适用年级:{{getGradeNameByProperty('高三|高考模拟|河北|2017年')}} 试卷类型:{{getTestPaperTypeName('高三|高考模拟|河北|2017年')}} 使用省份:{{getAreaName('高三|高考模拟|河北|2017年')}}
试卷年份:{{getYear('高三|高考模拟|河北|2017年')}}上传日期:2017-04-13题数:23
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题号:3533351
题型:选择题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image159.png)
,若关于
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image040.png)
的方程
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image160.png)
,恰好有4个不相等的实数根,则实数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image161.png)
的取值范围为( )
题号:3533352
题型:选择题
难易度:较难
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】某计算器有两个数据输入口
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image109.png)
,一个数据输出口
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image110.png)
,当
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image109.png)
分别输入正整数1时,输出口
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image110.png)
输出2,当
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image111.png)
输入正整数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image112.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image113.png)
输入正整数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image114.png)
时,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image110.png)
的输出是
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image087.png)
;当
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image111.png)
输入正整数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image112.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image113.png)
输入正整数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image115.png)
时,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image110.png)
的输出是
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image116.png)
;当
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image111.png)
输入正整数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image117.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image113.png)
输入正整数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image114.png)
时,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image110.png)
的输出是
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image118.png)
;当
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image111.png)
输入60,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image113.png)
输入50时,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image110.png)
的输出是( )
题号:3533353
题型:选择题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知点
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image019.png)
在角
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image020.png)
终边的延长线上,且
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image021.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image019.png)
的坐标为( )
题号:3533354
题型:选择题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
题号:3533355
题型:选择题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
题号:3534928
题型:选择题
难易度:较难
日期:2017-04-03
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知直线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image001.png)
与双曲线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image002.png)
交于
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image003.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image004.png)
两点,且
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image005.png)
中点
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image006.png)
的横坐标为
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image007.png)
,过
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image006.png)
且与直线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image001.png)
垂直的直线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image008.png)
过双曲线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/ec3e090b-efc4-4ca2-9f49-de94c6b04f94/paper.files/image009.png)
的右焦点,则双曲线的离心率为( )
题号:3534930
题型:选择题
难易度:较难
日期:2017-04-03
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】如图所示,网络纸上每个小格都是边长为1的正方形,粗线画出的是一个几何体的三视图,则该几何体的表面积为( )
![](http://static.zujuan.xkw.com/Upload/2017-04/03/66c55517-2a5f-4e7b-8820-cb12863b0bb0/paper.files/image001.png)
题号:3534932
题型:选择题
难易度:一般
日期:2017-04-03
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2017-04/03/c1337745-e727-447c-b550-bef16accf317/paper.files/image001.png)
,若
![](http://static.zujuan.xkw.com/Upload/2017-04/03/c1337745-e727-447c-b550-bef16accf317/paper.files/image002.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/03/c1337745-e727-447c-b550-bef16accf317/paper.files/image003.png)
都是从
![](http://static.zujuan.xkw.com/Upload/2017-04/03/c1337745-e727-447c-b550-bef16accf317/paper.files/image004.png)
任取的一个数,则满足
![](http://static.zujuan.xkw.com/Upload/2017-04/03/c1337745-e727-447c-b550-bef16accf317/paper.files/image005.png)
时的概率( )
题号:3534933
题型:选择题
难易度:较难
日期:2017-04-03
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】函数
![](http://static.zujuan.xkw.com/Upload/2017-04/03/561ed1c8-8173-4784-a60b-bc800e25b22e/paper.files/image001.png)
图象上的某点
![](http://static.zujuan.xkw.com/Upload/2017-04/03/561ed1c8-8173-4784-a60b-bc800e25b22e/paper.files/image002.png)
可以由函数
![](http://static.zujuan.xkw.com/Upload/2017-04/03/561ed1c8-8173-4784-a60b-bc800e25b22e/paper.files/image003.png)
上的某点
![](http://static.zujuan.xkw.com/Upload/2017-04/03/561ed1c8-8173-4784-a60b-bc800e25b22e/paper.files/image004.png)
向左平移
![](http://static.zujuan.xkw.com/Upload/2017-04/03/561ed1c8-8173-4784-a60b-bc800e25b22e/paper.files/image005.png)
个单位长度得到,则
![](http://static.zujuan.xkw.com/Upload/2017-04/03/561ed1c8-8173-4784-a60b-bc800e25b22e/paper.files/image006.png)
的最小值为( )
题号:3534934
题型:选择题
难易度:一般
日期:2017-04-03
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】在《九章算术》中有一个古典名题“两鼠穿墙”问题:今有垣厚五尺,两鼠对穿.大鼠日一尺,小鼠也日一尺.大鼠日自倍,小鼠日自半,问何日相逢?大意是有厚墙五尺,两只老鼠从墙的两边分别打洞穿墙.大老鼠第一天进一尺,以后每天加倍;小老鼠第一天也进一尺,以后每天减半.问几天后两鼠相遇?( )
题号:3534935
题型:选择题
难易度:一般
日期:2017-04-03
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】根据如图的程序框图,当输入
![](http://static.zujuan.xkw.com/Upload/2017-04/03/5bdd40f0-a2cc-470c-a42a-014c1ce24078/paper.files/image001.png)
为2017时,输出的
![](http://static.zujuan.xkw.com/Upload/2017-04/03/5bdd40f0-a2cc-470c-a42a-014c1ce24078/paper.files/image002.png)
为28,则判断框中的条件可以是( )
![](http://static.zujuan.xkw.com/Upload/2017-04/03/5bdd40f0-a2cc-470c-a42a-014c1ce24078/paper.files/image003.png)
题号:3534936
题型:选择题
难易度:一般
日期:2017-04-03
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】若
![](http://static.zujuan.xkw.com/Upload/2017-04/03/627430dc-562d-4e89-b8d1-db37233a27e2/paper.files/image001.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/03/627430dc-562d-4e89-b8d1-db37233a27e2/paper.files/image002.png)
,则( )
题号:3533348
题型:填空题
难易度:较难
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image096.png)
中,角
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image147.png)
为直角,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image205.png)
是边
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image206.png)
上一点,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image019.png)
是
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image207.png)
上一点,且
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image208.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image209.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image210.png)
__________.
题号:3533349
题型:填空题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
题号:3533350
题型:填空题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知二项式
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image184.png)
展开式中,则
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image185.png)
项的系数为__________.
题号:3534924
题型:填空题
难易度:一般
日期:2017-04-03
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2017-04/03/6c24dd1d-4240-4389-95f8-8cb2ccc80897/paper.files/image001.png)
,无论
![](http://static.zujuan.xkw.com/Upload/2017-04/03/6c24dd1d-4240-4389-95f8-8cb2ccc80897/paper.files/image002.png)
取何值,函数
![](http://static.zujuan.xkw.com/Upload/2017-04/03/6c24dd1d-4240-4389-95f8-8cb2ccc80897/paper.files/image003.png)
在区间
![](http://static.zujuan.xkw.com/Upload/2017-04/03/6c24dd1d-4240-4389-95f8-8cb2ccc80897/paper.files/image004.png)
总是不单调.则
![](http://static.zujuan.xkw.com/Upload/2017-04/03/6c24dd1d-4240-4389-95f8-8cb2ccc80897/paper.files/image005.png)
的取值范围是__________.
题号:3533343
题型:解答题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image391.png)
在
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image392.png)
处的切线与直线
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image393.png)
垂直.
(1)求函数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image394.png)
(
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image395.png)
为
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image199.png)
的导函数)的单调递增区间;
(2)记函数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image396.png)
,设
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image397.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image398.png)
是函数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image399.png)
的两个极值点,若
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image400.png)
,且
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image401.png)
恒成立,求实数
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image402.png)
的最大值.
题号:3533344
题型:解答题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知椭圆
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image345.png)
的离心率为
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image346.png)
,短轴长为
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image347.png)
,右焦点为
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image348.png)
.
(1)求椭圆
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image147.png)
的标准方程;
(2)若直线
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image349.png)
过点
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image350.png)
且与椭圆
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image147.png)
有且仅有一个公共点
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image253.png)
,过
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image253.png)
点作直线
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image351.png)
交椭圆与另一点
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image077.png)
.
①证明:当直线
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image352.png)
与直线
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image246.png)
的斜率
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image353.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image354.png)
均存在时,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image355.png)
为定值;
②求
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image356.png)
面积的最小值.
题号:3533345
题型:解答题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】某中学高二年级开设五门大学先修课程,其中属于数学学科的有两门,分别是线性代数和微积分,其余三门分别为大学物理,商务英语以及文学写作,年级要求每名学生只能选修其中一科,该校高二年级600名学生各科选课人数统计如下表:
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image310.png)
其中选修数学学科的人数所占频率为0.6,为了了解学生成绩与选课情况之间的关系,用分层抽样的方法从这600名学生中抽取10人进行分析.
(1)从选出的10名学生中随机抽取3人,求这3人中至少2人选修线性代数的概率;
(2)从选出的10名学生中随机抽取3人,记
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image040.png)
为选择线性代数人数与选择微积分人数差的绝对值,求随机变量
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image040.png)
的分布列和数学期望.
题号:3533346
题型:解答题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image245.png)
中,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image143.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image144.png)
分别为边
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image246.png)
上的两个三等分点,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image247.png)
为底边
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image246.png)
上的高,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image248.png)
,如图1.将
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image249.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image250.png)
分别沿
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image251.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image252.png)
折起,使得
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image253.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image077.png)
重合于点
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image147.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image145.png)
中点为
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image019.png)
,如图2.
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image254.png)
(1)求证:
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image255.png)
;
(2)若直线
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image256.png)
与平面
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image257.png)
所成角的正切值为2,求二面角
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image258.png)
的大小.
题号:3533347
题型:解答题
难易度:一般
日期:2017-04-13
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】已知数列
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image225.png)
前
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image087.png)
项和为
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image226.png)
,且满足
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image227.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image228.png)
.
(1)求数列
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image225.png)
的通项公式;
(2)令
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image229.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image230.png)
为
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image231.png)
的前
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image087.png)
项和,求证:
![](http://static.zujuan.xkw.com/Upload/2017-04/13/8ff91214-f18c-4173-96c4-86afd7cf557f/paper.files/image232.png)
.
题号:3534917
题型:解答题
难易度:一般
日期:2017-04-03
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】选修4-5:不等式选讲
已知函数
![](http://static.zujuan.xkw.com/Upload/2017-04/03/3337b045-333d-4f68-9777-5cd2f6688066/paper.files/image001.png)
.
(1)当
![](http://static.zujuan.xkw.com/Upload/2017-04/03/3337b045-333d-4f68-9777-5cd2f6688066/paper.files/image002.png)
时,求不等式
![](http://static.zujuan.xkw.com/Upload/2017-04/03/3337b045-333d-4f68-9777-5cd2f6688066/paper.files/image003.png)
的解集;
(2)设函数
![](http://static.zujuan.xkw.com/Upload/2017-04/03/3337b045-333d-4f68-9777-5cd2f6688066/paper.files/image004.png)
.当
![](http://static.zujuan.xkw.com/Upload/2017-04/03/3337b045-333d-4f68-9777-5cd2f6688066/paper.files/image005.png)
时,
![](http://static.zujuan.xkw.com/Upload/2017-04/03/3337b045-333d-4f68-9777-5cd2f6688066/paper.files/image006.png)
,求
![](http://static.zujuan.xkw.com/Upload/2017-04/03/3337b045-333d-4f68-9777-5cd2f6688066/paper.files/image007.png)
的取值范围.
题号:3534918
题型:解答题
难易度:一般
日期:2017-04-03
来源:【全国百强校word】河北省石家庄市第二中学2017届高三下学期模拟联考数学(理)试题
【题文】选修4-4:坐标系与参数方程
在平面直角坐标系
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image001.png)
中,曲线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image002.png)
和
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image003.png)
的参数方程分别是
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image004.png)
(
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image005.png)
是参数)和
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image006.png)
(
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image007.png)
为参数).以原点
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image008.png)
为极点,
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image009.png)
轴的正半轴为极轴建立极坐标系.
(1)求曲线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image002.png)
的普通方程和曲线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image003.png)
的极坐标方程;
(2)射线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image010.png)
与曲线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image002.png)
的交点为
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image008.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image011.png)
,与曲线
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image003.png)
的交点为
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image008.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image012.png)
,求
![](http://static.zujuan.xkw.com/Upload/2017-04/03/85a872fe-0627-4d11-8e68-7644b8d637b5/paper.files/image013.png)
的最大值.