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九年级英语测试答题卷

数学必修④学业水平测试题

一．选择题:本大题共8小题；每小题3分，共24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. ?

+45sin 15cos 15sin 45cos 的值等于( )

．

2 B ．21 C

．2

- D ．21-

2. 如图，在四边形ABCD 中AB BC OA ++等于( )

A ．?→?CD

B ．?→?O

C C ．?→

?DA D ．?→

?CO

3. 下列各式中，其值为

的是（） A ．2sin15cos15

B ．2

cos 15sin 15-

C ．2

2sin 151-

D ．2

sin 15cos 15+

4. 已知向量(1,0),(0,1)i j == ，则下列向量中与向量2i j +

垂直的向量是( )

A.2i j -

B.i j +

C.2i j -

D.i j -

5. 在下面给出的四个函数中，既是区间)2

,0(π

上的增函数，又是以π为周期的偶函数的是( )

A.x y 2cos =

B. x y 2sin =

C.|cos |x y =

D.|sin |x y =

6. 若=(2,1)，=(3,4)，则向量在向量方向上的投影为（） A. 52

B. 2

C.5

D.10

7. 在锐角△ABC 中，设.cos cos ,sin sin B A y B A x ?=?=则x , y 的大小关系为( ) A.y x ≤

B.y x >

C.y x <

D.y x ≥

8. 已知||2||0a b =≠ ,且关于x 的方程2

||0x a x a b ++?= 有实根,则a 与b 的夹角的取值范围

是( ) A.[0,

π] B.[,]3ππ C.2[,

]33ππ D.[,]6π

π 二.填空题:本大题共7个小题，每小题4分，共28分，将答案直接填写在题后的横线上. 9. 若)4,(m a =→

，且5||=→

a ，则m 的值是 .

10. 设扇形的半径长为8cm ，面积为2

4cm ，则扇形的圆心角的弧度数是 ,

11. 已知向量),3,1(=,则与向量平行的一个单位．．．．

向量是________． 12. 若角α的终边经过点(12)P -，，则tan 2α的值为 . 13. 设)(x f 是以4为周期的函数,且当]2,2[-∈x 时, x x f =)(,则

=)6.7(f .

14. 把函数sin ()y x x =∈R 的图象上所有的点向左平行移动3

个单位长度，再把所得图象上所有点的横坐标缩短到原来的1

2倍（纵坐标不变），得到的图象所表示的函数是____________.

15. 给出下列命题：

①第二象限角是钝角；

②若→

→b a ,是两个共线的单位向量，则→

→

=b a ； ③终边在y 轴上的角的集合是},2

2|{Z k k ∈-=

παα; ④不等式||||||||→

→

++≤++c b a c b a 恒成立.

其中真命题的序号是（写出所有正确命题的序号）

三.解答题:本大题共6小题，共48分.解答应写出文字说明、证明过程或演算步骤. 16．（本题满分7分）

已知函数)

sin()

6cos()(x x x f ++

ππ

（Ⅰ）求()f x 的定义域；

（Ⅱ）若角α在第一象限, 且3

cos 5

α=，求()f α．

17．（本题满分7分）

已知ABC △顶点的直角坐标分别为(34)A ，

，(00)B ，，(0)C c ，． (Ⅰ)若5c =，求sin A ∠的值； (Ⅱ)若A ∠是锐角，求c 的取值范围．

18. （本题满分7分）

如图，在同一平面内，向量→

a 与单位向量→

i 、→

j 的夹角分别为?30、?60，已知4||=→

a . (Ⅰ) 以→

i 和→j 为基底，表示→

a ； (Ⅱ) 若→

→

--=j i b 3，求证→

a 与→

b 共线.

19. （本题满分8分）

已知),2,0(,12

cos )

cos()2sin(2sin 3πθθθππ

θθ∈=?+-+

求θ的值.

20．(本小题满分9分)

如图,已知OPQ 是半径为1,圆心角为

的扇形,四边形ABCD 是其内接矩形,矩形的边BC 与扇形的弦PQ 平行,点E 、F 分别为BC 、AD 的中点,设θ=∠COE ,矩形ABCD 的面积为S .

（Ⅰ）求出矩形的面积S 与角θ的函数关系式;

（Ⅱ）当θ为何值时, 矩形ABCD 的面积S 有最大值,并求出这个最大值.

O Q

B C D E

21．(本小题满分10分)

如图，函数)sin(2?π+=x y (其中),2

0R x ∈≤≤π

?的图象与y 轴交于点（0，1）.

(Ⅰ)求出该函数的单调减区间；

(Ⅱ)设P 是图象上的最高点，M 、N 是图象与x 轴的交点，求

与的夹角的正弦值.

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