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2014丰台区高三一模文科数学试题含答案

2014丰台区高三一模文科数学试题含答案
2014丰台区高三一模文科数学试题含答案

丰台区2014学年度第二学期期中练习

高 三 数 学(文科) 2014.3

第一部分 (选择题 共40分)

一、选择题共8小题,每小题5分,共40分。在每小题列出的4个选项中,选出符合题目要求的一项。

(1)设集合{|11}A x R x =∈-≤≤,{|(3)0}B x R x x =∈-≤,则A B 等于 (A ) {|13}x R x ∈-≤≤ (B ) {|03}x R x ∈≤≤ (C ) {|10}x R x ∈-≤≤ (D ) {|01}x R x ∈≤≤ (2)已知等比数列{}n a 中,23a a +=1,45a a +=2,则67a a +等于 (A )2 (B )

(C )4 (D )

(3) 执行如图所示的程序框图,输出的x 值为

(A )85 (B )29

12

(C )53 (D )13

8

(4)已知函数()f x 是定义在R 上的偶函数,它在[0,)+∞上是减函数. 则下列各

式一定成立的是

(A )(0)(6)f f < (B )(3)(2)f f -> (C )(1)(3)f f -> (D )(2)(3)f f -<-

(5)设向量a =()21x ,-,b =()14x ,+,则“3x =”是“a //b ”的 (A )充分而不必要条件 (B )必要而不充分条件 (C )充分必要条件 (D )既不充分也不必要条件 (6)某企业开展职工技能比赛,并从参赛职工中选1人参加该行业全国技能大

赛.经过6轮选拔,甲、乙两人成绩突出,得分情况如茎叶图所示.若甲乙两 人的平均成绩分别是x 甲,x 乙,则下列说法正确的是 (A )x x >甲乙,乙比甲成绩稳定,应该选乙参加比赛 (B )x x >甲乙,甲比乙成绩稳定,应该选甲参加比赛 (C )x x <甲乙,甲比乙成绩稳定,应该选甲参加比赛

(D )x x <甲乙,乙比甲成绩稳定,应该选乙参加比赛 (7) 某三棱锥的三视图如图所示,

该三棱锥的体积是

(A

)(B

)(C

)(D

主视图

侧视图

俯视图

(8)在同一直角坐标系中,方程22ax by ab +=与方程0ax by ab ++=表示的曲线可能是

(A ) (B) (C) (D)

第二部分 (非选择题 共110分)

二、填空题共6小题,每小题5分,共30分。 (9)已知tan 2=α,则sin cos sin cos -+αα

αα

的值为_______________.

(10)复数

2i

i

+在复平面内对应的点的坐标是____________. (11) 以点(-1,1)为圆心且与直线0x y -=相切的圆的方程为

____________________.

(12)已知函数()2x f x =,点P(,a b )在函数1

(0)y x x

=

>图象上,那么()()f a f b ? 的最小值是____________.

(13) A ,B 两架直升机同时从机场出发,完成某项救灾物资空投任务.A 机到达

甲地 完成任务后原路返回;B 机路过甲地,前往乙地完成任务后原路返回.图中折线分别表示A ,B 两架直升机离甲地的距离s 与时间t 之间的函数关系. 假设执行任务过程中A,B 均匀速直线飞行,则B 机每小时比A 机多飞行 公里.

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