2019年10月28日云南省昆明市第一中学2020届高三联考第二次月考文科数学试题参考答案

第 1 页（共 5 页）

2020届昆一中高三联考卷第二期文科数学

参考答案及评分标准

命题、审题组教师杨昆华张宇甜顾先成鲁开红王海泉莫利琴吕文芬张远雄崔锦杨耕耘一、选择题

1. 解析：因为{}17A x x =-<<, 12B x x ??

=>-???

?,所以{}1A

B x x =>-,选C.

2. 解析：因为1i z =--,所以1i z =-+,选A.

3. 解析：由已知1a =, 得1

cos ,2

a b a b a b

,所以a 与b 的夹角为60,选C. 4. 解析：记4个班分别为甲、乙、丙、丁,则他们的比赛对阵场次为甲乙、甲丙、甲丁、乙丙、乙丁、丙

丁共6种,其中甲、乙两班至少有一个班参加的有5种,则所求概率5

p =,故选D ． 5. 解析：sin(2)cos22y x x π=+=,因为0,2x π∈（）

,所以()20,x π∈,所以sin(2)2

y x π

=+的周期为π,且在0,2

（）上为减函数,选A . 6. 解析：由已知11()33f =-,又因为()f x 是奇函数,所以111

()()333

f f -=-=,选B.

7. 解析：如果①为真,则②③为假,甲选篮球,

已选排球,丙选篮球,矛盾；如果②为真,则①③为假,若乙选篮球,丙选篮球,矛盾；

若乙选足球,丙选篮球,甲选排球,正确；

如果③为真,则①②为假,若丙选排球,乙选排球,矛盾；

若丙选足球

,乙选排球,甲选排球或足球,矛盾

综上,选C.

8. 解析：则()2ln f x ax x ax '=?+,由导数的几何意义得()11f a

'==,选B. 9. 解析：由1l β⊥,2l β⊥得1l ∥2l ,由因为2l α⊥,所以1l α⊥,选D ．

10. 解析：由已知,点A 的坐标为(,2

-,代入双曲线1C 得：2

()22122p --=,所以4p =,选B .

11. 解析：3sin()sin sin )=1326ππ

ααααα++=+=+,所以sin()=

6πα+, 所以211cos(2)=12sin 123633ππαα?

?+-+=-?= ??

?,选A.

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