2026届上海市浦东新区九年级数学中考冲刺模拟试卷（含答案详解与评分标准）

2026届九年级数学中考冲刺模拟试卷2026届上海市浦东新区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分题型：选择·填空·解答用途：考前综合检测题型与分值结构题型选择题填空题解答题合计分值30分18分72分120分注意事项1．本卷用于2026届九年级数学中考冲刺阶段考前综合检测，考试时间120分钟，满分120分。2．选择题每题只有一个正确答案；填空题直接填写最终结果；解答题须写出必要的演算过程、推理依据或文字说明。3．涉及作图、函数图像与几何关系时，可在题目所给条件基础上进行分析；题中图形仅作示意，若无特别说明，不作为精确比例依据。4．请将客观题答案填写在“学生作答区”对应栏内，解答题直接写在各题题后预留区域。一、选择题（本大题共10题，每题3分，共30分）1．计算的结果是（）。A．B．C．D．2．方程的较大实数根是（）。A．1B．2C．3D．63．若一次函数的图像经过点，则的值为（）。A．0B．2C．4D．54．一个不透明袋中装有2个红球和3个蓝球，除颜色外完全相同。随机不放回地连续摸出2个球，恰好都为红球的概率是（）。A．B．C．D．5．如图意可知，在⊙O中，点C位于优弧AB上，若圆心角，则圆周角的度数为（）。A．20°B．40°C．80°D．160°6．若△ABC与△DEF相似，且对应边之比，则面积之比为（）。A．4:9B．2:3C．3:2D．9:47．一组数据4，6，6，7，9的中位数是（）。A．5B．7C．8D．68．不等式的正整数解共有（）。A．2个B．3个C．4个D．无数个9．抛物线的对称轴是（）。A．B．C．D．10．在直角三角形ABC中，，，，则边BC的长为（）。A．6B．8C．10D．12二、填空题（本大题共6题，每题3分，共18分）11．分解因式：＝________________。12．若是方程的两个实数根，则＝________________。13．计算：＝________________。14．已知，，则＝________________。15．一个正多边形的每个内角都是150°，则这个正多边形的边数是________________。16．将标有1，2，3，4的四张卡片洗匀后，不放回地随机抽取两张，所得两个数字之和为奇数的概率是________________。三、学生作答区（客观题）选择题与填空题请将最终答案填入下表；第17—22题在各题题后预留区域内完成。题号12345678910答案题号111213141516答案四、解答题（本大题共6题，共72分）17．（本题10分）完成下列计算与求解。（1）化简下式，并写出使原式有意义的的取值限制：（2）解方程：。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本题10分）已知反比例函数的图像与直线相交于点和点B。（1）求、的值；（2）求点B的坐标；（3）求的面积。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本题12分）如图，△ABC中，，。点D是边BC的中点，过点D作，交AC于点E。（1）求线段AD的长；（2）证明：；（3）求线段DE的长及四边形ABDE的面积。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本题12分）某班20名学生参加“中考冲刺专题训练——代数综合”限时检测，成绩统计如下表。分数（分）708090100人数（人）3575（1）求这20名学生成绩的平均分；（2）写出这组成绩的众数与中位数；（3）随机抽取1名学生，求其得分不低于90分的概率；（4）从这20名学生中随机抽取2名，不放回，求恰有1名学生得100分的概率。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本题14分）已知抛物线与x轴交于A、B两点（点A在点B左侧），与y轴交于点C，顶点为D。（1）求点A、B、C、D的坐标；（2）求直线CD的解析式；（3）点E是线段BD上的一点，过点E作轴交抛物线于点F。若，求点E的横坐标。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（本题14分）学校准备在靠墙位置设置一个矩形“冲刺展示区”。其中一边靠墙，不设置围栏；其余三边使用总长36m的围栏。设垂直于墙的边长为，平行于墙的围栏边长为，展示区面积为。（1）用含的代数式表示，并写出的取值范围；（2）求展示区面积的最大值，并写出此时与的值；（3）若展示区面积不小于，求的取值范围。____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

参考答案与解析题号12345678910答案BCCBBADBCA题号111213141516答案(x-3)(x+3)4113122/3一、选择题答案与关键理由1．答案：B。理由：，，所以原式等于。2．答案：C。理由：，方程两根为2、3，较大根为3。3．答案：C。理由：将代入，得，所以。4．答案：B。理由：从5个球中任取2个共有种等可能结果，2个红球同时被取出有1种，概率为。5．答案：B。理由：同弧所对的圆周角等于圆心角的一半，因此。6．答案：A。理由：相似三角形面积之比等于相似比的平方，故。7．答案：D。理由：将数据从小到大排列后仍为4，6，6，7，9，中间的第3个