上海中学高三周测卷(一)

上海中学高三数学周练卷（一）

一. 填空题

1. 已知集合{1,3,21}A m =--，集合2{3,}B m =，若B A ?，则实数m =

2.

函数()f x =

3. 已知函数2log ,0()2,

0x x x f x x >?=?≤?，若1()2f a =，则a = 4. 若全集U R =，集合{|1}{|0}A x x x x =≥≤U ，则U C A =

5. 2{|10}A x ax x =++=是单元素集合，则a =

6. 全集U 的子集A 、B 、C 的关系如图所示，其中三个圆

分别表示集合A 、B 、C ，试用集合A 、B 、C 的运算结

果表述图中的阴影所代表的集合

7. 已知实数x 、y 、z 满足x y z xyz ++=，则以下命题中为真命题的是

（1）x 、y 、z 中若有两个互为相反数，则第三个数必为0；（2）x 、y 、z 中若有一个

为0，则另外两个必互为相反数；（3）1

x y z xy +=-； 8. 已知集合2{|280}A x x x =--<，22{|}B x x a =<（其中a 为正的常数），I R =，若 A B =?I ，则a 的取值范围是

9. 已知全集{(,)|,}U x y x y R =∈，若3{(,)|

1}2

y A x y x -==-，{(,)|1}B x y y x ==+， 则U B C A =I 10. 对实数a 、b ，定义运算“*”：22,,a ab a b a b b ab a b

?-≤?*=?->??，设()(21)(1)f x x x =-*-， 且关于x 的方程()f x m =恰有三个互不相等的实数根，则m 的取值范围为

11.

集合{(,)|1A x y y ==，{(,)|}B x y y x m ==+，若A B I 为单元素集，则 m 的取值范围为

12. 设{1,2,,1995}M =???，A 是M 的子集，且满足条件当x A ∈时，15x A ?，则A 中元 素个数最多是

二. 选择题

13. 设1x 、2x 都是实数，“13x >且23x >”是“126x x +>且129x x >”的（ ）

A. 充分不必要条件

B. 必要不充分条件

C. 充分必要条件

D. 既不充分也不必要条件

14. 若空间中有四个点，则“这四个点中有三点在同一直线上”是“这四个点在同一平面上” 的（ ）

A. 充分不必要条件

B. 必要不充分条件

C. 充分必要条件

D. 既不充分也不必要条件

15. 满足,{1,0,1,2}a b ∈-，且关于x 的方程220ax x b ++=有实数解的有序数对(,)a b 的 个数为（ ）

A. 14

B. 13

C. 12

D. 10

16. 旅游车上乘坐着日本、美国、法国三个国家的旅客，现知道日本游客有18人，法国游 客有9人；成年男游客中美国5人，法国3人；成年女游客中，法国3人，日本5人；男孩 中日本3人，美国2人；女孩中美国2人，法国1人；还知道成年女游客比成年男游客少2 人，而男孩和女孩一样多，则美国游客有（ ）人

A. 14

B. 13

C. 12

D. 10

三. 解答题

17. 已知集合265{|1}A x x x

=-≥，22(1)(1){|||,}22a a B x x a R +-=-≤∈，若A B ?， 求a 的取值范围；

18. 已知函数()||23f x x x a x =-+-，当[1,2]x ∈时，()22f x x ≤-恒成立，求实数a 的 取值范围；

19. 如图，直线v 、h 为正方形对边中点的连线，1l 、2l 为正方形对角线，定义变换v ：将 正方形以直线v 作为对称轴作对称变换，类似可定义对称变换h 、1l 、2l ；定义()r θ，θ∈

[0,2)π，将正方形以对称中心为中心逆时针旋转θ角；令集合12{|n i A x x x x =????∈ *12{,,,},}v h l l n N ∈，其中12n x x x ????表示对正方形先作变换n x ，再作变换1n x -，???，最 后作变换1x ，每个12n x x x ????都可进行化简，例如：()v h r π?=，请写出集合A 中所有的 元素；（用最简形式表示）

20. 对于数对序列11:(,)P a b 、22(,)a b 、…、(,)n n a b ，记111()T P a b =+，()k k T P b =+

112max{(),}k k T P a a a -++???+，其中112max{(),}k k T P a a a -++???+表示1()k T P -和 12k a a a ++???+两个数中的最大的数；

（1）对于数对序列:(2,5)P 、(4,1)，求1()T P 、2()T P 的值；

（2）记m 为a 、b 、c 、d 四个数中最小值，对于由两个数对(,)a b 、(,)c d 组成的数对序 列:(,)P a b 、(,)c d 和:(,)P c d '、(,)a b ，试分别对m a =和m d =时两种情况比较2()T P 和2()T P '的大小；

（3）在由5个数对(11,8)、(5,2)、(16,11)、(11,11)、(4,6)组成的所有数对序列中，写 出一个数对序列P ，使得5()T P 最小，并写出5()T P 的值；（只需写出结论）

参考答案

一. 填空题

1. 1

2. (,0]-∞

3. 1-(0,1) 5. 0或

14

6. ()U C A B C I I

7. ①②③

8. [4,)+∞

9. {(2,3)}

10. 1(0,)4 11. (1,3]{1--U 12. 1870

二. 选择题

13. A 14. A 15. B 16.B

三. 解答题 17. 1[,2]2 18. 3[,2]2 19. 123{,,,,(0),(),(),()}22

A v h l l r r r r πππ= 20.（1）1()7T P =，2()8T P =；（2）22()()T P T P '≤；

（3）(4,6)、(11,11)、(16,11)、(11,8)、(5,2)，5()52T P =；

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