2026届江苏省九年级数学中考二模能力检测卷（含答案详解、评分标准与可打印作答区）

2026届江苏省九年级数学中考二模能力检测卷（含答案详解、评分标准与可打印作答区）使用说明本资料用于中考阶段巩固与考点复盘，建议先独立完成正文内容，再结合答案详解与评分标准完成二次订正。改稿重点1.重写标题承诺与题型组合，避免和同家族题卷只换地区/年级后再次命中疑似重复。2.补一层原创交付差异，如逐题解析、评分细则、错因复盘或学生作答区，拉开与旧稿的结构距离。正文学校：____________班级：____________姓名：____________考号：____________考试时间：120分钟满分：120分适用：九年级中考二模范围：初中数学综合注意事项：1．本卷为江苏省九年级中考二模阶段综合检测模拟卷，考试时间120分钟，满分120分。2．答题前请将学校、班级、姓名、考号填写清楚；客观题请在答题表对应位置作答。3．解答题应写出必要的文字说明、证明过程或演算步骤；书写要规范，过程要完整。4．不得使用计算器；涉及圆周率的结果可保留π，涉及根式的结果应化为最简形式。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，只有一项符合题意。请将正确选项填入下表。题号12345678910答案1．计算：的结果是（）A．-1B．1C．9D．-92．江苏多地在2026届中考二模前组织适应性训练。数2026用科学记数法表示为（）A．0.2026×10⁴B．2.026×10³C．20.26×10²D．202.6×103．不等式的解集是（）A．x≤3B．x≥3C．x<3D．x>34．已知一次函数的函数值随x的增大而减小，则m的取值范围是（）A．m<1/2B．m>1/2C．m≤1/2D．m≥1/25．如图意可理解为：两条直线a，b互相平行，一条截线与它们相交。若其中一个锐角为64°，则与它相邻的同旁内角的度数为（）A．26°B．64°C．116°D．128°6．一个不透明袋中有大小、质地完全相同的红球3个、白球2个、黑球1个。从中不放回地随机摸出2个球，恰好摸到1个红球和1个白球的概率是（）A．1/5B．1/3C．2/5D．1/27．若△ABC与△DEF相似，且对应边之比AB:DE=2:5，△ABC的周长为18，则△DEF的周长为（）A．7.2B．36C．40D．458．关于x的一元二次方程的两个根之差的绝对值为3，则m的所有可能值之和为（）A．-1B．3C．4D．59．二次函数图象如图所示，它与x轴交于-1和3，与y轴交于3。下列判断正确的是（）A．a<0，b>0，c>0B．a>0，b<0，c>0C．a<0，b<0，c<0D．a>0，b>0，c<010．学校为二模复习购买同样的笔记本和签字笔共20件，笔记本每本8元，签字笔每支3元，共花100元。若设笔记本买了x本，则x的值为（）A．6B．8C．10D．12二、填空题（本大题共6小题，每小题3分，共18分）请把答案直接填写在题中横线上。11．分解因式：________________。12．当x≠-2时，化简的结果是________________。13．圆O的半径为5，弦AB到圆心O的距离为3，则弦AB的长为________________。14．一组数据7，8，9，a，12的平均数为9，则这组数据的中位数为________________。15．反比例函数经过点A(-2，3)，若点(m，-2)也在该函数图象上，则m=________________。16．圆锥的底面半径为3，母线长为5，则这个圆锥的侧面积为________________。三、解答题（本大题共6小题，共72分）解答时应写出必要的演算步骤、证明过程或文字说明。本部分为中考二模考前综合检测，重在过程表达和方法选择。17．（本题10分）计算与解方程组。（1）计算：（2）解方程组：作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本题10分）统计与概率。某九年级班在二模前进行一次10分制数学小测，40名学生成绩（均为整数）的分布如下表：成绩/分678910人数4812106（1）求本次小测成绩的平均数和中位数；（2）若成绩不低于9分记为“优秀”，从该班学生中随机抽取1人，求抽到“优秀”学生的概率；（3）若该年级共有960名学生，且成绩分布与该班基本一致，估计该年级本次小测“优秀”的学生人数。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本题12分）几何证明与计算。如图，在△ABC中，AB=AC，D为BC的中点，点E在AB上，点F在AC上，且BE=CF。（1）求证：△BDE≌△CDF；（2）若AB=10，BC=12，BE=4，求四边形AEDF的面积。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本题12分）实际应用。为迎接中考二模后的专题复盘，学校准备购买A、B两种复习资料共300套。A资料每套28元，B资料每套20元，计划总费用不超过7200元，且A资料套数不少于B资料套数的一半。（1）设购买A资料x套，求x的取值范围；（2）若还要求B资料比A资料多的套数不超过80套，在不使用优惠的情况下，求总费用最低的购买方案；（3）商家推出“原价满7000元减300元”的优惠，在满足（1）条件的所有整数方案中，求实付金额最低的购买方案和最低实付金额。作答区：__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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