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试卷年份:{{getYear('高三|高考模拟|福建|2015年')}}上传日期:2015-03-26题数:23
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题号:849787
题型:选择题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】已知集合
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image200.png)
(
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image201.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image202.png)
),若数列
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image203.png)
是等差数列,记集合
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image204.png)
的元素个数为
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image205.png)
,则
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image205.png)
关于
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image206.png)
的表达式为
.
题号:849791
题型:选择题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image123.png)
定义域
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image124.png)
,满足
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image125.png)
,当
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image126.png)
时,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image127.png)
,若函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image128.png)
,方程
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image129.png)
有三个实根,则实数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image130.png)
的取值范围是( )
题号:849812
题型:选择题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】已知抛物线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image086.png)
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image087.png)
(
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image088.png)
)的焦点
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image089.png)
到双曲线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image090.png)
的渐近线的距离为
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image091.png)
,过焦点
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image089.png)
斜率为
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image092.png)
的直线与抛物线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image093.png)
交于
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image094.png)
、
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image095.png)
两点,且
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image096.png)
,则
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image097.png)
( )
题号:849814
题型:选择题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】某程序框图如右图所示,若输出的
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image053.png)
,则判断框内应填( )
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image054.png)
题号:849815
题型:选择题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】
![](http://static.zujuan.xkw.com/Upload/2017-10/03/3c0b4444-b619-4d9c-b18b-0a29c2125d43/paper.files/image001.png)
的展开式中常数项为()
题号:849816
题型:选择题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】“
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image037.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image038.png)
且
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image039.png)
”是“数列
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image040.png)
为等比数列”的( )
A.必要不充分条件 | B.充分不必要条件 |
C.充分必要条件 | D.既不充分也不必要条件 |
题号:849817
题型:选择题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image029.png)
的图象大致为( )
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image030.png)
A. B. C. D.
题号:849818
题型:选择题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】某几何体的三视图如图,则该几何体的体积为( )
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image018.png)
题号:849819
题型:选择题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
题号:849820
题型:选择题
难易度:较易
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
题号:4899793
题型:选择题
难易度:较易
日期:2017-09-09
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
题号:849788
题型:填空题
难易度:较易
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image170.png)
(
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image171.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image172.png)
)的部分图象如图所示,则
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image173.png)
的值为
.
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image174.png)
题号:849789
题型:填空题
难易度:较易
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】复数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image162.png)
为纯虚数,若
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image163.png)
(
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image164.png)
为虚数单位),则实数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image070.png)
的值为
.
题号:849790
题型:填空题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
题号:4183074
题型:填空题
难易度:较易
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】在平面直角坐标系
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image193.png)
中,设
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image194.png)
是由不等式组
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image195.png)
表示的区域,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image094.png)
是到原点的距离不大于
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image021.png)
的点构成的区域,向
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image094.png)
中随机投一点,则所投点落在
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image194.png)
中的概率是
.
题号:849779
题型:解答题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】(本小题满分7分)选修4-5:不等式选讲
已知函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image491.png)
.
(1)若不等式
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image492.png)
的解集为
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image493.png)
,求实数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image130.png)
的值;
(2)若实数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image070.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image071.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image222.png)
满足
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image494.png)
,求
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image495.png)
的最大值.
题号:849780
题型:解答题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】(本小题满分7分)选修4-4:坐标系与参数方程
已知直线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image476.png)
的参数方程:
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image477.png)
(
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image478.png)
为参数)和圆
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image093.png)
的极坐标方程:
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image479.png)
.
(1)求圆
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image093.png)
的直角坐标方程;
(2)判断直线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image476.png)
与圆
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image093.png)
的位置关系.
题号:849781
题型:解答题
难易度:较易
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】(本小题满分7分)选修4-2:矩阵与变换
已知矩阵
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image453.png)
.
(1)矩阵
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image453.png)
对应的变换把直线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image355.png)
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image454.png)
变为直线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image455.png)
,求直线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image455.png)
的方程;
(2)求
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image094.png)
的逆矩阵
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image456.png)
.
题号:849782
题型:解答题
难易度:容易
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】(本小题满分14分)已知函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image396.png)
(
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image397.png)
).
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image398.png)
(1)若
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image399.png)
为函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image400.png)
的极值点,求
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image222.png)
的值;
(2)若
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image401.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image357.png)
已知
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image402.png)
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image403.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image404.png)
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image405.png)
,若直线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image406.png)
、
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image407.png)
及直线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image408.png)
与函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image123.png)
的图象所围成的封闭图形如阴影部分所示,求阴影面积
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image365.png)
关于
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image222.png)
的函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image409.png)
的最小值
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image130.png)
;
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image358.png)
证明不等式:
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image410.png)
.
题号:849783
题型:解答题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】(本小题满分13分)已知中心在原点,焦点在
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image351.png)
轴上的椭圆
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image093.png)
过点
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image352.png)
,离心率
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image353.png)
.
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image354.png)
(1)求椭圆
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image093.png)
的方程;
(2)如图,动直线
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image355.png)
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image356.png)
与椭圆
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image093.png)
有且仅有一个公共点,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image357.png)
求
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image092.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image130.png)
满足的关系式;
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image358.png)
如图,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image359.png)
、
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image360.png)
为椭圆
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image093.png)
的左、右焦点,作
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image361.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image362.png)
,垂足分别为
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image194.png)
、
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image363.png)
,四边形
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image364.png)
的面积
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image365.png)
是否存在最大值?若存在,求出该最大值;若不存在,请说明理由.
题号:849784
题型:解答题
难易度:一般
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】(本小题满分13分)如图1,在
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image280.png)
中,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image281.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image282.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image283.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image284.png)
、
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image285.png)
分别为
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image286.png)
、
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image287.png)
的中点,连接
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image288.png)
并延长交
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image289.png)
于
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image089.png)
,将
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image290.png)
沿
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image287.png)
折起,使平面
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image291.png)
平面
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image292.png)
,如图2所示.
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image293.jpg)
(1)求证:
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image294.png)
平面
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image292.png)
;
(2)求平面
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image295.png)
与平面
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image296.png)
所成的锐二面角的余弦值;
(3)在线段
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image297.png)
上是否存在点
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image194.png)
使得
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image298.png)
平面
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image296.png)
?若存在,请指出点
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image194.png)
的位置;若不存在,说明理由.
题号:849785
题型:解答题
难易度:较易
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】(本小题满分13分)根据新修订的《环境空气质量标准》指出空气质量指数在
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image250.png)
,各类人群可正常活动.某市环保局在2014年对该市进行为期一年的空气质量检测,得到每天的空气质量指数,从中随机抽取50个作为样本进行分析报告,样本数据分组区间为
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image251.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image252.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image253.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image254.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image255.png)
,由此得到样本的空气质量指数频率分布直方图,如图.
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image256.png)
(1)求
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image070.png)
的值;
(2)根据样本数据,试估计这一年度的空气质量指数的平均值;
(3)用这50个样本数据来估计全年的总体数据,将频率视为概率.如果空气质量指数不超过20,就认定空气质量为“最优等级”.从这一年的监测数据中随机抽取2天的数值,其中达到“最优等级”的天数为
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image257.png)
,求
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image257.png)
的分布列和数学期望.
题号:849786
题型:解答题
难易度:较易
日期:2015-03-26
来源:2015届福建省漳州市普通高中毕业班质量检查理科数学试卷(带解析)
【题文】(本小题满分13分)已知函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image220.png)
.
(1)求函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image123.png)
的最小正周期和函数
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image123.png)
的单调递增区间;
(2)在
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image221.png)
中,角
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image094.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image095.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image093.png)
所对的边分别为
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image070.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image071.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image222.png)
,若
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image223.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image224.png)
,
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image221.png)
的面积为
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image225.png)
,求边长
![](http://static.zujuan.xkw.com/Upload/2015-03/26/22da9670-ed0c-46f5-ad0d-9f7c7a375c12/paper.files/image070.png)
的值.