 eV - (-8 eV) = 3 eV; the 3 \u00e2\u0086\u0092 1 transition would emit a -5 eV - (-12 eV) = 7 eV photon; and the 2 \u00e2\u0086\u0092 1 transition would result in the emission of -8 eV - (-12 eV) = 4 eV. Therefore, if the atom is initially in the n = 3 state, it could emit photons of energy 3 eV, 4 eV, or 7 eV.", "ImagePath": "Physics/195" }, { "Question": "\nThe above picture shows a converging mirror and an object, as well as the image, which is formed from standard ray tracing. After the image is formed, an opaque block, also shown in the picture, is inserted to block the top half of the mirror. What changes, if any, will be observed in the image?\nA. The image will remain complete but will be diminished in brightness.\nB. Part of the image will be absent, but the rest will be as bright was it was before the insertion of the block.\nC. Part of the image will be absent and the part which remains will be diminished in brightness.\nD. No change will be observed.\n", "Answer (final answer highlighted)": "A All of the rays which originate at the tip of the image and travel along paths that remain above the optic axis will be blocked. However, all of the rays which originate at the tip of the image and travel along paths that are below the optic axis at the plane of the block will be unaltered. As a result, fewer rays will converge at the image location, resulting in a less bright image.", "ImagePath": "Physics/196" }, { "Question": "\nThe above picture shows a converging mirror and an object, as well as the image, which is formed from standard ray tracing. Also shown, a dotted vertical line indicates the image place for this configuration. Also shown in a ray that travels from the top of the image to the point P on the curved mirror. The point P lies above the line which is parallel to the optic axis from the tip of the image. Where will the reflected ray from point P intersect the image plane?\nA. On the optic axis\nB. Below the optic axis but above the tip of the image\nC. At the tip of the image\nD. Farther from the optic axis than the tip of the image\n", "Answer (final answer highlighted)": "C Every ray, regardless of whether it is a principle ray or not, which originates at the tip of an object and strikes mirror, will converge at the tip of the image.", "ImagePath": "Physics/197" }, { "Question": "A beam of light in air is incident upon the smooth surface of a piece of flint glass, as shown:A beam of light in air is incident upon the smooth surface of a piece of flint glass, as shown:\nA beam of light in air is incident upon the smooth surface of a piece of flint glass, as shown:As the incident angle is increased toward \u00ce\u00b8 = 90\u00c2\u00b0, what observation is made of the refracted ray? All angle references are relative to the surface as shown for both rays.\nA. The refracted ray angle increases as the incident angle increases, but the value of the refracted angle is always smaller than the incident angle.\nB. The refracted ray angle increases as the incident angle increases, but the value of the refracted angle is always larger than the incident angle.\nC. The refracted ray angle increases as the incident angle increases until at some angle total internal reflection begins to occur.\nD. The refracted ray angle decreases as the incident angle increases, but the value of the refracted angle is always smaller than the incident angle.\n", "Answer (final answer highlighted)": "B As light travels into an optically dense medium, it will refract in toward the normal and away from the surface. So the light in the glass will always be at a greater angle from the surface than the light in the air, so (B) is correct. Note that total internal reflection, (C), will not occur in this situation because it only happens with the initial medium being more optically dense. https://img.apstudy.net/ap/physics-2/br20/Page_323_Image_0001.jpg", "ImagePath": "Physics/198" }, { "Question": "As shown in the figures below, a bar magnet is moved as a constant speed through a loop of wire. Figure A shows the bar magnet when it is as a position below the loop of wire and figure B shows the loop of wire after it has passed completely through the loop.As shown in the figures below, a bar magnet is moved as a constant speed through a loop of wire. Figure A shows the bar magnet when it is as a position below the loop of wire and figure B shows the loop of wire after it has passed completely through the loop.\nAs shown in the figures below, a bar magnet is moved as a constant speed through a loop of wire. Figure A shows the bar magnet when it is as a position below the loop of wire and figure B shows the loop of wire after it has passed completely through the loop.Which of the following best describes the direction or directions of the current induced in the loop when the loop is looked at from above? Note that when looking at the loop from above, the bar magnet will be moving toward the viewer.\nA. Always clockwise\nB. Always counterclockwise\nC. First clockwise, then counterclockwise\nD. First counterclockwise, then clockwise\n", "Answer (final answer highlighted)": "C First, you can eliminate (A) and (B). By definition, magnetic field lines emerge from the north pole and enter at the south pole. The magnetic field from the bar magnet will always point toward a viewer who is looking down at the loop from above. As the north pole gets closer to the loop, the field at the loop grows in strength, but as the south pole recedes from the loop, the magnetic field strength shrinks. Because of this, the flux changes from growing to shrinking as the magnet passes through the loop and the induced current must also change directions. Therefore, (A) and (B) are wrong. To determine whether (C) or (D) is correct, look at the first half of the motion. As the north pole get closer to the loop, the magnetic flux increases. To oppose an increasing flux, the direction of the magnetic field generated by induced current must be downward. Looking from above, a clockwise-induced current generates a downward magnetic field. Therefore, (C) is correct.", "ImagePath": "Physics/199" }, { "Question": "A conducting rod of length 0.2 m and resistance 10 ohms between its endpoints slides without friction along a U-shaped conductor in a uniform magnetic field B of magnitude 0.5 T perpendicular to the plane of the conductor, as shown in the diagram below.A conducting rod of length 0.2 m and resistance 10 ohms between its endpoints slides without friction along a U-shaped conductor in a uniform magnetic field B of magnitude 0.5 T perpendicular to the plane of the conductor, as shown in the diagram below.\nA conducting rod of length 0.2 m and resistance 10 ohms between its endpoints slides without friction along a U-shaped conductor in a uniform magnetic field B of magnitude 0.5 T perpendicular to the plane of the conductor, as shown in the diagram below.If the rod is moving with velocity v = 3 m/s to the left, what is the magnitude and direction of the current induced in the rod?\nA conducting rod of length 0.2 m and resistance 10 ohms between its endpoints slides without friction along a U-shaped conductor in a uniform magnetic field B of magnitude 0.5 T perpendicular to the plane of the conductor, as shown in the diagram below.Current \u00a0\u00a0\u00a0\u00a0 Direction\nA. 0.03 A \u00a0\u00a0\u00a0\u00a0 down\nB. 0.03 A \u00a0\u00a0\u00a0\u00a0 up\nC. 0.3 A \u00a0\u00a0\u00a0\u00a0 down\nD. 0.3 A \u00a0\u00a0\u00a0\u00a0 up\n", "Answer (final answer highlighted)": "A As we discussed in this chapter, the magnitude of the emf induced between the ends of the rod is \u00ce\u00b5 = BLv = (0.5 T)(0.2 m)(3 m/s) = 0.3 V. Since the resistance is 10 \u00ce\u00a9, the current induced will be I = V/R = (0.3 V)/(10 \u00ce\u00a9) = 0.03 A. To determine the direction of the current, note that since positive charges in the rod are moving to the left and the magnetic field points into the plane of the page, the right-hand rule states that the magnetic force, qv \u00c3\u0097 B, points downward. Since the resulting force on the positive charges in the rod is downward, so is the direction of the induced current.", "ImagePath": "Physics/200" }, { "Question": "What is the direction of force acting on the current-carrying wire as shown below?What is the direction of force acting on the current-carrying wire as shown below?\nA. To the bottom of the page\nB. Into the page\nC. Out of the page\nD. To the right of the page\n", "Answer (final answer highlighted)": "C Magnetic fields point from north to south. Therefore, the magnetic field between the two magnets is toward the right of the page. Use the right-hand rule. Because the B field is to the right and the charges through the wire flow to the bottom of the page, the force must be out of the page.", "ImagePath": "Physics/201" }, { "Question": "Here is a section of a wire with a current moving to the right. Where is the magnetic field strongest and pointing INTO the page?Here is a section of a wire with a current moving to the right. Where is the magnetic field strongest and pointing INTO the page?\nA. A\nB. B\nC. C\nD. D\n", "Answer (final answer highlighted)": "C Use the right-hand rule for wires. If you point your thumb to the right and wrap your fingers along the wire, you will note that the magnetic field goes into the page when you are below the wire and comes out of the page above the wire. This allows you to eliminate (A) and (B). Because https://img.apstudy.net/ap/physics-2/br20/Page_319_Image_0003.jpg , the closer you are to the wire, the stronger the magnetic field. Choice (C) is closer, so it is the correct answer.", "ImagePath": "Physics/202" }, { "Question": "In the figure below, what is the magnetic field at the Point P, which is midway between the two wires?In the figure below, what is the magnetic field at the Point P, which is midway between the two wires?\nA. 2\u00ce\u00bc0I/(\u00cf\u0080d), into the plane of the page\nB. \u00ce\u00bc0I/(2\u00cf\u0080d), out of the plane of the page\nC. \u00ce\u00bc0I/(2\u00cf\u0080d), into the plane of the page\nD. Zero\n", "Answer (final answer highlighted)": "D The strength of the magnetic field at a distance r from a long, straight wire carrying a current I is given by the equation B = (\u00ce\u00bc0/2\u00cf\u0080)(I/r). Therefore, the strength of the magnetic field at Point P due to either wire is B = (\u00ce\u00bc0/2\u00cf\u0080)(I/ https://img.apstudy.net/ap/physics-2/br20/1by2.jpg d). By the right-hand rule, the direction of the magnetic field at P due to the top wire is into the plane of the page and the direction of the magnetic field at P due to the bottom wire is out of the plane of the page. Since the two magnetic field vectors at P have the same magnitude and opposite directions, the net magnetic field at Point P is zero.", "ImagePath": "Physics/203" }, { "Question": "In the figure below, what must be the direction of the particle's velocity, v?In the figure below, what must be the direction of the particle's velocity, v?\nA. Downward, in the plane of the page\nB. Upward, in the plane of the page\nC. Out of the plane of the page\nD. Into the plane of the page\n", "Answer (final answer highlighted)": "C Since FB is always perpendicular to v, v cannot be upward or downward in the plane of the page; this eliminates (A) and (B). Because the charge is positive, the direction of FB will be the same as the direction of v \u00c3\u0097 B. In order for v \u00c3\u0097 B to be downward in the plane of the page, the right-hand rule implies that v must be out of the plane of the page.", "ImagePath": "Physics/204" }, { "Question": "A particle of charge -q moves to the left at speed v through a uniform magnetic field B which points into the second quadrant, as shown below.A particle of charge -q moves to the left at speed v through a uniform magnetic field B which points into the second quadrant, as shown below.\nA particle of charge -q moves to the left at speed v through a uniform magnetic field B which points into the second quadrant, as shown below.A second experiment is performed which results in the same magnitude and same direction of the magnetic force on the particle. Which of the following could NOT be the conditions for the new experiment?\nA. B is unchanged, but q is now positive and v is directed to the right.\nB. The charge is still negative, but v and B are rotated 90\u00c2\u00b0 into the plane of the paper so that v is directed along the -z-axis.\nC. The charge is still negative, but v and B are rotated 90\u00c2\u00b0 counterclockwise so that v is directed along the -y-axis.\nD. V is unchanged, but q is now positive and B is rotated 180\u00c2\u00b0 to point into the fourth quadrant.\n", "Answer (final answer highlighted)": "B All of the new experimental set-ups have the same magnitude of force as the original. In order to have the new experiment result in the same magnitude of the force, FB = |q||v||B| sin(\u00ce\u00b8) must be unchanged. Changing the signs of q, v, or B do not change the strength of the force. Rotating v and B by the same amount leaves \u00ce\u00b8 unchanged, and rotating B by 180\u00c2\u00b0 results in the same value for sin(\u00ce\u00b8). Thus, the invalid experiment must have a different direction of the magnetic force. Using the right-hand rule, rotating your thumb and fingers by 90\u00c2\u00b0 into the plane of the paper causes the magnetic force to rotate from the original direction of into the plane (recalling q is negative) to finally point to the right.", "ImagePath": "Physics/205" }, { "Question": "\nIf each of the capacitors in the array shown above is C, what is the capacitance of the entire combination?\nA. C/2\nB. 2C/3\nC. 5C/6\nD. 2C\n", "Answer (final answer highlighted)": "D https://img.apstudy.net/ap/physics-2/br20/Page_316_Image_0001.jpg Capacitors 1 and 2 are in series, so their equivalent capacitance is C1-2 = C/2. (This is obtained from the equation 1/C1-2 = 1/C1 + 1/C2 = 1/C + 1/C = 2/C.) Capacitors 4 and 5 are also in series, so their equivalent capacitance is C4-5 = C/2. The capacitances C1-2, C3, and C4-5 are in parallel, so the overall equivalent capacitance is (C/2) + C + (C/2) = 2C.", "ImagePath": "Physics/206" }, { "Question": "\nWhat is the voltage drop across the 12 \u00ce\u00a9 resistor in the portion of the circuit shown above?\nA. 24 V\nB. 36 V\nC. 48 V\nD. 72 V\n", "Answer (final answer highlighted)": "B The three parallel resistors are equivalent to a single 2 \u00ce\u00a9 resistor, because https://img.apstudy.net/ap/physics-2/br20/Page_315_Image_0003.jpg . This 2 \u00ce\u00a9 resistance is in series with the given 2 \u00ce\u00a9 resistor, so their equivalent resistance is 2 \u00ce\u00a9 + 2 \u00ce\u00a9 = 4 \u00ce\u00a9. Therefore, three times as much current will flow through this equivalent 4 \u00ce\u00a9 resistance in the top branch as through the parallel 12 \u00ce\u00a9 resistor in the bottom branch, which implies that the current through the bottom branch is 3 A, and the current through the top branch is 9 A. The voltage drop across the 12 \u00ce\u00a9 resistor is therefore V = IR = (3 A)(12 \u00ce\u00a9) = 36 V.", "ImagePath": "Physics/207" }, { "Question": "\nThree identical light bulbs are connected to a source of emf, as shown in the diagram above. What will happen if the middle bulb burns out?\nA. The light intensity of the other two bulbs will decrease (but they won't go out).\nB. The light intensity of the other two bulbs will increase.\nC. The light intensity of the other two bulbs will remain the same.\nD. More current will be drawn from the source of emf.\n", "Answer (final answer highlighted)": "C If each of the identical bulbs has resistance R, then the current through each bulb is \u00ce\u00b5/R. This is unchanged if the middle branch is taken out of the parallel circuit. (What will change is the total amount of current provided by the battery.)", "ImagePath": "Physics/208" }, { "Question": "\nThe circuit shown above has a constant voltage between points a and b. The voltage has been flowing for a long time. What is the resistance of the circuit?\nA. 0.47 \u00ce\u00a9\nB. 1.5 \u00ce\u00a9\nC. 2.1 \u00ce\u00a9\nD. 10 \u00ce\u00a9\n", "Answer (final answer highlighted)": "C Because the voltage has been established for a long time, the capacitor will be full, so it behaves like an open switch. This puts 4 \u00ce\u00a9 resistor and the top 3 \u00ce\u00a9 resistor in series with one another, making an equivalent resistor of 7 \u00ce\u00a9. That combination in parallel with the other 3 \u00ce\u00a9 resistor, so https://img.apstudy.net/ap/physics-2/br20/Page_315_Image_0002.jpg .", "ImagePath": "Physics/209" }, { "Question": "A charge Q creates an electric field through which a second charge q moves, as shown below. q is initially at point B and is moved to point A. The potential from Q at position A is VA = 100 V and at B is VB = 200 V. The charge on q is negative. What is the sign of Q and the sign of the work done by the electric field of Q as q is moved from B to A?A charge Q creates an electric field through which a second charge q moves, as shown below. q is initially at point B and is moved to point A. The potential from Q at position A is VA = 100 V and at B is VB = 200 V. The charge on q is negative. What is the sign of Q and the sign of the work done by the electric field of Q as q is moved from B to A?\nA. Q is positive and the work done by the electric field is positive.\nB. Q is positive and the work done by the electric field is negative.\nC. Q is negative and the work done by the electric field is positive.\nD. Q is negative and the work done by the electric field is negative.\n", "Answer (final answer highlighted)": "B The charge Q must be positive because the potential decreases as the distance from the charge increases. A negative charge will be attracted to a positive charge. This means that the electric field of Q would do positive work if q were brought closer, and it would do negative work if q were moved farther away.", "ImagePath": "Physics/210" }, { "Question": "\nWhich points in this uniform electric field (between the plates of the capacitor) shown above lie on the same equipotential?\nA. 1 and 3 only\nB. 2 and 4 only\nC. None lie on the same equipotential.\nD. 1, 2, 3, and 4 all lie on the same equipotential since the electric field is uniform.\n", "Answer (final answer highlighted)": "B Because E is uniform, the potential varies linearly with distance from either plate (\u00ce\u0094V = Ed). Since Points 2 and 4 are at the same distance from the plates, they lie on the same equipotential. (The equipotentials in this case are planes parallel to the capacitor plates.)", "ImagePath": "Physics/211" }, { "Question": "Below is shown a section near the center of a parallel plate capacitor. There are 4 labeled positions between the plates shown as A, B, C, and D. Relative to A, which point has the largest potential difference and why?Below is shown a section near the center of a parallel plate capacitor. There are 4 labeled positions between the plates shown as A, B, C, and D. Relative to A, which point has the largest potential difference and why?\nA. Point A because the potential difference is infinite when the position between points is 0 m.\nB. Point B because it is the same distance from the -Q plate as A.\nC. Point C because it is farther in distance from Point A.\nD. Point D because it is closest to the +Q Plate.\n", "Answer (final answer highlighted)": "D Equipotential curves for a parallel plate capacitor are horizontal lines. Both (A) and (B) are at the same potential as (A), so their potential difference is 0 V. As one moves closer to the +Q plate, the potential will increase, so (D) is correct.", "ImagePath": "Physics/212" }, { "Question": "What is the total work performed on the gas as it is transformed from state a to state c, along the path indicated?What is the total work performed on the gas as it is transformed from state a to state c, along the path indicated?\nA. 1,500 J\nB. 3,000 J\nC. 4,500 J\nD. 9,500 J\n", "Answer (final answer highlighted)": "C No work is done during the step from state a to state b because the volume doesn't change. Therefore, the work done from a to c is equal to the work done from b to c. Since the pressure remains constant (this step is isobaric), find that W = -P\u00ce\u0094V = -(3.0 \u00c3\u0097 105 Pa)[(10 - 25) \u00c3\u0097 10-3 m3] = 4,500 J", "ImagePath": "Physics/213" }, { "Question": "\nThe figure above shows a portion of a conduit for water, one with rectangular cross sections. If the flow speed at the top is v, what is the flow speed at the bottom?\nA. 4v\nB. 8v\nC. 12v\nD. 16v\n", "Answer (final answer highlighted)": "D Each side of the rectangle at the bottom of the conduit is 1/4 the length of the corresponding side at the top. Therefore, the cross-sectional area at the bottom is (1/4)2 = 1/16 the cross-sectional area at the top. The Continuity Equation states that the flow speed, v, is inversely proportional to the cross-sectional area, A. So, if A at the bottom is 1/16 the value of A at the top, then the flow speed at the bottom is 16 times the flow speed at the top.", "ImagePath": "Physics/214" }, { "Question": "\nA ball is tied to a string and placed in a container of water as shown. The water is slowly drained from the container until the water level is below the position of the ball shown, but the draining stops while there is still water in the container. The tension in the string is measured while this occurs. Which describes why the tension measurements decrease?\nA. The tension decreases because there is less pressure on the ball when the water level drops because of the change in the water depth.\nB. The tension decreases because there is less pressure on the ball when the water level drops because the water is moving at a faster speed.\nC. The tension decreases because the force of gravity on the ball decreases.\nD. The tension decreases because the buoyant force on the ball decreases.\n", "Answer (final answer highlighted)": "D The upward force on the ball is the buoyant force. The downward forces are gravity and tension. Gravity will remain constant, so you can eliminate (C). The change in tension results from a change in the buoyant force and not because of pressure, so you can eliminate (A) and (B).", "ImagePath": "Physics/215" } ] }