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试卷年份:{{getYear('高三|高考模拟|河北|2017年')}}上传日期:2017-06-01题数:23
提示:单击题文可显示答案与解析。
题号:3722436
题型:选择题
难易度:困难
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】已知偶函数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image120.png)
满足
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image121.png)
,且当
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image122.png)
时,
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image123.png)
,关于
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image072.png)
的不等式
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image124.png)
在
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image125.png)
上有且只有200个整数解,则实数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image020.png)
的取值范围是( )
题号:3722437
题型:选择题
难易度:较难
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】已知向量
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image104.png)
满足
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image105.png)
,若
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image106.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image107.png)
的最大值和最小值分别为
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image108.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image109.png)
等于( )
题号:3722438
题型:选择题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】数列
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image025.png)
为非常数列,满足:
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image088.png)
,且
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image089.png)
对任何的正整数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image074.png)
都成立,则
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image090.png)
的值为( )
题号:3722439
题型:选择题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image080.png)
的展开式中各项系数的和为16,则展开式中
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image081.png)
项的系数为( )
A.![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image082.png) | B.![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image083.png) | C.57 | D.33 |
题号:3722440
题型:选择题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】数列
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image025.png)
为正项等比数列,若
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image026.png)
,且
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image027.png)
,则此数列的前5项和
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image028.png)
等于 ( )
题号:3722441
题型:选择题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
题号:3722455
题型:选择题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】20世纪30年代,德国数学家洛萨---科拉茨提出猜想:任给一个正整数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image083.png)
,如果
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image083.png)
是偶数,就将它减半;如果
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image083.png)
是奇数,则将它乘3加1,不断重复这样的运算,经过有限步后,一定可以得到1,这就是著名的“
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image084.png)
”猜想.如图是验证“
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image084.png)
”猜想的一个程序框图,若输出
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image085.png)
的值为8,则输入正整数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image086.png)
的所有可能值的个数为( )
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image087.png)
题号:3722457
题型:选择题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】已知二次函数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image061.png)
的两个零点分别在区间
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image062.png)
和
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image063.png)
内,则
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image064.png)
的取值范围是 ( )
题号:3722458
题型:选择题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】在
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image057.png)
中,“
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image058.png)
”是“
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image059.png)
”的( )
A.充分不必要条件 | B.必要不充分条件 | C.充要条件 | D.既不充分也不必要条件 |
题号:3722459
题型:选择题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】已知
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image045.png)
、
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image046.png)
分别是双曲线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image047.png)
的左、右焦点,以线段
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image048.png)
为边作正三角形
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image049.png)
,如果线段
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image050.png)
的中点在双曲线的渐近线上,则该双曲线的离心率
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image051.png)
等于( )
题号:3722463
题型:选择题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】已知集合
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image008.png)
,则集合
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image009.png)
等于( )
题号:4817994
题型:选择题
难易度:一般
日期:2017-08-14
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】如图,一个简单几何体的正视图和侧视图都是边长为2的等边三角形,若该简单几何体的体积是
![](http://static.zujuan.xkw.com/Upload/2017-08/14/7a7149ad-8915-4d83-afe2-b8db2c8159e6/paper.files/image055.png)
,则其底面周长为( )
![](http://static.zujuan.xkw.com/Upload/2017-08/14/7a7149ad-8915-4d83-afe2-b8db2c8159e6/paper.files/image056.png)
题号:3722435
题型:填空题
难易度:较难
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】已知两平行平面
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image158.png)
间的距离为
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image041.png)
,点
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image159.png)
,点
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image160.png)
,且
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image161.png)
,若异面直线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image162.png)
与
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image163.png)
所成角为60°,则四面体
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image164.png)
的体积为__________.
题号:3722449
题型:填空题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】已知
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image179.png)
是过抛物线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image180.png)
焦点
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image181.png)
的直线与抛物线的交点,
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image182.png)
是坐标原点,且满足
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image183.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image184.png)
的值为__________.
题号:3722451
题型:填空题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】将函数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image148.png)
的图象向右平移
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image086.png)
个单位(
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image149.png)
),若所得图象对应的函数为偶函数,则
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image086.png)
的最小值是__________.
题号:3722452
题型:填空题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】为稳定当前物价,某市物价部门对本市的5家商场的某商品的一天销售量及其价格进行调查,5家商场商品的售价
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image083.png)
元和销售量
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image142.png)
件之间的一组数据如下表所示:
价格![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image083.png)
| 8.5
| 9
| 9.5
| 10
| 10.5
|
销售量![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image142.png)
| 12
| 11
| 9
| 7
| 6
|
由散点图可知,销售量
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image142.png)
与价格
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image083.png)
之间有较好的线性相关关系,其线性回归方程是
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image143.png)
,则
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image144.png)
__________.
题号:3722431
题型:解答题
难易度:困难
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】已知函数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image319.png)
,其中
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image040.png)
为自然对数的底数.(参考数据:
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image320.png)
)
(1)讨论函数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image120.png)
的单调性;
(2)若
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image321.png)
时,函数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image322.png)
有三个零点,分别记为
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image323.png)
,证明:
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image324.png)
.
题号:3722432
题型:解答题
难易度:较难
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】如图,小华和小明两个小伙伴在一起做游戏,他们通过划拳(剪刀、石头、布)比赛决胜谁首先登上第3个台阶,他们规定从平地开始,每次划拳赢的一方登上一级台阶,输的一方原地不动,平局时两个人都上一级台阶,如果一方连续两次赢,那么他将额外获得一次上一级台阶的奖励,除非已经登上第3个台阶,当有任何一方登上第3个台阶时,游戏结束,记此时两个小伙伴划拳的次数为
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image259.png)
.
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image260.png)
(1)求游戏结束时小华在第2个台阶的概率;
(2)求
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image259.png)
的分布列和数学期望.
题号:3722433
题型:解答题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】如图,已知圆锥
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image207.png)
和圆柱
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image208.png)
的组合体(它们的底面重合),圆锥的底面圆
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image209.png)
半径为
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image210.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image211.png)
为圆锥的母线,
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image162.png)
为圆柱
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image208.png)
的母线,
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image212.png)
为下底面圆
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image213.png)
上的两点,且
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image214.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image215.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image216.png)
.
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image217.png)
(1)求证:平面
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image218.png)
平面
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image219.png)
;
(2)求二面角
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image220.png)
的正弦值.
题号:3722434
题型:解答题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】如图,已知
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image046.png)
关于
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image184.png)
边的对称图形为
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image185.png)
,延长
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image186.png)
边交
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image187.png)
于点
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image188.png)
,且
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image189.png)
,
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image190.png)
.
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image191.png)
(1)求
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image186.png)
边的长;
(2)求
![](http://static.zujuan.xkw.com/Upload/2017-06/01/f60e2d9b-2298-4261-b4c3-fd0bc0e92202/paper.files/image192.png)
的值.
题号:3722442
题型:解答题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】选修4-5:不等式选讲
已知实数
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image374.png)
满足
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image375.png)
.
(1)求
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image376.png)
的取值范围;
(2)若
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image377.png)
,求证:
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image378.png)
.
题号:3722443
题型:解答题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(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/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image343.png)
中直线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image344.png)
的倾斜角为
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image345.png)
,且经过点
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image346.png)
,以坐标系
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image343.png)
的原点为极点,
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image083.png)
轴的非负半轴为极轴,建立极坐标系
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image347.png)
,曲线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image240.png)
的极坐标方程为
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image348.png)
,直线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image344.png)
与曲线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image240.png)
相交于
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image179.png)
两点,过点
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image271.png)
的直线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image349.png)
与曲线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image240.png)
相交于
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image350.png)
两点,且
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image351.png)
.
(1)平面直角坐标系中,求直线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image344.png)
的一般方程和曲线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image240.png)
的标准方程;
(2)求证:
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image352.png)
为定值.
题号:3722445
题型:解答题
难易度:一般
日期:2017-06-01
来源:【全国百强校】河北省衡水中学2017届高三下学期第三次摸底考试数学(理)试题
【题文】如图,已知
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image268.png)
为椭圆
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image269.png)
上的点,且
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image270.png)
,过点
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image271.png)
的动直线与圆
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image272.png)
相交于
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image179.png)
两点,过点
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image271.png)
作直线
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image184.png)
的垂线与椭圆
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image240.png)
相交于点
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image273.png)
.
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image274.png)
(1)求椭圆
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image240.png)
的离心率;
(2)若
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image275.png)
,求
![](http://static.zujuan.xkw.com/Upload/2017-06/01/584b1d01-9c8d-446b-9170-ca4563d5c124/paper.files/image276.png)
.