2026届浙江省九年级数学中考三模模拟试卷（含答案详解与评分标准）

2026届浙江省九年级数学中考三模模拟试卷（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分注意事项：1．本卷为九年级数学中考三模考前综合检测卷，试题覆盖数与式、方程与不等式、函数、图形与几何、统计与概率、综合应用等内容。2．全卷共22题。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．请在规定区域内作答，书写过程要清楚，关键步骤不能缺失；作图或说明题应保留必要的依据。4．允许使用直尺、圆规、三角板等常规作图工具；不得使用具有符号运算功能的计算设备。一、选择题（本题有10小题，每小题3分，共30分）每小题只有一个选项符合题意。请把正确选项填在题后括号内。1．实数－3的相反数是（）A．－3B．3C．1/3D．－1/32．下列运算正确的是（）A．B．C．D．3．某学习小组7名同学的数学三模限时训练成绩（单位：分）为8，9，7，10，6，9，11，则这组数据的中位数是（）A．8B．8.5C．9D．104．不等式的解集是（）A．B．C．D．5．若反比例函数的图象经过点（－2，3），则它的图象位于（）A．第一、三象限B．第一、二象限C．第二、三象限D．第二、四象限6．已知三角形的两边长分别为2和5，第三边长为整数x，则x的可能取值个数是（）A．1B．2C．3D．47．半径为6cm的圆中，圆心角为120°的弧长为（）A．B．C．D．8．若一元二次方程有两个相等的实数根，则m的值为（）A．－4B．0C．4D．89．两个相似三角形的面积比为9∶16，其中较小三角形的一条边长为6，则较大三角形中对应边的长为（）A．8B．9C．10D．1210．二次函数的图象与x轴交于A、B两点。下列说法正确的是（）A．当－1＜x＜3时，y＜0B．图象的对称轴是直线x＝－1C．图象的顶点坐标是（1，4）D．当x＞3时，y随x的增大而减小二、填空题（本题有6小题，每小题3分，共18分）请把答案直接写在题中横线上。11．分解因式：________________。12．一个不透明袋中装有大小、形状完全相同的3个红球和2个白球，从中随机摸出1个球，摸到红球的概率是________________。13．点P（m，2）在一次函数的图象上，则m＝________________。14．一个正六边形的边长为4，则它的周长是________________。15．若，则________________。16．在Rt△ABC中，∠C＝90°，AC＝6，BC＝8，则△ABC的内切圆半径为________________。三、解答题（本题有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10分）计算与解方程。（1）计算：；（2）解方程：。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本题10分）某校九年级在三模前进行一次数学专题限时训练，随机抽取40名学生成绩并整理如下表。成绩x（分）60≤x＜7070≤x＜8080≤x＜9090≤x≤100合计人数410161040（1）求80≤x＜90这一组所占的百分比；（2）在扇形统计图中，90≤x≤100这一组对应的圆心角为多少度？（3）若该校九年级共有500名学生，请估计成绩达到90分及以上的人数。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本题12分）为迎接中考三模后的针对性复习，某班准备印制一批数学专题资料。甲、乙两家印刷店的收费方式如下：印刷店收费方式甲店先收制版费100元，再按每份0.30元收费乙店不收制版费，按每份0.50元收费设印制资料x份，在甲店的费用为y₁元，在乙店的费用为y₂元。（1）分别写出y₁、y₂关于x的函数表达式；（2）当印制多少份时，两店收费相同？（3）若全年级实际需要印制680份，选择哪家店更省钱？可节省多少元？________________________________________________________________________________________________________________________________________________________________________________________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_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（本题14分）综合探究：如图，在矩形ABCD中，AB＝8，BC＝6。点P从A出发沿AB向B运动，设AP＝t（0≤t≤8）；同时点Q在BC上运动，且BQ＝3t/4。连接DP、DQ、PQ。（1）用含t的式子表示△DPQ的面积S；（2）求S的最小值，并写出此时t的值；（3）当S＝20时，求t的值；（4）若R为PQ的中点，求点R运动路径的长度。_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析评分总则：选择题每题3分，选对得3分，不选、错选、多选均不得分；填空题每题3分，结果正确得3分，等价形式正确同样得分；解答题按步骤给分，关键思想正确但书写有小误差时，可依据评分标准酌情给过程分。一、选择题题号12345678910答案BBCBDCBCAA1．－3的相反数是3，故选B。2．幂的乘方底数不变、指数相乘，故（a²）³＝a⁶。其余选项分别混淆了合并同类项、同底数幂相除和积的乘方，故选B。3．将数据从小到大排列为6，7，8，9，9，10，11，第4个数为9，故中位数为9，选C。4．由2x－1＜5得2x＜6，故x＜3，选B。5．把点（－2，3）代入y＝k/x，得k＝－6＜0，反比例函数图象位于第二、四象限，选D。6．由三角形三边关系得5－2＜x＜5＋2，即3＜x＜7。整数x可取4，5，6，共3个，选C。7．弧长等于圆周长按圆心角比例取值，即120°/360°×2π×6＝4πcm，选B。8．方程有两个相等实数根时判别式为0，即16－4m＝0，得m＝4，选C。9．相似三角形面积比为对应边长比的平方，所以对应边长比为3∶4。较大三角形对应边长为6×4/3＝8，选A。10．二次函数y＝x²－2x－3＝（x＋1）（x－3），零点为－1和3，开口向上，故－1＜x＜3时y＜0，选A。二、填空题题号111213141516答案（x＋3）（x－3）3/532413211．平方差公式：x²－9＝x²－3²＝（x＋3）（x－3）。12．共有5个球，其中红球3个，随机摸出红球的概率为3/5。13．将P（m，2）代入y＝2x－4，得2＝2m－4，解得m＝3。14．正六边形六条边相等，周长为6×4＝24。15．x²＋y²＝（x＋y）²－2xy＝25－12＝13。16．直角三角形斜边AB＝10，内切圆半径r＝（AC＋BC－