2026届广东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届广东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分注意事项：1．本卷为广东省九年级数学中考冲刺阶段模拟检测，试题覆盖数与式、方程与不等式、函数、几何、统计与概率等核心内容。2．答题前请将学校、班级、姓名、考号填写清楚；作图、计算和证明均写在相应作答区内。3．选择题每题只有一个正确选项；填空题只填写最终结果；解答题须写出必要的推理、计算过程和结论。4．全卷共三大题，22小题，满分120分。请合理安排时间，保持卷面整洁。题型题量分值合计选择题10题；填空题6题；解答题6题共22题30分+18分+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答案）1．计算的结果是（）A．B．C．D．2．某校九年级数学线上冲刺练习的总点击量为1280000次，将1280000用科学记数法表示为（）A．B．C．D．3．下列因式分解正确的是（）A．B．C．D．4．不等式组的解集是（）A．B．C．D．5．在直角三角形ABC中，，，，则的值为（）A．B．C．D．6．一个不透明袋中有3个红球、2个白球、1个蓝球，除颜色外完全相同。随机摸出1个球，摸到的球不是红球的概率是（）A．B．C．D．7．一组九年级学生的数学小测成绩为86，90，92，90，88，则这组数据的中位数和众数分别是（）A．88，90B．90，92C．92，90D．90，908．如图形条件所述：AB为圆O的直径，点C在圆O上，若，则的度数为（）A．B．C．D．9．二次函数的图象的顶点坐标和最小值分别是（）A．，4B．，C．，D．，410．直线与坐标轴分别交于A、B两点，点O为坐标原点，则O到直线AB的距离为（）A．B．C．D．二、填空题（本大题共6小题，每小题3分，共18分。请把答案填写在横线上）11．若，则=__________。12．一元二次方程的较小根是__________。13．半径为6、圆心角为的扇形弧长为__________。14．反比例函数经过点，当时，=__________。15．直角三角形的两条直角边长分别为9和12，则其内切圆半径为__________。16．观察数列：3，8，15，24，35，……，它的第n项可表示为，则第10项为__________。三、解答题（本大题共6小题，每小题12分，共72分。解答应写出文字说明、证明过程或演算步骤）17．（12分）本题考查实数运算与分式化简，是考前冲刺中常见的基础计算题。（1）计算：；（2）先化简，再求值：，其中。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（12分）为了解九年级学生在中考冲刺阶段的数学复习效果，某校从九年级随机抽取50名学生，按一次模拟检测成绩分成A、B、C、D、E五个等级，整理得到如下统计表。等级成绩范围人数频率A108～12080.16B96～10718nC84～95m0.30D72～8360.12E72以下30.06（1）求表中m、n的值；（2）若该校九年级共有800名学生，请估计成绩达到B等级及以上的学生人数；（3）A等级的8名学生中有3名男生、5名女生，若从这8名学生中随机抽取2名作为经验分享代表，求恰好抽到1名男生和1名女生的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（12分）某文具店为服务中考冲刺复习，购进A、B两种数学资料共80套，A种资料每套进价18元，B种资料每套进价24元，共花费1740元。销售时，A种资料每套售价25元，B种资料每套售价32元。（1）求第一次购进A、B两种资料各多少套；（2）若第二次仍按相同进价和售价购进100套资料，且B种资料数量不超过A种资料数量的2倍，总利润不低于760元，求第二次购进A种资料的最少套数。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（12分）如图，在中，，，。点D在AB上，且，过点D作，垂足为E。（1）求AB、BD的长；（2）证明，并求AE、DE的长；（3）求与四边形BCED的面积比。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（12分）在平面直角坐标系中，一次函数的图象与反比例函数的图象交于点P、Q。已知点，点Q在第一象限，直线与x轴交于点A。（1）求k的值；（2）求点Q的坐标；（3）点M在x轴正半轴上，且在点A的右侧，若，求点M的坐标。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（12分）如图，抛物线与x轴交于A、B两点，与y轴交于C点。点P在抛物线位于线段CB上方的部分上，过P作轴，交直线BC于E。设点P的横坐标为t。（1）求A、B、C三点坐标及抛物线顶点D的坐标；（2）用含t的式子表示PE的长，并求面积的最大值；（3）若，求点P的坐标。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析一、选择题答案与关键理由12345678910BCDABCDCCD选择题评分标准：每小题3分，选对得3分，未选、多选、错选均不得分。解析部分给出判定依据，阅卷时以选项字母为准；若学生在草稿或题旁保留了正确计算过程但最终选项错误，选择题仍按最终选项判定。1．，，故原式为，选B。2．科学记数法要求写成的形式，其中。，选C。3．寻找乘积为6、和为5的两个数为2和3，且中间项为负，因此，选D。4．由得；由得，公共部分为，选A。5．在中，，选B。6．不是红球的共有白球2个、蓝球1个，共3个；总球数6个，概率为，选C。7．数据从小到大排列为86，88，90，90，92，中间数为90，出现次数最多的数也是90，故中位数、众数均为90，选D。8．AB为直径，故。在三角形ABC中，，选C。9．函数已写成顶点式，顶点为，开口向上，最小值为，选C。10．直线可化为，点O到直线的距离为，选D。二、填空题答案与解析填空题评分标准：每小题3分，只看最终结果。结果等价即可得分；含根式、分式或π的答案应保持精确形式，若小数近似未按题意要求且造成精度变化，不得满分。11．答案：。解析：，因，可约去。12．答案：。解析：，两根为1和3，较小根为1。13．答案：。解析：弧长公式，代入得。14．答案：。解析：由点得，所以；当时，。15．答案：。解析：斜边为，直角三角形内切圆半径。16．答案：。解析：。三、解答题参考答案、详解与评分标准评分说明：以下给出一种规