2026届河南省高三数学高考二模模拟试卷（含答案详解与评分标准）

2026届河南省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：高考二模学科：数学注意事项：1．本卷用于2026届河南省高三数学高考二模模拟检测，全卷共22题，考试时间120分钟，满分150分。2．答题前请将学校、班级、姓名、考号填写清楚；选择题用2B铅笔填涂，非选择题用黑色签字笔作答。3．本卷包含单项选择题、填空题和解答题。解答题须写出必要的文字说明、证明过程或演算步骤。4．可使用符合考试规定的作图工具；保持卷面整洁，答案写在相应作答区域内。题型单项选择题填空题解答题合计题量与分值10题×3分=30分6题×3分=18分6题=102分150分一、单项选择题：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．设集合，，则等于（）A．[2，3]B．[2，3)C．(1，3)D．(2，3]2．若复数满足，则的值为（）A．1B．√2C．2D．2√23．已知，则的值为（）A．-3/4B．-1/2C．1/2D．3/44．已知向量，。若与垂直，则的值为（）A．-1B．0C．1/2D．25．二项式展开式中的常数项为（）A．-160B．-80C．80D．1606．函数在处取得极值，则实数等于（）A．1/4B．1/2C．1D．27．一个袋中有4个红球、2个蓝球，除颜色外完全相同。一次不放回任取2个球，取到同色球的概率为（）A．2/5B．7/15C．8/15D．3/58．数列满足，，则的值为（）A．15B．31C．32D．639．棱长为2的正方体的外接球体积为（）A．4πB．4√3πC．8πD．(32/3)π10．若函数有三个不同的零点，则实数的取值范围是（）A．(-∞，-2)B．(-2，2)C．(2，+∞)D．(-∞，2)选择题答题栏：题号12345678910答案二、填空题：本大题共6小题，每小题3分，共18分。11．等差数列中，若，则前9项和__________。12．若，则实数__________。13．椭圆的离心率为__________。14．用数字1，2，3，4，5组成没有重复数字的三位偶数，共有__________个。15．曲线在点处的切线方程为__________。16．已知随机变量，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15分）在中，内角所对的边分别为。已知，，。（1）求边c的长和三角形ABC的面积；（2）求sin(A-B)的值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18．（本小题17分）已知正项数列满足，。（1）证明数列{1/a_n}为等差数列，并求a_n；（2）设c_n=a_na_{n+1}，求T_n=c_1+c_2+...+c_n。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19．（本小题17分）在四棱锥中，底面是边长为2的正方形，PA⊥平面ABCD，且。（1）证明BD⊥平面PAC；（2）求点D到平面PBC的距离；（3）求二面角D-PB-C的余弦值。作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20．（本小题17分）已知椭圆，其左、右焦点分别为，右顶点为。（1）求椭圆C的离心率及焦点坐标；（2）过F_2的直线l:y=k(x-2)与椭圆C交于M，N两点，且弦MN的中点横坐标为8/7。求直线l的斜率k及弦长|MN|。作答区：_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22．（本小题18分）某校在高三数学高考二模模拟检测后，对一道满分10分的综合题进行抽样分析。设随机抽取一名学生在该题上的得分为，其分布列如下表。X0246810P0.060.100.18p0.24q已知。（1）求p，q的值；（2）若得分不低于8分记为“达标”，从同类学生中独立抽取4人，求恰有3人达标的概率以及至少2人达标的概率；（3）现有一个10人学习小组，其中6人达标、4人未达标。从该小组中不放回随机抽取3人，设抽到的达标人数为Z，求Z的分布列与数学期望。作答区：____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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