2026届苏州市九年级数学中考二模模拟试卷（含答案详解与评分标准）

2026届苏州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：中考二模适用对象：九年级注意事项1．本卷用于九年级中考二模阶段检测，试题覆盖数与式、方程与不等式、函数、统计与概率、图形与几何、综合应用等核心内容。2．全卷共三大题22小题，满分120分。选择题10题，每题3分；填空题6题，每题3分；解答题6题，共72分。3．答题前请将学校、班级、姓名、考号填写清楚；作答时书写要规范，计算题和证明题须写出必要步骤。4．选择题每题只有一个正确选项；填空题只需写出最后结果；解答题请在题后作答区内完成。题型选择题填空题解答题总分分值30分18分72分120分一、选择题（本大题共10小题，每小题3分，共30分）每小题给出的四个选项中，只有一个选项符合题意。1．的值是（）A．B．C．D．2．的计算结果是（）A．B．C．D．3．苏州市某区九年级二模数学线上错题推送量约为920000条，将920000用科学记数法表示为（）A．B．C．D．4．不等式的解集是（）A．B．C．D．5．一组数据3，4，4，5，8的中位数和众数分别是（）A．3，4B．4，4C．4，5D．5，46．点关于轴对称的点的坐标是（）A．B．C．D．7．若正比例函数的图象经过第一、第三象限，则的取值范围是（）A．B．C．D．8．二次函数的顶点坐标是（）A．B．C．D．9．一个不透明袋中有3个红球、2个黄球、1个蓝球，这些球除颜色外完全相同。随机摸出1个球，摸到“不是黄球”的概率为（）A．B．C．D．10．如图形问题中常见的直径模型：在圆中，为直径，点在圆上，若，，则圆的半径是（）A．B．C．D．选择题答题栏题号12345678910答案二、填空题（本大题共6小题，每小题3分，共18分）11．＝答案：________________12．分式方程的解是答案：________________13．一次函数的图象经过点和，则的值为答案：________________14．半径为6、圆心角为的扇形面积为答案：________________15．二次函数的最小值为答案：________________16．用一根长40米的围栏围成一个矩形菜地，若一边靠墙且靠墙一边不需要围栏，则围成矩形面积的最大值为答案：________________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。17．（本题8分）计算与化简：（1）计算：；（2）化简：，并写出的取值限制。作答区________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本题10分）某校九年级数学组在中考二模复习阶段，随机抽取20名学生，调查他们“一周内主动整理数学错题的次数”，得到如下统计表：整理次数012345人数136532（1）求这20名学生一周主动整理数学错题次数的平均数、中位数和众数；（2）若该校九年级共有900名学生，请估计一周内主动整理数学错题不少于3次的学生人数；（3）结合数据，从备考习惯角度写出一条合理建议。作答区________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本题12分）如图象综合题中，已知一次函数与反比例函数的图象交于点和点。（1）求的值及点的坐标；（2）求的面积，其中为坐标原点；（3）根据函数图象或代数推理，写出不等式的解集。作答区________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本题12分）在中，，，。点为从向作垂线的垂足，过点作交于点。（1）求和的长；（2）求与的长；（3）以点为圆心、为半径作圆，判断直线与该圆的位置关系，并说明理由。作答区________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本题14分）为配合九年级中考二模后的错题订正活动，某文具店购进一种复习记录本。每本进价10元，规定销售单价满足。经调查，当销售单价为20元时，每天可售出120本；销售单价每提高1元，每天少售出4本。设每天销售量为本，每天销售利润为元。（1）求与之间的函数关系式；（2）求与之间的函数关系式，并求每天销售利润的最大值；（3）若商店希望每天销售利润不低于1500元，同时尽量让利给学生，请确定销售单价应如何安排。作答区________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（本题16分）如图，在平面直角坐标系中，抛物线经过点、、，其解析式可记为。（1）求该抛物线的解析式；（2）求抛物线的顶点的坐标，并写出当时函数的最小值与最大值；（3）在抛物线第四象限部分是否存在点，使？若存在，求点的坐标；若不存在，请说明理由；（4）点在直线上，若，求点的坐标，并判断其中是否有点与顶点重合。作答区_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________