2026届安徽省高三数学高考三模模拟试卷（含答案详解与评分标准）

2026届安徽省高三数学高考三模模拟试卷（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：高考三模注意事项1．本卷为高考三模考前综合检测卷，重点考查基础知识、关键能力、综合运用与规范表达。2．答题前，考生务必将学校、班级、姓名、考号填写清楚；选择题用规定方式填涂，非选择题写在相应作答区内。3．全卷共22题，满分150分。选择题10题，每题3分，共30分；填空题6题，每题3分，共18分；解答题6题，共102分。4．解答题应写出必要的文字说明、证明过程或演算步骤；只写最后结果且缺少关键过程的，按评分标准酌情给分。一、选择题：本大题共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．已知复数，则等于（）A．B．C．D．2．设集合，，则为（）A．B．C．D．3．在二项式的展开式中，常数项为（）A．120B．160C．240D．3204．已知非零向量满足，则等于（）A．B．C．D．5．某校高三三模数学成绩近似服从正态分布。若，则120名考生中成绩在90分到110分之间的人数约为（）A．68B．76C．82D．906．函数的最小正周期为（）A．B．C．D．7．等差数列中，，，则前5项和等于（）A．25B．28C．30D．358．已知曲线在点处的切线方程为（）A．B．C．D．9．双曲线的离心率为，则其渐近线斜率的绝对值为（）A．B．C．D．10．设函数。若方程在内有两个不同实根，则实数的取值范围是（）A．B．C．D．二、填空题：本大题共6小题，每小题3分，共18分。请把答案填写在题中横线上。11．曲线在处的切线方程是____________。12．从5名男生和3名女生中随机选3人参加三模试卷讲评，至少选到1名女生的概率为____________。13．定积分的值为____________。14．等比数列的首项为2，前三项和为14，且公比为正数，则公比为____________。15．圆的圆心到直线的距离为____________。16．若且，则的值为____________。三、解答题：本大题共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．（14分）已知函数。（1）求函数的最小正周期和最大值；（2）求不等式在区间上的解集；（3）若锐角α满足f(α)=1，求tanα的值。作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（16分）在直三棱柱ABC-A₁B₁C₁中，底面ABC为等腰直角三角形，AB=AC=2，∠BAC=90°，AA₁=2。点E是B₁C₁的中点。（1）证明：AE⊥B₁C₁；（2）求平面AEC₁与平面ABC所成锐二面角的余弦值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（17分）某校高三年级在高考三模前进行一次数学专题检测，随机抽取100名学生的得分并按分数段统计如下表。分数段[60,70)[70,80)[80,90)[90,100]人数10304020（1）用各组组中值估计这100名学生的平均得分；（2）若按分层抽样从这100名学生中抽取10人参加试卷讲评，求各分数段应抽取的人数；（3）在得分不低于90分的20名学生中，有8名学生选择“函数与导数”作为最需要强化的专题，其余12名学生选择“解析几何”。现从这20名学生中随机抽取3人，设其中选择“函数与导数”的人数为X，求X的分布列和数学期望。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（19分）已知函数，其中a为实数。（1）当时，求函数的单调区间和极值；（2）求方程在内有两个不同实根时a的取值范围；（3）当时，设方程的两个不同正根为，证明：。作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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