西城区2020年高三二模数学试题及答案(WORD版)

西城区2020年高三二模数学试题及答案(WORD版)
西城区2020年高三二模数学试题及答案(WORD版)

西 城 区 高 三 诊 断 性 测 试

数 学2020.5

第Ⅰ卷(选择题 共40分)

一、选择题:本大题共10小题,每小题4分,共40分.在每小题列出的四个选项中,选出符合题目要求

的一项. 01.设集合{}

3A x x =<,{}2,B x x k k ==∈Z ,则A B I =

(A ){}0,2

(B ){}2,2-

(C ){}2,0,2-

(D ){}2,1,0,1,2--

02.若复数z 满足i 1i z ?=-+,则在复平面内z 对应的点位于

(A )第一象限 (B )第二象限 (C )第三象限 (D )第四象限

03.下列函数中,值域为R 且区间(0,)+∞上单调递增的是

(A )3y x =-

(B )y x x =

(C )1y x -=

(D )y =

04.抛物线24x y =的准线方程为

(A )1x = (B )1x =-

(C )1y = (D )1y =-

05.在ABC ?中,若::4:5:6a b c =,则其最大内角的余弦值为

(A )18

(B )

14

(C )

310 (D )35

06.设0.23a =,3log 2b =,0.2log 3c =,则

(A )a c b >> (B )a b c >> (C )b c a >> (D )b a c >>

07.某几何体的三视图如图所示,则该几何体的体积是

(A )6

(B )4

(C )3

(D )2

08.若圆22420x y x y a +-++=与x 轴,y 轴均有公共点,则实数a 的取值范围是

(A )(,1]-∞

(B )(,0]-∞

(C )[0,)+∞

(D )[5,)+∞

09.若向量a 与b 不共线,则“0?+a b a b ”的

(A )充分而不必要条件 (B )必要而不充分条件

(C )充要条件

(D )既不充分也不必要条件

10.设函数()(1)e x f x x =-.若关于x 的不等式()1f x ax <-有且仅有一个整数解,则正数a 的取值范围是

(A )(0,e]

(B )2

(0,e ]

(C )2e 1,2?? ???

(D )2e 11,2??+ ??

?

第Ⅱ卷(非选择题 共110分)

二、填空题:本大题共5小题,每小题5分,共25分. 11.设平面向量(1,2)=-a ,(,2)k =b 满足⊥a b ,则=b ____.

12.若双曲线22

21(0)16

x y a a -=>经过点(2,0),则该双曲线渐近线的方程为____.

13.设函数2()sin 22cos f x x x =+,则函数()f x 的最小正周期为____;若对于任意x ∈R ,都有()f x m ≤成立,则实数m 的最小值为____.

14.甲、乙、丙、丁四人参加冬季滑雪比赛,其中有两人最终获奖.在比赛结果揭晓之前,四人的猜测如

下表,其中“√”表示猜测某人获奖,“×”表示猜测某人未获奖,而“○”则表示对某人是否获奖____,____.

15.在四棱锥P -,,,E F H 分别是棱

,,PB BC PD 的中点,对于平面EFH 截四棱锥P ABCD -所得的截面多边形,有以下三个结论:

①截面的面积等于

②截面是一个五边形;

③截面只与四棱锥P ABCD -四条侧棱中的三条相交. 其中,所有正确结论的序号是______.

三、解答题:本大题共6小题,共85分.解答应写出必要的文字说明、证明过程或演算步骤. 16.(本小题满分14分)

如图,在几何体ABCDEF 中,底面ABCD 是边长为2的正方形,DE ⊥平面ABCD ,DE BF ∥,且22DE BF ==.

(Ⅰ)求证:平面BCF ∥平面ADE ; (Ⅱ)求钝二面角D AE F --的余弦值.

17.(本小题满分14分)

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