重庆市第三十中学2020-2021学年高一数学10月月考试题(无答案)

重庆市第三十中学2020-2021学年高一数学10月月考试题（无答案）

考试时间：150分；考试时间：120分钟

第I 卷（选择题 共60分）

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

每小题5分，共60分） 1. 满足{1}{1,2,3}A ??的集合A 的个数为( ) A.1

B.2

C.3

D.4

2. 已知集合{}{}2R |13,R |4P x x Q x x =

∈≤≤=∈≥,则R ()P

Q = ( )

A. [2,3]

B.

(]2,3- C. ()1,2 D. (][),21,-∞-+∞

3．下列四组函数中,表示相同函数的一组是( )

A. ()21

,()11

x g x x f x x -==+- B. ()()2

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

C. ()2,()x g x f x x ==

D. ()21,()1x x a g f x x x =+?-=-

4. 已知函数()1

,22(3),2

x x x f x f x x +?>?

=-??+≤?,则(2)f 的值等于( )

A. 4

B. 3

C. 2

D.无意义

5. 已知函数()f x 的定义域为()1,0-,则函数()21f x +的定义域为( ) A. ()1,1- B. 11,2??--

??? C. ()1,0- D. 1,12?? ???

6. 小明和小华进行自行车比赛(比赛过程中，两人均匀速行驶），刚开始小华领先，但关键时刻自行车掉了链子，小明赶超小华，小华修好车后，奋起直追，但为时已晚，小明还是先到了终点.如果用12,s s 分别表示小明和小华所行走的路程，t 表示时间，则下图中与该事件符合的是( )

A

. B.

C. D.

7．下列函数中，既是偶函数又在区间()0,+∞上单调递增的为( ) A.1y x

=

B.1y x =+

C.1y x =+

D.2

1y x =-+ 8. .设偶函数()f x 在()0,+∞上是增函数，且()20f =，则不等式()()

0f x f x x

+-<的解

集为( ) A.()

()2,02,-+∞ B.()(),20,2-∞- C.()(),22,-∞-+∞ D.()()2,00,2-

9．下列各式中成立的是( )

A. 7

1

7

7n n m m ??= ???

B. ()4

31233-=-

C. ()33

3

4

4

x y x y +=+

D.

3

393=

10．函数①x y a =;②x y b =;③x

y c =;④x

y d =的图像如图所示, ,,,a b c d 分别是下列四个数:

514

,3,,4311

中的一个,则,,,a b c d 的值分别是( )

A. 5143,,43115413,,,4113 C. 415

,3,1134

D. 145,,33114

11．已知()f x 是定义在R 上的奇函数,当0x <时, ()2

f x x x =-,则当0x >时, ()f x =

( )

A. 2x x -

B. 2x x --

C. 2x x -+

D. 2x x +

12. 45.在下列图像中,二次函数2

y ax bx =+及指数函数x

b y a ??

= ???

的图像只可能是( )

A.

B. C. D.

第Ⅱ卷（非选择题 共90分）

二、填空题（本大题共4小题，每小题5分，共20分，把答案填写在答题卡中的横线上。）

13. 函数的定义域为 .(用区间表示)

14. .若函数()()()2

212f x m x m x =-+-+是偶函数，则()f x 的单调递增区间

是 . 15．函数2y x x =+

-的值域为 .

16. 设01a <<则关于x 的不等式22

232

223

x x x

x a a -++->的解集为________.

三、解答题（本大题共6小题，共70分．解答应写出文字说明、证明过程或演算步骤。）

17．（本题满分12分）已知函数()35,05,0128,1x x f x x x x x +≤??

=+<≤??-+>?

（1）.求()31,,12πf f f ????

- ? ?????

的值;

（2）.画出这个函数的图像

（3）.求()f x 的最大值。

18．（本题满分10分）已知函数()m

f x x x

=+

，且此函数的图像过点()1,5. （1）.求实数m 的值；（2）.判断并证明()f x 的奇偶性。

19. （本题满分12分）某公司计划投资,A B 两种金融产品,根据市场调查与预测A 产品的利润()f x 与投资量x 成正比, ()f x 与x 的关系如图1所示, B 产品的利润()g x 与投资量x 的算术平方根成正比, ()g x 与x 的关系如图2所示(注:利润与投资量的单位均为万元)。

（1）.求()f x 和()g x 的解析式。

（2）.已知该公司有10万元资金,并全部投入,A B 两种产品中,问:怎样分配这10万元资金,才能使公司获得最大利润?最大利润为多少万元?

20．（本题满分12分）求函数223

3x x y -++=的定义域、值域和单调区间

21．（本题满分12分）

设,

,如果

,求实数的取值范围。

22. （本题满分12分）已知函数()f x 的定义域是R ，对任意实数,x y ，均有

()()()f x y f x f y +=+，且当0x >时，()0f x >.

（1）.证明()f x 在R 上是增函数。

（2）.若()12f -=-，求不等式()

244f a a +-<的解集。

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