| {"question": "有理数通常能写成什么样的形式？", "options": ["$\\sqrt{pq} $( $p, q$为整数且$p\\ne0$)", "$sin(pq)$( $p, q$为整数且$p\\ne0$)", "$\\frac{q}{p}$( $p, q$为整数且$p\\ne0$)", "$ q^{p}$( $p, q$为整数且$p\\ne0$)"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "什么数既不是正数也不是负数？", "options": ["0", "无理数", "超越数", "循环小数"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "$\\pi$是什么数？", "options": ["实数", "有理数", "无限循环小数", "无理数"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "分数除了正分数，还有可能是什么数？", "options": ["自然数", "无理数", "负分数", "0"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有理数除了是整数，还有可能是什么数？", "options": ["虚数", "分数", "复数", "循环小数"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "整数除了正整数，0，还有可能是什么数？", "options": ["复数", "循环小数", "虚数", "负整数"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有理数按照符号分，除了正有理数和负有理数，还有什么数？", "options": ["循环小数", "超越数", "无理数", "0"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "正有理数除了正整数，还有什么数？", "options": ["正分数", "无理数", "超越数", "循环小数"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "负有理数除了负整数，还有什么数？", "options": ["无理数", "超越数", "负分数", "循环小数"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "在构建一个数轴时，下列哪个要素不是必须明确指定的？", "options": ["正方向", "负方向", "原点", "单位长度"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "什么是数轴？", "options": ["数轴是规定了原点、正方向、单位长度的一条直线。", "数轴是规定了原点、负方向、单位长度的一条直线。", "数轴是规定了原点、正方向、单位长度的一条曲线。", "数轴是规定了原点、负方向的一条曲线。"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "相反数的和为0或者是$a+b=0$，可以推导出以下哪个结论？", "options": ["$a,b$都小于零", "$a,b$都大于零", "$a,b$互为质数", "$a,b$互为相反数"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "什么情况下，我们说一个数是另一个数的相反数？", "options": ["只有符号不同的两个数", "相减的绝对值为1的两个数", "相加的绝对值为1的两个数", "相乘的绝对值为1的两个数"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "0的相反数是什么？", "options": ["2", "1", "3", "0"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "正数的绝对值是什么？", "options": ["其立方数", "其平方数", "其相反数", "其本身"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "0的绝对值是什么？", "options": ["0", "3", "2", "1"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "负数的绝对值是什么？", "options": ["其立方数", "其本身", "其平方数", "其相反数"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "绝对值的意义是什么？", "options": ["数轴上表示某数的点离开原点的距离的立方", "数轴上表示某数的点离开原点的距离的平方", "数轴上表示某数的点离开原点的距离的相反数", "数轴上表示某数的点离开原点的距离"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "$|a|$大于零时是什么？", "options": ["$-a$", "$a$", "0", "$a^2$"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "$|a|$小于零时是什么？", "options": ["$a^2$", "$a$", "0", "$-a$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "绝对值的问题通常需要如何处理？", "options": ["建立球坐标系", "画图", "分类讨论", "建立直角坐标系"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "在有理数比大小的过程中，正数的绝对值越大会怎么样？", "options": ["无法判断", "这个数越大", "这个数越小", "这个数的相反数越大"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有一个数，正数永远比它大，负数永远比他小，这个数是什么？", "options": ["1", "0", "2", "3"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "正数永远大于什么数？", "options": ["一切有理数", "一切整数", "一切负数", "一切无理数"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "两个负数比大小，绝对值大的数值怎么样？", "options": ["小", "大", "相等", "无法判断"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "数轴上的两个数，右边的数总比左边的数怎么样？", "options": ["相等", "小", "大", "无法判断"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "大数减去小数的结果值是怎么样的？", "options": ["大于零", "小于零", "无法判断", "等于零"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "小数减去大数的结果值是怎么样的？", "options": ["大于零", "无法判断", "小于零", "等于零"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "怎么样的两个数互为倒数？", "options": ["乘积为1的两个数互为倒数", "乘积为0的两个数互为倒数", "乘积为2的两个数互为倒数", "乘积为3的两个数互为倒数"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "0有没有倒数？", "options": ["没有", "无法判断", "有时候有倒数有时候没有", "有"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "若$a\\ne 0$，那么$a$的倒数是什么？", "options": ["$\\frac{2}{a} $", "$\\frac{1}{a} $", "$\\frac{3}{a} $", "$\\frac{4}{a} $"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "若$ab=1$，那么$a,b$互为什么关系？", "options": ["互为相反数", "相等", "互为质数", "倒数关系"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "若$ab=-1$，那么$a,b$互为什么关系？", "options": ["互为质数", "互为相反数", "负倒数关系", "相等"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "在同号两数相加的过程中，应该取相同的符号，然后怎么做？", "options": ["再把绝对值相加", "乘以1", "乘以零", "乘以2"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "在异号两数相加的过程中，应该取绝对值较大的符号，然后怎么做", "options": ["用较大绝对值加上较小绝对值", "用较大绝对值除以较小绝对值", "用较大绝对值乘以较小绝对值", "用较大绝对值减去较小绝对值"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "一个数与零相加，结果是什么？", "options": ["这个数的负数", "这个数的平方数", "0", "这个数"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "加法的交换律是什么？", "options": ["$a+b=b-a$", "$a+b=-b+a$", "$a+b=b*a$", "$a+b=b+a$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "加法的结合律是什么？", "options": ["$(a+b)+c=a+(b-c)$", "$(a+b)+c=a+(b*c)$", "$(a+b)+c=a+(-b+c)$", "$(a+b)+c=a+(b+c)$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有理数的减法法则是什么？", "options": ["减去一个数等于加上这个数的2倍", "减去一个数等于加上这个数的相反数", "减去一个数等于加上这个数的3倍", "减去一个数等于加上这个数的4倍"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有理数的减法法则的数学形式是什么？", "options": ["$a-b=a+(-4b)$", "$a-b=a+(-2b)$", "$a-b=a+(-3b)$", "$a-b=a+(-b)$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "在有理数的乘法法则中，两数相乘时，符号的规则是什么？", "options": ["同号为负，异号为负", "同号为负，异号为正", "同号为正，异号为正", "同号为正，异号为负"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "在有理数的乘法法则中，两数相乘时，值的规则是什么？", "options": ["绝对值相乘", "绝对值相减", "绝对值相加", "绝对值相除"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "在有理数的乘法法则中，任何数与零相乘的结果是什么？", "options": ["1", "3", "0", "2"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "在有理数的乘法法则中，几个数相乘有一个因式为0，则积是什么数？", "options": ["2", "3", "1", "0"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "在有理数的乘法法则中，各个因式都不为0，则积的符号由什么决定？", "options": ["所有因式的个数", "正因式的个数", "负因式的个数", "无法决定"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "乘法的交换律是什么？", "options": ["$ab=ba+1$", "$ab=ba+3$", "$ab=ba+2$", "$ab=ba$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "乘法的结合律是什么？", "options": ["$(ab)c=a(bc)$", "$(ab)c=a(bc)+2$", "$(ab)c=a(bc)+1$", "$(ab)c=a(bc)+3$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "乘法的分配律是什么？", "options": ["$a(b+c)=ab+ac+2$", "$a(b+c)=ab+ac$", "$a(b+c)=ab+ac+3$", "$a(b+c)=ab+ac+1$"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有理数的除法法则是什么？", "options": ["除以一个数等于乘以这个数的相反数", "除以一个数等于乘以这个数的平方数", "除以一个数等于乘以这个数的倒数（0不能做除数）", "除以一个数等于乘以这个数的绝对值"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有理数的乘方法则中，正数的任何次幂式什么数？", "options": ["无限循环小数", "正数", "负数", "无限不循环小数"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有理数的乘方法则中，负数的奇次幂是什么数？", "options": ["无限不循环小数", "无限循环小数", "正数", "负数"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有理数的乘方法则中，负数的正奇次幂有什么样的等式？", "options": ["$(-a)^{n} =-(a^{4n} )$", "$(-a)^{n} =-(a^{n} )$", "$(-a)^{n} =-(a^{2n} )$", "$(-a)^{n} =-(a^{3n} )$"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有理数的乘方法则中，负数的偶次幂是什么数？", "options": ["无限不循环小数", "无限循环小数", "负数", "正数"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有理数的乘方法则中，若n为偶数，那么负数的正偶次幂有什么样的等式？", "options": ["$(-a)^{n} =-a^{2n} )$", "$(-a)^{n} =a^{n} )$", "$(-a)^{n} =-a^{4n} )$", "$(-a)^{n} =-a^{3n} )$"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "乘方的定义是什么？", "options": ["求相同因式积的运算叫做乘方", "求相同因式绝对值的运算叫做乘方", "求相同因式差的运算叫做乘方", "求相同因式和的运算叫做乘方"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "乘方中，相同的因式叫做什么？", "options": ["底数", "加数", "乘数", "除数"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "乘方中，相同的因式的个数叫做什么？", "options": ["指数", "加数", "乘数", "除数"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "乘方中，乘方的结果叫做什么？", "options": ["积", "幂", "和", "差"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "科学计数法的定义是什么？", "options": ["把一个大于10的数记成$a\\times 30^{n} $的形式，其中$a$是整数数位只有一位的数", "把一个大于10的数记成$a\\times 40^{n} $的形式，其中$a$是整数数位只有一位的数", "把一个大于10的数记成$a\\times 10^{n} $的形式，其中$a$是整数数位只有一位的数", "把一个大于10的数记成$a\\times 20^{n} $的形式，其中$a$是整数数位只有一位的数"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "近似数的精确位是到哪一位？", "options": ["四舍五入之后三位", "四舍五入那一位", "四舍五入之后一位", "四舍五入之后两位"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "有效数字的位数是什么样的情况？", "options": ["从左边第一个不为零的数字起，到精确的位数止", "从左边第三个不为零的数字起，到精确的位数止", "从左边第四个不为零的数字起，到精确的位数止", "从左边第二个不为零的数字起，到精确的位数止"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "什么是混合运算法则？", "options": ["先乘除，后乘方，最后加减", "先乘方，后乘除，最后加减", "先乘方，后加减，最后乘除", "先加减，后乘除，最后乘方"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "什么是单项式？", "options": ["在代数式中，若只含有乘法（包括乘方）运算。或虽含有除法运算，且除式中含字母一类的代数式叫单项式。", "在代数式中，若只含有加法运算。或虽含有除法运算，但除式中不含字母一类的代数式叫单项式。", "在代数式中，若只含有减法运算。或虽含有除法运算，但除式中不含字母一类的代数式叫单项式。", "在代数式中，若只含有乘法（包括乘方）运算。或虽含有除法运算，但除式中不含字母一类的代数式叫单项式。"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "什么是单项式的系数？", "options": ["单项式中不为零的数字因数", "单项式中为零的数字因数", "单项式中为2的数字因数", "单项式中为1的数字因数"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "什么是单项式的次数？", "options": ["单项式系数不为零时，单项式中所有字母指数的差。", "单项式系数不为零时，单项式中所有字母指数的积。", "单项式系数为零时，单项式中所有字母指数的和。", "单项式系数不为零时，单项式中所有字母指数的和。"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "什么是多项式的定义？", "options": ["几个单项式的积叫做多项式", "几个单项式的乘方叫做多项式", "几个单项式的差叫做多项式", "几个单项式的和叫做多项式"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "什么是多项式的项数？", "options": ["多项式中所含单项式的个数的四次方", "多项式中所含单项式的个数", "多项式中所含单项式的个数的平方", "多项式中所含单项式的个数的立方"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "什么是多项式的次数？", "options": ["多项式里，次数第三高项的次数", "多项式里，次数最高项的次数", "多项式里，次数最低项的次数", "多项式里，次数第二高项的次数"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "一元一次方程的定义是什么？", "options": ["只含有一个未知数，并且未知数的次数是1，并且含未知数项的系数不是零的整式方程", "只含有一个未知数，并且未知数的次数是2，并且含未知数项的系数不是零的整式方程", "只含有一个未知数，并且未知数的次数是3，并且含未知数项的系数不是零的整式方程", "只含有一个未知数，并且未知数的次数是4，并且含未知数项的系数不是零的整式方程"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "一元一次方程的标准形式是什么？", "options": ["$a^2x+b=0$($x$是未知数，$a、b$是已知数，且$a\\ne 0$)", "$ax+b=0$($x$是未知数，$a、b$是已知数，且$a\\ne 0$)", "$a^4x+b=0$($x$是未知数，$a、b$是已知数，且$a\\ne 0$)", "$a^3x+b=0$($x$是未知数，$a、b$是已知数，且$a\\ne 0$)"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "下面有一些一元一次方程解法的一般步骤，哪一个顺序是正确的？", "options": ["整理方程、去分母、去括号、移项、合并同类项、系数化为一、检验方程的解", "整理方程、系数化为一、去括号、移项、合并同类项、去分母、检验方程的解", "整理方程、检验方程的解、去括号、移项、合并同类项、系数化为一、去分母", "整理方程、合并同类项、去括号、移项、去分母、系数化为一、检验方程的解"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "使用读题分析法解一元一次方程的应用题，多用于哪些问题？", "options": ["火箭发射问题", "鸡兔同笼问题", "卫星轨道计算问题", "和，差，倍，分问题"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "使用画图分析法解一元一次方程的应用题，多用于哪些问题？", "options": ["和，差，倍，分问题", "行程问题。", "逻辑推理问题，数独问题", "组合问题，鸡兔同笼问题"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "使用画图分析法解一元一次方程的应用题，找到什么关系是解题关键？", "options": ["通过图形找相等关系是解决问题的关键", "通过方程式找相等关系是解决问题的关键", "通过文字信息找相等关系是解决问题的关键", "通过语音信息找相等关系是解决问题的关键"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "在列方程解应用题的过程中，行程问题有哪些常用公式？", "options": ["顺流速度=静水速度+水流速度、逆流速度=静水速度-水流速度", "$距离=速度\\cdot 时间$、$速度=\\frac{距离}{时间}$ 、$时间=\\frac{距离}{速度} $", "$工作量=工效\\cdot 工时$、$工效=\\frac{工作量}{工时}$、$工时=\\frac{工作量}{工效}$", "$部分=全体\\cdot 比率$、$比率=\\frac{部分}{全体}$、$全体=\\frac{部分}{比率}$"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "在列方程解应用题的过程中，工程问题有哪些常用公式？", "options": ["$工作量=工效\\cdot 工时$、$工效=\\frac{工作量}{工时}$、$工时=\\frac{工作量}{工效}$", "$部分=全体\\cdot 比率$、$比率=\\frac{部分}{全体}$、$全体=\\frac{部分}{比率}$", "顺流速度=静水速度+水流速度、逆流速度=静水速度-水流速度", "$距离=速度\\cdot 时间$、$速度=\\frac{距离}{时间}$ 、$时间=\\frac{距离}{速度} $"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "在列方程解应用题的过程中，工程问题有哪些常用公式？", "options": ["$距离=速度\\cdot 时间$、$速度=\\frac{距离}{时间}$ 、$时间=\\frac{距离}{速度} $", "$工作量=工效\\cdot 工时$、$工效=\\frac{工作量}{工时}$、$工时=\\frac{工作量}{工效}$", "$部分=全体\\cdot 比率$、$比率=\\frac{部分}{全体}$、$全体=\\frac{部分}{比率}$", "顺流速度=静水速度+水流速度、逆流速度=静水速度-水流速度"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "在列方程解应用题的过程中，工程问题有哪些常用公式？", "options": ["$距离=速度\\cdot 时间$、$速度=\\frac{距离}{时间}$ 、$时间=\\frac{距离}{速度} $", "$部分=全体\\cdot 比率$、$比率=\\frac{部分}{全体}$、$全体=\\frac{部分}{比率}$", "$工作量=工效\\cdot 工时$、$工效=\\frac{工作量}{工时}$、$工时=\\frac{工作量}{工效}$", "顺流速度=静水速度+水流速度、逆流速度=静水速度-水流速度"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "在列方程解应用题的过程中，商品价格问题有哪些常用公式？", "options": ["$工作量=工效\\cdot 工时$、$工效=\\frac{工作量}{工时}$、$工时=\\frac{工作量}{工效}$", "$距离=速度\\cdot 时间$、$速度=\\frac{距离}{时间}$ 、$时间=\\frac{距离}{速度} $", "$售价=定价\\cdot 折\\cdot \\frac{1}{10}$、利润=售价-成本、$利润率=\\frac{售价-成本}{成本}\\cdot 100%$", "$部分=全体\\cdot 比率$、$比率=\\frac{部分}{全体}$、$全体=\\frac{部分}{比率}$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} |
| {"question": "在列方程解应用题的过程中，周长问题有哪些常用公式？", "options": ["$部分=全体\\cdot 比率$、$比率=\\frac{部分}{全体}$、$全体=\\frac{部分}{比率}$", "$C_{圆} =2\\pi R$、$C_{长方形} =2(a+b)$、$C_{正方形} =4a$", "$V_{长方体} =abc$、$V_{正方体} =a^3$、$V_{圆柱} =\\pi R^2h$、$V_{圆锥} =\\frac{1}{3}\\pi R^2h$", "$S_{圆} =\\pi R^2$、$S_{长方形} =ab$、$S_{正方形} =a^2$、$S_{环形} =\\pi (R^2-r^2)$"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "在列方程解应用题的过程中，面积问题有哪些常用公式？", "options": ["$部分=全体\\cdot 比率$、$比率=\\frac{部分}{全体}$、$全体=\\frac{部分}{比率}$", "$V_{长方体} =abc$、$V_{正方体} =a^3$、$V_{圆柱} =\\pi R^2h$、$V_{圆锥} =\\frac{1}{3}\\pi R^2h$", "$S_{圆} =\\pi R^2$、$S_{长方形} =ab$、$S_{正方形} =a^2$、$S_{环形} =\\pi (R^2-r^2)$", "$C_{圆} =2\\pi R$、$C_{长方形} =2(a+b)$、$C_{正方形} =4a$"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "在列方程解应用题的过程中，体积问题有哪些常用公式？", "options": ["$S_{圆} =\\pi R^2$、$S_{长方形} =ab$、$S_{正方形} =a^2$、$S_{环形} =\\pi (R^2-r^2)$", "$C_{圆} =2\\pi R$、$C_{长方形} =2(a+b)$、$C_{正方形} =4a$", "$V_{长方体} =abc$、$V_{正方体} =a^3$、$V_{圆柱} =\\pi R^2h$、$V_{圆锥} =\\frac{1}{3}\\pi R^2h$", "$部分=全体\\cdot 比率$、$比率=\\frac{部分}{全体}$、$全体=\\frac{部分}{比率}$"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "两条直线相交所构成的四个角中，有公共顶点且有一条公共边的两个角是？", "options": ["互补角", "平行角", "邻补角", "对顶角"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "一个角的两边分别是另一个角的两边的反向延长线，像这样的两个角互为？", "options": ["对顶角", "互补角", "邻补角", "平行角"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "两条直线相交成直角时，叫做互相垂直，其中一条叫做另一条的？", "options": ["平行线", "相交线", "补线", "垂线"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "在同一平面内，不相交的两条直线叫做？", "options": ["相交线", "垂线", "平行线", "补线"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "判断一件事情的语句叫？", "options": ["命题", "定义", "描述", "描绘"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "在平面内，将一个图形沿某个方向移动一定的距离，图形的这种移动叫做？", "options": ["平移", "右移", "左移", "移动"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "平移后得到的新图形中每一点，都是由原图形中的某一点移动后得到的，这样的两个点叫做？", "options": ["对等点", "对应点", "类似点", "相似点"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "对顶角的大小关系是？", "options": ["相等", "二倍", "无关系", "不相等"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "过一点有且只有几条直线与已知直线垂直？", "options": ["3", "1", "2", "4"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "连接直线外一点与直线上各点的所有线段中，哪一种线段最短？", "options": ["平行线段", "垂线段", "相交不垂直线段", "不存在最短线段"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "经过直线外一点有且只有几条直线与已知直线平行？", "options": ["4", "2", "1", "3"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "如果两条直线都与第三条直线平行，那么这两条直线的位置关系是？", "options": ["无关系", "互相垂直", "相交", "互相平行"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "两直线平行，则同位角的大小关系是？", "options": ["二倍", "相等", "无关", "三倍"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "两直线平行，则内错角的大小关系是？", "options": ["无关", "三倍", "二倍", "相等"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "两直线平行，则同旁内角的大小关系是？", "options": ["相等", "互补", "二倍", "三倍"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "同位角相等，两直线的位置关系是？", "options": ["相交", "平行", "无关", "垂直"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "内错角相等，两直线的位置关系是？", "options": ["垂直", "平行", "无关", "相交"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "同旁内角相等，两直线的位置关系是？", "options": ["无关", "平行", "相交", "垂直"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "有顺序的两个数a与b组成的数对叫做？", "options": ["数对", "有序数组", "数组", "有序数对"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "在平面内，两条互相垂直且有公共原点的数轴组成？", "options": ["数轴集", "数轴空间", "坐标空间", "平面直角坐标系"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "水平的数轴称为？竖直的数轴称为？两坐标轴的交点为平面直角坐标系的？", "options": ["x轴；y轴；原点", "y轴；y轴；原点", "y轴；x轴；原点", "x轴；x轴；原点"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "对于平面内任一点，过该点分别向x轴，y轴作垂线，垂足分别在x轴，y轴上，对应的数a，b分别叫该点的？", "options": ["横坐标；纵坐标", "纵坐标；横坐标", "纵坐标；纵坐标", "横坐标；横坐标"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "两条坐标轴把平面分成四个部分，右上部分叫？按逆时针方向依次叫？", "options": ["第一象限；第三象限；第二象限；第四象限", "第一象限；第二象限；第三象限；第四象限", "第一象限；第二象限；第四象限；第三象限", "第二象限；第一象限；第三象限；第四象限"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "由不在同一直线上的三条线段首尾顺次相接所组成的图形叫做？", "options": ["正方形", "三角形", "圆形", "长方形"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "三角形任意两边的和与第三边的大小关系是怎样的，任意两边的差与第三边的大小呢？", "options": ["小于；小于", "大于；小于", "小于；大于", "大于；大于"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "从三角形的一个顶点向它的对边所在直线作垂线，顶点和垂足间的线段叫做三角形的？", "options": ["交线", "中线", "高", "中位线"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "在三角形中，连接一个顶点和他的对边中点的线段叫做三角形的？", "options": ["中位线", "交线", "中线", "高"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "三角形的一个内角的平分线与这个角的对边相交，这个角的顶点和交点之间的线段叫做三角形的？", "options": ["角平分线", "交线", "高", "中位线"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "三角形的形状是固定的，三角形的这个性质叫做三角形的？", "options": ["稳重性", "稳定性", "稳固性", "三角性"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "在平面内，由一些线段首尾顺次相接组成的图形叫做？", "options": ["三角形", "多边形", "多角形", "图形"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "多边形相邻两边组成的角叫做它的？", "options": ["同位角", "外角", "内角", "对顶角"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "多边形的一边与它的邻边的延长线组成的角叫做多边形的？", "options": ["内角", "对顶角", "外角", "同位角"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "连接多边形不相邻的两个顶点的线段，叫做多边形的？", "options": ["对角线", "垂线", "临边", "对边"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "在平面内，各个角都相等，各条边都相等的多边形叫做？", "options": ["正多边形", "多边形", "平行多边形", "正多面体"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "用一些不重叠摆放的多边形把平面的一部分完全覆盖，叫做？", "options": ["用多边形遮盖平面", "用多边形覆盖平面", "用多边形覆盖空间", "用多边形掩盖平面"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "三角形的内角和是？", "options": ["$180{^\\circ}$", "$270{^\\circ}$", "$360{^\\circ}$", "$90{^\\circ}$"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "三角形的一个外角等于和它不相邻的两个内角的？", "options": ["平方和", "差", "和", "积"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "三角形的一个外角和任何一个和它不相邻的内角的大小关系是？", "options": ["小于", "大于", "等于", "无关"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "n边形的内角和等于？", "options": ["$( (n-1) × 180{^\\circ} )$", "$( (n+1) × 180{^\\circ} )$", "$( (n-3) × 180{^\\circ} )$", "$( (n-2) × 180{^\\circ} )$"], "answer": "D", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "多边形的外角和等于？", "options": ["$270{^\\circ}$", "$360{^\\circ}$", "$90{^\\circ}$", "$180{^\\circ}$"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "从n边形的一个顶点出发可以引几条对角线，把多边形分成几个三角形？", "options": ["$n-3$；$n-2$", "$n-2$；$n-3$", "$n-3$；$n-3$", "$n-2$；$n-2$"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "n边形共有几条对角线？", "options": ["$\\frac{n(n-3)}{2}$", "$\\frac{(n-1)(n-3)}{2}$", "$\\frac{n(n-1)}{2}$", "$\\frac{n(n-2)}{2}$"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "二元一次方程含有两个未知数，并且未知数的指数都是1，像这样的方程叫做什么？", "options": ["二元一次方程", "一元一次方程", "一元二次方程", "二元二次方程"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} |
| {"question": "二元一次方程一般形式是什么？", "options": ["$ax+by=c(a\\neq 0,b\\neq 0)$", "$ax+by=0(a\\neq 0,b\\neq 0)$", "$ax+by=c(a\\neq 0)$", "$ax+by=c(b\\neq 0)$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} |
| {"question": "把两个二元一次方程合在一起，就组成了一个什么？", "options": ["二元一次方程组", "二元二次方程组", "一元二次方程组", "一元一次方程组"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} |
| {"question": "什么叫做二元一次方程的解？", "options": ["一般地，使二元一次方程两边的值相等的x的值叫做二元一次方程组的解。", "一般地，使二元一次方程两边的值相等的指数的值叫做二元一次方程组的解。", "一般地，使二元一次方程两边的值相等的系数的值叫做二元一次方程组的解。", "一般地，使二元一次方程两边的值相等的未知数的值叫做二元一次方程组的解。"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} |
| {"question": "什么叫做二元一次方程组的解？", "options": ["一般地，二元一次方程组的两个方程的其中两组解叫做二元一次方程组。", "一般地，二元一次方程组的两个方程的所有解叫做二元一次方程组。", "一般地，二元一次方程组的两个方程的其中一组解叫做二元一次方程组。", "一般地，二元一次方程组的两个方程的公共解叫做二元一次方程组。"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} |
| {"question": "将未知数的个数由多化少，逐一解决的想法，叫做什么思想？", "options": ["增元思想", "化简思想", "消元思想", "解元思想"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} |
| {"question": "将一个未知数用含有另一个未知数的式子表示出来，再代入另一方程，实现消元，进而求得这个二元一次方程组的解，这种方法叫做<<<Answer>>>，简称代入法。", "options": ["加减消元法", "穷举法", "代入消元法", "换元法"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} |
| {"question": "当两个方程中同一未知数的系数相反或相等时，将两个方程的两边分别相加或相减，就能消去这个未知数，这种方法叫做<<<Answer>>>，简称加减法。", "options": ["换元法", "加减消元法", "穷举法", "代入消元法"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} |
| {"question": "用哪些符号表示大小关系的式子叫做不等式？", "options": ["$<,>$", "$<,>,\\leq,\\req$", "$<,>,\\leq,\\req,\\neq$", "$<,>,\\leq,\\req,=$"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} |
| {"question": "什么叫做不等式的解？", "options": ["使不等式两端相等的系数的值", "使不等式成立的未知数的值", "使不等式成立的系数的值", "使不等式两端相等的未知数的值"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} |
| {"question": "一个含有未知数的不等式的所有解，组成这个不等式的什么？", "options": ["解集", "集合", "特征值", "解"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} |
| {"question": "不等式的左、右两边都是<<<Answer1>>>，只有一个未知数，并且未知数的最高次数是<<<Answer2>>>，像这样的不等式，叫做一元一次不等式", "options": ["整式，2", "整式，1", "单项式，2", "单项式，1"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} |
| {"question": "一般地，关于同一未知数的几个一元一次不等式合在一起，就组成了一个什么？", "options": ["一元一次方程", "一元一次不等式组", "一元一次方程组", "一元一次不等式"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} |
| {"question": "考察不等式的性质。不等式的两边都加上（或减去）同一个数（或式子），不等号的方向怎么变？", "options": ["不变", "改变", "不一定", "都不是"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} |
| {"question": "考察全体对象的调查方式叫做什么？", "options": ["全面调查", "片面调查", "抽样调查", "普遍调查"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} |
| {"question": "调查部分数据，根据部分来估计总体的调查方式称为什么？", "options": ["抽样调查", "普遍调查", "全面调查", "片面调查"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} |
| {"question": "要考察的全体对象称为什么？", "options": ["全集", "总集", "局部", "总体"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} |
| {"question": "组成总体的每一个考察对象称为什么？", "options": ["总体", "个体", "局部", "全集"], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} |
| {"question": "被抽取的所有个体组成了一个什么？", "options": ["全集", "样本", "总体", "个体"], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} |
| {"question": "样本中个体的数目称为什么？", "options": ["样本体积", "样本个数", "样本总和", "样本容量"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} |
| {"question": "一般地，我们称落在不同小组中的数据个数为该组的<<<Answer>>>", "options": ["频数", "概率", "容量", "频率"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} |
| {"question": "频数与数据总数的比为<<<Answer>>>", "options": ["频率", "帧率", "斜率", "概率"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} |
| {"question": "在统计数据时，把数据按照一定的范围分成若干组，分成组的个数称为<<<Answer1>>>，每一组两个端点的差叫做<<<Answer2>>>", "options": ["类数，组差", "组别，距离", "组距，组数", "组数，组距"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} |
| {"question": "两个三角形的形状、大小都一样时，其中一个可以经过平移、旋转、对称等运动（或称变换）使之与另一个重合，这两个三角形称为<<<Answer>>>", "options": ["全等三角形", "等腰三角形", "等边三角形", "相似三角形"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "考察全等三角形的性质：全等三角形的对应角<<<Answer1>>>，对应边<<<Answer2>>>", "options": ["相等，相等", "不等，相等", "相等，不等", "不等，不等"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "三角形全等的\"边角边\"简称是什么？", "options": ["ASA", "AAS", "SSS", "SAS"], "answer": "D", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "三角形全等的\"角边角\"简称是什么？", "options": ["SAS", "SSS", "AAS", "ASA"], "answer": "D", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "三角形全等的\"边边边\"简称是什么？", "options": ["ASA", "SSS", "AAS", "SAS"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "三角形全等的\"角角边\"简称是什么？", "options": ["SAS", "ASA", "SSS", "AAS"], "answer": "D", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "斜边和直角边相等的两直角三角形简称是什么？", "options": ["HL", "AAS", "SSS", "SAS"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "角的内部到角的两边的距离相等的点在角的<<<Answer>>>上", "options": ["延长线", "平分线", "垂线", "中线"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "证明两个三角形全等或利用它证明线段或角相等的基本方法步骤顺序依次是？", "options": ["回顾三角形判定，确定已知条件，正确地书写证明格式", "确定已知条件，回顾三角形判定，正确地书写证明格式", "确定已知条件，正确地书写证明格式，回顾三角形判定", "正确地书写证明格式，确定已知条件，回顾三角形判定"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "如果一个图形沿某条直线折叠后，直线两旁的部分能够互相重合，那么这个图形叫做？", "options": ["正方形", "轴对称图形", "中心对称图形", "全等图形"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "轴对称图形关于什么对称？", "options": ["中心", "一条边", "对称轴线", "对角线"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "轴对称图形的对称轴，是任何一对对应点所连线段的什么？", "options": ["中心", "一条边", "垂直平分线", "对角线"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "等腰三角形的两个底角?", "options": ["不等", "不确定", "相等", "和为90°"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "等腰三角形的角平分线、底边上的高、底边上的中线有什么关系？", "options": ["重合", "互相平行", "互相垂直", "两两垂直"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "等腰三角形如何判定？", "options": ["两边之和大于第三边", "存在两条边互相垂直", "等角对等边", "一个角为直角"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "等腰三角三个角有什么特点？", "options": ["一个角为直角", "只有两个角相等", "相等，都为60°", "没有关系"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "直角三角形中，30°角所对的直角边等于斜边的？", "options": ["一半", "三分之一", "没有关系", "四分之一"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "直角三角形斜边上的中线等于斜边的？", "options": ["没有关系", "四分之一", "三分之一", "一半"], "answer": "D", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "一般地，如果一个正数$x$的平方等于$a$，即$x^2=a$，那么正数x叫做$a$的？", "options": ["算术平方根", "立方根", "几何平方根", "算术立方根"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "0的算术平方根为？", "options": ["-1", "不存在", "1", "0"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "一般地，如果一个数$x$的平方等于$a$，即$x^2=a$，那么数x叫做$a$的？", "options": ["算术立方根", "平方根", "几何平方根", "立方根"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "按正负性分，一个什么样的数的平方等于$a$，即$x^2=a$，该数x叫做$a$的平方根？", "options": ["正负数都不行", "负数", "正负数都可以", "正数"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "0有几个平方根？", "options": ["0个", "3个", "1个", "2个"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "正数的立方根是？", "options": ["不存在", "0", "正数", "负数"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "负数的立方根是？", "options": ["负数", "不存在", "正数", "0"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "0的立方根是？", "options": ["-1", "1", "0", "不存在"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "数$a$的相反数是？", "options": ["$-a$", "$a+1$", "$a$", "$-a+1$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "负数的绝对值是？", "options": ["它的相反数", "它的立方", "它的平方", "它本身"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "0的绝对值是？", "options": ["1", "-1", "不存在", "0"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} |
| {"question": "若两个变量x,y间的关系式可以表示成$y=kx+b(k\\ne 0)$\n的形式，则称y是x的？", "options": ["指数函数", "三角函数", "一次函数", "二次函数"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} |
| {"question": "若两个变量x,y间的关系式可以表示成$y=kx+b(k\\ne 0)$\n的形式，则称y是x的一次函数，当b怎么样时，称y是x的正比例函数？", "options": ["$b\\ge 0$", "$b<0$", "$b=0$", "$b>0$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} |
| {"question": "正比例函数一定经过坐标哪里？", "options": ["原点", "没有", "x轴", "y轴"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} |
| {"question": "正比例函数$y=kx$，当$k>0$时，直线经过哪几个象限？", "options": ["二、四", "只有三", "一、三", "只有一"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} |
| {"question": "正比例函数$y=kx$，当$k<0$时，直线经过哪几个象限？", "options": ["二、四", "只有二", "只有四", "一、三"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} |
| {"question": "正比例函数$y=kx(k>0)$经过一、三象限时，y随着x的增大而？", "options": ["减小", "先增大后减小", "增大", "不变"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} |
| {"question": "正比例函数$y=kx(k<0)$经过二、四象限时，y随着x的增大而？", "options": ["减小", "不变", "增大", "先减小后增大"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} |
| {"question": "已知两点坐标求函数解析式可以使用什么方法？", "options": ["待定系数法", "因式分解法", "配方法", "参数方程法"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} |
| {"question": "下面哪个是同底数幂的乘法法则？", "options": ["$a^m × b^m = (a×b)^m$", "$(ab)^n = a^n × b^n$", "$a^m\\cdot a^n=a^{m+n}$", "$(a^m)^n = a^{mn}$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "$(a^m)^n$等于什么？", "options": ["$a^{mn}$", "$a^{m-n}$", "$a^{m^n}$", "$a^{m+n}$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "对于单项式乘法法则，以下哪个是正确的？", "options": ["对于只在一个单项式里含有的字母，连同它的指数需要舍弃", "系数相乘，相同字母相除", "系数、相同字母分别相除", "它们的系数、相同字母分别相乘"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "单项式与多项式相乘是通过乘法对加法的什么律，把它转换成单项式乘以单项式？", "options": ["反结合律", "交换律", "分配律", "结合律"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "对于多项式乘以多项式，以下哪个是正确的？", "options": ["两个多项式中的每一项按顺序只需要对应相乘再相加", "先用一个多项式中的每一项乘以另一个多项式的每一项，再把所得的积相加", "两个多项式中的每一项按顺序只需要对应相乘再相减", "先用一个多项式中的每一项乘以另一个多项式的每一项，再把所得的积相减"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "平方差公式是下面的哪个？", "options": ["$(a+b)^2 = a^2 + 2ab + b^2$", "$(a-b)^2 = a^2 - 2ab + b^2$", "$(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$", "$(a+b)(a-b)=a^2-b^2$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "$(a\\pm b)^2=a^2\\pm 2ab+b^2$是哪个公式？", "options": ["平方差公式", "平方和与差公式", "平方和公式", "完全平方公式"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "$a^0(a\\ne 0)=$？", "options": ["0", "a", "-1", "1"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "任何不等于0的数的-p次幂，等于这个数的p次幂的？", "options": ["倒数", "平方根", "对数", "立方根"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "当a满足什么条件时，$a^{-p}$的值一定是正的？", "options": ["$a\\ge 0$", "$a\\le 0$", "$a<0$", "$a>0$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "对于单项式除以单项式，以下哪个是正确的？", "options": ["系数、同底数幂分别相除", "对于只在被除式里含有的字母需要舍弃", "系数、同底数幂分别相乘", "系数相乘，同底数幂相除"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "对于多项式除以单项式，以下哪个是正确的？", "options": ["先把这个多项式的每一项乘以单项式，再把所得的商相减", "先把这个多项式的每一项除以单项式，再把所得的商相减", "先把这个多项式的每一项乘以单项式，再把所得的积相加", "先把这个多项式的每一项除以单项式，再把所得的商相加"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "把一个多项式化成几个整式的积的形式，这种变形叫做把这个多项式？", "options": ["分组分解", "十字相乘", "分解因式", "提取公因式"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "下面哪个不是分解因式的一般方法？", "options": ["十字相乘法", "运用公式法", "提公共因式法", "主元法"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "因式分解的最后结果必须是？", "options": ["几个分式的乘积", "几个整式相减", "几个整式相加", "几个整式的乘积"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "有关因式分解步骤错误的是？", "options": ["第二步，看能否用公式法", "先看各项有没有公因式，若有则先提取公因式", "因式分解的最后结果必须是几个整式的相加", "因式分解的结果必须进行到每个因式在有理数范围内不能再分解为止"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} |
| {"question": "形如$A/B$，A、B是整式，B中含有未知数且B不等于0，这样的式子叫做分式，其中A和B分别叫做分式的什么？", "options": ["分母、分母", "分子、分子", "分母、分子", "分子、分母"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "分式有意义的条件是什么？", "options": ["分子分母不相等", "分子不等于1", "分母不等于0", "分子分母都不等于0"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "把一个分式的分子和分母的公因式（不为1的数）约去，这种变形称为？", "options": ["约分", "通分", "化简", "通项"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "异分母的分式可以化为同分母的分式，这一过程叫做？", "options": ["通分", "通项", "化简", "约分"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "分式的分子和分母同时乘以一个不为0的整式，分式的值如何变化？", "options": ["变小", "变大", "不变", "不确定"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "分式的分子和分母同时除以一个不为0的整式，分式的值如何变化？", "options": ["不确定", "变大", "变小", "不变"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "一个分式的分子和分母没有公因式时，这个分式称为？", "options": ["最简分式", "无公因式分式", "单调分式", "简单分式"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "同分母的分式相加减的规则是什么？", "options": ["分母不变，分子相加减", "分母不变，分母相加减", "分子不变，分母相加减", "分子不变，分子相加减"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "异分母的分式相加减，需要先进行什么操作，使其化为同分母的分式进行计算，然后再按照同分母分式的法则进行计算。", "options": ["约分", "化简", "通分", "乘上最小公倍数"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "两个分式相乘，积的分子和分母分别是？", "options": ["分子相乘的积、分母相乘的积", "分母相乘的积、分母相乘的积", "分子相乘的积、分子相乘的积", "分母相乘的积、分子相乘的积"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "两个分式相除，需要把什么的分子和分母颠倒位置后再与什么相乘。", "options": ["除式、被除式", "较大的分式、较小的分式", "被除式、除式", "较小的分式、较大的分式"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "分式方程指的是分式的哪里含有未知数？", "options": ["分子", "不确定", "分母", "任意地方"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "分式方程求解的正确顺序是？", "options": ["求解未知数、去分母、验根", "去分母、求解未知数、验根", "去分母、求解未知数", "求解未知数、验根"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Fractions"} |
| {"question": "形如$y=\\frac{k}{x} $（k为常数，$k \\ne 0$）的函数被称为？", "options": ["反比例函数", "双曲线函数", "常函数", "单调函数"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} |
| {"question": "反比例函数的图像属于？", "options": ["弧线", "抛物线", "曲线", "双曲线"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} |
| {"question": "反比例函数的图像属于哪种对称图形？", "options": ["既不是轴对称，也不是中心对称", "只是轴对称", "只是中心对称", "既是轴对称，也是中心对称"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} |
| {"question": "反比例函数的对称中心是？", "options": ["$(0,1)$", "$(1,0)$", "原点", "$(1,1)$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} |
| {"question": "关于双曲线函数的图像，当$k>0$时，双曲线的两支分别位于什么象限？", "options": ["第二、第三", "第二、第四", "第一、第三", "第一、第四"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} |
| {"question": "关于双曲线函数的图像，当$k<0$时，双曲线的两支分别位于什么象限？", "options": ["第一、第四", "第二、第四", "第一、第三", "第二、第三"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} |
| {"question": "关于双曲线函数的图像，当$k>0$时，在每个象限内y值随着x值的增大而？", "options": ["不变", "减小", "增大", "不确定"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} |
| {"question": "关于双曲线函数的图像，当$k<0$时，在每个象限内y值随着x值的增大而？", "options": ["减小", "增大", "不变", "不确定"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} |
| {"question": "关于反比例函数$y=\\frac{k}{x}$，其中$|k|$的几何意义是？", "options": ["截距的绝对值", "不确定", "反比例函数图像上的点向两坐标所作的垂线段与两坐标围成的矩形的面积", "斜率的绝对值"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} |
| {"question": "根据勾股定理与逆定理，下列说法正确的是:", "options": ["$a^{2} +b^{2} <c^{2}$", "$a^{2} +b^{2} =c^{2}$", "根据勾股定理逆定理，如果三角形边长$a$,$b$,$c$满足$a^{2} +b^{2} =c^{2}$，那么这个三角形是等边三角形", "$a^{2} +b^{2} >c^{2}$"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "下列关于定理描述正确的是:", "options": ["未经过证明被认证正确的命题", "经过证明被认证错误的命题", "经过证明被认证正确的命题", "未经过证明被认证错误的命题"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "下列关于互逆命题说法正确的是:", "options": ["题设、结论都相同", "题设相同，结论相反", "题设、结论都相反", "题设相反，结论相同"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "下列关于平行四边形定义说法正确的是:", "options": ["有一组对边平行", "有一个角一定是钝角", "有一个角是直角", "有两组对边分别平行"], "answer": "D", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于平行四边形性质说法错误的是:", "options": ["平行四边形的对角相等", "平行四边形有且仅有一个角是直角", "平行四边形的对角线互相平分", "平行四边形的对边相等"], "answer": "B", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于平行四边形的判定条件说法错误的是:", "options": ["一组对边平行且相等", "两组对边分别相等", "两组对角分别相等", "对角线相等"], "answer": "D", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "关于三角形中位线下列说法正确的是:", "options": [":三角形的中位线垂直于三角形的第三边", ":三角形的中位线平行于三角形的第三边", "三角形中位线等于三角形周长的一半", "三角形的中位线等于第三边"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "下列关于直角三角形斜边上的中线说法正确的是:", "options": ["等于斜边的一半", "等于斜边", "和斜边长度没有必然联系", "等于斜边的两倍"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "下列关于矩形的定义说法正确的是：", "options": ["有一个角是直角的四边形", "有一个角是锐角的四边形", "有一个角是锐角的平行四边形", "有一个角是直角的平行四边形"], "answer": "D", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于矩形的性质说法错误的是:", "options": ["四个角都是直角", "对角线相等", "对角线平分", "四条边都相等"], "answer": "D", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于举行判定定理说法错误的是:", "options": ["对角线相等的平行四边形是矩形", "有一个角是直角的平行四边形是矩形", "有一个角是直角的四边形是矩形", "有三个角是直角的四边形是矩形"], "answer": "C", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于菱形说法正确的是:", "options": ["对角线相等的平行四边形", "有一个角为直角的四边形", "邻边相等的四边形", "邻边相等的平行四边形"], "answer": "D", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于菱形的性质说法错误的是:", "options": ["菱形的每一条对角线平分一组对角", "菱形的四条边都相等", "菱形两条对角线相等", "菱形的两条对角线互相垂直"], "answer": "C", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于菱形的判定定理说法错误的是:", "options": ["四条边相等的四边形是菱形", "对角线互相垂直的平行四边形是菱形", "一组邻边相等的平行四边形是菱形", "一组邻边相等的四边形是菱形"], "answer": "D", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于菱形说法正确的是:", "options": ["$S_{菱形}=\\frac{1}{2} ab$", "对角线互相垂直的四边形是菱形", "菱形两条对角线相等", "一组邻边相等的四边形是菱形"], "answer": "A", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于正方形说法错误的是:", "options": ["既是矩形，又是菱形", "四个角都是直角", "四条边都相等", "一个角是直角的菱形或邻边相等的平行四边形"], "answer": "D", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于正方形说法错误的是:", "options": ["四条边都相等", "既是矩形，又是菱形", "四个角都是直角", "对角线不一定垂直"], "answer": "D", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于正方形判定定理说法正确的是:", "options": ["有一个角是直角的平行四边形是正方形", "邻边相等的矩形是正方形", "对角线垂直的四边形是正方形", "邻边相等的平行四边形是正方形"], "answer": "B", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于梯形的定义说法正确的是:", "options": ["对角线垂直的四边形", "对角线相互平分的四边形", "有且仅有一个角为直角的四边形", "一组对边平行，另一组对边不平行的四边形"], "answer": "D", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于直角梯形说法正确的是:", "options": ["有一个角是直角的平行四边形是直角梯形", "有一个角是直角的梯形是直角梯形", "一组对边一组对边平行，另一组对边不平行的四边形是直角梯形", "对角线垂直的四边形是直角梯形"], "answer": "B", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于等腰梯形说法正确的是:", "options": ["邻边相等的平行四边形是等腰梯形", "一组对边一组对边平行，另一组对边不平行的四边形是等腰梯形", "两腰相等的梯形是等腰梯形", "对角线垂直的四边形是等腰梯形"], "answer": "C", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于等腰梯形说法错误的是:", "options": ["等腰梯形的两条对角线相等", "等腰梯形一组对边平行，另一组对边不平行", "等腰梯形有一个角为直角", ":等腰梯形同一底边上的两个角相等"], "answer": "C", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "下列关于等腰梯形说法错误的是:", "options": ["等腰梯形同一底边上的两个角不相等", ":等腰梯形同一底边上的两个角相等", "等腰梯形的两条对角线相等", "等腰梯形一组对边平行，另一组对边不平行"], "answer": "A", "topic": "Middle--Basic Geometry--Quadrilaterals"} |
| {"question": "加权平均数中“权”代表了什么？", "options": ["数据的波动", "一组数据的中位数", "某个数据在整个数据中的重要程度", "一组数据的众数"], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} |
| {"question": "将一组数据按照由小到大（或由大到小）的顺序排列，如果数据的个数是奇数，则这组数据的中位数是哪个数？", "options": ["处于结束位置的数", "处于开始位置的数", "处于中间位置的数", "处于随机位置的数"], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} |
| {"question": "将一组数据按照由小到大（或由大到小）的顺序排列，如果数据的个数是奇数，则这组数据的中位数是哪个数？", "options": ["处于结束位置的数", "处于中间位置的数", "处于开始位置的数", "中间两个数据的平均数"], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} |
| {"question": "一组数据中出现次数最多的数据是这组数据的什么？", "options": ["方差", "中位数", "平均数", "众数"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} |
| {"question": "组数据中的最大数据与最小数据的差叫做这组数据的什么？", "options": ["众数", "极差", "平均数", "中位数"], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} |
| {"question": "数据的波动与方差大小的变化关系？", "options": ["数据波动和方差大小的关系不明", "数据波动和方差大小无关", "数据波动越大，方差越大", "数据波动越大，方差越小"], "answer": "C", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} |
| {"question": "一般地，形如$\\sqrt{a} (a \\ge 0)$的代数式叫做什么？", "options": ["三次根式", "一次根式", "四次根式", "二次根式"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "当$a > 0$时，$\\sqrt{a}$ 表示什么？", "options": ["a的算术平方根", "a的积分平方根", "a的微分平方根", "a的几何平方根"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "$\\sqrt{0}$ 是多少？", "options": ["0", "3", "2", "1"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "$\\sqrt{a} (a \\ge 0)$的结果是什么类型的数？", "options": ["有理数", "负数", "非负数", "整数"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "$(\\sqrt{a})^{2} (a \\ge 0) $的结果是什么？", "options": ["a", "-a", "1", "0"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "$\\sqrt{a^{2}} (a \\leq 0)$的结果是什么？", "options": ["a", "-a", "1", "0"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "一元二次方程的方程两边都是什么？", "options": ["不定式", "分式", "不等式", "整式"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "一元二次方程有几个未知数？", "options": ["1", "0", "3", "2"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "一元二次方程的未知数的最高次数是几次？", "options": ["1", "3", "0", "2"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "一元二次方程的一般形式是什么？", "options": ["$\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1 $", "$a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0$", "$\\frac{a}{b}\\pm \\frac{c}{d}= \\frac{ad \\pm bc}{bd} $", "$y-y_{1}=k \\left( x-x_{1}\\right) $"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "一元二次方程经过整理化成$a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0$后，其中$a\\mathop{{x}}\\nolimits^{{2}}$、$bx$、$b$、$c$分别是什么？", "options": ["二次项, 一次项，常数项，一次项系数", "二次项, 一次项系数，一次项，常数项", "二次项, 一次项，一次项系数，常数项", "一次项, 二次项，一次项系数，常数项"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "运用配方法解一元二次方程$a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0$时，左边配成一个完全平方式，变形为$(x+p)^{2} = q$的形式，解是什么？", "options": ["如果$q \\ge 0$，方程的根是$\\frac{{-b \\pm \n \\sqrt{{\\mathop{{b}}\\nolimits^{{2}}-4ac}}}}{{2a}}$，如果$q< 0$，方程无实根", "无实根", "0", "$\\frac{{-b \\pm \n \\sqrt{{\\mathop{{b}}\\nolimits^{{2}}-4ac}}}}{{2a}}$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "运用公式法解一元二次方程$a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0且a\\neq0$时，当$\\mathop{{b}}\\nolimits^{{2}}-4ac> 0$，方程的根是什么？", "options": ["1", "0", "无实根", "$\\frac{{-b \\pm \n \\sqrt{{\\mathop{{b}}\\nolimits^{{2}}-4ac}}}}{{2a}}$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} |
| {"question": "在平面内，将一个图形绕一个定点按某个方向转动一个角度，这样的运动是什么？", "options": ["对称", "中心对称", "平移", "旋转"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "如果把一个图形绕着某一点旋转180度后能与自身重合，那么这个图形具有什么特性？", "options": ["平移对称", "旋转对称", "无", "中心对称"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "关于旋转对称，一个图形旋转多少度能够首次与自身重合，且这个角度应该满足什么条件？", "options": ["0；360", "360；720", "180；360", "0；180"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "旋转对称图形的定义是什么？", "options": ["一个图形如果能够绕着一个固定点旋转任意角度后与自身重合，则称为旋转对称图形。", "一个图形如果能够绕着一个固定点旋转360度后与自身重合，则称为旋转对称图形。", "一个图形如果能够绕着一个固定点旋转特定的角度（不是360度）后与自身重合，则称为旋转对称图形。", "一个图形如果能够沿着一条直线翻转后与自身重合，则称为旋转对称图形。"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "如果把一个图形移动后与另一个图形重合，那么这两个图形成什么？", "options": ["平移对称", "旋转对称", "上下对称", "中心对称"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "中心对称的两个图形是什么关系？", "options": ["重合", "全等", "没有特定关系", "相似但不全等"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "中心对称的两个图形，对称点连线经过哪一点？", "options": ["对称中心", "图形外的点", "图形上的点", "不过定点"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "中心对称的两个图形，对应线段是什么关系", "options": ["平行且相等", "相等但不平行", "相交", "平行但不相等"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} |
| {"question": "平面上到定点的距离等于等长的所有点组成的图形叫做", "options": ["正方形", "直线", "以上都不是", "圆"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "平面上到定点的距离等于等长的所有点组成的图形是圆，则定点称为", "options": ["都不是", "圆心", "中心", "驻点"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "经过圆心的弦称为", "options": ["周长", "都不是", "半径", "直径"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "顶点在圆心上的角叫做", "options": ["圆周角", "钝角", "锐角\nE: 圆角", "圆心角"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "顶点在圆周上，且它的两边分别与圆有另一个交点的角叫做", "options": ["圆周角", "钝角", "锐角\nE: 圆角", "圆心角"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "过三角形三个顶点的圆叫做三角形的", "options": ["都不是", "关联圆", "外接圆", "内切圆"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "和三角形三边都相切的圆叫做这个三角形的", "options": ["内切圆", "关联圆", "都不是", "外接圆"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "扇形由什么组成？", "options": ["三段弧", "两条半径和一段弧", "都不是", "一条弦和一段弧"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "在圆上，由两条半径和一段弧围成的图形叫做", "options": ["内接圆", "都不是", "外切圆", "扇形"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "圆锥侧面展开图是一个扇形，这扇形的什么称为圆锥的母线？", "options": ["都不是", "半径", "弦", "弧"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "圆和点的位置关系中，以点P与圆O为例（设P是一点，则PO是点到圆心的距离），当P在圆O外时，PO和圆O的半径大小关系是", "options": ["PO小于圆O的半径", "都不是", "PO大于圆O的半径", "PO等于圆O的半径"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "圆和点的位置关系中，以点P与圆O为例（设P是一点，则PO是点到圆心的距离），当P在圆O上时，PO和圆O的半径大小关系是", "options": ["PO小于圆O的半径", "PO大于圆O的半径", "都不是", "PO等于圆O的半径"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "圆和点的位置关系中，以点P与圆O为例（设P是一点，则PO是点到圆心的距离），当P在圆O内时，PO和圆O的半径大小关系是", "options": ["PO大于圆O的半径", "都不是", "PO等于圆O的半径", "PO小于圆O的半径"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "圆和点的位置关系有几种？", "options": ["3种", "无数种", "2种", "都不是"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "圆和直线有几种位置关系？", "options": ["1种", "无数种", "2种", "3种"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "两圆有几种位置关系", "options": ["2种", "3种", "5种", "4种"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "经过半径外端并且垂直于这条半径的直线是圆的", "options": ["割线", "切线", "都不是", "交线"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "经过切点垂直于切线的直线经过圆心吗？", "options": ["不一定经过", "一定经过", "都不是", "一定不经过"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "圆的切线垂直于经过切点的半径吗？", "options": ["一定不经过", "一定经过", "不一定经过", "都不是"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "平分弦（不是直径）的直径与弦一定有什么关系？", "options": ["平行", "都不是", "垂直", "重合"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "平分弦（不是直径）的直径怎么分弦所对的两条弧", "options": ["1/4分", "平分", "都不是", "1/3分"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "在同圆或等圆中，相等的圆心角所对的弧相等吗？", "options": ["不一定相等", "一定相等", "都不是", "一定不相等"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "在同圆或等圆中，相等的圆心角所对的弦相等吗？", "options": ["一定不相等", "一定相等", "都不是", "不一定相等"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "在同圆或等圆中，同弧等弧所对的圆周角相等吗？", "options": ["都不是", "一定不相等", "不一定相等", "一定相等"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "半圆（或直径）所对的圆周角是", "options": ["平角", "钝角", "直角", "锐角"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "90°的圆周角所对的弦是", "options": ["任意一条弦", "都不是", "半径", "直径"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "以下哪个是正确的圆周长公式？", "options": ["$C=4 \\pi r=2 \\pi d$", "$C= \\pi r=\\pi d$", "都不是", "$C=2 \\pi r=\\pi d$"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "以下哪个是正确的圆面积公式？", "options": ["$S= 2 \\pi r^{2}$", "$S= \\pi r^{4}$", "$S= \\pi r^{2}$", "都不是"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "以下哪个是正确的弧长公式？", "options": ["都不是", "$l=n \\pi r/90$", "$l=n \\pi r/360$", "$l=n \\pi r/180$"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "以下哪个是正确的扇形面积公式？", "options": ["$S= \\pi ( R^{2}-r^{2} )$", "$S= 2\\pi ( r^{2}-R^{2} )$", "$S=2 \\pi ( R^{2}-r^{2} )$", "$S= \\pi ( r^{2}-R^{2} )$"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Circles"} |
| {"question": "一般地，自变量x和因变量y之间存在如下哪个关系，则称y为x的二次函数？", "options": ["$y=ax^{2}+bx+c （a、b、c为常数）$", "以上都不是", "$y=ax^{2}+bx+c$", "$y=ax^{2}+bx+c （a≠0，a、b、c为常数）$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "一般地，自变量x和因变量y之间存在如下关系：一般式：$y=ax^{2}+bx+c （a≠0，a、b、c为常数）$，则称y为x的", "options": ["二次函数", "一次函数", "三次函数", "都不是"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "以下哪个解析式是二次函数的一般式？", "options": ["$y=ax^{2}+bx+c （a≠0）$", "$y=a(x-h)^{2}+k$", "$y=a(x-x_{1} )(x-x_{2})$", "$y=a(x-\\frac{b}{2a} )^{2}+\\frac{4ac-b^{2}}{4a} $"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "以下哪个解析式是二次函数的顶点式？", "options": ["都不是", "$y=a(x-x_{1} )(x-x_{2})$", "$y=a(x-\\frac{b}{2a} )^{2}+\\frac{4ac-b^{2}}{4a} $", "$y=ax^{2}+bx+c （a≠0）$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "以下哪个解析式是二次函数的交点式？", "options": ["$y=a(x-\\frac{b}{2a} )^{2}+\\frac{4ac-b^{2}}{4a} $", "都不是", "$y=ax^{2}+bx+c （a≠0）$", "$y=a(x-x_{1} )(x-x_{2})$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "二次函数的对称轴如何表示？", "options": ["都不是", "$x=-\\frac{b}{a} $", "$x=-\\frac{2b}{a} $", "$x=-\\frac{b}{2a} $"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "二次函数顶点坐标如何表示？", "options": ["$(-\\frac{b}{2a} ,\\frac{4ac-b^{2}}{4a} )$", "$(-\\frac{b}{2a} ,\\frac{4ac-b^{2}}{2a} )$", "都不是", "$(-\\frac{b}{a} ,\\frac{4ac-b^{2}}{4a} )$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "二次函数与y轴交点如何表示？", "options": ["$(0,c)$", "$(0,b)$", "$(0,a)$", "都不是"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "二次函数$y=ax^{2}+bx+c （a≠0）$ 中，当$a > 0$时，对称轴左边，y随x增大而如何变化？对称轴右边，y随x增大而如何变化？", "options": ["减小，减小", "增大，增大", "减小，增大", "增大，减小"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "二次函数$y=ax^{2}+bx+c （a≠0）$ 中，当$a > 0$时，对称轴左边，y随x增大而如何变化？对称轴右边，y随x增大而如何变化？", "options": ["减小，减小", "增大，减小", "减小，增大", "增大，增大"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "二次函数图像画法草图有什么关键点？", "options": ["开口方向", "顶点\nE: 与x轴交点\nF: 与y轴交点", "以下都是", "对称轴"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "二次函数$y=a(x-h)^{2}+k$，平移规则是什么？", "options": ["x轴左减右加，y轴上加下减", "x轴左加右减，y轴上加下减", "x轴左减右加，y轴上减下加", "x轴左加右减，y轴上减下加"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "二次函数当横坐标为$x_{1}$,$x_{2}$，其对应的纵坐标相等那么对称轴为", "options": ["$x=\\frac{x_{1}^{2}+x_{2}^{2}}{2}$", "$x=\\frac{x_{1}^{2}-x_{2}^{2}}{2}$", "$x=\\frac{x_{1}+x_{2}}{2} $", "$x=\\frac{x_{1}-x_{2}}{2} $"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "二次函数$y=ax^{2}+bx+c （a≠0）$中，a用来判断", "options": ["顶点位置", "开口方向", "都不是", "函数图像位置"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "抛物线$y=ax^{2}+bx+c （a≠0）$，当$b^{2}-4ac>0$时，一元二次方程有几个实根，二次函数图像与x轴有几个交点？", "options": ["1,2", "2,1", "1,1", "2,2"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "抛物线$y=ax^{2}+bx+c （a≠0）$，当$b^{2}-4ac=0$时，一元二次方程有几个实根，二次函数图像与x轴有几个交点", "options": ["1,2", "1,1", "2,1", "2,2"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} |
| {"question": "相似三角形一定满足？", "options": ["对应边上的高相等", "对应边相等", "对应角相等", "对应角平分线相等"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "哪个条件不能判定两个三角形相似？", "options": ["三组对应角相等", "三组对应边的比相等", "两组对应角相等", "两组对应边相等"], "answer": "D", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "相似三角形的判定方法不包括？", "options": ["如果一个三角形的两个角与另一个三角形的两个角对应相等，那么这两个三角形相似。", "平行于三角形一边的直线（或两边的延长线）和其他两边相交，所构成的三角形与原三角形相似。", "如果两个三角形的两组对应边的比相等，且有一个对应角相等，那么这两个三角形相似。", "如果两个三角形的二组对应边的比相等，且任意角相等，那么这两个三角形相似。"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "哪个条件不能判定两个直角三角形相似？", "options": ["两条直角边对应成比例", "斜边对应成比例", "一组锐角对应相等", "斜边与一条直角边对应成比例"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "直角三角形相似判定定理包括？", "options": ["直角三角形被斜边上的高分成的两个直角三角形与原直角三角形相似，并且分成的两个直角三角形也相似。", "面积的比等于相似比", "周长的比等于相似比", "一切对应线段成比例"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "相似三角形不满足？", "options": ["面积的比等于相似比", "对应角平分线的比等于相似比", "对应外接圆半径的比等于相似比", "对应内切圆半径的比等于相似比"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "相似三角形的相似比不等于？", "options": ["周长的比", "对应中线的比", "对应角平分线的比", "面积的比"], "answer": "D", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "相似三角形的相似比等于？", "options": ["内切圆面积的比", "面积的比", "外接圆半径的比", "对应角的比"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "在$Rt\\triangle ABC$中，$\\angle A$的正弦是？", "options": ["$\\angle A$的斜边与对边的比值", "$\\angle A$的邻边与对边的比值", "$\\angle A$的对边与邻边的比值", "$\\angle A$的对边与斜边的比值"], "answer": "D", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "在$Rt\\triangle ABC$中，$\\angle A$的余弦是？", "options": ["$\\angle A$的对边与邻边的比值", "$\\angle A$的对边与斜边的比值", "$\\angle A$的邻边与对边的比值", "$\\angle A$的邻边与斜边的比值"], "answer": "D", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "在$Rt\\triangle ABC$中，$\\angle A$的正切是？", "options": ["$\\angle A$的邻边与对边的比值", "$\\angle A$的对边与斜边的比值", "$\\angle A$的对边与邻边的比值", "$\\angle A$的斜边与对边的比值"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "在$Rt\\triangle ABC$中，$\\angle A$的余切是？", "options": ["$\\angle A$的对边与斜边的比值", "$\\angle A$的邻边与对边的比值", "$\\angle A$的对边与邻边的比值", "$\\angle A$的斜边与对边的比值"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "下列正弦三角函数值正确的是？", "options": ["$\\sin45^{\\circ}=\\frac{\\sqrt{2}}{2}$", "$\\sin60^{\\circ}=\\frac{\\sqrt{1}}{2}$", "$\\sin60^{\\circ}=\\frac{\\sqrt{2}}{2}$", "$\\sin30^{\\circ}=\\frac{\\sqrt{3}}{2}$"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "下列余弦三角函数值正确的是？", "options": ["$\\cos30^{\\circ}=\\frac{\\sqrt{3}}{2}$", "$\\cos30^{\\circ}=\\frac{\\sqrt{1}}{2}$", "$\\cos60^{\\circ}=\\frac{\\sqrt{3}}{2}$", "$\\cos30^{\\circ}=\\frac{\\sqrt{2}}{2}$"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "下列正切三角函数值正确的是？", "options": ["$\\tan45^{\\circ}=\\frac{\\sqrt{2}}{2}$", "$\\tan30^{\\circ}=\\frac{\\sqrt{3}}{2}$", "$\\tan45^{\\circ}=1$", "$\\tan30^{\\circ}=\\frac{\\sqrt{1}}{2}$"], "answer": "C", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
| {"question": "下列余切三角函数值正确的是？", "options": ["$\\cot30^{\\circ}=1$", "$\\cot30^{\\circ}=\\sqrt{3}$", "$\\cot45^{\\circ}=\\frac{\\sqrt{2}}{2}$", "$\\cot30^{\\circ}=\\frac{\\sqrt{3}}{3}$"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} |
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