2018年福建省普通高中毕业班4月质量检查理科数学试题及答案

'2015年福建省普通高中毕业班质量检查数学(理科)第Ⅰ卷（选择题共50分）一、选择题1.已知集合，，则等于A.B.C.D2.执行如图所示的程序框图，则输出结果为A.15B.16C.25D.363.展开式的二项式系数和为64，则其常数项为A.-20B.-15C.15D.204.某校为了解本校高三学生学习心里状态，采用系统抽样方法从800人中抽取40人参加某种测试，为此将题目随机编号，分组后再第一组采用简单随机抽样的方法抽到号码为18，抽到的40人中，编号落入区间的人做试卷，编号落入区间的人做试卷,其余的人做试卷，则做试卷的人数为A.10B.12C.18D.285.是已知双曲线的中心在原点，焦点再轴上，若双曲线的一条渐近线的倾斜角等于60°，则双曲线的离心率等于·22· A.B.C.D.2·22· 2.函数的图像大致是3.已知集合.且,的最小值为A.B.C.3D.54.在中，,,,若为的内心，则的值为A.6B.10C.12D.155.系的纸张规格如图，其特点是：②所有规格的纸张的长宽比都相同；②对裁后可以得到两张。·22· 对裁后可以得到两张对裁后可以得到两张若每平方厘米重量为克的纸各一张，其中纸的较短边的长为厘米，记这张纸的重量之和为，则下列判断错误的是A.存在，使得B.存在，使得C.对于任意，都有D.对于任意，都有2.定义在上的可导函数满足，且。现给出关于函数的下列结论①函数在上单调递增②函数的最小值为③函数有且只有一个零点④对于任意，都有A.6B.10C.12D.15第Ⅱ卷（选择题共50分）3.已知且，则等于_________4.设等差数列的前项和为，且，则_______5.在中，,,，若在线段上任取一点,则为锐角的概率是______·22· 2.正方体的棱长为2，则三棱锥公共部分的体积等于_______3.定义在上函数满足：，，若取芯在处的切线方程，该曲线在的切线方程为________三、解答题：·22· 2.已知函数，（Ⅰ）若，求的值；（Ⅱ）若函数的图像是由函数的图像上所有的电向右平移个单位长度而得到，且在内是单调函数，求实数m的最大值。3.如图，四棱锥的底面为直角梯形，，90°，平面,,,过作一平面分别相交,于电Ⅰ求证Ⅱ设，求于平面所成的角的大小4.“抢红包“的网络游戏给2015年的春节增添了一份趣味。”掐女红包“有多种玩法，小明参加一种接龙红包游戏：小明在红包里装了9元现金，然后发给朋友A，并给出金额所在区间，让A猜（所猜金额为整数元；下同），如果A猜中,A将获得红包里的金额；如果A未猜中，A将当前的红包转发给朋友B，同时给出金额所在区间，让B猜，如果B猜中，A和B可以评分红包里的金额；如果B未猜中，B要将当前的红包转发个朋友C，同时给出金额所在区间，让C猜，如果C猜中，A、B和C可以评分红包里的金额；如果C未猜中，红包里的资金将退回小明的账户。Ⅰ求A恰好得到3元的概率Ⅱ设A所获得的金额为X元，求X的分布列及数学期望·22· Ⅲ从统计学的角度而言，A所获得的金额是否超过B和C两人所获得的金额之和?并说明理由·22· 2.已知椭圆的左、右焦点分别为,及椭圆的短轴端点为顶点的三角形是等边三角形，椭圆的右定点到右焦点的距离为Ⅰ求椭圆的方程：Ⅱ如图，直线与椭圆有且只有一个公共点，且交于轴于点，过点作垂直于的直线交轴于点,求证：五点共圆3.已知函数的图象在点处的切线方程为Ⅰ求的值及的单调区间Ⅱ是否存在实数，使得射线与曲线有三个公共点？若存在，求出的取值范围；若不存在，说明理由Ⅲ设，为正实数，且，证明：21、选做题（1）选修4-2：矩阵与变换已知曲线C：，矩阵，且曲线C在矩阵M对应的变换的作用下得到曲线.·22· （I）求曲线的方程；（II）求曲线C的离心率以及焦点坐标.（1）选修4-4：极坐标与参数方程在平面直角坐标系中，点M的坐标为（-1,2），在极坐标系（与直角坐标系取相同的长度单位，且以原点O为极点，以x轴正半轴为极轴）中，直线的方程为（I）判断点M与直线的位置关系；（II）设直线与抛物线相交于A,B两点，求点M到A,B两点的距离之积（2）选修4-5：不等式选讲设函数（I）若对任意恒成立，求实数m的取值范围（II）当，求的最大值.·22· ·22· ·22· ·22· ·22· ·22· ·22· ·22· ·22· ·22· ·22· ·22· 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