2026届武汉市高三数学高考一模模拟试卷（含答案详解与评分标准）

2026届武汉市高三数学高考一模模拟试卷2026届武汉市高三数学高考一模模拟试卷（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：150分考试节点：高考一模适用对象：2026届高三注意事项：1．本卷用于2026届武汉市高三数学高考一模前阶段检测，满分150分，考试时间120分钟。2．答题前，请将学校、班级、姓名、考号填写清楚；选择题请把答案填入答案栏。3．解答题应写出必要的文字说明、证明过程或演算步骤，只写结果不得满分。4．全卷分为选择题、填空题和解答题三部分；参考答案与解析从新页开始。一、选择题：本题共10小题，每小题3分，共30分。在每小题给出的四个选项中，只有一项符合题目要求。1．设全集为实数集，集合，，则（）A．B．C．D．2．已知复数，则（）A．B．C．D．3．向量，，若，则（）A．2B．3C．D．4．函数的最大值为（）A．B．C．D．5．等差数列中，，公差，则前10项和（）A．125B．155C．165D．1806．一枚质地均匀的硬币连续抛掷4次，正面向上的次数为，则（）A．B．C．D．7．已知，，则（）A．B．C．D．8．正方体的棱长为2，则异面直线与所成的角为（）A．B．C．D．9．曲线在点处的切线方程为（）A．B．C．D．10．椭圆的离心率为（）A．B．C．D．选择题答案栏题号12345678910答案二、填空题：本题共6小题，每小题3分，共18分。请把答案填写在相应题号后的横线上。11．已知，曲线在处的切线斜率为2，则________。12．的展开式中的系数为________。13．已知，且，则________。14．若直线与圆相切，且，则________。15．双曲线的一条渐近线方程为，则该双曲线的离心率为________。16．若函数在区间内存在极小值点，则实数的取值范围为________。填空题答案栏题号111213141516答案三、解答题：本题共6小题，共102分。解答应写出必要的文字说明、证明过程或演算步骤。17．（14分）已知函数。（1）求的最小正周期，并写出它的单调递增区间与单调递减区间；（2）若，且，求的值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（16分）已知数列满足，。（1）求数列的通项公式；（2）设，求。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

19．（17分）某校为了解2026届高三学生在高考一模前对“函数与导数”专题的掌握情况，从一次限时训练中随机抽取50名学生的成绩，整理如下表。成绩区间[60,70)[70,80)[80,90)[90,100]人数6142010（1）用各组中点估计这50名学生的平均成绩；（2）已知成绩在的10名学生中有6名男生、4名女生，从中随机选取2名参加讲评展示，求至少选到1名女生的概率；（3）若该校高三全体800名学生在同类训练中的成绩近似服从正态分布，且，估计成绩不低于90分的人数。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（17分）在四棱锥中，底面是边长为2的正方形，底面，且。点为的中点。（1）证明：平面；（2）求直线与平面所成角的正弦值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

21．（18分）已知椭圆，点。过点且斜率为的动直线与椭圆交于两点，设的中点为。（1）求点的轨迹方程，并写出范围；（2）求弦长的最小值及此时直线的方程。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（20分）已知函数，其中为实数。（1）讨论函数的单调性；（2）若对任意，都有，求的取值范围；（3）当时，证明方程在内有且只有一个实数根，并指出该根所在的一个长度为1的区间。作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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