2026届深圳市高三数学高考冲刺模拟试卷（含答案详解与评分标准）

2026届深圳市高三数学高考冲刺模拟试卷（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届高三高考冲刺学科：数学注意事项：1．本试卷用于2026届深圳市高三数学高考冲刺阶段限时检测，考试时间120分钟，满分150分。2．选择题作答时，必须将唯一正确选项填在答题卡相应位置；填空题只写最终结果，结果可用精确值表示。3．解答题应写出必要的文字说明、证明过程或演算步骤；书写要规范，计算要准确。4．答卷前请填写学校、班级、姓名和考号；考试结束后交回答题卷，本试卷可作为复盘订正材料。一、选择题（本大题共10小题，每小题3分，共30分。每小题只有一个选项符合题意。）1．已知复数，则的值为（）A．B．C．D．2．设集合，，则为（）A．B．C．D．3．已知向量，。若，则实数的值为（）A．B．C．D．4．函数在处的切线方程为（）A．y＝2B．y＝2x＋2C．y＝－2x＋2D．y＝x＋25．一个不透明袋中有5个红球、3个蓝球，除颜色外完全相同。现不放回任取2个球，恰有1个红球、1个蓝球的概率为（）A．B．C．D．6．已知正项等比数列满足，，则前5项和等于（）A．B．C．D．7．方程在区间内的解的个数为（）A．1B．2C．3D．48．双曲线的一条渐近线为，焦距为4，则等于（）A．B．C．D．9．若函数在实数集上有两个不同的极值点，则实数的取值范围为（）A．B．C．D．10．在三角形中，，，，则三角形的面积为（）A．B．C．D．二、填空题（本大题共6小题，每小题3分，共18分。请将答案填写在横线上。）11．二项式的展开式中的常数项为__________。12．若直线与圆相切，且，则__________。13．随机变量X的取值为0，1，2，且P(X=0)=1/4，P(X=1)=p，E(X)=1，则p=__________。14．三棱锥P－ABC中，PA垂直于平面ABC，△ABC为直角三角形，AB=3，AC=4，PA=6，则该三棱锥的体积为__________。15．已知函数的最大值为0，则__________。16．数列满足，，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．（15分）在高考冲刺三角函数专题检测中，设的内角所对边分别为，已知（1）求角的大小；（2）若，，求的面积。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（17分）某校高三年级在考前进行一次数学限时训练，教研组抽取60份试卷统计“运算错误数”，得到如下频数表：运算错误数0123人数1521186（1）求这60份试卷运算错误数的平均数，并说明冲刺复盘中应重点关注的错误层级；（2）若按运算错误数分层抽取20份试卷进行二次复盘，求各层应抽取的份数；（3）在第（2）问抽取的“错误数为2”和“错误数为3”的试卷中任选2份做课堂展示，求至少有1份来自“错误数为3”的概率。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（17分）如图意，四棱锥P－ABCD的底面ABCD为边长为2的正方形，PA垂直于底面ABCD，且PA=2。点M为PB的中点。（1）证明：CD垂直于平面PAD；（2）求直线CM与平面PCD所成角的正弦值；（3）求平面PBC与底面ABCD夹角的余弦值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（17分）已知椭圆，点在椭圆上。过点作直线，交椭圆于另一点。（1）求点B的坐标；（2）求△OAB面积的表达式，其中O为坐标原点；（3）求△OAB面积的最大值及此时k的取值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________21．（18分）设函数。（1）讨论函数f(x)的单调性；（2）若对任意x>0恒有f(x)≤0，求实数a的值；（3）当时，证明不等式对任意成立，并写出等号成立条件。作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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