2021-2022年高三第二次月考(数学文)

2021年高三第二次月考（数学文）

2011年10月本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分．共150分，考试时间120分钟．

注意事项：

1．答题前，考生务必将自己的姓名、准考证号、考试科目用铅笔涂写在答题卡上． 2．选择题每小题选出答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案，不能答在试题上．

3．填空题的答案和解答题的解答过程直接写在答题卡Ⅱ上．

4．考试结束，监考人将本试题和答题卡一并收回．

第Ⅰ卷（选择题，共50分）

一、选择题：本大题共10小题，每题5分，共50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．集合，则（）

A．{1} B．{0} C．{0，1} D．{– 1，0，1}

2．，则（）

A．b > a > c B．a > b > c C．c > a > b D．b > c > a

3．若曲线的一条切线l与直线垂直，则l的方程为（）

A．B．C．D．

4．函数是（）

A．最小正周期是2的奇函数B．最小正周期是2的偶函数

C．最小正周期是的奇函数D．最小正周期是的偶函数

5．设等差数列{a n}的前n项和为S n，若，则S9等于（）

A．18 B．36 C．45 D．60

实用文档

6．已知向量

1

(11cos)(1cos)//

2

a b a b

θθ

=-=+

，，，，且，则锐角等于（）

A．30°B．45°C．60°D．75°

7．已知函数的图象上各点的横坐标伸长到原来的3倍，再向右平移个单位，得到的函数的一个对称中心是（）

A．B．C．D．

8．若，则（）

A．B．C．D．

9．已知a > 0，b > 0，a、b的等差中项是，且，则x + y的最小值是（）A．6 B．5 C．4 D．3

10．已知函数（b、c、d为常数），当时，只有一个实根，当时，有3个相异实根，现给出下列4个命题：

①函数有2个极值点；②函数有3个极值点；③有一个相同的实根；④有一个相同的实

根。

其中正确命题的个数是（）

A．1 B．2 C．3 D．4

第Ⅱ卷（非选择题，共100分）

二、填空题：本大题共5小题，每题5分，共25分．各题答案必须填写在答题卡II上（只填

结果，不要过程）

11．______________．

12．不等式的解集是________________．

13．在等比数列{a n}中，，则______________．

14．，则______________．

15．函数是定义在R上的奇函数，且满足对一切都成立，又当时，，则下列四个命题：

①函数是以4为周期的周期函数

②当时，

③函数的图象关于x = 1对称

④函数的图象关于点（2，0）对称

其中正确命题序号是_______________．

三、解答题：本题共6小题，共75分．各题解答必须答在答题卡II上（必须写出必要的文字

实用文档

说明、演算步骤或推理过程）．

16．(本小题满分13分)

求的值．

17．(本小题满分13分)

已知三点A（3，0），B（0，3），C，．

(1)若，求角；

(2)若，求的值．

18．(本小题满分12分)

设函数，已知是奇函数．

(1)求b、c的值；

(2)求的单调区间与极值．

19．(本小题满分13分)

已知，函数．

(1)求函数的最小正周期；

(2)求函数的单调减区间；

(3)当时，求函数的值域．

20．(本小题满分12分)

设a > 1，函数．

(1)求的反函数；

(2)若在[0，1]上的最大值与最小值互为相反数，求a的值；

(3)若的图象不经过第二象限，求a的取值范围．

21．(本小题满分12分)

实用文档

已知函数，数列，满足条件：

．

(1)求证：数列为等比数列；

(2)令，T n是数列的前n项和，求使成立的最小的n值．实用文档

实用文档

西南大学附属中学高xx 级第二次月考

数学试题参考答案（文）

一、选择题：本大题共10小题，每题5分，共50分．

1．A 2．B 3．A 4．D 5．C 6．B 7．D 8．C 9．B 10．C

二、填空题：本大题共5小题，每题5分，共25分．

11． 12．– 13．240 14． 15．①②③④

三、解答题：本题共6小题，共75分．

16．解：原式 ································································································································· 6分 ································································································································· 9分 ······························································································································· 11分 ······························································································································· 13分

17．解：(1) ∵ (cos 3sin )(cos sin 3)AC BC αααα=-=-，，， ················································· 2分

由得 ··························································································································· 4分 整理得

∴ ······························································································································ 6分 ∵ ∴ ············································································································ 7分

(2) ∵

∴ ······························································································································· 8分 即 ······························································································································· 9分 ∴

∴ ··························································································································· 10分

∴ 22sin sin 22sin (sin cos )52sin cos sin cos 1tan 9

cos ααααααααααα

++===-++ ························· 13分 18．解：(1) ∵ ································································································································1分

∴ 32()()'()(3)(2)g x f x f x x b x c b x c =-=+-+-- ··············································3分 ∵ 是奇函数 ∴ 恒成立

即 3232(3)(2)(3)(2)x b x c b x c x b x c b x c -+----=-----+

∴ ∴ ··················································································································7分

(2) ∵

∴

由

由

∴ 的递增区间为 ······································································································11分 的递减区间为

·····························································································································13分

19．解：

22sin cos 2cos sin 4cos x x x x x x =+++ ·················································2分

····································································································································5分 ····································································································································6分