江苏省徐州市2019-2020学年高二下学期数学期中考试试卷
一、单选题
5. 已知函数
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的图象如图所示,则其导函数
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的图象可能是( )
6. 已知函数
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,则
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( )
7. 若函数
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在区间
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上是单调减函数,则实数
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的取值范围是( )
8. 设
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是定义在R上的奇函数,
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,当
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时,有
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恒成立,则
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的解集为( )
二、多选题
9. 已知不等式
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对任意的
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恒成立,则满足条件的整数
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的可能值为( )
10. 已知函数
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,下列说法中正确的有( )
11. 若函数
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在
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上单调递减,则称
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为
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函数,下列函数中为
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函数的是( )
12. 设函数
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,
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,给定下列命题,其中是正确命题的是( )
三、填空题
13. 函数
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的单调递减区间为
.
14. 若函数
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在区间
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上不单调,则实数a的取值范围为
.
15. 已知函数
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,若函数
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有四个不同的零点,则
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的取值范围为
16. 已知函数
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,
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(
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),若曲线
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与曲线
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相交,且在交点处有相同的切线,则
,切线的方程为
(直线的方程写成一般式).
四、解答题
17. 已知复数
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,其中
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为虚数单位.若
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满足下列条件,求实数
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的值:
(1)
为实数;
(2)
为纯虚数;
(3)
在复平面内对应的点在直线
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上.
18. 已知函数
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.
(1)求函数
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的单调区间;
(2)求函数
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在
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上的最大值和最小值.
19. 已知函数
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(
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).
(2)讨论函数
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的单调性.
20. 如图,已知海岛
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与海岸公路
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的距离
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为
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,
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,
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间的距离为

,从
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到
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,需要先乘船至海岸公路
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上的登陆点
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,船速为
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,再乘汽车至
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,车速为
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.设
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.
(1)用
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表示从海岛
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到
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所用的时间

,并写出

的取值范围;
(2)登陆点
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应选在何处,能使从
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到
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所用的时间最少?
21. 已知函数
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(
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).
(1)若

在其定义域内单调递增,求实数

的取值范围;
(2)若
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,且

有两个极值点

,其中
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,求

的取值范围.
22. 已知函数
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,
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.
(2)若不等式
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在
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上恒成立,求实数

的取值范围.
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