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莱芜四中高一上学期期末必修一三四(6)

莱芜四中2014-2015年度期末考试模拟试题（6）

高一数学

2015.01

一、选择题（每题5分共50分）

1、若,0n m <<则下列结论正确的是（）

A 、n m

> B 、n m 5.05.0< C 、n m 22log log > D 、n m 5.05.0log log >

2、若函数23)23(++=+x f x

，则)3(f 的值是（）

A ．3

B ．6

C ．17

D ．32

3、先后抛掷两枚骰子，设出现的点数之和是12,11,10的概率依次是P 1，P 2，P 3，则( )

A ．P 1＝P 2

B ．P 3＝P 2

C ．P 1

D ．P 1

A 、x x f -=3)(

B 、x x x f 3)(2-=

C 、1

)(+-=x x f D 、x x f -=)( 5、下列各组角中，终边相同的角是（）

A ．π2

k 与 ()2k k Z ππ+

∈ B ．)(3k

3Z k k ∈±

πππ与

C ．ππ)14()12(±+k k 与 )(Z k ∈

D ．)(6

Z k k k ∈±

ππ

π与

6、如图，A 是圆上固定的一点，在圆上其他位置任取一点A ′，

连结AA ′，它是一条弦，它的长度大于或等于半径长度的概率为 ( )

A.12

B.23

C.32

D.12

7、已知集合}1,log |{2>==x x y y A ，}1,)2

(|{>==x y y B x

，则=B A （）

A 、}210|{<

B 、}10|{<

C 、 }12

=-+q x x 的解集为N ，且N M =}2{，

那么=+q p （）

A 、6

B 、7

C 、 8

D 、21

9、如果点)cos 2,cos (sin θθθP 位于第三象限，那么角θ所在的象限是（）

A 、第一象限

B 、第二象限

C 、第三象限

D 、第四象限 10、执行如图所示的程序框图，输出的s 值为 ( )．

A ．－3

B ．－12 C.1

3 D ．2

二、填空题（每题5分共25分）

11、()f x 的图像如右图，则()f x 的值域为

12、已知sin cos θθ-=

，则44sin cos θθ+= 13、将2本不同的数学书和1本语文书在书架上随机排成一行，则2本数学书相邻的概率为____ 14、若23

cos 4m m

α-=

-，且α为第二象限角，则m 的取值范围是．

15、设函数()113,1,,1,

x e x f x x x -?

=??≥?则使得()2f x ≤成立的x 的取值范围是_______

三、解答题（共75分）

16.（1）设{}{}

(),1,05,U U R A x x B x x C A B ==≥=<<求和()U A

C B .

（2）已知集合A ＝{x |1＜x ＜2}，B ＝{x |x ＜a }，若B A ?，求实数a 的取值范围.

、已知3

tan 2

απαπ=<<,求sin cos αα-的值.

19、袋中有5张卡片，其中红色红色卡片3张，标号分别为1、2、3；蓝色卡片两张，标号分别为1,2

（1）从以上5张卡片任取两张，求这两张卡片颜色不同且标号之和小于4的概率；

（2）现袋中再放入一张标号为0的绿色卡片，从这6张卡片中任取两张，求这两张卡片颜色不同且标号之和小于4的概率。

20、（本小题13分）扇形AOB 的周长为cm 8 （1）若这个扇形的面积为2

3cm ，求圆心角的大小；（2）求这个扇形的面积取得最大值时圆心角的大小和弦长AB

21、（本小题14分）已知函数)(12)(2

为实数a a x ax x f -+-= （1）若1=a ，作函数)(x f 的图象并写出单调区间；（2）当4

≤a 时，求)(x f 在区间]2,1[上的最小值；

（（（（（（21题答题纸上的图形：）））））

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Men start to change their focus from the workplace to other things after age 30, while women do not do so until eight years later. Both, however, care most about fashion at age 16. The research used anonymous(匿名的) data donated by thousands of Facebook users, recording the statuses, ‘likes’and ‘interests’they had posted on their profiles. It found the average woman talks about television most at 44, while men peak much younger, at age 31. Men are also most likely to see a film in a cinema at age 31, while women go out to see films most when they are only 19. Men are most interested in travel at 29, women at 27, while women talk most about food and drink at 35, and men at 38. And if you are middle aged, a safe topic for any audience is the weather, which is a key interest for many as they approach 60. Stephen Wolfram, the British scientist who carried out the research, says, “It’s almost shocking how much this tells us about the changes of people’s typical interests. “People talk less about video games as they get older, and more about politics.” 21. When do women love books best? A. At the age of 22. B. At the age of 50. C. At the age of 30. D. At the age of 15. 22. Men tend to ______ once they are 30.

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