2026届苏州市九年级数学中考冲刺模拟试卷（含答案详解与评分标准）

第页2026届苏州市九年级数学中考冲刺模拟试卷（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分适用：九年级中考冲刺日期：2026年____月____日注意事项：1．本卷为苏州市九年级数学中考冲刺模拟训练，全卷共三大题，22小题，满分120分，考试时间120分钟。2．答题前，请将学校、班级、姓名和考号填写在指定位置；作答时书写工整，步骤完整，单位明确。3．选择题每题只有一个正确答案；填空题只需填写最终结果；解答题应写出必要的推理、计算或证明过程。4．本卷允许使用直尺、圆规、三角板等常规作图工具，计算结果可按题目要求保留精确值或近似值。题型与分值结构：题型题量每题分值小计选择题10题3分30分填空题6题3分18分解答题6题见题内标注72分合计22题—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。请将正确选项填在题后括号内。1．下列运算正确的是（）A．a²＋a³＝a⁵B．(a²)³＝a⁶C．a⁶÷a²＝a³D．(ab)²＝ab²2．关于x的一元二次方程有两个不相等的实数根，则m的取值范围是（）A．m＞4B．m＝4C．m＜4D．m≤43．在△ABC中，AB＝AC，∠A＝40°，则∠B的度数为（）A．40°B．50°C．70°D．80°4．一个不透明袋中有3个红球和2个白球，除颜色外完全相同。从中任取1个球，取到红球的概率是（）A．2/5B．3/5C．1/2D．3/25．一次函数的函数值大于0时，x的取值范围是（）A．x＞3B．x＜3C．x＞−3D．x＜−36．点P(−2，3)关于原点对称的点P′的坐标是（）A．(2，3)B．(−2，−3)C．(2，−3)D．(−3，2)7．在⊙O中，点A、B、C都在圆上，若∠ACB＝35°，则同弧AB所对的圆心角∠AOB为（）A．35°B．55°C．70°D．110°8．若两个相似三角形的相似比为2∶3，则它们面积的比为（）A．2∶3B．4∶9C．3∶2D．9∶49．关于二次函数，下列说法错误的是（）A．图象开口向上B．对称轴为直线x＝1C．最小值为−4D．当x＞1时，y随x的增大而减小10．在矩形ABCD中，AB＝6，BC＝8，点E是BC的中点，连接AE，则AE的长为（）A．10B．2√13C．5√2D．4√5二、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中横线上。11．分解因式：x²−9＝________________。12．若一组数据7，8，8，9，a的平均数为8.4，则a＝________________。13．计算下式的值：________________。14．已知扇形半径为6cm，圆心角为60°，则该扇形的面积为________________cm²。15．若二元一次方程组2x＋y＝7，x−y＝2的解为(x，y)，则x＋y＝________________。16．二次函数的最大值是________________。三、解答题（本大题共6小题，共72分）解答应写出文字说明、证明过程或演算步骤。17．（本题8分）（1）计算：（2）解分式方程：作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本题10分）某校九年级数学备课组组织一次中考冲刺模拟检测，随机抽取40名学生的数学成绩进行整理，得到如下频数分布表：成绩x（分）频数备注60≤x＜704基础待巩固70≤x＜808基本达标80≤x＜9014稳定提升90≤x＜10010优秀100≤x≤1204优秀（1）求这40名学生成绩的中位数所在组；（2）若成绩90分及以上记为“优秀”，求本次抽样中优秀率；（3）已知90分及以上的14名学生中男生6人、女生8人。若从这些优秀学生中随机抽取2人担任讲题员，求恰好抽到1名男生和1名女生的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本题10分）为完成考前实践测量任务，某小组在水平地面上测量一栋教学楼的高度。点C为楼底，P为楼顶，A、B、C在同一直线上，B在A与C之间，AB＝20m。小组在A处测得楼顶P的仰角为37°，在B处测得楼顶P的仰角为53°。先不计测角仪高度，取tan37°≈3/4，tan53°≈4/3。（1）求BC的长；（2）求教学楼PC的高度；（3）若测角仪高度为1.6m，求教学楼的实际高度（结果精确到0.1m）。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本题12分）图形描述：在等腰直角三角形ABC中，AB＝AC＝6，∠A＝90°。点D在BC上，过D分别作DE⊥AB于E，DF⊥AC于F。（1）证明四边形AEDF是矩形；（2）若BD∶DC＝1∶2，求矩形AEDF的面积；（3）当点D在BC上运动时，求矩形AEDF面积的最大值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本题14分）某文具店为中考冲刺阶段准备一种套装。该套装进价为24元/套，原售价为40元/套时每天可售100套。市场调查发现，在保证售价不低于原售价且销售单价为整数元的条件下，每提高1元，每天少售2套。设每套提高x元，每天利润为W元。（1）写出W关于x的函数表达式，并写出x的取值范围；（2）当每套售价为多少元时，每天利润最大？最大利润是多少元？（3）若商店希望每天利润不少于2100元，求每套售价的整数取值范围。作答区：_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析一、选择题答案与解析题号12345678910答案BCCBBCCBDB分值33333333331．B。幂的乘方底数不变，指数相乘，(a²)³＝a⁶。A中a²与a³不是同类项，不能合并为a⁵；C应为a⁴；D应为a²b²。2．C。判别式Δ＝(−4)²−4m＝16−4m。方程有两个不相等实数根，需Δ＞0，所以m＜4。3．C。AB＝AC，底角相等，∠B＝∠C＝(180°−40°)÷2＝70°。4．B。共有5个球，其中红球3个，任取一个球为红球的概率为3/5。5．B。由−2x＋6＞0，得−2x＞−6，故x＜3。6．C。关于原点对称的两个点横、纵坐标均互为相反数，故P′(