2026届杭州高三数学高考三模考前模拟试卷第007套强证据校准版（含答案详解与评分标准）

2026届杭州高三数学高考三模考前模拟试卷第007套强证据校准版（含答案详解与评分标准）考试名称2026届杭州高三数学高考三模考前模拟卷考试时间120分钟满分120分试卷形态Word文本版，可打印可作答，参考答案新页内容侧重函数导数、解析几何、数列压轴与综合运算学校：________________班级：____________姓名：____________考号：________________注意事项1.本卷共18题。选择题1-8题共40分，填空题9-12题共20分，解答题13-18题共60分。2.答题前请填写学校、班级、姓名和考号；选择题请把唯一正确选项填入答题栏，填空题请在横线上写出最终结果。3.解答题必须写出必要的推理、计算和结论。涉及函数、导数、解析几何、数列递推时，应写清变量范围、等价变形和关键依据。4.本卷为杭州高三三模节点考前模拟训练，请按正式考试节奏完成。选择题答题栏题号12345678答案一、单项选择题（本大题共8小题，每小题5分，共40分。每小题只有一个选项符合题意）1.设集合，，则为2.复数，则等于3.已知函数满足，则的值域为4.一组数据6，8，8，10，13的平均数为，方差为。若每个数据都增加2，得到新数据的平均数与方差分别为，则5.正方体的棱长为2，则直线与平面所成角的正弦值为6.椭圆的离心率为7.曲线在点处的切线方程为8.数列满足，则二、填空题（本大题共4小题，每小题5分，共20分。请把答案写在横线上）9.方程在区间内的解为：________________。10.二项式的展开式中项的系数为：________________。11.直线被圆截得的弦长为：________________。12.函数恰有两个不同实零点，则实数的取值集合为：________________。三、解答题（本大题共6小题，每小题10分，共60分。解答应写出文字说明、证明过程或演算步骤）13.（10分）在中，角的对边分别为，已知，且。求：（1）的值；（2）的面积。作答区域：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________14.（10分）某班进行三模前数学限时训练，12名同学完成第18题第一问的用时（单位：分钟）统计如下：8分钟2人，10分钟3人，12分钟4人，14分钟2人，16分钟1人。（1）求这组用时的平均数；（2）从完成质量较高的5名同学与其余7名同学中随机抽取3人组成讲评小组，求恰有2名来自完成质量较高同学的概率。作答区域：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________15.（10分）如图形文字描述：在棱长为2的正方体中，底面为水平面，在的正上方。（1）证明：⊥平面；（2）求点到平面的距离。作答区域：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________16.（10分）已知椭圆的离心率为，且点在椭圆上。（1）求椭圆的标准方程；（2）过点的直线与椭圆交于两点，设线段的中点为，求点的轨迹方程及取值范围。作答区域：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________17.（10分）已知数列满足。记。（1）证明是等比数列；（2）求的通项公式，并求。作答区域：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.（10分）已知函数。（1）求的最小值；（2）求实数的最小值，使得对任意，都有；（3）讨论方程在区间上的实根个数。作答区域：__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________