2026届广东省九年级数学中考二模模拟试卷（含答案详解与评分标准）

2026届广东省九年级数学中考二模模拟试卷2026届广东省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分题型：选择、填空、解答考试节点：中考二模注意事项：本卷用于2026届九年级数学中考二模考前综合检测，重点考查阶段复习质量、基础知识迁移能力与综合解题规范。请将答案写在相应作答区内，作图题保留必要辅助线，解答题必须写出主要推理或计算过程。题型选择题填空题解答题合计分值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。每小题只有一个正确选项）1．计算的结果是（）A．B．C．D．2．把小数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．若一次函数的图象随的增大而减小，则的取值范围是（）A．B．C．D．5．一个不透明袋中有2个白球和1个黑球，除颜色外其余完全相同。从袋中不放回地一次取出2个球，恰好取到1个白球和1个黑球的概率是（）A．B．C．D．6．方程的两个根是（）A．B．C．D．7．某学习小组5名同学一次二模专题测试成绩为76，82，88，90，94。则这组数据的中位数是（）A．82B．86C．88D．908．边长为的正方形内切圆的面积是（）A．B．C．D．9．在中，，点在上，点在上，且，则等于（）A．B．C．D．10．关于二次函数，下列结论正确的是（）A．图象开口向下B．图象的对称轴是直线x=-1C．函数的最小值为-4D．图象与y轴的交点为（0，-4）二、填空题（本大题共6小题，每小题3分，共18分）11．分解因式：________________。12．方程的解是________________。13．抛物线的顶点坐标是________________。14．若一元二次方程有两个相等的实数根，则________________。15．半径为、圆心角为的扇形面积是________________。16．直线与两坐标轴围成的三角形面积为，且，则________________。三、解答题（本大题共6小题，每小题12分，共72分。解答应写出文字说明、证明过程或演算步骤）17．（12分）本题考查数式运算与不等式组，是中考二模基础运算规范检测。（1）计算：；（2）解不等式组：，，并写出它的整数解。（请在此处作答，写出必要的计算、证明或说明过程。）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（12分）某校九年级数学组为了解二模阶段复习效果，从全年级200名学生中随机抽取40名学生的数学模拟测试成绩，整理成如下频数分布表。成绩x（分）频数组中值60≤x<7046570≤x<8087580≤x<90168590≤x≤1001295（1）求样本中成绩达到90分及以上的优秀率，并估计全年级达到优秀的学生人数；（2）用组中值估计这40名学生的平均成绩；（3）若学校把80分及以上视为二模复习“达标”，请估计全年级达标人数，并结合数据给出一句复习建议。（请在此处作答，写出必要的计算、证明或说明过程。）________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）为迎接中考二模后的专题提升，某班准备统一购买数学训练册。甲、乙两家书店的促销方式如下：甲店每本原价18元，购买超过30本时，前30本按原价付款，超出部分按八折付款；乙店不设门槛，全部按九折付款。设购买训练册x本，且x>30。（1）分别写出在甲店、乙店购买所需费用y1、y2与x的函数关系式；（2）若该班购买50本，选择哪家书店更省钱？省多少钱？（3）当购买数量满足什么条件时，甲店更省钱？（请在此处作答，写出必要的计算、证明或说明过程。）____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（12分）如图形探究题中不另给坐标图，请根据文字条件建立平面直角坐标系。已知抛物线经过、、三点。（1）求该抛物线的函数表达式，并写出顶点坐标；（2）点在抛物线的对称轴上，若，求点的坐标；（3）点在抛物线位于第四象限的部分上，过点作轴于点。求四边形面积的最大值。（请在此处作答，写出必要的计算、证明或说明过程。）___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________