| {"id": "CAP_mathematics-102-1", "question": "算式 $-6+2 \\times [16-(-32) \\div 8]$ 之值為何？", "correct_choices": ["3"], "incorrect_choices": ["-24", "-4", "30"], "metadata": {"timestamp": "2023-10-29 01:58:12.626441", "source": "CAP_mathematics-102"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-102-2", "question": "數線上A、B兩點所表示的數分別為a、b，且$a<b$, $|a-b|=9$。若從A點向右移動3單位到達C點，則B、C兩點的距離為何？ ", "correct_choices": ["6"], "incorrect_choices": ["3", "9", "12"], "metadata": {"timestamp": "2023-10-29 01:58:12.626494", "source": "CAP_mathematics-102"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-102-6", "question": "若 A、Ｂ分別表示多項式 $2x=3$與$3x+1$，則$\\frac{3A+B}{2}-\\frac{A-3B}{3}$與下列哪一個式子相同？", "correct_choices": ["$\\frac{41x-12}{6}$"], "incorrect_choices": ["$\\frac{13x-12}{6}$", "$\\frac{13x-36}{6}$", "$\\frac{41x-36}{6}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.626531", "source": "CAP_mathematics-102"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-102-7", "question": "在30~50的正整數中，將與48互質的數由小到大排列，則第5個數為何？", "correct_choices": ["43"], "incorrect_choices": ["37", "41", "47"], "metadata": {"timestamp": "2023-10-29 01:58:12.626564", "source": "CAP_mathematics-102"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-102-8", "question": "算式 $\\frac{6}{\\sqrt{7}-\\sqrt{5}} - \\frac{12}{\\sqrt{11}+\\sqrt{5}}$之值為何？", "correct_choices": ["$3\\sqrt{7} + 5\\sqrt{5} - 2\\sqrt{11}$"], "incorrect_choices": ["$3\\sqrt{2}-3$", "$6\\sqrt{3} - 2\\sqrt{6}$", "$3\\sqrt{7} - 5\\sqrt{5} - 2\\sqrt{11}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.626602", "source": "CAP_mathematics-102"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-102-9", "question": "已知一等差數列的公差是2，前20項和是500，求此等差數列的首項為何？", "correct_choices": ["6"], "incorrect_choices": ["5", "10", "12"], "metadata": {"timestamp": "2023-10-29 01:58:12.626632", "source": "CAP_mathematics-102"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-102-12", "question": "已知在KTV唱歌消費，除了唱歌的費用外，還需多付10%的服務費。若小明在KTV唱歌，含服務費共花了x元，則他付的服務費可用下列哪一個式子表示？", "correct_choices": ["$\\frac{1}{11}x$"], "incorrect_choices": ["$\\frac{1}{10}x$", "$\\frac{9}{10}x$", "$\\frac{9}{11}x$"], "metadata": {"timestamp": "2023-10-29 01:58:12.626658", "source": "CAP_mathematics-102"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-102-13", "question": "座標平面上有一矩形ABCD，其中直線AC的方程式為x+2y=7。若B點座標為(1,1)，且AB與y軸平行，則D點座標為何？", "correct_choices": ["(5,3)"], "incorrect_choices": ["(1,3)", "(3,5)", "(5,1)"], "metadata": {"timestamp": "2023-10-29 01:58:12.626684", "source": "CAP_mathematics-102"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-102-14", "question": "算式$2 \\times (2000^{2}-1) - 2001^{2} -1999^{2}$之值為何？", "correct_choices": ["-4"], "incorrect_choices": ["4", "7998", "-8002"], "metadata": {"timestamp": "2023-10-29 01:58:12.626709", "source": "CAP_mathematics-102"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-102-22", "question": "若干對夫妻參加新婚座談會，座談會有提供參加的夫妻每人一杯飲料，其中飲料有茶、咖啡、果汁三種選擇。若座談會中丈夫選擇茶、咖啡、果汁的杯數比為5:3:2，妻子選擇茶、咖啡、果汁的杯數比為2:2:1，則所有參加者選擇茶、咖啡、果汁的杯數比為何？", "correct_choices": ["9 : 7 : 4"], "incorrect_choices": ["7 : 5 : 3", "16 : 12 : 7", "20 : 16 : 9"], "metadata": {"timestamp": "2023-10-29 01:58:12.626735", "source": "CAP_mathematics-102"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-1", "question": "算式 $(\\sqrt{6}+ \\sqrt{10} × \\sqrt{15})× \\sqrt{3}$ 之值為何?", "correct_choices": ["$18\\sqrt{2}$"], "incorrect_choices": ["$2\\sqrt{42}$", "$12\\sqrt{5}$", "$12\\sqrt{13}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.626782", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-2", "question": "若A為一數，且A = $2^{5} × 7^{6} × 11^{4}$，則下列選項中所表示的數，何者是A的因數?", "correct_choices": ["$2^{4} \\times 7^{4} \\times 11^{4}$"], "incorrect_choices": ["$2^{4} \\times 5$", "$7^{7} \\times 11^{3}$", "$2^{6} \\times 7^{6} \\times 11^{6}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.626805", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-4", "question": "有一箱子裝有 3 張分別標示 4 、5 、6 的號碼牌，已知小武以每次取一張且取 後不放回的方式，先後取出 2 張牌，組成一個二位數，取出第 1 張牌的號碼為 十位數，第 2 張牌的號碼為個位數。若先後取出 2 張牌組成二位數的每一種 結果發生的機會都相同，則組成的二位數為 6 的倍數的機率為何?", "correct_choices": ["$\\frac{1}{6}$"], "incorrect_choices": ["$\\frac{1}{4}$", "$\\frac{1}{3}$", "$\\frac{1}{2}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.626828", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-5", "question": "算式 743 × 369 − 741 × 370 之值為何?", "correct_choices": ["-3"], "incorrect_choices": ["-2", "2", "3"], "metadata": {"timestamp": "2023-10-29 01:58:12.626851", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-6", "question": "若二元一次聯立方程式 $5x-y=5, y=\\frac{1}{5}x$ 的解為x=a，y=b，則a+b之值為何?", "correct_choices": ["$\\frac{5}{4}$"], "incorrect_choices": ["$\\frac{75}{13}$", "$\\frac{31}{25}$", "$\\frac{29}{25}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.626874", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-7", "question": "已知果農販賣的番茄，其重量與價錢成線型函數關係，今小華向果農買一竹籃 的番茄，含竹籃秤得總重量為 15 公斤，付番茄的錢 250 元。若他再加買 0.5 公斤的番茄，需多付 10 元，則空竹籃的重量為多少公斤?", "correct_choices": ["2.5"], "incorrect_choices": ["1.5", "2", "3"], "metadata": {"timestamp": "2023-10-29 01:58:12.626949", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-14", "question": "小明在網路上搜尋到水資源的資料如下:「地球上水的總儲量為 $1.36 \\times 10^{18}$ 立方公尺，其中可供人類使用的淡水只占全部的 0.3%。」根據他搜尋到的資 料，判斷可供人類使用的淡水有多少立方公尺?", "correct_choices": ["$4.08 \\times 10^{15}$"], "incorrect_choices": ["$4.08 \\times 10^{14}$", "$4.08 \\times 10^{16}$", "$4.08 \\times 10^{17}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.626975", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-15", "question": "計算多項式 $10x^{3} + 7x^{2} + 15x − 5$ 除以 5x^{2} 後，得餘式為何?", "correct_choices": ["$15x-5$"], "incorrect_choices": ["$\\frac{15x-5}{5x^{2}}$", "$2x^{2}+15x-5$", "$3x-1$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627000", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-17", "question": "$(3x+2)(−x^{6}+3x^{5})+(3x+2)(−2x^{6}+x^{5})+(x+1)(3x^{6}−4x^{5})$ 與下列哪 一個式子相同?", "correct_choices": ["$-( 3x^{6} − 4x^{5} )( 2x + 1 )$"], "incorrect_choices": ["$( 3x^{6} − 4x^{5} )( 2x + 1 )$", "$( 3x^{6} − 4x^{5} )( 2x + 3 )$", "$-( 3x^{6} − 4x^{5} )( 2x + 3 )$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627024", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-23", "question": "若有一等差數列，前九項和為 54，且第一項、第四項、第七項的和為 36 ， 則此等差數列的公差為何?", "correct_choices": ["-6"], "incorrect_choices": ["-3", "3", "6"], "metadata": {"timestamp": "2023-10-29 01:58:12.627047", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-25", "question": "有甲、乙兩個箱子，其中甲箱內有 98 顆球，分別標記號碼 1 ~ 98 ，且號碼為 不重複的整數，乙箱內沒有球。已知小育從甲箱內拿出 49 顆球放入乙箱後， 乙箱內球的號碼的中位數為 40。若此時甲箱內有 a 顆球的號碼小於 40 ，有 b 顆球的號碼大於 40 ，則關於 a 、 b 之值，下列何者正確?", "correct_choices": ["b = 34"], "incorrect_choices": ["a = 16", "a = 24", "b = 24"], "metadata": {"timestamp": "2023-10-29 01:58:12.627070", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-103-26", "question": "已知 a、h、k 為三數，且二次函數 $y = a( x − h )^{2} + k$ 在坐標平面上的圖形通 過(0,5 )、(10,8 )兩點。若$a<0$，$0<h<10$，則h之值可能為下列何者?", "correct_choices": ["7"], "incorrect_choices": ["1", "3", "5"], "metadata": {"timestamp": "2023-10-29 01:58:12.627093", "source": "CAP_mathematics-103"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-104-1", "question": "算式$(−1 \\frac{1}{2}) \\times (−3 \\frac{1}{4}) \\times \\frac{2}{3}$之值為何?", "correct_choices": ["$\\frac{13}{4}$"], "incorrect_choices": ["$\\frac{1}{4}$", "$\\frac{11}{12}$", "$\\frac{11}{4}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627117", "source": "CAP_mathematics-104"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-104-4", "question": "算式 $(−3)^{4} − 7^{2} − \\frac{2^{6}}{(−2)^{3}}$ 之值為何?", "correct_choices": ["40"], "incorrect_choices": ["-138", "-122", "24"], "metadata": {"timestamp": "2023-10-29 01:58:12.627139", "source": "CAP_mathematics-104"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-104-6", "question": "計算多項式 $−2x (3x − 2)^{2} + 3$ 除以 $3x − 2$ 後，所得商式與餘式兩者之和為何?", "correct_choices": ["$$−6x^{2} +4x+3"], "incorrect_choices": ["$−2x + 3$", "$−6x^{2} + 4x$", "$−6x^{2} −4x+3$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627162", "source": "CAP_mathematics-104"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-104-8", "question": "下列哪一個選項中的等式不成立?", "correct_choices": ["$ \\sqrt{(−5)^{6}} = (−5)^{3}$"], "incorrect_choices": ["$ \\sqrt{3^{8}}=3^{4}$", "$ \\sqrt{3^{4} \\times 5^{10}}= 3^{2} \\times 5^5$", "$ \\sqrt{(-3)^{4} \\times (-5)^{8}}= (-3)^{2} \\times (-5)^4$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627184", "source": "CAP_mathematics-104"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-104-14", "question": "判斷一元二次方程式 $x^{2} − 8x − a = 0$ 中的 a 為下列哪一個數時，可使得此 方程式的兩根均為整數?", "correct_choices": ["20"], "incorrect_choices": ["12", "16", "24"], "metadata": {"timestamp": "2023-10-29 01:58:12.627206", "source": "CAP_mathematics-104"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-104-16", "question": "判斷下列各式的值，何者最大?", "correct_choices": ["$16 \\times 17^{2} −18^{2}$"], "incorrect_choices": ["$25 \\times 13^{2} −15^{2}$", "$9 \\times 21^{2} −13^{2}$", "$4 \\times 31^{2} −12^{2}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627229", "source": "CAP_mathematics-104"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-104-21", "question": "坐標平面上，二次函數 $y = −x^{2} + 6x − 9$ 的圖形的頂點為 A，且此函數圖形與 y 軸交於 B 點。若在此函數圖形上取一點 C，在 x 軸上取一點 D ，使得 四邊形 ABCD 為平行四邊形，則 D 點坐標為何?", "correct_choices": ["(9,0)"], "incorrect_choices": ["(6,0)", "(-6,0)", "(-9,0)"], "metadata": {"timestamp": "2023-10-29 01:58:12.627252", "source": "CAP_mathematics-104"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-104-22", "question": "已知甲校原有 1016 人，乙校原有 1028 人，寒假期間甲、乙兩校人數變動的 原因只有轉出與轉入兩種，且轉出的人數比為 1 : 3，轉入的人數比也為 1 : 3。 若寒假結束開學時甲、乙兩校人數相同，則乙校開學時的人數與原有的人數 相差多少?", "correct_choices": ["18"], "incorrect_choices": ["6", "9", "12"], "metadata": {"timestamp": "2023-10-29 01:58:12.627275", "source": "CAP_mathematics-104"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-104-24", "question": "將甲、乙、丙三個正分數化為最簡分數後，其分子分別為6、15、10， 其分母的最小公倍數為 360。判斷甲、乙、丙三數的大小關係為何?", "correct_choices": ["乙 > 甲 > 丙"], "incorrect_choices": ["乙 > 丙 > 甲", "甲 > 乙 > 丙", "甲 > 丙 > 乙"], "metadata": {"timestamp": "2023-10-29 01:58:12.627297", "source": "CAP_mathematics-104"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-105-1", "question": "x=−3，y=1為下列哪一個二元一次方程式的解?", "correct_choices": ["$x + 2y = −1$"], "incorrect_choices": ["$x − 2y = 1$", "$2x + 3y = 6$", "$2x − 3y = −6$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627319", "source": "CAP_mathematics-105"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-105-2", "question": "算式$[−5−(−11)] \\div (\\frac{3}{2} \\times 4)$之值為何?", "correct_choices": ["1"], "incorrect_choices": ["16", "$-\\frac{8}{3}$", "$-\\frac{128}{3}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627341", "source": "CAP_mathematics-105"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-105-3", "question": "計算$(2x+1)(x−1)−(x^{2} +x−2)$的結果，與下列哪一個式子相同?", "correct_choices": ["$x^{2} −2x+1$"], "incorrect_choices": ["$x^{2} −2x-3$", "$x^{2} +x-3$", "$x^{2} −3$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627364", "source": "CAP_mathematics-105"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-105-9", "question": "小昱和阿帆均從同一本書的第 1 頁開始，逐頁依順序在每一頁上寫一個數。小昱 在第 1 頁寫 1，且之後每一頁寫的數均為他在前一頁寫的數加 2;阿帆在第 1 頁 寫 1，且之後每一頁寫的數均為他在前一頁寫的數加 7。若小昱在某頁寫的數為 101，則阿帆在該頁寫的數為何?", "correct_choices": ["351"], "incorrect_choices": ["350", "356", "358"], "metadata": {"timestamp": "2023-10-29 01:58:12.627408", "source": "CAP_mathematics-105"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-105-10", "question": "甲箱內有4顆球，顏色分別為紅、黃、綠、藍;乙箱內有3顆球，顏色分別 為紅、黃、黑。小賴打算同時從甲、乙兩個箱子中各抽出一顆球，若同一箱中 每球被抽出的機會相等，則小賴抽出的兩顆球顏色相同的機率為何?", "correct_choices": ["$\\frac{1}{6}$"], "incorrect_choices": ["$\\frac{1}{3}$", "$\\frac{2}{7}$", "$\\frac{7}{12}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627430", "source": "CAP_mathematics-105"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-105-11", "question": "坐標平面上有一個二元一次方程式的圖形，此圖形通過 ( − 3 , 0 )、( 0 , − 5 ) 兩點。 判斷此圖形與下列哪一個方程式的圖形的交點在第三象限?", "correct_choices": ["y + 4 = 0"], "incorrect_choices": ["x − 4 = 0", "x + 4 = 0", "y − 4 = 0"], "metadata": {"timestamp": "2023-10-29 01:58:12.627452", "source": "CAP_mathematics-105"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-105-13", "question": "若一正方形的面積為20平方公分，周長為x公分，則x的值介於下列哪兩個 整數之間?", "correct_choices": ["1718"], "incorrect_choices": ["1617", "1819", "1920"], "metadata": {"timestamp": "2023-10-29 01:58:12.627474", "source": "CAP_mathematics-105"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-105-17", "question": "已知 a、b、c 為三正整數，且 a、b 的最大公因數為 12，a、c 的最大公因數 為 18。若 a 介於 50 與 100 之間，則下列敘述何者正確?", "correct_choices": ["8 是 a 的因數，8 不是 b 的因數"], "incorrect_choices": ["8 是 a 的因數，8 是 b 的因數", "8 不是 a 的因數，8 是 c 的因數", "8 不是 a 的因數，8 不是 c 的因數"], "metadata": {"timestamp": "2023-10-29 01:58:12.627496", "source": "CAP_mathematics-105"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-105-21", "question": "坐標平面上，某二次函數圖形的頂點為(2,−1)，此函數圖形與x軸相交於P、Q 兩點，且 $\\overline{PQ} = 6$ 。若此函數圖形通過 ( 1 , a )、( 3 , b )、( −1 , c )、( −3 , d ) 四點，則 a、b 、c 、d 之值何者為正?", "correct_choices": ["d"], "incorrect_choices": ["a", "b", "c"], "metadata": {"timestamp": "2023-10-29 01:58:12.627518", "source": "CAP_mathematics-105"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-1", "question": "算式$(−2) \\times |−5| − |−3|$ 之值為何?", "correct_choices": ["-13"], "incorrect_choices": ["13", "7", "-7"], "metadata": {"timestamp": "2023-10-29 01:58:12.627540", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-2", "question": "下列哪一個選項中的等式成立?", "correct_choices": ["$\\sqrt{2^{2}} = 2$"], "incorrect_choices": ["$\\sqrt{3^{3}} = 2$", "$\\sqrt{4^{4}} = 4$", "$\\sqrt{5^{5}} = 5$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627562", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-3", "question": "計算 $6x \\dot (3 − 2x)$ 的結果，與下列哪一個式子相同?", "correct_choices": ["$−12x^{2} + 18x$"], "incorrect_choices": ["$−12x^{2} + 3$", "$16x$", "$6x$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627586", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-5", "question": "已知坐標平面上有兩直線相交於一點 (2,a)，且兩直線的方程式分別為 $2x + 3y = 7$、$3x − 2y = b$，其中 a、b 為兩數。求 a + b 之值為何?", "correct_choices": ["5"], "incorrect_choices": ["1", "-1", "-5"], "metadata": {"timestamp": "2023-10-29 01:58:12.627608", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-6", "question": "阿信、小怡兩人打算搭乘同一班次電車上學。若此班次電車共有 5 節車廂，且 阿信從任意一節車廂上車的機會相等，小怡從任意一節車廂上車的機會相等， 則兩人從同一節車廂上車的機率為何?", "correct_choices": ["$\\frac{1}{5}$"], "incorrect_choices": ["$\\frac{1}{2}$", "$\\frac{1}{10}$", "$\\frac{1}{25}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627631", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-7", "question": "平面上有 A、B、C 三點，其中 AB = 3，BC = 4，AC = 5。若分別以 A、B、C 為圓心，半徑長為 2 畫圓，畫出圓 A、圓 B、圓 C，則下列敘述何者正確?", "correct_choices": ["圓 A 與圓 C 外離，圓 B 與圓 C 外切"], "incorrect_choices": ["圓 A 與圓 C 外切，圓 B 與圓 C 外切", "圓 A 與圓 C 外切，圓 B 與圓 C 外離", "圓 A 與圓 C 外離，圓 B 與圓 C 外離"], "metadata": {"timestamp": "2023-10-29 01:58:12.627653", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-8", "question": "下列選項中所表示的數，哪一個與 252 的最大公因數為 42 ?", "correct_choices": ["$2 × 3 × 5^{2} × 7^{2}$"], "incorrect_choices": ["$2 × 3^{2} × 5 × 7^{2}$", "$2^{2} × 3 × 5^{2} × 7$", "$2^{2} × 3^{2} × 5 × 7$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627675", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-9", "question": "某高中的籃球隊成員中，一、二年級的成員共有 8 人，三年級的成員有 3 人。 一、二年級的成員身高 ( 單位:公分 ) 如下:\n172、172、174、174、176、176、178、178。 若隊中所有成員的平均身高為 178 公分，則隊中三年級成員的平均身高為幾公分?", "correct_choices": ["186"], "incorrect_choices": ["178", "181", "183"], "metadata": {"timestamp": "2023-10-29 01:58:12.627697", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-10", "question": "已知在卡樂芙超市內購物總金額超過 190 元時， 購物總金額有打八折的優惠。 安妮帶 200 元到卡樂芙超市買棒棒糖，若棒棒糖每根 9 元，則她最多可買多少 根棒棒糖?", "correct_choices": ["27"], "incorrect_choices": ["22", "23", "28"], "metadata": {"timestamp": "2023-10-29 01:58:12.627720", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-12", "question": "一元二次方程式$x^{2}−8x=48$可表示成$(x−a)^{2}=48+b$的形式，其中a、b 為整數。求 a + b 之值為何?", "correct_choices": ["20"], "incorrect_choices": ["12", "-12", "-20"], "metadata": {"timestamp": "2023-10-29 01:58:12.627742", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-15", "question": "威立到小吃店買水餃，他身上帶的錢恰好等於 15 粒蝦仁水餃或 20 粒韭菜 水餃的價錢。若威立先買了 9 粒蝦仁水餃，則他身上剩下的錢恰好可買多少粒 韭菜水餃?", "correct_choices": ["8"], "incorrect_choices": ["6", "9", "12"], "metadata": {"timestamp": "2023-10-29 01:58:12.627764", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-17", "question": "若a、b為兩質數且相差2，則ab+1之值可能為下列何者?", "correct_choices": ["$42^2$"], "incorrect_choices": ["$39^2$", "$40^2$", "$41^2$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627786", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-106-22", "question": "已知坐標平面上有兩個二次函數 $y = a(x + 1)(x − 7)$、$y = b(x + 1)(x − 15)$ 的 圖形，其中 a、b 為整數。判斷將二次函數 $y = b(x + 1)(x − 15)$ 的圖形依下列 哪一種方式平移後，會使得此兩圖形的對稱軸重疊?", "correct_choices": ["向左平移 4 單位"], "incorrect_choices": ["向右平移 4 單位", "向左平移 8 單位", "向右平移 8 單位"], "metadata": {"timestamp": "2023-10-29 01:58:12.627809", "source": "CAP_mathematics-106"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-2", "question": "已知 $a=({\\frac{3}{14}}-{\\frac{2}{15}}~)-{\\frac{1}{16}},b={\\frac{3}{14}}-({\\frac{2}{15}}-{\\frac{1}{16}}{}),c={\\frac{3}{14}}-{\\frac{2}{15}}-{\\frac{1}{16}}$，判斷下列敘述何者正確", "correct_choices": ["$a=c, b\\neq c$"], "incorrect_choices": ["$a=c, b=c$", "$a\\neq c, b=c$", "$a\\neq c, b\\neq c$"], "metadata": {"timestamp": "2023-10-29 01:58:12.627831", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-3", "question": "已知坐標平面上，一次函數$y=3x+a$的圖形通過點$(0,-4)$，其中$a$為一數，求$a$的值為何？", "correct_choices": ["-4"], "incorrect_choices": ["-12", "4", "12"], "metadata": {"timestamp": "2023-10-29 01:58:12.627854", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-4", "question": "已知某文具店販售的筆記本每本售價均相等且超過 10 元，小錦和小勳在此 文具店分別購買若干本筆記本。若小錦購買筆記本的花費為36 元，則小勳 購買筆記本的花費可能為下列何者?", "correct_choices": ["48元"], "incorrect_choices": ["16元", "27元", "30元"], "metadata": {"timestamp": "2023-10-29 01:58:12.627876", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-5", "question": "若二元一次聯立方程式$\\begin{cases} 7x-3y=8 \\\\ 3x-y=8 \\end{cases}$ 的解為 $x=a$，$y=b$，則$a+b$之值為何？", "correct_choices": ["24"], "incorrect_choices": ["0", "-4", "-8"], "metadata": {"timestamp": "2023-10-29 01:58:12.627898", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-7", "question": "算式 $\\sqrt{6} \\times (\\frac{1}{\\sqrt{3}}-1)$ 之值為何？", "correct_choices": ["$\\sqrt{2}-\\sqrt{6}$"], "incorrect_choices": ["$\\sqrt{2}-1$", "$2-\\sqrt{6}$", "1"], "metadata": {"timestamp": "2023-10-29 01:58:12.627921", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-8", "question": "若一元二次方程式 $x^2-8x-3\\times 11=0$ 的兩根為 a、b，且 $a>b$，則 $a-2b$ 之值為何？", "correct_choices": ["17"], "incorrect_choices": ["-25", "-19", "5"], "metadata": {"timestamp": "2023-10-29 01:58:12.627943", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-16", "question": "若小舒從 1 ~ 50 的整數中挑選 4 個數，使其由小到大排序後形成一等差 數列，且 4 個數中最小的是7，則下列哪一個數不可能出現在小舒挑選的數之中?", "correct_choices": ["30"], "incorrect_choices": ["20", "25", "35"], "metadata": {"timestamp": "2023-10-29 01:58:12.627965", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-17", "question": "已知 $a=3.1\\times 10^{-4}$，$b=5.2\\times 10^{-8}$，判斷下列關於 $a-b$ 之值的敘述何者正確？", "correct_choices": ["介於 0、1 之間"], "incorrect_choices": ["比 1 大", "介於 -1、0 之間", "比 -1 小"], "metadata": {"timestamp": "2023-10-29 01:58:12.627988", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-21", "question": "已知坐標平面上有一直線 $L$，其方程式為 $y+2=0$，且 $L$ 與二次函數 $y=3x^2+a$ 的圖形相交於 $A$、$B$ 兩點；與二次函數$y=-2x^2+b$ 的圖形相交於$C$、$D$ 兩點，其中 $a$、$b$ 為整數。若 ${\\overline{AB}}=2$，${\\overline{CD}}=4$，則 $a+b$ 之值為何？", "correct_choices": ["1"], "incorrect_choices": ["9", "16", "24"], "metadata": {"timestamp": "2023-10-29 01:58:12.628010", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-23", "question": "小柔想要搾果汁，她有蘋果、芭樂、柳丁三種水果，且其顆數比為 9:7:6。 小柔搾完果汁後，蘋果、芭樂、柳丁的顆數比變為 6:3:4。已知小柔搾果汁 時沒有使用柳丁，關於她搾果汁時另外兩種水果的使用情形，下列敘述何者正確?", "correct_choices": ["只使用芭樂"], "incorrect_choices": ["只使用蘋果", "使用蘋果及芭樂，且使用的蘋果顆數比使用的芭樂顆數多", "使用蘋果及芭樂，且使用的芭樂顆數比使用的蘋果顆數多"], "metadata": {"timestamp": "2023-10-29 01:58:12.628032", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-107-25", "question": "某商店將巧克力包裝成方形、圓形禮盒出售，且每盒方形禮盒的價錢相同， 每盒圓形禮盒的價錢相同。阿郁原先想購買 3 盒方形禮盒和 7 盒圓形禮盒， 但他身上的錢會不足 240 元，如果改成購買 7 盒方形禮盒和 3 盒圓形禮盒， 他身上的錢會剩下 240 元。若阿郁最後購買 10 盒方形禮盒，則他身上的錢會剩下多少元?", "correct_choices": ["600"], "incorrect_choices": ["360", "480", "720"], "metadata": {"timestamp": "2023-10-29 01:58:12.628054", "source": "CAP_mathematics-107"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-108-1", "question": "算式 $-{\\frac{5}{3}}-(-{\\frac{1}{6}})$ 之值為何？", "correct_choices": ["$-\\frac{3}{2}$"], "incorrect_choices": ["$-\\frac{4}{3}$", "$-\\frac{11}{6}$", "$-\\frac{4}{9}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628076", "source": "CAP_mathematics-108"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-108-3", "question": "計算 $(2x-3)(3x+4)$ 的結果，與下列哪一個式子相同？", "correct_choices": ["$6x^2-x-12$"], "incorrect_choices": ["$-7x+4$", "$-7x-12$", "$6x^2-12$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628098", "source": "CAP_mathematics-108"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-108-5", "question": "若 $\\sqrt{44}=2\\sqrt{a}, \\sqrt{54}=3\\sqrt{b}$，則 $a+b$ 之值為何？", "correct_choices": ["17"], "incorrect_choices": ["13", "24", "40"], "metadata": {"timestamp": "2023-10-29 01:58:12.628120", "source": "CAP_mathematics-108"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-108-6", "question": "民國 106 年 8 月 15 日，大潭發電廠因跳電導致供電短少約 430 萬瓩，造成 全臺灣多處地方停電。已知 1 瓩等於 1 千瓦，求 430 萬瓩等於多少瓦？", "correct_choices": ["$4.3 \\times 10^{9}$"], "incorrect_choices": ["$4.3 \\times 10^{7}$", "$4.3 \\times 10^{8}$", "$4.3 \\times 10^{10}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628144", "source": "CAP_mathematics-108"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-108-8", "question": "若多項式 $(5x^2+17x-12)$ 可因式分解成 $(x+a)(bx+c)$ ，其中$a$ 、 $b$ 、 $c$ 均為整數，則$a+c$ 之值為何?", "correct_choices": ["1"], "incorrect_choices": ["7", "11", "13"], "metadata": {"timestamp": "2023-10-29 01:58:12.628167", "source": "CAP_mathematics-108"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-108-14", "question": "箱子內裝有 53 顆白球及 2 顆紅球，小芬打算從箱子內抽球，以每次抽出一球後將 球再放回的方式抽 53 次球。若箱子內每顆球被抽到的機會相等， 且前 52 次中 抽到白球 51 次及紅球 1 次，則第53 次抽球時，小芬抽到紅球的機率為何？", "correct_choices": ["$\\frac{2}{55}$"], "incorrect_choices": ["$\\frac{1}{2}$", "$\\frac{1}{3}$", "$\\frac{2}{53}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628189", "source": "CAP_mathematics-108"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-108-16", "question": "小涵與阿嘉一起去咖啡店購買同款咖啡豆，咖啡豆每公克的價錢固定，購買時 自備容器則結帳金額再減 5 元。若小涵購買咖啡豆 250 公克且自備容器，需支付 295 元；阿嘉購買咖啡豆 x 公克但沒有自備容器，需支付 y 元， 則 y 與x 的關係式為下列何者？", "correct_choices": ["$y=\\frac{300}{250}x$"], "incorrect_choices": ["$y=\\frac{295}{250}x$", "$y=\\frac{295}{250}x+5$", "$y=\\frac{300}{250}x+5$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628211", "source": "CAP_mathematics-108"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-108-22", "question": "若正整數 $a$ 和 420 的最大公因數為 35 ，則下列敘述何者正確？", "correct_choices": ["20 不可能是 $a$ 的因數，25 可能是 $a$ 的因數"], "incorrect_choices": ["20 可能是 $a$ 的因數，25 可能是 $a$ 的因數", "20 可能是 $a$ 的因數，25 不可能是 $a$ 的因數", "20 不可能是 $a$ 的因數，25 不可能是$a$ 的因數"], "metadata": {"timestamp": "2023-10-29 01:58:12.628234", "source": "CAP_mathematics-108"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-109-1", "question": "已知 $a=(-12)×(-23)×(-34)×(-45)$ ， $b=(-123)×(-234)×(-345)$， 判斷下列敘述何者正確？", "correct_choices": ["$a$ 為正數，$b$ 為負數"], "incorrect_choices": ["$a$ 、 $b$ 皆為正數", "$a$ 、 $b$ 皆為負數", "$a$ 為負數，$b$ 為正數"], "metadata": {"timestamp": "2023-10-29 01:58:12.628256", "source": "CAP_mathematics-109"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-109-2", "question": "算式 $2^3 \\times 5^3$ 之值為何？", "correct_choices": ["1000"], "incorrect_choices": ["30", "90", "1000000"], "metadata": {"timestamp": "2023-10-29 01:58:12.628278", "source": "CAP_mathematics-109"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-109-3", "question": "小真煮好了 25 顆湯圓，其中 15 顆為芝麻湯圓，10 顆為花生湯圓。已知小真想從煮好的湯圓中撈一顆，若每顆湯圓被小真撈到的機會相等，則他撈到花生湯圓的機率為何？", "correct_choices": ["$\\frac{2}{5}$"], "incorrect_choices": ["$\\frac{1}{2}$", "$\\frac{2}{3}$", "$\\frac{1}{10}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628300", "source": "CAP_mathematics-109"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-109-4", "question": "算式 $\\sqrt{2} \\times (\\sqrt{48} - \\sqrt{12})$ 之值為何？", "correct_choices": ["$2\\sqrt{6}$"], "incorrect_choices": ["$6\\sqrt{2}$", "$2\\sqrt{21}$", "$4\\sqrt{6} - 2\\sqrt{3}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628323", "source": "CAP_mathematics-109"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-109-7", "question": "計算 $2x^2-3$ 除以 $x+1$ 後，得商式和餘式分別為何？", "correct_choices": ["商式為 $2x-2$，餘式為 -1"], "incorrect_choices": ["商式為 2，餘式為 -5", "商式為 $2x-5$，餘式為 5", "商式為 $2x+2$，餘式為 -1"], "metadata": {"timestamp": "2023-10-29 01:58:12.628345", "source": "CAP_mathematics-109"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-109-8", "question": "下列何者可表示成兩個質數的乘積？", "correct_choices": ["82"], "incorrect_choices": ["81", "83", "84"], "metadata": {"timestamp": "2023-10-29 01:58:12.628367", "source": "CAP_mathematics-109"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-109-9", "question": "已知小薇住家的西方 100 公尺處為車站，住家的北方 200 公尺處為學校，且從學校往東方走 100 公尺，再往南方走 400 公尺可到達公園。若小薇將住家、車站、學校分別標示在坐標平面上的$(2,0)$、$(0,0)$、$(2,4)$ 三點，則公園應標示在此坐標平面上的哪一點？", "correct_choices": ["$(4,-4)$"], "incorrect_choices": ["$(4,12)$", "$(0,-4)$", "$(0,12)$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628390", "source": "CAP_mathematics-109"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-109-10", "question": "若一元二次方程式$5(x−4)^2=125$ 的解為 $a$ 、$b$ ，且 $a>b$ ，則 $2a+b$ 之值為何？", "correct_choices": ["17"], "incorrect_choices": ["-7", "-1", "11"], "metadata": {"timestamp": "2023-10-29 01:58:12.628412", "source": "CAP_mathematics-109"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-2", "question": "算式 $(-8)+(-2) \\times (-3)$ 之值為何？", "correct_choices": ["-2"], "incorrect_choices": ["-14", "18", "30"], "metadata": {"timestamp": "2023-10-29 01:58:12.628456", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-3", "question": "若二元一次聯立方程式$\\begin{cases} x=4y \\\\ 6y-x=10 \\end{cases}$ 的解為 $x=a$，$y=b$，則 $a+b$ 之值為何？", "correct_choices": ["25"], "incorrect_choices": ["-15", "-3", "5"], "metadata": {"timestamp": "2023-10-29 01:58:12.628478", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-5", "question": "$5^6$ 是 $5^3$ 的多少倍？", "correct_choices": ["125"], "incorrect_choices": ["2", "3", "25"], "metadata": {"timestamp": "2023-10-29 01:58:12.628500", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-6", "question": "下列等式何者不成立？", "correct_choices": ["$4\\sqrt{3} \\times 2\\sqrt{3}=8\\sqrt{3}$"], "incorrect_choices": ["$4\\sqrt{3}+2\\sqrt{3}=6\\sqrt{3}$", "$4\\sqrt{3}-2\\sqrt{3}=2\\sqrt{3}$", "$4\\sqrt{3} \\div 2\\sqrt{3}=2$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628522", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-8", "question": "利用乘法公式判，下列等式何者成立？", "correct_choices": ["$248^2+2 \\times 248 \\times 52+52^2 =300^2$"], "incorrect_choices": ["$248^2+248 \\times 52+52^2=300^2$", "$248^2-248 \\times 48-48^2=200^2$", "$248^2-2 \\times 248 \\times 480-48^2 =200^2$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628547", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-10", "question": "將一半徑為 6 的圓形紙片，沿著兩條半徑剪開形成兩個扇形。若其中一個扇形的弧長為 $5\\pi$ ，則另一個扇形的圓心角度數是多少？", "correct_choices": ["210"], "incorrect_choices": ["30", "60", "105"], "metadata": {"timestamp": "2023-10-29 01:58:12.628569", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-12", "question": "美美和小儀到超市購物，且超市正在舉辦摸彩活動，單次消費金額每滿 100 元可以拿到 1 張摸彩券。已知美美一次購買 5 盒餅乾拿到 3 張摸彩券；小儀一次購買 5 盒餅乾與 1 個蛋糕拿到 4 張摸彩券。若每盒餅乾的售價為 $x$ 元，每個蛋糕的售價為 150 元，則 $x$ 的範圍為下列何者？", "correct_choices": ["$60 \\leq x<70$"], "incorrect_choices": ["$50 \\leq x<60$", "$70 \\leq x<80$", "$80 \\leq x<90$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628592", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-13", "question": "已知 $a_1$ ， $a_2$ ， $......$ ，$a_{40}$ 為一等差數列，其中$a_1$ 為正數，且$a_{20}+a_{22}=0$。判斷下列敘述何者正確？", "correct_choices": ["$a_{21}+a_{22}<0$"], "incorrect_choices": ["$a_{21}+a_{22}>0$", "$a_{21} \\times a_{22}>0$", "$a_{21} \\times a_{22}<0$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628614", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-14", "question": "已知 $a=-\\frac{5}{223}$ ，$b=\\frac{6}{263}$ ， $c=-\\frac{7}{293}$ ，判斷下列各式之值何者最大？", "correct_choices": ["$|a-b+c|$"], "incorrect_choices": ["$|a+b+c|$", "$|a+b-c|$", "$|a-b-c|$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628636", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-18", "question": "若坐標平面上二次函數$y=a(x+b)^2+c$ 的圖形，經過平移後可與 $y=(x+3)^2$ 的圖形完全疊合，則 $a$ 、 $b$ 、 $c$ 的值可能為下列哪一組？", "correct_choices": ["$a=1$ ， $b=0$ ， $c=-2$"], "incorrect_choices": ["$a=2$ ， $b=6$ ， $c=0$", "$a=-1$ ， $b=-3$ ，$c=0$", "$a=-2$ ， $b=3$ ，$c=-2$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628658", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-20", "question": "已知捷立租車行有甲、乙兩個營業據點，顧客租車後當日須於營業結束前在任意一個據點還車。某日營業結束清點車輛時，發現在甲歸還的自行車比從甲出租的多 4 輛。若當日從甲出租且在甲歸還的自行車為 15 輛，從乙出租且在乙歸還的自行車為 13 輛，則關於當日從甲、乙出租的自行車數量，下列比較何者正確？", "correct_choices": ["從甲出租的比從乙出租的少 2 輛"], "incorrect_choices": ["從甲出租的比從乙出租的多 2 輛", "從甲出租的比從乙出租的多 6 輛", "從甲出租的比從乙出租的少 6 輛"], "metadata": {"timestamp": "2023-10-29 01:58:12.628681", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-22", "question": "若 $a$ 、 $b$ 為正整數，且 $a \\times b=2^5 \\times 3^2 \\times 5$，則下列何者不可能為 $a$ 、$b$ 的最大公因數？", "correct_choices": ["8"], "incorrect_choices": ["1", "6", "12"], "metadata": {"timestamp": "2023-10-29 01:58:12.628703", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-110-24", "question": "小文原本計畫使用甲、乙兩臺影印機於 10:00 開始一起印製文件並持續到下午，但 10:00 時有人正在使用乙，於是他先使用甲印製，於10:05 才開始使用乙一起印製，且到 10:15 時乙印製的總張數與甲相同，到 10:45 時甲、乙印製的總張數合計為 2100 張。若甲、乙的印製張數與印製時間皆成正比，則依照小文原本的計畫，甲、乙印製的總張數會在哪個時間達到 2100 張？", "correct_choices": ["0.445833333"], "incorrect_choices": ["0.444444444", "0.445138889", "0.446527778"], "metadata": {"timestamp": "2023-10-29 01:58:12.628725", "source": "CAP_mathematics-110"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-111-2", "question": "計算多項式 $6x^2+4x$ 除以$2x^2$ 後，得到的餘式為何？", "correct_choices": ["$4x$"], "incorrect_choices": ["2", "4", "$2x$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628747", "source": "CAP_mathematics-111"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-111-3", "question": "下列何者為 156 的質因數？", "correct_choices": ["13"], "incorrect_choices": ["11", "12", "14"], "metadata": {"timestamp": "2023-10-29 01:58:12.628769", "source": "CAP_mathematics-111"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-111-5", "question": "算式 $\\frac{9}{22}+\\frac{11}{18}-(\\frac{23}{22}-\\frac{7}{18})$ 之值為何？", "correct_choices": ["$\\frac{4}{11}$"], "incorrect_choices": ["$\\frac{9}{10}$", "$\\frac{1}{9}$", "$\\frac{5}{4}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628791", "source": "CAP_mathematics-111"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-111-6", "question": "$\\sqrt{2022}$ 的值介於下列哪兩個數之間？", "correct_choices": ["40，45"], "incorrect_choices": ["25，30", "30，35", "35，40"], "metadata": {"timestamp": "2023-10-29 01:58:12.628813", "source": "CAP_mathematics-111"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-111-7", "question": "已知坐標平面上有一直線 $L$ 與一點 $A$ 。若 $L$ 的方程式為$x=-2$ ， $A$ 點坐標為 $(6,5)$，則 $A$ 點到直線 $L$ 的距離為何？", "correct_choices": ["8"], "incorrect_choices": ["3", "4", "7"], "metadata": {"timestamp": "2023-10-29 01:58:12.628835", "source": "CAP_mathematics-111"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-111-8", "question": "多項式 $39x^2+5x-14$ 可因式分解成 $(3x+a)(bx+c)$ ，其中 $a$ 、 $b$ 、 $c$ 均為整數，求$a+2c$ 之值為何？", "correct_choices": ["-12"], "incorrect_choices": ["-3", "3", "12"], "metadata": {"timestamp": "2023-10-29 01:58:12.628857", "source": "CAP_mathematics-111"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-111-9", "question": "箱子內有分別標示號碼 1 ～ 6 的球，每個號碼各 2 顆，總共 12 顆。已知小茹先 從箱內抽出 5 顆球且不將球放回箱內，這 5 顆球的號碼分別是 1、2、2、3、5。今阿純打算從此箱內剩下的球中抽出 1 顆球，若箱內剩下的每顆球被他抽出 的機會相等，則他抽出的球的號碼，與小茹已抽出的 5 顆球中任意一顆球的號碼相同的機率是多少？", "correct_choices": ["$\\frac{3}{7}$"], "incorrect_choices": ["$\\frac{3}{6}$", "$\\frac{4}{6}$", "$\\frac{4}{7}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628879", "source": "CAP_mathematics-111"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-111-10", "question": "已知一元二次方程式 $(x-2)^2=3$ 的兩根為 $a$ 、 $b$，且$a>b$，求 $2a+b$ 之值為何？", "correct_choices": ["$6+\\sqrt{3}$"], "incorrect_choices": ["9", "-3", "$-6+\\sqrt{3}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628901", "source": "CAP_mathematics-111"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-111-12", "question": "已知 $p=7.52×10^{-6}$ ，下列關於 $p$ 值的敘述何者正確？", "correct_choices": ["介於 0 與 1 兩數之間，兩數中比較接近 0"], "incorrect_choices": ["小於 0", "介於 0 與 1 兩數之間，兩數中比較接近1", "大於 1"], "metadata": {"timestamp": "2023-10-29 01:58:12.628924", "source": "CAP_mathematics-111"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-112-2", "question": "下列何者為多項式 $x^2-36$ 的因式？", "correct_choices": ["$x-6$"], "incorrect_choices": ["$x-3$", "$x-4$", "$x-9$"], "metadata": {"timestamp": "2023-10-29 01:58:12.628990", "source": "CAP_mathematics-112"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-112-4", "question": "化簡 $\\sqrt{135}$ 的結果為下列何者？", "correct_choices": ["$3\\sqrt{15}$"], "incorrect_choices": ["$3\\sqrt{5}$", "$27\\sqrt{5}$", "$9\\sqrt{15}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.629012", "source": "CAP_mathematics-112"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-112-5", "question": "坐標平面上，一次函數 $y=-2x-6$ 的圖形通過下列哪一個點？", "correct_choices": ["$(-4,2)$"], "incorrect_choices": ["$(-4,1)$", "$(-4,-1)$", "$(-4,-2)$"], "metadata": {"timestamp": "2023-10-29 01:58:12.629035", "source": "CAP_mathematics-112"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-112-6", "question": "已知 $a=-1$ ， $b=-1\\frac{3}{4}$ ， $c=-1\\frac{8}{5}$ ，下列關於$a$、$b$、$c$ 三數的大小關係，何者正確？", "correct_choices": ["$a>c>b$"], "incorrect_choices": ["$a>b>c$", "$b>c>a$", "$c>b>a$"], "metadata": {"timestamp": "2023-10-29 01:58:12.629057", "source": "CAP_mathematics-112"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-112-9", "question": "有多少個正整數是 18 的倍數，同時也是 216 的因數？", "correct_choices": ["6"], "incorrect_choices": ["2", "10", "12"], "metadata": {"timestamp": "2023-10-29 01:58:12.629079", "source": "CAP_mathematics-112"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-112-10", "question": "利用公式解可得一元二次方程式$3x^2-11x-1=0$ 的兩解為$a$、$b$，且 $a>b$， 求 $a$ 值為何？", "correct_choices": ["$\\frac{11+\\sqrt{133}}{6}$"], "incorrect_choices": ["$\\frac{-11+\\sqrt{109}}{6}$", "$\\frac{-11+\\sqrt{133}}{6}$", "$\\frac{11+\\sqrt{109}}{6}$"], "metadata": {"timestamp": "2023-10-29 01:58:12.629103", "source": "CAP_mathematics-112"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-112-15", "question": "若想在等差數列 1,2,3,4,5 中插入一些數，使得新的數列也是等差數列，且新的數列的首項仍是 1，末項仍是 5，則新的數列的項數可能為下列何者？", "correct_choices": ["33"], "incorrect_choices": ["11", "15", "30"], "metadata": {"timestamp": "2023-10-29 01:58:12.629126", "source": "CAP_mathematics-112"}, "human_evaluation": {"quality": "", "comments": ""}} | |
| {"id": "CAP_mathematics-112-16", "question": "已知某速食店販售的套餐內容為一片雞排和一杯可樂，且一份套餐的價錢比單點一片雞排再單點一杯可樂的總價錢便宜 40 元。阿俊打算到該速食店買兩份套餐，若他發現店內有單點一片雞排就再送一片雞排的促銷活動， 且單點一片雞排再單點兩杯可樂的總價錢，比兩份套餐的總價錢便宜 10 元， 則根據題意可得到下列哪一個結論？", "correct_choices": ["單點一片雞排的價錢必為 90 元"], "incorrect_choices": ["一份套餐的價錢必為 140 元", "一份套餐的價錢必為 120 元", "單點一片雞排的價錢必為 70 元"], "metadata": {"timestamp": "2023-10-29 01:58:12.629148", "source": "CAP_mathematics-112"}, "human_evaluation": {"quality": "", "comments": ""}} | |