2026年广东省新九年级数学开学诊断摸底测试卷

新九年级数学开学诊断测试卷学校：__________班级：__________姓名：__________得分：__________2026年广东省新九年级数学开学诊断摸底测试卷八下核心复习+九上预习衔接，含答案详解与压轴题解析适用对象八升九学生、九年级开学诊断与中考一轮前基础摸底考试时间100分钟满分120分，附加模块20分试卷结构选择题30分，填空题24分，解答题46分，预习探究20分考查重点二次根式、方程、函数、几何证明、统计与二次函数初步考生须知·请在规定时间内独立完成，书写清楚，答题位置规范。·选择题请将答案填入答题表；非选择题应写出必要过程、依据或表达要点。·教师可根据班级实际情况选择整卷检测，也可拆分为基础诊断、能力提升和专项训练模块。·本卷含学生版、答题区、参考答案、评分细则与错因诊断表，适用于开学前后摸底、分层辅导与课堂讲评。

一、选择题（10小题，每小题3分，共30分）1.下列式子中，是最简二次根式的是（）A.√12B.√18C.√5D.√502.函数y=2x-1的图象不经过第（）象限A.一B.二C.三D.四3.一元二次方程x^2-5x+6=0的两个根是（）A.1和6B.2和3C.-2和-3D.0和64.若反比例函数y=k/x的图象经过点(2,-3)，则k=（）A.-6B.-1C.1D.65.在Rt△ABC中，∠C=90°，AC=6，BC=8，则AB=（）A.10B.12C.14D.166.一组数据的方差越小，说明这组数据（）A.平均数越大B.波动越小C.中位数越小D.众数越多7.若a>b>0，则下列结论正确的是（）A.1/a>1/bB.a^2>b^2C.-a>-bD.a-b<08.抛物线y=(x-1)^2+2的顶点坐标是（）A.(1,2)B.(-1,2)C.(1,-2)D.(-1,-2)9.平行四边形ABCD中，∠A=70°，则∠C=（）A.70°B.90°C.110°D.140°10.已知x=1是方程x^2+mx-2=0的一个根，则m=（）A.-1B.0C.1D.2二、填空题（8小题，每小题3分，共24分）11.计算：√27-√12=__________。12.若点A(3,y)在直线y=-2x+5上，则y=__________。13.方程x^2=16的解为__________。14.某校九年级一班40名学生体育测试平均分为48分，则总分为__________分。15.菱形的两条对角线长分别为6cm和8cm，则它的面积为__________cm²。16.一个不透明袋中有3个红球、2个白球，随机摸出1个球，摸到白球的概率为__________。17.若二次函数y=x^2-4x+1写成顶点式为__________。18.若关于x的方程x^2-2x+c=0有两个相等实数根，则c=__________。三、解答题（5小题，共46分）19.（8分）计算：2√8-3√2+√18。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（8分）解方程：x^2-4x-5=0。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.（10分）如图意，在平行四边形ABCD中，E为BC中点，连接AE并延长交DC延长线于F。求证：△ABE≌△FCE。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（10分）某校调查九年级学生每天阅读时间，抽取50名学生得到：0.5小时10人，1小时18人，1.5小时14人，2小时8人。求样本平均阅读时间，并说明该结果可用于什么。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.（10分）已知一次函数y=kx+b经过点A(0,3)，B(2,-1)。求函数解析式，并判断点C(3,-3)是否在该函数图象上。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________四、九上预习探究题（2小题，每小题10分，共20分）24.已知抛物线y=x^2-2x-3。

（1）求它与x轴的交点坐标；

（2）求它的对称轴；

（3）当x为何值时，y随x增大而增大？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25.某商店销售一种文具，进价为每件8元。若售价为每件12元，每天可售出60件；售价每提高1元，每天少售出5件。设售价提高x元，每天利润为W元。

（1）写出W与x的关系式；

（2）当x=2时，每天利润是多少？

（3）根据关系式说明利润是否可能达到400元。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

附加模块中考基础衔接专项（不计入总分）S1.已知a=√3+1，b=√3-1，求ab与a^2+b^2。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________S2.用配方法解方程x^2+6x+5=0。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________S3.直角三角形两直角边为5和12，斜边上的中线长是多少？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________S4.二次函数y=-x^2+4x-1的最大值是多少？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

答题卡选择题（1-10）12345678910填空题：11.______12.______13.______14.______15.______16.______17.______18.______19.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与评分细则选择题：1.C2.B3.B4.A5.A6.B7.B8.A9.A10.C填空题：11.√312.-113.x=±414.192015.2416.2/517.y=(x-2)^2-318.119.2√8-3√2+√18=4√2-3√2+3√2=4√2。20.x^2-4x-5=0，(x-5)(x+1)=0，x=5或x=-1。21.因ABCD为平行四边形，AB∥DC，且F在DC延长线上，所以AB∥FC。E为BC