2026届福建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届福建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：九年级考试节点：中考冲刺注意事项：1．答题前，考生务必将学校、班级、姓名、考号填写清楚。2．本卷用于2026届九年级数学中考冲刺阶段考前检测，满分120分，考试时间120分钟。3．选择题每小题只有一个正确选项；填空题只写最终结果；解答题应写出必要的文字说明、证明过程或演算步骤。4．全卷共三大题，22小题。试卷结构：选择题10题共30分，填空题6题共18分，解答题6题共72分。题型选择题填空题解答题合计分值10题×3分=30分6题×3分=18分6题=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．-5B．3C．7D．112．据统计，某地常住人口约为4180000人，将4180000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．不等式的整数解中，最大的一个是（）A．0B．1C．2D．35．一个不透明袋中有除颜色外完全相同的红球3个、黄球2个、蓝球1个，从中任取1个球，取到红球的概率为（）A．B．C．D．6．一次函数的图象不经过的象限是（）A．第一象限B．第二象限C．第三象限D．第四象限7．在△ABC中，D在AB上，E在AC上，且DE∥BC。若AD=2，DB=3，AE=4，则EC的长为（）A．2B．4C．5D．68．一个正多边形的每个内角都是150°，则这个正多边形的边数是（）A．8B．10C．12D．159．圆O的半径为5，点P到圆心O的距离为13，过点P作圆O的切线，切点为T，则PT的长为（）A．8B．10C．12D．1310．二次函数中。比较函数值、、的大小，正确的是（）A．B．C．D．题号12345678910答案二、填空题（本大题共6小题，每小题3分，共18分）11．因式分解：________________。12．在Rt△ABC中，∠C=90°，∠A为锐角，若，则________________。13．一组数据6，7，8，8，9，10的中位数是________________。14．反比例函数的图象经过点（-2，3），则当时，________________。15．半径为6、圆心角为120°的扇形弧长为________________。16．二次函数当________时取得最大值，最大值为________。题号111213141516答案三、解答题（本大题共6小题，共72分。解答应写出必要过程）17．（本小题8分）完成下列计算与求解。（1）计算：；（2）解方程组：。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本小题10分）某校九年级数学中考冲刺复习需要购买A、B两种作业本。已知购买3本A和2本B共需18元，购买2本A和5本B共需23元。（1）求A、B两种作业本的单价；（2）若某班计划购买A、B两种作业本共35本，总费用不超过130元，且A本数量不少于B本数量的2倍，则最多能购买多少本B？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本小题12分）为了解九年级学生中考冲刺阶段“每日数学自主复习时长”，学校从九年级随机抽取40名学生进行调查，按时长t（单位：小时）分组，得到如下统计表。请根据表中信息回答问题。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________组别时长t（小时）人数A0.5≤t<16B1≤t<1.514C1.5≤t<212D2≤t<2.58（1）补全频数分布表中的总人数信息，并写出本次调查样本容量；（2）若该校九年级共有200名学生，估计每日数学自主复习时长不少于1.5小时的学生人数；（3）学校从甲、乙、丙、丁4名复习表现优秀的学生中随机选2名担任学习小导师，求甲、乙两人同时被选中的概率。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本小题12分）如题设，△ABC中，AB=AC=10，BC=12，D为BC的中点，E为AC的中点。（1）求证：AD⊥BC，并求AD的长；（2）求证：DE∥AB，并求四边形ABDE的周长；（3）求△ADE的面积。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本小题14分）某文创店销售“中考冲刺资料包”，每套进价20元。设每套售价为x元，日销量为y套，市场调查发现，且。设该店每日利润为W元。（1）当售价为35元时，求日销量和日利润；（2）求W关于x的函数表达式，并求日利润最大时的售价及最大利润；（3）若要求日销量不少于40套，且日利润不少于750元，求售价x的取值范围。___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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