2026届南京市九年级数学中考三模模拟试卷（含答案详解与评分标准）

第页2026届南京市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．本试卷为九年级数学中考三模考前检测卷，试题覆盖数与式、方程与不等式、函数、图形与几何、统计与概率等重点内容。2．全卷共22题，其中选择题10题，每题3分；填空题6题，每题3分；解答题6题，每题12分。总分120分。3．请将选择题、填空题答案填写在答题栏内，解答题写出必要的文字说明、演算步骤或证明过程。4．作答时可使用黑色字迹签字笔、铅笔、直尺、圆规、三角板等常用作图工具。保持卷面整洁，计算结果应化为最简形式。选择题答题栏题号12345678910答案填空题答题栏111213141516一、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．（本题3分）计算的结果是（）A．B．C．D．2．（本题3分）把用科学记数法表示为（）A．B．C．D．3．（本题3分）函数中，自变量的取值范围是（）A．B．C．D．4．（本题3分）若一个多边形的内角和为，则这个多边形的边数是（）A．6B．7C．8D．95．（本题3分）一元二次方程的两个根是（）A．B．C．D．6．（本题3分）一个不透明袋中有3个红球、2个白球、1个蓝球，这些球除颜色外完全相同。从中一次随机取出2个球，取出的2个球同色的概率是（）A．B．C．D．7．（本题3分）在圆中，为直径，点在圆上，且。则与弧对应的圆心角的度数为（）A．B．C．D．8．（本题3分）不等式组的整数解的个数为（）A．1B．2C．3D．49．（本题3分）抛物线经过点，对称轴为直线，则当时，函数值为（）A．0B．1C．2D．310．（本题3分）在平面直角坐标系中，将点先向左平移4个单位，再向上平移5个单位，得到点。点所在象限是（）A．第一象限B．第二象限C．第三象限D．第四象限二、填空题（本大题共6小题，每小题3分，共18分）11．（本题3分）分解因式：____________________________。12．（本题3分）方程的解为____________________________。13．（本题3分）在平面直角坐标系中，点、的中点坐标为____________________________。14．（本题3分）一组数据的方差是____________________________。15．（本题3分）同一时刻，身高的同学影长为，学校旗杆影长为，则旗杆高为____________________________m。16．（本题3分）半径为6的扇形圆心角为，则该扇形的面积为____________________________。三、解答题（本大题共6小题，每小题12分，共72分。解答应写出必要步骤）17．（本题12分）计算与解方程。（1）计算：；（2）解分式方程：。解答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本题12分）为了解九年级学生在中考三模阶段数学复习中最需要突破的内容，某校随机调查了200名学生，每名学生只能从A、B、C、D四类中选择一类。调查结果如下表：类别A数与式B函数C图形与几何D统计与概率人数5070m30（1）求表中的值；（2）求扇形统计图中“B函数”所对应扇形圆心角的度数；（3）若该校九年级共有600名学生，请估计其中最需要突破“图形与几何”的学生人数。解答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本题12分）有四张除正面数字外完全相同的卡片，正面分别写有1、2、3、4。将它们背面朝上充分混合后，随机不放回地抽取两张，按抽取顺序记为有序数对。（1）用列表法或树状图法列出所有等可能结果；（2）求“为偶数且”的概率。解答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本题12分）在等腰三角形中，，。点为的中点，点在上，点在上，且。（1）求证：；（2）求四边形的面积。解答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本题12分）中考前某校开展交通安全专题教育，数学兴趣小组记录汽车在干燥平直路面上的制动距离。设汽车行驶速度为km/h，制动距离为m，近似满足二次函数关系。根据测试，当时，；当时，。（1）求关于的函数表达式；（2）当时，估计制动距离；（3）若校门前某路段可视停车距离为60m，为保证车辆从发现情况到完全停止的制动距离不超过60m，求速度的最大整数值。解答：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（本题12分）在平面直角坐标系中，抛物线与轴交于点、，其中点在点的左侧，与轴交于点。点是抛物线在第一象限内的一点，过点作轴，垂足为，且与直线交于点。（1）求点、、的坐标，并求直线的函数表达式；（2）设点的横坐标为，用含的式子表示，并求的最大值；（3）当时，求点的坐标。解答：___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析一、选择题答案与关键理由1．C。，，所以原式为。2．B。小数点向右移动7位得到3.7，因此。3．B。分母不能为0，由得。4．C。设边数为，则，解得。5．B。，所以根为、。6．C。总取法数；同色取法数，概率为。7．C。为直径，则。由得。圆周角与圆心角对应同弧，因此。8．B。由得；由得，整数解为1、2，共2个。9．A。对称轴为，且点在抛物线上，点与关于对称，所以当时函数值为0。10．B。平移后，横坐标负、纵坐标正，在第二象限。二、填空题答案与解析11．。先提公因式3，得；再利用平方差公