2026年成都市新初三数学暑期一轮诊断卷

成都新初三数学暑期一轮诊断卷第页2026年成都市新初三数学暑期一轮诊断卷方程函数·几何综合·统计概率·压轴训练·答案详解适用对象新初三暑期一轮复习、开学摸底与分层训练建议用时120分钟满分150分能力目标基础稳准、模型迁移、几何推理、综合表达使用提示：本册按“试卷、答题区、答案详解、评分标准、考点回扣”组织，适合暑期诊断、考前复盘和分层训练。建议先限时完成，再对照解析订正，并把错题归入文末的错因表。

一、一轮诊断考点与复盘路径模块重点内容能力要求常见失分点复盘动作数与式实数、整式、分式、二次根式能准确化简、求值和变形符号与限制条件遗漏先写定义域或取值条件方程与不等式一元二次方程、分式方程、不等式组能选择合适方法求解漏检验、根的判别式误用解后代回检验函数一次函数、反比例函数、二次函数基础能读图像、求解析式、分析增减性坐标代入错误，图像意义不清画草图标关键点几何三角形、四边形、相似、圆基础能写出证明过程和辅助线思路理由跳步，条件未用全按“已知-推出-结论”书写统计概率平均数、中位数、方差、概率能解释数据结论只计算不解释实际意义补一句结论判断作答规范提醒函数题先求关键点坐标，再结合图像回答范围问题。几何证明题要避免只写“显然”，每一步都要有依据。分式方程、实际问题必须检验，含单位的题目必须写答句。压轴题按小问分步得分，不要因最后一问不会而放弃前两问。

二、试题部分试卷说明全卷共28题，满分150分。选择题每题4分，填空题每题4分，解答题按过程给分。A.选择题（共40分）1.-2的相反数是A.2B.-2C.1/2D.-1/22.下列计算正确的是A.a²+a³=a⁵B.a²·a³=a⁶C.(a²)³=a⁶D.a⁶÷a²=a³3.若分式1/(x-3)有意义，则x的取值应满足A.x≠3B.x=3C.x≠0D.x>34.一元二次方程x²-5x+6=0的根是A.1和6B.2和3C.-2和-3D.无实根5.函数y=2x-1的图像经过的象限是A.一、二、三B.一、三、四C.一、二、四D.二、三、四6.若反比例函数y=k/x的图像经过点(2,-3)，则k=A.-6B.6C.-1D.17.一组数据2，3，3，5，7的中位数是A.2B.3C.4D.58.袋中有3个红球、2个白球，随机摸出1个球，摸到红球的概率是A.2/5B.3/5C.1/2D.3/29.若两个相似三角形的相似比为2:3，则面积比为A.2:3B.4:9C.3:2D.9:410.圆的半径为6，圆心到直线l的距离为6，则直线l与圆的位置关系是A.相离B.相交C.相切D.无法判断B.填空题（共24分）11.分解因式：x²-9=__________。12.若√(a-1)有意义，则a的取值范围是__________。13.已知一次函数y=kx+2经过点(1,5)，则k=__________。14.方程x²=16的解是__________。15.已知扇形半径为3，圆心角为120°，则弧长为__________。16.若一组数据的平均数为8，新增一个数据8后，新的平均数为__________。C.解答题（共86分）17.计算：(√12-√3)×√3+|1-√2|。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.解分式方程：2/(x-1)=3/(x+2)。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.解不等式组：{2x-1≤7，x+3>0}，并写出整数解。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.已知一次函数图像经过A(-1,1)、B(2,7)。求函数解析式，并判断点C(3,9)是否在该图像上。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.某校篮球队8名队员身高（cm）为：168，170，172，172，174，176，178，180。求平均数和中位数，并说明哪一个更能反映中间水平。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.如图，在△ABC中，D、E分别在AB、AC上，且DE∥BC。若AD=3，DB=2，AE=4，求EC的长。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.某商店购进A、B两种商品共100件，A商品进价20元，B商品进价35元，总进价2900元。求A、B两种商品各购进多少件。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.已知二次函数y=x²-4x+3。求顶点坐标、对称轴，并写出当x为何值时y随x的增大而增大。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25.在平面直角坐标系中，反比例函数y=k/x与一次函数y=x-3交于点P(6,3)。求k，并求另一个交点坐标。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26.如图，AB为圆O的直径，点C在圆O上，连接AC、BC。若∠A=35°，求∠B和∠ACB的度数，并说明依据。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________27.某校为了解学生每天运动时间，抽样调查得到：不足30分钟12人，30-60分钟28人，60-90分钟36人，90分钟以上24人。请计算样本容量，估计运动时间不少于60分钟的学生比例，并提出一条合理建议。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________28.综合题：已知抛物线y=x²-2x-3与x轴交于A、B两点（A在B左侧），与y轴交于C点。

（1）求A、B、C坐标；

（2）求△ABC面积；

（3）若点P在抛物线上，且横坐标为m，试写出当点P在x轴下方时m的取值范围。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

三、答题卡选择题答题区题号/选项题号/选项题号/选项题号/选项题号/选项题号/选项1.ABCD2.ABCD3.ABCD4.ABCD5.ABCD6.ABCD7.ABCD8.ABCD9.ABCD10.ABCD填空题答题区11.__________________12.__________________13.__________________14.__________________15.__________________16.__________________解答题答题区17.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________27.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________28.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

四、答案详解与评分标准选择题：1.A2.C3.A4.B5.B6.A7.B8.B9.B10.C填空题：11.(x+3)(x-3)；12.a≥1；13.3；14.x=±4；15.2π；16.8。17.√12=2√3，