2026届九年级数学中考一模模拟试卷（含答案详解与评分标准）第013套

2026届九年级数学中考一模模拟试卷（含答案详解与评分标准）第013套学校：__________________班级：__________姓名：__________考号：__________________考试时间：120分钟满分：120分注意事项1．本试卷共26题，满分120分。答题前，请将学校、班级、姓名、考号填写清楚。2．选择题每题只有一个正确选项；填空题只填写最后结果；解答题须写出必要的文字说明、演算步骤或证明过程。3．作图题或几何题可在草稿处辅助作图，最终答案以文字、式子和步骤为准。4．请合理安排时间，保持卷面整洁；所有题目均按中考一模综合检测要求命制。一、选择题（本大题共12小题，每小题3分，共36分。每小题只有一个选项符合题意）1．下列各数中，的相反数是（）A．B．C．D．2．把用科学记数法表示为（）A．B．C．D．3．下列运算正确的是（）A．B．C．D．4．一个多边形的内角和为，则这个多边形的边数是（）A．B．C．D．5．不等式组的解集是（）A．B．C．D．6．一元二次方程的两个根分别为（）A．B．C．D．7．在下列四组数据中，方差最小的是（）A．2，2，2，2B．1，2，3，4C．0，2，4，6D．3，3，4，48．从数字1，2，3，4中随机取两个不同的数字组成一个两位数，则这个两位数能被3整除的概率是（）A．B．C．D．9．若一次函数的函数值随的增大而减小，则的取值范围是（）A．B．C．D．10．如为圆的直径，点在圆上，且，则的度数为（）A．B．C．D．11．反比例函数的图象经过点，下列结论正确的是（）A．k=6，图象在第一、三象限B．k=6，图象在第二、四象限C．k=−6，图象在第一、三象限D．k=−6，图象在第二、四象限12．二次函数在上的最大值是（）A．B．C．D．选择题答题栏123456789101112二、填空题（本大题共6小题，每小题3分，共18分）13．因式分解：________________。14．若，则________________。15．一组数据2，4，5，6，的平均数为5，则________________。16．一个正多边形的每一个外角都是，则它的边数是________________。17．抛物线的顶点坐标是________________。18．半径为6，圆心角为的扇形弧长为________________。三、解答题（本大题共8小题，共66分。解答应写出文字说明、证明过程或演算步骤）19．（本题6分）计算与化简：（1）计算：；（2）化简：。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本题8分）解方程与不等式组：（1）解分式方程：；（2）解不等式组：。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本题8分）某校为了解九年级学生体育中考跳绳项目的阶段性训练情况，从九年级随机抽取40名学生，记录他们一分钟跳绳个数，并按如下分组整理成频数表：跳绳个数x频数组中值120≤x<1404130140≤x<16010150160≤x<x<2008190200≤x<2202210请根据表中信息解答下列问题：（1）这40名学生一分钟跳绳个数的众数所在组是哪一组？（2）用组中值估计这40名学生一分钟跳绳个数的平均数；（3）若全校九年级共有900名学生，请估计一分钟跳绳个数达到180个及以上的学生人数。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（本题8分）一个不透明袋中有3个红球、2个白球，这些球除颜色外完全相同。小明从袋中不放回地随机摸出2个球。（1）请用列表或树状图表示所有等可能的结果；（2）求摸出的2个球颜色不同的概率。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23．（本题8分）某文具店准备购进A、B两种笔记本共80本。A种笔记本进价6元/本，售价10元/本；B种笔记本进价8元/本，售价13元/本。设购进A种笔记本本。（1）若总进货成本不超过560元，且B种笔记本不少于30本，求的取值范围；（2）在（1）的条件下，若两种笔记本全部售出，求共有多少种进货方案，并指出哪种方案获得的利润最大，最大利润是多少元。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24．（本题9分）已知中，，点分别为的中点。（1）求证：；（2）若，求的度数；（3）若，底边上的高，求的面积。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25．（本题9分）如是的直径，点在上，且。过点作圆的切线，与的延长线交于点，且在的外侧。（1）说明的理由；（2）求切线段的长。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26．（本题10分）在平面直角坐标系中，抛物线与轴交于两点（点在点左侧），与轴交于点。点是抛物线第一象限内的一点，过点作轴交直线于点。（1）求点的坐标；（2）求线段关于的表达式，并写出的取值范围；（3）求面积的最大值；（4）当的面积为15时，求点的坐标。__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析及评分标准评分说明：客观题按标准答案给分；解答题按步骤给分，若方法正确但表述不同，可参照相应步骤酌情给分。一、选择题答案123456789101112BABCBCABABDC1．相反数只有符号相反，故为2026。2．小数点向右移动3位得到3.2，因此0.0032=3.2×10⁻³，应选A。3．幂的乘方底数不变，指数相乘，(a²)³=a⁶。4．由(n−2)×180°=1080°，得n=8。5．两个不等式分别给出x<3和x≥−2，交集为−2≤x<3。6．x²−5x+6=(x−2)(x−3)，两根为2和3。7．四个数据完全相同，离散程度为0，方差最小。8．有12个等可能有序结果，能被3整除的有12、21、24、42共4个，概