2026届湖北省九年级数学中考二模模拟试卷（含答案详解与评分标准）

2026届湖北省九年级数学中考二模模拟试卷（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分考试范围：九年级数学中考二模阶段综合检测注意事项：1．本试卷分选择题、填空题、解答题三部分，共22题。请在规定位置作答，书写要工整，步骤要完整。2．答题前请填写学校、班级、姓名和考号。选择题每题只有一个正确选项。3．可使用直尺、圆规、三角板和无存储功能计算器。所有答案均应化简，解答题应写出必要推理过程。题型选择题填空题解答题总分分值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）每小题给出的四个选项中，只有一项符合题意。请把正确选项填在答题卡对应位置。题号12345678910答案1．在中考二模考前体温记录中，某天清晨气温为，这个数的相反数是（）A．B．C．D．2．某校二模复习资料的厚度约为m，用科学记数法表示为（）A．B．C．D．3．如图形语言所示，两条直线被第三条直线所截，若一组同位角中，则与它对应的同位角的度数是（）A．B．C．D．4．化简的结果是（）A．B．C．D．5．不等式的解集是（）A．B．C．D．6．某学习小组在一次二模专题练习中的得分为，这组数据的众数与中位数分别是（）A．B．C．D．7．二次函数的顶点坐标和对称轴分别是（）A．B．C．D．8．在直角三角形中，，，斜边，则的值为（）A．B．C．D．9．圆中，弦，圆心到弦的距离为，则圆的面积是（）A．B．C．D．10．若关于的一元二次方程有两个相等的实数根，则的值是（）A．B．C．D．二、填空题（本大题共6小题，每小题3分，共18分）请将答案直接填写在题中横线上。11．计算：__________。12．分解因式：__________。13．方程的解是__________。14．一个不透明袋中有个红球和个蓝球，这些球除颜色外完全相同。从袋中不放回地连续摸出两个球，两球都是蓝球的概率是__________。15．在圆中，若圆心角，点在优弧上，则圆周角__________。16．抛物线与轴交于两点，顶点为，则的面积为__________。题号111213141516答案三、解答题（本大题共6小题，共72分）解答应写出文字说明、证明过程或演算步骤。17．（本题10分）二模复习中，计算与方程是基础得分点。完成下列各题：（1）计算：；（2）解方程组：。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本题10分）某校九年级在中考二模后开展“错题整理促提升”活动，随机抽取名学生，统计他们每周数学错题整理次数，得到下表：整理次数0次1次2次3次4次人数37m106（1）求表中m的值；（2）求这40名学生每周错题整理次数的众数、中位数和平均数；（3）若该校九年级共有1200名学生，请估计每周整理错题至少3次的学生人数。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本题12分）如图形条件所示，在中，，点是的中点。过点作，交于点；过点作，交于点。（1）证明四边形AEDF是菱形；（2）若，，求菱形的面积。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本题12分）二模质量分析后，某校准备印制型专题卷和型综合卷共份。型每份元，型每份元，预算不超过元，且型份数不少于型份数的一半。（1）设A型专题卷印制x份，求x的取值范围；（2）若每份型卷能提供个压轴题训练位，学校要求压轴题训练位不少于个，求满足条件的所有印制方案中的范围；（3）印刷厂优惠后，型每份实际元，型每份实际元。在满足（2）条件下，怎样印制实际费用最少？最少费用是多少？________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本题14分）在中，，，。以为直径作圆，交于点（点不与重合）。过点作圆的切线，交于点。（1）证明CD⊥AB；（2）求的长；（3）求的长。__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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