2026届广东省高三数学高考一模模拟试卷（含答案详解与评分标准）

第页2026届广东省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分适用：2026届高三高考一模阶段检测注意事项1．本试卷共22题，分选择题、填空题和解答题三部分。答题前，考生务必将学校、班级、姓名、考号填写清楚。2．选择题每题只有一个正确选项；填空题只写最后结果；解答题应写出必要的文字说明、推理过程和演算步骤。3．本卷用于高三一轮复习后高考一模阶段检测，重点考查基础知识、关键能力和综合应用能力。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，只有一项是符合题目要求的。1．已知复数，则等于（）A．B．C．D．2．设集合，，则为（）A．B．C．D．3．已知向量，，且。若，则的值为（）A．1B．2C．D．4．等差数列中，，，则前10项和等于（）A．135B．145C．150D．1555．函数在实数集上的单调性为（）A．在上单调递增B．在上单调递减C．先增后减D．先减后增6．6名同学独立地从甲、乙、丙三个学习小组中任选一个加入，且每个小组被选中的概率相同，则三个小组人数都为2的概率为（）A．B．C．D．7．已知，且，则的值为（）A．0B．C．D．8．椭圆的离心率为（）A．B．C．D．9．二项式的展开式中的系数为（）A．80B．40C．160D．3210．在棱长为1的正方体中，直线与平面所成角为，则等于（）A．B．C．D．二、填空题：本大题共6小题，每小题3分，共18分。11．不等式的解集为__________。12．曲线在点处的切线方程为__________。13．等比数列中，，公比。若前项和，则__________。14．一个盒中有5个红球、3个白球，从中不放回地任取2个，则至少取到1个白球的概率为__________。15．若函数的两个极值点分别为与，则__________。16．直线与圆相切，且，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．（本小题满分17分）已知函数。（1）化简，并求它的最小正周期和最大值；（2）求方程在区间上的解。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本小题满分17分）某校高三年级在一模前进行“每日数学限时训练”调研，随机抽取50名学生，统计某天自主训练用时（单位：小时），得到如下频数分布表。[0,1)[1,2)[2,3)[3,4)[4,5]61418102（1）用各组中点估计该样本的平均训练用时和方差；（2）规定训练用时不少于2小时为“达标”。从该校高三学生中随机抽取3人，若每人达标情况相互独立，且达标概率用样本频率估计，求恰有2人达标的概率。作答区：_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（本小题满分17分）设函数，定义域为。（1）当时，证明；（2）若方程有两个不同的正根，求实数的取值范围。作答区：__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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