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重庆一中高2020级高三下5月月考试题

重庆一中高2020级高三下5月月考试题
重庆一中高2020级高三下5月月考试题

绝密★启用前【考试时间:5月15日15:00-17:00】

重庆一中高2020级高三下期5月月考

理 科 数 学 试 题 卷

第I 卷(选择题)

一、选择题:(本大题 12个小题,每小题5分,共60分,每小题有且只有一项是正确的). 1.已知复数)2)(1(i i z +-=,则=?z z ( ) A .2

B .5

C .10

D .18

2.已知非空集合{

}

022

<--∈?x x N x A ,则满足条件的集合A 的个数是 ( ) A .1

B .2

C .3

D .4

3.函数x x f ln )(=过点)(0,0的切线方程为 ( ) A.x y =

B .x e

y 2

=

C .x y 2

1=

D.x e

y 1=

4.双曲线13

22

=-x y 的渐近线与圆03422=+-+y y x 的位置关系是 ( ) A .相切 B .相离 C .相交 D .不确定

5.已知10<< B .3

23

2b a >

C .ab b a <+

D .3

3

ab b a <

6. 秦九韶是我国南宋时期的数学家,普州(现四川省安岳县) 人,他在所著的《数书九章》中提出的多项式求值的秦九韶 算法,至今仍是比较先进的算法.如图所示的程序框图给出了 利用秦九韶算法求某多项式值的一个实例,若输入n ,x 的

值分别为3,2,则输出v 的值为( )

A.9

B.18

C.20

D.35 7.甲、乙、丙、丁4人排成一纵列,现已知甲不排首位,则乙不 排末位的概率为 ( ) A .21 B .127 C .32 D .9

7

8.下列说法中正确的个数是 ( )

①若三个平面两两相交有三条交线,则三交线相互平行

①三个平面最多将空间分为8个部分

①一平面截一正方体,则截面不可能为五边形

①过空间任意一点有且只有一条直线与两异面直线垂直

A .1

B .2

C .3

D .4

9.已知点P 在以12,F F 为左,右焦点的椭圆22

22:1(0)2x y C b b b +=>上,在21F PF ?中,若 βα=∠=∠1221,F PF F PF ,则=

++βαβαsin sin )

sin( ( )

A .

2

1 B .

2

2 C .

2

3 D .2

10.函数??

?

???∈+=2,

0cos 22sin )(πx x x x f ,的单调递减区间是 ( ) A .??

?

???6,

0π B .??????2

6ππ,

C .??

?

???3,

0π D .??

?

?

??2,3ππ 11.(原创)某中学高三年级在返校复学后,为了做好疫情防护工作,一位防疫督察员要将2盒完全相同的

95N 口罩和3盒完全相同的普通医用口罩全部分配给3个不同的班,每个班至少分得一盒,则不同的 分法种数是 ( ) A .21 B .24 C .27 D .30 12.(原创)锐角ABC ?的内角C B A ,,的对边分别为,,,c b a 且,1=a 1cos cos =-B A b ,若B A ,变化时,

A B 2sin 2sin λ-存在最大值,则正数λ的取值范围是( )

A .???

? ??

330,

B .??

? ??

210,

C .??

?

?

??2233, D .??

?

??121,

第II 卷(非选择题)

二、填空题:(本大题4个小题,每小题5分,共20分).

13.若定义在R 上的函数

()

f x 满足

()()

3f x f x +=,且当(]3,0∈x 时,x x f 4log )(=,则=

)2021(f ________.(结果用分数表示) 14.已知0,0>>b a 且1=+b a ,则

b

a 1

13++的最小值为________. 15.(原创),于点,中,在D BC AD A ABC ⊥=∠?0

90且 AC AB AD 4

3

41+=

,则=∠C ______. 16.(原创)已知半径为7的球面上有三点C B A 、、,32=AB ,球心为O ,二面角O AB C --的大小为

060,当直线OC 与平面OAB 所成角最大时,三棱锥ABC O -的体积为_______.

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