2026届广州市高三数学高考二模模拟试卷（含答案详解与评分标准）

2026届广州市高三数学高考二模模拟试卷（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：150分考试节点：高考二模适用对象：2026届高三注意事项：1．本试卷用于高考二模阶段复习质量检测，重点考查主干知识、通性通法、综合应用与规范表达。2．全卷共22题，选择题10题共30分，填空题6题共18分，解答题6题共102分，满分150分。3．作答前请填写学校、班级、姓名和考号；客观题答案填入答题栏，主观题写出必要的文字说明、证明过程或演算步骤。4．不得使用计算器；作图可先用铅笔，最终结果应清楚、完整、规范。一、选择题（本大题共10小题，每小题3分，共30分。每小题只有一个正确选项。）题号12345678910答案1．设全集，集合，，则为（）A．B．C．D．2．已知复数，则复数在复平面内对应的点所在象限及分别为（）A．第二象限，B．第一象限，C．第三象限，D．第四象限，3．已知向量，，且，则实数的值为（）A．B．C．D．4．函数在区间上取得最大值的点的个数为（）A．1个B．2个C．3个D．4个5．展开式中项的系数为（）A．B．C．D．6．从数字中不放回地任取两个不同数字，记事件为“两数之和为偶数”，事件为“至少有一个数为3”。则等于（）A．B．C．D．7．曲线在点处的切线方程为（）A．B．C．D．8．正项等比数列满足，，则等于（）A．B．C．D．9．棱长为2的正方体中，点为棱的中点，则线段的长为（）A．B．C．D．10．若函数有三个不同的零点，则实数的取值范围为（）A．B．C．D．或二、填空题（本大题共6小题，每小题3分，共18分。请把答案填在答题栏内。）题号111213141516答案11．方程的解为________。12．若直线与圆相切，则________。13．一个盒中有2个红球、3个蓝球，从中不放回地任取2个球，记取到红球的个数为，则________。14．曲线与直线围成图形的面积为________。15．椭圆的焦距为________。16．若函数在上的最小值为0，则________。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．（17分）已知函数（1）化简函数，并求它的最小正周期；（2）求方程在区间上的全部解；（3）在三角形中，为锐角，且，求的最大值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（17分）广州市某校在高考二模阶段进行数学专题复盘。现随机抽取100名高三学生，记录其一周专题训练时长（单位：小时）和本周小测是否达到80分，统计如下表。训练时长[0,2)[2,4)[4,6)[6,8)[8,10]合计人数1022342410100达标人数3102218962（1）用组中值估计这100名学生的一周专题训练时长平均数，并指出中位数所在的组；（2）若按训练时长分层抽样抽取10名学生参加学习访谈，请给出各组抽取人数的一种合理方案；（3）从训练时长在这一组的学生中随机抽取2人，求至少有1人达标的概率。作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（17分）已知函数，其中为实数。（1）讨论函数的单调性；（2）若对任意恒成立，求的取值范围；（3）设，证明：并指出等号成立的条件。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（17分）已知数列满足，且对任意有（1）证明数列为等差数列，并求；（2）设，求；（3）求满足的最小正整数。作答区：_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析一、选择题答案与解析题号12345678910答案