2026届河南省高三数学高考三模模拟试卷（含答案详解与评分标准）

2026届河南省高三数学高考三模模拟试卷数学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分适用：高考三模命题范围：高中数学综合注意事项：1．本卷用于2026届高三高考三模考前检测，试题共22题，满分150分，考试时间120分钟。2．请将选择题答案填涂在答题卡相应位置，非选择题写在指定作答区内。3．作答时应书写清楚、步骤完整，凡需说明理由的题目，应写出必要的推理过程。一、选择题：本题共10小题，每小题3分，共30分。每小题只有一个选项符合题意。1．（3分）设集合，，则（）A．B．C．D．2．（3分）复数的虚部为（）A．B．C．D．3．（3分）已知，且，则（）A．B．C．D．4．（3分）若函数在上有且仅有一个零点，则实数的值为（）A．B．C．D．5．（3分）已知向量与满足，，夹角为，则（）A．B．C．D．6．（3分）随机变量，则（）A．B．C．D．7．（3分）样本数据的平均数为，方差为，则数据的方差为（）A．B．C．D．8．（3分）圆的半径为（）A．B．C．D．9．（3分）等差数列满足，，则（）A．B．C．D．10．（3分）在正方体中，异面直线与所成的角为（）A．B．C．D．二、填空题：本题共6小题，每小题3分，共18分。11．（3分）不等式的解集为__________。12．（3分）曲线在点处的切线方程为__________。13．（3分）数列是等比数列，，，则__________。14．（3分）椭圆的离心率为__________。15．（3分）二项式展开式中的常数项为__________。16．（3分）若满足约束条件，，，则的最大值为__________。三、解答题：本题共6小题，共102分。解答应写出文字说明、证明过程或演算步骤。17．（17分）已知函数。（1）化简；（2）求在区间上的最大值、最小值及相应的的取值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

18．（17分）数列满足，。（1）求的通项公式；（2）求前项和。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

19．（17分）在四棱锥的底面为正方形，，，。（1）求四棱锥的体积；（2）求直线与平面所成角的正弦值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

20．（17分）某校高三三模数学训练后，教师统计发现每名学生独立答对某综合题的概率约为。现随机抽取名学生，设答对该题的人数为。（1）写出的分布列；（2）求与；（3）求至少人答对的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

21．（17分）已知抛物线，直线与交于两点。（1）设，，证明；（2）若，求实数的值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

22．（17分）已知函数，定义域为。（1）讨论的单调性；（2）若对任意恒成立，求实数的取值范围；（3）当时，证明。作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________