-2018年上海市南模中学高三上十月月考上课讲义

-2018年上海市南模中学高三上十月月考上课讲义
-2018年上海市南模中学高三上十月月考上课讲义

2017-2018年上海市南模中学高三上十月

月考

2017学年南模中学高三年级十月份月考试卷

2017.10

一、填空题

1.

若α是第四象限角,则22απ-所在象限是第________象限 2. 已知集合2|,,{|40}32A x k x k k Z B x x ππππ??=+≤<+∈=-≥????

,则A B =____________.

3. 函数3cos 3cos x y x

-=+的值域为____________. 4.

已知tan 2α=,则2sin cos αα=____________. 5. 函数12

()log cos 34x f x π??=+ ???的单调递增区间为____________. 6.

若()21(0)f x x ωω=+>在区间3,22ππ??-????上为增函数,则ω的最大值是____________.

7. 有一个解三角形的题因纸张破损有一个条件不清,具体如下“在ABC 中,角,,A B C 所对的边分别为,,a b c

,已知4a B π==

,__________. 求角A ”。经推断破损处的条件为三角形的一边的长度,且答案提示3A π=

,试将条件补充完整 8. 函数2max min 2(1)sin (),(),()1

x x f x f x M f x m x ++===+,则M m +=____________. 9.

已知函数1()sin 2cos 2122f x x x =-+,若2()log f x t ≥对x R ∈恒成立,则t 的取值范围为____________.

10. 设12,R αα∈,且121122sin 2sin(2)

αα+=++,则12|10|παα--的最小值等于____________.

11. 设,,[0,2)a b R c π∈∈,若对任意实数x 都有2sin 3sin()3x a bx c π??-=+ ??

?,则满足条件的有序实数组(,,)a b c 的组数为____________.

12. 关于x 的方程11|sin ||1|12

x x π=--在[2016,2016]-上解的个数是____________. 二、选择题

13.

在ABC 中,222sin sin sin sin sin A B C B C ≤+-,则角A 的取值范围是( ) A. (0,]6π B. [,)6ππ C. (0,]3π D.

[,)3π

π

14. 把(cos 2sin 2)2y x x =-的图像作适当的移动得sin 2y x =的图像,这样的移动可以是( )

A. 向右平移38

π个单位 B. 向左平移38π个单位 C. 向右平移34π个单位 D. 向左平移

34π个单位 15. 将函数1y x

=-的图像按向量(1,0)a =平移,得到的函数图像与函数2sin (24)y x x π=-≤≤的图像的所有交点的横坐标之和等于( )

A. 2

B. 4

C. 6

D. 8 16.

存在函数()f x 满足:对任意x R ∈都有( )

A. (sin 2)sin f x x =

B. 2(sin 2)f x x x =+

C. 2(1)|1|f x x +=+

D. 2(2)|1|f x x x +=+

三、解答题

17. 已知函数221()cos sin ,(0,)2

f x x x x π=-+∈ (1)求()f x 的单调递增区间;

(2)设ABC 为锐角三角形,角A 所对边a =,角B 所对边5b =,若()0f A =,求ABC 的面积

18. 设函数2()cos 2sin 24f x x x π??=++ ??

? (1)求函数()f x 的最小正周期;

(2)设函数()g x 对任意x R ∈,有()2g x g x π??+= ???,且当0,2x π??∈????时,1()()2g x f x =-,求函数()g x 在[,0]π-上的解析式

19. 如图所示,湖面上甲、乙、丙三艘船沿着同一条直线航行,某一时刻,甲船在最前面的A 点处,乙船在中间的B 点处,丙船在最后的C 点处,且:3:1BC AB =,一架无人机在空中的P 点处对它们进行数据测量,在同一时刻测得30,90APB BPC ∠=?∠=?(船只与无人机的大小及其他因素忽略不计)

(1)求此时无人机到甲、丙两船的距离之比;

(2)若此时甲、乙两船相距100米,求无人机到丙船的距离(精确到1米)

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