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题号:750493
题型:选择题
难易度:较易
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】定义:分子为1且分母为正整数的分数成为单位分数,我们可以把1分拆为若干个不同的单位分数之和.如:
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image106.png)
,依次类推可得:
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image107.png)
,其中
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image108.png)
.设
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image109.png)
,则
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image110.png)
的最小值为( )
题号:750494
题型:选择题
难易度:较易
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】在一个棱长为4的正方体内,你认为最多放入的直径为1的球的个数为( )
题号:750496
题型:选择题
难易度:较易
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】如图所示是一几何体的三视图,正视图是一等腰直角三角形,且斜边
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image074.png)
长为2,侧视图是一直角三角形,俯视图为一直角梯形,且
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image075.png)
,则异面直线
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image076.png)
与
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image077.png)
所成角的正切值是( )
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image078.png)
题号:750497
题型:选择题
难易度:一般
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
题号:750498
题型:选择题
难易度:较易
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】已知
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image050.png)
是椭圆
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image051.png)
的右焦点,
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image052.png)
是
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image053.png)
上一点,
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image054.png)
,当
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image055.png)
周长最小时,其面积为( )
A.4 | B.8 | C.![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image056.png) | D.![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image057.png) |
题号:750499
题型:选择题
难易度:较易
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】函数
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image035.png)
是定义在区间
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image036.png)
上可导函数,其导函数为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image037.png)
,且满足
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image038.png)
,则不等式
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image039.png)
的解集为( )
题号:750500
题型:选择题
难易度:较易
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image029.png)
中三边上的高依次为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image030.png)
,则
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image029.png)
为( )
A.锐角三角形 | B.直角三角形 | C.钝角三角形 | D.不存在这样的三角形 |
题号:750502
题型:选择题
难易度:较易
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】设
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image005.png)
且
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image006.png)
,若复数
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image007.png)
(
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image008.png)
为虚数单位)是实数,则( )
题号:750503
题型:选择题
难易度:较易
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】设命题甲:
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image001.png)
的解集是实数集
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image002.png)
;命题乙:
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image003.png)
,则命题甲是命题乙成立的( )
A.充分不必要条件 | B.充要条件 |
C.必要不充分条件 | D.既不充分也不必要条件 |
题号:3916242
题型:选择题
难易度:较难
日期:2017-07-27
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】已知
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image127.png)
,直线
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image128.png)
与函数
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image129.png)
的图像在
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image130.png)
处相切,设
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image131.png)
,若在区间
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image132.png)
上,不等式
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image133.png)
恒成立,则实数
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image084.png)
()
题号:3916249
题型:选择题
难易度:较易
日期:2017-07-27
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】等差数列
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image021.png)
中,
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image033.png)
是一个与
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image034.png)
无关的常数,则该常数的可能值的集合为()
题号:750488
题型:填空题
难易度:一般
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】已知
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image029.png)
的面积为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image199.png)
,内角
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image200.png)
所对的边分别为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image201.png)
,且
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image202.png)
成等比数列,
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image203.png)
,则
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image204.png)
的最小值为
.
题号:750490
题型:填空题
难易度:一般
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】在直角坐标系
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image161.png)
中,已知点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image162.png)
和点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image163.png)
,若点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image053.png)
在
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image164.png)
的平分线上,且
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image165.png)
,则
.
题号:750491
题型:填空题
难易度:较难
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image146.png)
的图像在点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image147.png)
处的切线与直线
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image148.png)
垂直,执行如图所示的程序框图,输出的
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image149.png)
值是
.
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image150.png)
题号:3916238
题型:填空题
难易度:较易
日期:2017-07-27
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】如图,将平面直角坐标系中的纵轴绕原点
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image205.png)
顺时针旋转
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image206.png)
后,构成一个斜坐标平面
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image207.png)
.在此斜坐标平面
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image207.png)
中,点
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image208.png)
的坐标定义如下:过点
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image209.png)
作两坐标轴的平分线,分别交两轴于
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image210.png)
两点,则
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image211.png)
在
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image212.png)
轴上表示的数为
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image213.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image214.png)
在
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image215.png)
轴上表示的数为
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image216.png)
.那么以原点
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image205.png)
为圆心的单位圆在此斜坐标系下的方程为
.
![](http://static.zujuan.xkw.com/Upload/2017-07/27/65f09620-1de5-4f87-8c66-3ea289934938/paper.files/image217.png)
题号:750460
题型:解答题
难易度:较易
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image449.png)
.
(1)当
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image450.png)
时,求函数
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image035.png)
的最大值;
(2)解关于
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image184.png)
的不等式
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image451.png)
.
题号:750481
题型:解答题
难易度:较易
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】已知曲线
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image430.png)
(
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image431.png)
为参数),
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image432.png)
(
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image433.png)
为参数).
(1)化
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image434.png)
的方程为普通方程,并说明他们分别表示什么曲线;
(2)若
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image302.png)
上的点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image052.png)
对应的参数为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image435.png)
为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image305.png)
上的动点,求
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image319.png)
的中点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image182.png)
到直线
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image436.png)
(
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image431.png)
为参数)距离的最小值.
题号:750482
题型:解答题
难易度:一般
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】如图,
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image029.png)
内接于直径为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image267.png)
的圆
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image178.png)
,过点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image408.png)
作圆
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image178.png)
的切线交
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image409.png)
的延长线于点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image410.png)
的平分线分别交
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image267.png)
和圆
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image178.png)
于点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image411.png)
,若
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image412.png)
.
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image413.png)
(1)求证:
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image414.png)
;
(2)求
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image415.png)
的值.
题号:750483
题型:解答题
难易度:困难
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】设
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image221.png)
为实数,函数
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image352.png)
.
(1)当
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image353.png)
时,求
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image035.png)
在
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image354.png)
上的最大值;
(2)设函数
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image355.png)
当
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image140.png)
有两个极值点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image356.png)
时,总有
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image357.png)
,求实数
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image312.png)
的值(
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image037.png)
为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image035.png)
的导函数).
题号:750484
题型:解答题
难易度:困难
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】已知椭圆
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image299.png)
的离心率为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image080.png)
,其短轴的下端点在抛物线
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image300.png)
的准线上.
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image301.png)
(1)求椭圆
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image302.png)
的方程;
(2)设
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image178.png)
为坐标原点,
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image182.png)
是直线
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image303.png)
上的动点,
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image050.png)
为椭圆的右焦点,过点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image050.png)
作
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image304.png)
的垂线与以
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image304.png)
为直径的圆
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image305.png)
相交于
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image306.png)
两点,与椭圆
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image302.png)
相交于
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image307.png)
两点,如图所示.
①若
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image308.png)
,求圆
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image305.png)
的方程;
②设
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image305.png)
与四边形
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image309.png)
的面积分别为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image310.png)
,若
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image311.png)
,求
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image312.png)
的取值范围.
题号:750485
题型:解答题
难易度:一般
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】电子商务在我国发展迅猛,网上购物成为很多人的选择.某购物网站组织了一次促销活动,在网页的界面上打出广告:高级口香糖,10元钱三瓶,有8种口味供你选择(其中有一种为草莓口味).小王点击进入网页一看,只见有很多包装完全相同的瓶装口香糖排在一起,看不见具体口味,由购买者随机点击进行选择(各种口味的高级口香糖均超过3瓶,且各种口味的瓶数相同,每点击选择一瓶后,网页自动补充相应的口香糖).
(1)小王花10元钱买三瓶,请问小王共有多少种不同组合选择方式?
(2)小王花10元钱买三瓶,由小王随机点击三瓶,请列出有小王喜欢的草莓味口香糖瓶数
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image280.png)
的分布列,并计算其数学期望和方差.
题号:750486
题型:解答题
难易度:较难
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】如图,四边形
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image246.png)
是直角梯形,
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image247.png)
,又
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image248.png)
,直线
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image249.png)
与直线
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image250.png)
所成的角为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image251.png)
.
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image252.png)
(1)求证:
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image253.png)
;
(2)求二面角
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image254.png)
的余弦值;
(3)求点
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image255.png)
到平面
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image256.png)
的距离.
题号:750487
题型:解答题
难易度:较难
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】设等比数列
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image015.png)
的前
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image017.png)
项和为
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image222.png)
,已知,
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image223.png)
,且
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image224.png)
成等差数列.
(1)求数列
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image015.png)
的通项公式;
(2)设
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image225.png)
,求数列
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image226.png)
的前
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image017.png)
项和
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image227.png)
.
题号:750495
题型:解答题
难易度:较难
日期:2016-05-09
来源:【百强校】2016届河北省衡水中学高三下学期一模考试理科数学试卷(带解析)
【题文】某学校课题组为了研究学生的数学成绩和物理成绩之间的关系,随机抽取高二年级20名学生某次考试成绩(百分制)如下表所示:
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image091.png)
若数学成绩90分(含90分)以上为优秀,物理成绩85(含85分)以上为优秀.有多少把握认为学生的学生成绩与物理成绩有关系( )
参考数据公式:①独立性检验临界值表
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image096.png)
②独立性检验随机变量
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image097.png)
的值的计算公式:
![](http://static.zujuan.xkw.com/Upload/2016-05/09/79819238-0589-4094-a5d6-83e1b476a555/paper.files/image098.png)