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题号:3526576
题型:选择题
难易度:较易
日期:2017-04-12
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
题号:3533827
题型:选择题
难易度:较易
日期:2017-04-11
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】已知平面向量
![](http://static.zujuan.xkw.com/Upload/2017-04/11/ccc7a277-df12-4f41-b435-41924cfed2cd/paper.files/image020.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/11/ccc7a277-df12-4f41-b435-41924cfed2cd/paper.files/image021.png)
夹角为
![](http://static.zujuan.xkw.com/Upload/2017-04/11/ccc7a277-df12-4f41-b435-41924cfed2cd/paper.files/image022.png)
,且
![](http://static.zujuan.xkw.com/Upload/2017-04/11/ccc7a277-df12-4f41-b435-41924cfed2cd/paper.files/image023.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/11/ccc7a277-df12-4f41-b435-41924cfed2cd/paper.files/image024.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-04/11/ccc7a277-df12-4f41-b435-41924cfed2cd/paper.files/image025.png)
( )
A.1 | B.![](http://static.zujuan.xkw.com/Upload/2017-04/11/ccc7a277-df12-4f41-b435-41924cfed2cd/paper.files/image026.png) | C.2 | D.![](http://static.zujuan.xkw.com/Upload/2017-04/11/ccc7a277-df12-4f41-b435-41924cfed2cd/paper.files/image027.png) |
题号:3799695
题型:选择题
难易度:较易
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】设抛物线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image100.png)
的焦点为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image101.png)
,点
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image102.png)
在
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image026.png)
上,
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image103.png)
,若
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image104.png)
轴上存在点
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image105.png)
,使得
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image106.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image107.png)
的值为 ( )
题号:3799696
题型:选择题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image089.png)
,若
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image090.png)
,使得
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image091.png)
成立,则实数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image092.png)
的取值范围为 ( )
题号:3799697
题型:选择题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image076.png)
的图象过点
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image077.png)
,若
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image078.png)
对
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image079.png)
恒成立,则
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image080.png)
的最小值为 ( )
题号:3799698
题型:选择题
难易度:较易
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】设实数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image062.png)
满足约束条件
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image063.png)
,则目标函数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image064.png)
的最大值为 ( )
题号:3799699
题型:选择题
难易度:较易
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】已知
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image053.png)
为第二象限角,
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image054.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image055.png)
的值为 ( )
题号:3799700
题型:选择题
难易度:较易
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
题号:3799701
题型:选择题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】已知双曲线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image025.png)
的一条渐近线的倾斜角为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image016.png)
,则双曲线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image026.png)
的离心率为( )
题号:3799702
题型:选择题
难易度:较易
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】设复数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image008.png)
,则复数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image009.png)
的摸为( )
题号:3799703
题型:选择题
难易度:较易
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】已知集合
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image001.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image002.png)
( )
题号:3799721
题型:选择题
难易度:较易
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】执行如图所示的程序框图,若输入
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image043.png)
,则输出
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image044.png)
( )
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image045.png)
题号:3799691
题型:填空题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】已知
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image139.png)
是函数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image140.png)
的极小值点,则实数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image141.png)
的取值范围是__________.
题号:3799692
题型:填空题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】若直线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image129.png)
都是正实数)与圆
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image130.png)
相交于
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image131.png)
两点,当
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image132.png)
是坐标点)时,
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image133.png)
的最大值为__________.
题号:3799693
题型:填空题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】在
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image119.png)
中,
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image120.png)
是角
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image121.png)
所对的边,
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image122.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image123.png)
__________.
题号:3799694
题型:填空题
难易度:较易
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】设
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image111.png)
是定义在
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image112.png)
上的奇函数,当
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image113.png)
时,
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image114.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image115.png)
__________.
题号:3799686
题型:解答题
难易度:较难
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image251.png)
.
(1)若
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image252.png)
,求曲线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image253.png)
在点
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image254.png)
处的切线方程;
(2)若
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image255.png)
对任意 在
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image256.png)
恒成立,求实数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image257.png)
的取值范围.
题号:3799687
题型:解答题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】在平面直角坐标系
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image212.png)
中,过椭圆
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image213.png)
右焦点
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image101.png)
的直线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image214.png)
交
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image026.png)
于
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image131.png)
两点 ,
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image215.png)
为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image216.png)
的中点,且
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image217.png)
的斜率为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image057.png)
.
(1)求椭圆
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image026.png)
的标准方程;
(2)设过点
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image101.png)
的直线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image218.png)
(不与坐标轴垂直)与椭圆交于
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image219.png)
两点,若在线段
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image220.png)
上存在点
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image221.png)
,
使得
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image222.png)
,求
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image223.png)
的取值范围.
题号:3799688
题型:解答题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】如图,四棱锥
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image173.png)
中,底面
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image174.png)
是矩形,平面
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image175.png)
平面
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image174.png)
,且
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image176.png)
是边长为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image013.png)
的等边三角形,
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image177.png)
,点
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image102.png)
是
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image178.png)
的中点.
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image179.png)
(1)求证:
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image180.png)
平面
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image181.png)
;
(2)求四面体
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image182.png)
的体积.
题号:3799689
题型:解答题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】某城市为了满足市民出行的需要和节能环保的要求,在公共场所提供单车共享服务,某部门为了对该城市共享单车进行监管,随机选取了
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image157.png)
位市民对共享单车的情况逬行问卷调査,并根根据其满意度评分值(滿分
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image158.png)
分)制作的茎叶图如图所示:
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image159.png)
(1)分别计算男性打分的平均数和女性打分的中位数;
(2)从打分在
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image160.png)
分以下(不含
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image160.png)
分)的市民抽取
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image161.png)
人,求有女性被抽中的概率.
题号:3799690
题型:解答题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】已知数列
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image032.png)
满足
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image144.png)
,且
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image145.png)
.
(1)求数列
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image032.png)
的通项公式;
(2)若
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image146.png)
,设数列
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image147.png)
的前
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image148.png)
项和
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image149.png)
,证明
![](http://static.zujuan.xkw.com/Upload/2017-06/16/8aa56368-d4d2-4b77-be5c-b63ca290f722/paper.files/image150.png)
.
题号:3799704
题型:解答题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】选修4-5:不等式选讲
已知函数
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image347.png)
.
(1)解不等式,
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image348.png)
;
(2)若
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image349.png)
,求证:
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image350.png)
.
题号:3799705
题型:解答题
难易度:一般
日期:2017-06-16
来源:【全国百强校】辽宁省庄河市高级中学2017届高三第四次模拟考试数学(文)试题
【题文】选修4-4:坐标系与参数方程
已知极坐标系的极点为平面直角坐标系
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image262.png)
的原点,极轴为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image246.png)
轴正半轴,两种坐标系中的长度单位相同,曲线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image138.png)
的参数方程为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image329.png)
为参数),直线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image268.png)
过点
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image330.png)
,且斜率为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image331.png)
,射线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image332.png)
的极坐标方程为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image333.png)
.
(1)求曲线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image138.png)
和直线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image268.png)
的极坐标方程;
(2)已知射线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image332.png)
与圆
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image138.png)
的交点为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image334.png)
,与直线
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image268.png)
的交点为
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image335.png)
,求线段
![](http://static.zujuan.xkw.com/Upload/2017-06/16/7599f234-cd34-4678-bf35-d8fb81b47a22/paper.files/image336.png)
的长.