2026届重庆市九年级数学中考二模模拟试卷（含答案详解与评分标准）

第页2026届重庆市九年级数学中考二模模拟试卷（含答案详解与评分标准）学校：______________班级：______________姓名：______________考号：______________考试时间：120分钟满分：120分考试节点：中考二模适用年级：九年级注意事项：1．本试卷为重庆市九年级中考二模阶段检测模拟卷，满分120分，考试时间120分钟。2．答题前请将学校、班级、姓名、考号填写清楚。3．选择题请将唯一正确选项填入答题位置；解答题应写出必要的文字说明、证明过程或演算步骤。4．作图、计算和书写应清楚规范，结果需化简；答案与解析从新页开始，供阅卷与复盘使用。一、选择题（本大题共10小题，每小题3分，共30分）每小题只有一个选项符合题意。请结合二模复习要求，认真审题、独立判断。1．计算的结果是（3分）A．1B．5

C．7D．132．2026年重庆某区二模质量分析中提到，某种芯片导线的直径约为0.00000046米，将0.00000046用科学记数法表示为（3分）A．B．

C．D．3．若，则化简后的结果是（3分）A．B．

C．D．4．在中，，，则的度数为（3分）A．50°B．60°

C．70°D．80°5．一次函数的图象随的增大而减小，则的取值范围是（3分）A．B．

C．D．6．不等式组的解集是（3分）A．B．

C．D．7．已知圆的半径为6，圆心角所对弧长为（3分）A．B．

C．D．8．袋中有5个红球和3个白球，它们除颜色外完全相同。从中任意摸出1个球，摸到红球的概率为（3分）A．B．

C．D．9．若关于的方程的两个根为，则的值为（3分）A．4B．6

C．10D．1610．已知一次函数的图象经过点与，则点位于（3分）A．第一象限B．第二象限

C．第三象限D．第四象限二、填空题（本大题共6小题，每小题3分，共18分）请把正确答案填写在题后横线上。11．计算：＝__________。（3分）12．因式分解：＝__________。（3分）13．若点关于轴对称的点为，则的坐标为__________。（3分）14．已知反比例函数的图象经过点，则＝__________。（3分）15．一个正多边形的每个外角均为45°，则这个正多边形的边数为__________。（3分）16．一组数据6，8，10，，12的平均数为10，则＝__________。（3分）三、解答题（本大题共6小题，共72分）解答应写出必要的文字说明、证明过程或演算步骤。每题后方保留作答区，可在空白处继续书写。17．计算与解方程。（12分）（1）先化简，再求值：，其中。（2）解分式方程：。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

18．为迎接中考体育模拟测试，某校准备购买篮球和足球共40个，已知篮球每个80元，足球每个60元，计划总费用不超过2800元，且篮球数量不少于足球数量的。设购买篮球个。（12分）（1）求的取值范围；（2）若学校希望篮球数量尽可能多，同时费用不超过预算，最多可以买多少个篮球？此时总费用是多少元？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

19．如平面内有三角形，点在上，点在上，且。已知，，。（12分）（1）证明：；（2）求的长；（3）若，求的长。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

20．某区九年级二模复习周开展“每天数学基础练习用时”调查，随机抽取20名学生，统计结果如下表。（12分）用时（分钟）20253035人数3584（1）求这20名学生每天数学基础练习用时的平均数；（2）直接写出这组数据的中位数和众数；（3）从用时为20分钟的3名学生中选2名参加访谈，其中甲、乙恰好都被选中的概率是多少？作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

21．某文具店在二模备考季推出两种购买中性笔芯的方案。方案甲：每支0.8元，不收其他费用；方案乙：先购买10元会员卡，再按每支0.5元购买。设购买笔芯支，甲、乙两种方案的总费用分别为元。（12分）（1）分别写出与的函数关系式；（2）当购买多少支时，两种方案费用相同？（3）若九年级某班计划购买60支，选择哪种方案更省钱？请说明理由；（4）结合函数关系，给出购买数量与方案选择的建议。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

22．在平面直角坐标系中，抛物线与轴交于点（点在点左侧），与轴交于点，顶点为。（12分）（1）求点的坐标；（2）若直线过点和，求直线的解析式；（3）在抛物线对称轴上是否存在点，使的值最小？若存在，求点的坐标及最小值；若不存在，请说明理由。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析一、选择题答案与关键理由题号12345678910答案CBACBCBBCA分值33333333331．答案：C。先算乘方与绝对值，。2．答案：B。小数点向右移动7位得到4.6，所以。3．答案：A。同底数幂相乘、相除，指数先加后减，。4．答案：C。三角形内角和为180°，。5．答案：B。一次函数随自变量增大而减小，斜率应小于0，即。6．答案：C。由两个不等式分别得，取公共部分为。7．答案：B。弧长公式，代入得。8．答案：B。总球数为8个，红球5个，摸到红球的概率为。9．答案：C。方程可化为，两根为3和-1，平方和为。10．答案：A。由两点求斜率，代入得，所以，点在第一象限。二、填空题答案与解析题号111213141516答案√2(x+3)(x-3)(2,3)10814分值33333311．12．13．关于轴对称时，横坐标不变，纵坐标变为相反数，故。14．反比例函数经过，得。15．正多边形外角和为360°，边数。16．由平均数公式，，解得。

三、解答题答案详解与评分标准评分说明：以下给出一种标准解法和分步给分点。学生采用其他正确方法，只要逻辑严密、结果正确，可按相应步骤等值给分；若过程合理但计算失误，应根据错误影响范围酌情扣分。17．答案详解与评分标准（12分）（1）原式==。当时，原式=。（2）方程两边同乘（且），得。化简得，故原方程对所有满足的实数均成立，解集为。评分标准：第（1）问展开正确2分，合并为2分，代入求值2分；第（2）问写出定义域限制2分，正确去分母2分，说明恒等成立并给出解集2分。18．答案详解与评分标准（12分）设篮球个，则足球个。由费用不超过2800元，得，化简得，即。由篮球数量不少于