2026届河南省九年级数学中考冲刺模拟试卷（含答案详解与评分标准）

2026届河南省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分适用对象：九年级用途：中考冲刺检测注意事项：1．本试卷为中考冲刺阶段综合模拟训练，内容覆盖数与式、方程与不等式、函数、图形与几何、统计与概率等核心板块。2．全卷共三大题，22小题，满分120分。选择题10小题，每小题3分，共30分；填空题6小题，每小题3分，共18分；解答题6小题，共72分。3．答题前请将学校、班级、姓名、考号填写清楚。作答时应写出必要的文字说明、证明过程或演算步骤。4．可使用直尺、圆规、三角板和无编程功能计算器。请保持卷面整洁，最终结果应化为最简形式或按题意保留。题型题量分值合计选择题10题；填空题6题；解答题6题22题30+18+72120分一、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正确）1．下列各数中，绝对值最大的是（）A．-5B．0C．3D．42．2026年河南省九年级中考冲刺复习中，某校统计参加数学限时训练约有1.08×10人次。将这个数写成普通记数法为（）A．108B．1080C．10800D．1080003．下列计算正确的是（）A．B．C．D．4．不等式组的整数解共有（）A．1个B．2个C．3个D．4个5．一个不透明袋中装有形状、大小完全相同的红球2个、白球3个、黑球1个，从中随机摸出1个球，摸到白球的概率是（）A．B．C．D．6．若一次函数的图象经过点（1，2）和（3，6），则这个函数的表达式为（）A．B．C．D．7．某班进行数学冲刺测验，40名学生成绩的平均数为92分。若去掉1名成绩为100分的学生后，剩余39名学生成绩的平均数为（）A．分B．92分C．分D．90分8．在圆O中，弦AB所对的圆周角，则劣弧AB所对的圆心角等于（）A．B．C．D．9．关于x的一元二次方程有两个相等的实数根，则m的值是（）A．-4B．0C．4D．810．二次函数的图象向右平移1个单位，再向下平移3个单位，得到的新图象的顶点坐标是（）A．（1，8）B．（3，2）C．（3，8）D．（1，2）选择题作答栏：12345678910二、填空题（本大题共6小题，每小题3分，共18分）11．计算：=__________。12．分解因式：=__________。13．点P（-2，3）关于y轴的对称点为Q，则点Q的坐标是__________。14．一组数据2，4，4，5，6，9的中位数是__________。15．若正六边形的边长为4，则它的周长是__________，面积是__________。16．若反比例函数的图象经过点（-2，6），则k=__________；当x<0时，y随x的增大而__________。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．（10分）考前冲刺阶段，整理代数运算与不等式是提高得分稳定性的关键。完成下列各题：（1）计算：；（2）解不等式组：，并把它的解集在数轴上表示出来。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（10分）某校九年级进行中考数学冲刺模拟检测，随机抽取40名学生的成绩（满分120分）进行整理，得到如下频数分布表：成绩x（分）频数等级60≤x<724基础巩固72≤x<848稳步提升84≤x<96m达标冲刺96≤x<10812优秀提升108≤x≤1206拔高突破（1）求m的值，并判断这40名学生成绩的中位数所在的分数段；（2）若把成绩不低于96分记为“优秀”，求样本中的优秀率；（3）学校从获得“进步星”的4名学生（2名男生、2名女生）中随机抽取2名参加经验交流，求抽到的2名学生恰好为1男1女的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）如图，在平面直角坐标系中，反比例函数与一次函数的图象交于A（2，4），B（4，2）两点。（1）求反比例函数和一次函数的表达式；（2）根据图象直接写出不等式的解集；（3）求三角形AOB的面积。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）如图，在△ABC中，AB=AC=10，BC=12，AD⊥BC于点D。点E在AB上，AE=4，过点E作EF∥BC交AC于点F，连接DE、DF。（1）证明△AEF∽△ABC；（2）求EF的长和四边形EBCF的面积；（3）证明DE=DF。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（14分）如图，二次函数的图象与x轴交于A、B两点（A在B的左侧），与y轴交于点C。点P在该抛物线第一象限部分上，设P的横坐标为t。（1）求A、B、C三点的坐标；（2）用含t的式子表示三角形PAB的面积，并求该面积的最大值及此时点P的坐标；（3）若直线与该抛物线在第一象限内有两个不同交点，求m的取值范围。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（14分）综合与探究：如图，矩形ABCD中，AB=8，AD=6，点E在AB上，AE=x（0<x≤6）。将△ADE沿直线DE折叠，点A的对应点为P，连接DP、EP、PC。（1）以A为坐标原点，AB所在直线为x轴，AD所在直线为y轴，建立平面直角坐标系，求点P的坐标（用x表示）；（2）当点P恰好在对角线BD上时，求AE的长；（3）当0<x<6时，设三角形PCD的面积为S，写出S关于x的函数关系式，并判断S的取值范围。作答区：_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析一、选择题答案与解析12345678910ABDBCAACCB1．答案：A。解析：绝对值分别为5，0，3，4，其中最大的是5，所以选A。评分标准：选对得3分；错选、多选或不选得0分。2．答案：B。解析：科学记数法还原时，小数点向右移动3位，1.08×10³=1080。评分标准：选对得3分；错选、多选或不选得0分。3．答案：D。解析：同类项才能合并，幂的乘方指数相乘，同底数幂相除指数相减，只有（-2a）²=4a²正确。评分标准：选对得3分；错选、多选或不选得0分。4．答案：B。解析：由x-1>0得x>1；由2x-5≤1得x≤3，所以整数解为2、3，共2个。评分标准：选对得3分；错选、多选或不选得0分。5．答案：C。解析：袋中共有6个球，白球3个，摸到白球的概率为3/6=1/2。评分标准：选对得3分；错选、多选或不选得0分。6．答案：A。解析：两点斜率为（6-2）÷（3-1）=2，代入（1，2）得b=0，所以y=2x。评分标准：选对得3分；错选、多选或不选得0分。7．答案：A。解析：总分为40×92=3680，去掉100分后总分为3580，平均数为3580÷39=91又31/39分。评分标准：选对得3分；错选、多选或不选得0分。8．答案：C。解析：同弧所对圆心角等于圆周角的2倍，所以∠AOB=76°。评分标准：选对得3分；错选、多选或不选得0分。9．答案：C。解析：方程有两个相等实数根时判别式为0，即16-4m=0，得m=4。评分标准：选对得3分；错选、多选或不选得0分。10．答案：B。解析：原顶点为（2，5），右移1个单位得横坐标3，下移3个单位得纵坐标2。评分标准：选对得3分；错选、多选或不选得0分。二、填空题答案与解析11．。解析：答案为√3。先把√12化为2√3，再合并同类二次根式。评分标准：化简正确得2分，结果正确得3分。12．。解析：答案为3（x-2）（x+2）。先提公因式3，再用平方差公式。评分标准：提公因式得1分，完全分解得3分。13．解析：答案为（2，3）。关于y轴对称，横坐标互为相反数，纵坐标不变。评分标准：横纵坐标均正确得3分。14．解析：答案为4.5。数据已按从小到大排列，共6个数，中位数为第3个和第4个数的平均数，即（4+5）÷2=4.5。评分标准：位置判断正确得1分，结果正确得3分。15．。解析：答案为24，24√3。正六边形周长为6×4=24；它可分成6个边长为4的等边三角形，面积为6×（4²√3÷4）=24√3。评分标准：周长1分，面积2分。16．。解析：答案为-12，增大。把点（-2，6）代入y=k/x，得6=k/（-2），所以k=-12；当k<0时，反比例函数在每个象限内y随x的增大而增大。评分标准：k值2分，单调性1分。三、解答题答案详解与评分标准17．（10分）（1）原式。（2）由得；由得。所以不等式组的解集为。在数轴上表示时，3处画实心点