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2018-2019学年吉林省长春外国语学校第二学期高一年级开学考试试卷与答案

2018-2019学年吉林省长春外国语学校第二学期高一年级开学考试试卷与答案
2018-2019学年吉林省长春外国语学校第二学期高一年级开学考试试卷与答案

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2018-2019学年吉林省长春外国语学校第二学期高一年级开学考试

数学试题

一、选择题:本题共12小题,每小题5分。在每小题给出的四个选项中,只有一项是符合题目要求的。

1.设U ={1,2,3,4,5},A ={1,2,3},B ={2,3,4},则下列结论中正确的是( ) A .A ?B B .A ∩B ={2} C .A ∪B ={1,2,3,4,5}

D .A ∩(?U B )=

{1}

2.函数)6

5

2cos(3π

-=x y 的最小正周期是( )

A .

52π B .

2

5π C .π2 D .π5

3.函数y =1

x +log 2(x +3)的定义域是( ) A .R

B .(-3,+∞)

C .(-∞,-3)

D .(-3,0)∪(0,+∞)

4.下列函数中,既是偶函数又在(0)+∞,上单调递增的是( )

A .2()f x x =-

B .()2x f x -=

C .()ln ||f x x =

D .()||f x x =-

5.设0.2

611log 7,,24a b c ??

=== ???

,则,,a b c 的大小关系是( )

A .a b c >>

B .b c a <<

C .b c a >>

D .a b c <<

6.当10<

A B C D

7.方程2x =2-x 的根所在区间是( )

A .(-1,0)

B .(2,3)

C .(1,2)

D .(0,1)

8.若函数()f x =ln ,0

91,x x x x -???

>+≤0,则3((1))(log 2)f f f +-的值是( )

A .2

B .3

C .5

D .7

9.定义在R 上的偶函数()f x 满足(1)()f x f x +=-,且当x ∈[1,0]-时()12x

f x ??

= ???,则

2(log 8)f 等于( )

A .3

B .18

C .2-

D .2

10.将函数sin()3y x π

=-的图象上所有点的横坐标伸长到原来的2倍(纵坐标不

变),再将所得的图象向左平移3

π

个单位,得到的图象对应的僻析式是( ) A .1

sin 2

y x =

B .1sin()22

y x π

=-

C .1sin()26y x π

=-

D .sin(2)6

y x π

=-

11.函数)32sin(2π

+=x y 的图象( )

A .关于原点对称

B .关于点(-

,0)对称

C .关于y 轴对称

D .关于直线x=

6

π

对称 12.函数sin(),2

y x x R π

=-∈是( )

A .[,]22

ππ

-

上是增函数 B .[0,]π上是减函数

C .[,0]π-上是减函数

D .[,]ππ-上是减函数

一、填空题(本题包括4个小题,每小题5分,共20分)

13.已知f (x )是定义在R 上的偶函数,且当x >0时,f (x )=2x -3,则f (-2)=______.

14.若指数函数f (x )与幂函数g (x )的图象相交于一点(2,4),则f (x )=___________,g (x )=__________. 15.已知31)2

sin(=

+

π

α,)(0.2

-πα∈,则αtan =________. 16.函数)3

2sin(3)(π

-=x x f 的图象为C ,

①图象C 关于直线x =11

12π对称; ②函数f (x )在区间]125.

12[π

π-

内是增函数;

③由y =3sin2x 的图象向右平移π

3个单位长度可以得到图象C , 其中正确命题的序号为_________________.

二、解答题(17题10分,其他题每题12分,共70分。解答时请写出必要的文字说明,方程式和重要的演算步骤)

17.已知集合}023|{2=+-=x x x A ,}0)1(|{2=-+-=a ax x x B ,

}02|{2=+-=mx x x C ;若A B A = ,C C A = ,求实数m a ,的值或取值范

围 .

18.已知方程)4cos(23-sin παπα-=)(,

)

sin()2

3sin(2)

2cos(5)sin(απαπ

απαπ+---+-的值.

19.已知函数f (x )=1-2

x .

(1)若g (x )=f (x )-a 为奇函数,求a 的值;

(2)试判断f (x )在(0,+∞)内的单调性,并用定义证明。 20.已知函数f (x )是定义在R 上的奇函数,当x >0时,f (x )=log 2x . (1)求f (x )的解析式; (2)解关于x 的不等式f (x )≤1

2.

21.已知函数y =A sin (ωx +φ)(A >0,ω>0,2

π

φ≤

)的图象过点)0,12

(

π

P ,图

象与P 点最近的一个最高点坐标为)

,(53π

. (1)求函数解析式;

(2)求函数的最小值,并写出相应的x 值的集合;

(3)当]2

,0[π

∈x 时,求函数的值域.

22.已知函数).(2sin 2cos )(22a g a x a x x f ,其最大值记为--+=

(1)求函数)(a g 解析式;

(2)判断函数)(a g 的奇偶性(给出结论即可);

(3)若方程.)(的取值范围数根,求实数有且只有两个不等的实b b a g =

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2018-2019学年吉林省长春外国语学校第二学期高一年级开学考试

数学试题参考答案

一、选择题:

13.1 14.2)(,2)(x x g x f x ==

15.22-

16.(1)(2)

三、解答题:

17.}3{)22,22(.32 -∈=b a 或

18.43-

19.

增函数)()2(,11=a

20.(1)???

??<--=>=)

0)((log )0(0)0(log )(22x x x x x x f

(2)]2,0[]2

2

,( --∞

21.(1))

6

2sin(5π-=x y

(2)最小值-5; (3)]5.25

[-

22.(1)??

?

??≥-+-<<---≤---=)1(22)11(1)1(22)(22a a a a a a a a g

(2)偶函数 (3)b<-1

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