2026届浙江省高三数学高考三模模拟试卷（含答案详解与评分标准）

2026届浙江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：高考三模适用对象：2026届高三注意事项：1．本卷用于浙江省2026届高三高考三模考前综合检测，分选择题、填空题和解答题三部分。2．选择题每题只有一个符合题意的选项；填空题只写最后结果；解答题应写出必要的文字说明、演算步骤和推理过程。3．所有答案须写在相应作答区内；不得在密封线外作答；保持卷面整洁，画图题可用铅笔辅助作图。4．本卷共22题，选择题10题30分，填空题6题18分，解答题6题102分，合计150分。题型选择题填空题解答题总分分值3018102150得分一、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。1．（3分）已知复数z为下式的值，则z等于A．B．C．D．2．（3分）设集合A与B满足下列条件，则A∩B为A．B．C．D．3．（3分）已知向量如下，若所给两向量垂直，则λ的值为A．B．C．D．4．（3分）二项式展开式中的常数项为A．B．C．D．5．（3分）一个袋中有3个红球、2个蓝球，从中不放回地任取2个球，恰有1个红球的概率为A．B．C．D．6．（3分）若函数如下，并且在实数集R上单调递增，则实数a的取值范围为A．B．C．D．7．（3分）若α满足下列条件，则下列值正确的是A．B．C．D．8．（3分）一个圆锥的底面半径为3，高为4，则该圆锥的侧面积为A．B．C．D．9．（3分）数列的前n项和满足下式，则第10项为A．B．C．D．10．（3分）双曲线的焦距为4，离心率如下，则它的实轴长为A．B．C．D．二、填空题：本大题共6小题，每小题3分，共18分。11．（3分）极限的值为答：____________________12．（3分）点P到直线l的距离为答：____________________13．（3分）方程的实数解为答：____________________14．（3分）圆的半径为答：____________________15．（3分）若随机变量X满足下列条件，则所求概率为答：____________________16．（3分）曲线在指定点处的切线方程为答：____________________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f(x)如下。（1）求f(x)的最小正周期，并写出它的单调递增区间；（2）求不等式在区间上的解集。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（17分）某校高三年级在高考三模考前检测后，对一个班50名学生的数学成绩进行整理，得到如下分组统计表。作答区：分数段[60,70)[70,80)[80,90)[90,100]人数6121814组中值65758595（1）用组中值估计该班本次检测的平均分，并估计中位数；（2）已知90分及以上学生中男生8人、女生6人。从该组随机抽取2名参加答题展示，求至少抽到1名女生的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（17分）四棱锥P-ABCD的底面ABCD为边长为2的正方形，PA⊥平面ABCD，PA的长度如下。设AC与BD交于O。（1）证明：BD⊥平面PAC；（2）求直线PC与平面PBD所成角的正弦值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（17分）已知椭圆C的方程如下，O为坐标原点。（1）写出椭圆C的焦点坐标和离心率；（2）过点的直线与椭圆C相交于A、B两点，设直线斜率为，求△OAB面积的最大值，并求此时的值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（17分）已知函数如下，其中x>0，a为实数。（1）讨论f(x)的单调性；（2）若方程x-alnx=a有两个不同的正根，求a的取值范围，并说明较小根所在的区间。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

22．（17分）已知数列满足下列条件，且对任意正整数n有递推关系（1）求数列{a_n}的通项公式；（2）设，求，并证明。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________解答题附加作答区（若前面空间不足，可在此继续作答并注明题号）：_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________