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开封高中16届高一文科下学期第二次月考试卷

开封高中16届高一文科下学期第二次月考试卷
开封高中16届高一文科下学期第二次月考试卷

开封高中2016届高一下期数学试题

一、选择题(每题5分)

1.若(2,1)a =,(3,4)b =,则向量a 在向量b 方向上的投影为( ) A .52 B .2 C .5 D .10 2.将十进制2010化为七进制数是 ( )

A .6600(7)

B .5661(7)

C .6660(7)

D .5601(7) 3、在△ABC 中,内角A,B,C 的对边分别是a,b,c ,若22

3a b bc -=,sin 23sin C B =,则A= ( ) A 0

30 B 0

60 C 0

120 D 0

150 4. 已知函数的部分图象,如图所示,其中,则的解析式为( ) A .)3

2sin(2π

-

=x y B. 2sin(2)3

y x π

=+

C. )621sin(2π-=x y

D. )6

21sin(2π

+=x y

5.若函数)6

(sin 2π

+

=x y 与函数sin 2cos 2y x a x =+的图像的对称轴相同,则实数a 的值为

( ) A .3 B.3- C.

3

3

D.33-

6、在ABC ?中,内角A ,B ,C 所对的边分别是c b a ,,,已知8b=5c ,C=2B ,则cosC=

(A )257 (B )257- (C )257± (D )25

24

7.如图BC 是单位圆A 的一条直径, F 是线段AB 上的点,且

FC BF 2

1

=,若DE 是圆A 中绕圆心A 运动的一条直径,则

FD FE ?的值是( )

A .34-

B .89

- C..14- D .91-

()sin(),f x A x x R ω?=+∈0,0,02

A π

ω?>><<()f x A

B

C

D

E

F

2

2-

o 6

π 12

11π

x

y

8.设向量(1,0),(0,1)i j ==,若向量a 满足|2|||5a i a j -+-=,则|2|j a +的取值范围

是( ) A .]3,22[ B. ]22,556[

C. ]4,5[

D.]3,5

5

6[ 二、填空题(每题5分)

1、设△ABC 的内角A ,B ,C 所对的边分别为a ,b ,c . 若()()a b c a b c ab +-++=,则角C = .

2、三个数115,161,805的最大公约数是

3、在△ABC 中,D 为边BC 上一点,BD=1

2

DC ,∠ADB=120°,AD=2,若△ADC 的面积为33-,则∠BAC=_______

4、设错误!未找到引用源。为锐角,若错误!未找到引用源。,则错误!未找到引用源。的值为 .

选择题答案填入答题框

1 2

3

4

5

6

7

8

填空题

1 2 3 4

三、解答题(第1题12分,第2,3 题每题14分)

1、在ABC ?中,角,,A B C 所对的边分别为,,a b c ,且满足25cos

25

A =, 3A

B A C

?=. (I )求ABC ?的面积; (II )若1c =,求a 的值.

2、设函数22()(sin cos )2cos (0)f x x x x ωωωω=++>的最小正周期为23

π

.(Ⅰ)求ω的值.(Ⅱ)若函数()y g x =的图像是由()y f x =的图像向右平移

2

π

个单位长度得到,求()y g x =的单调增区间.

3、设函数2()sin(

)2cos 1468

x x

f x ππ

π=--+.(Ⅰ)求()f x 的最小正周期.(Ⅱ)若函数()y g x =与()y f x =的图像关于直线1x =对称,求当4

[0,]3

x ∈时()y g x =的最大值.

参考答案选择题BDAADABD 填空题

1.2

3

π 2. 23 3.

1

3

π 4.

172

50

解答题

1.(1)2 (2)25

2.(1)

3

2

ω=(2)

5212

,()

123123

k k

k z

ππ

ππ

??

-+-+∈

??

??

3.(1)8 (2)

3 2

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