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四川省成都七中2014届高三4月第二次周练 数学(理) Word版含答案

四川省成都七中2014届高三4月第二次周练 数学(理) Word版含答案
四川省成都七中2014届高三4月第二次周练 数学(理) Word版含答案

成都七中2014级高三数学测试题(理科)

一、选择题(每小题5分,共50分)

1.若复数z ,满足:12z z i +=+,则z 的虚部为( ) A. 2i B. 1 C. 2 D. i

2.设全集U 是实数集R ,{}234M x x x =-≥,13log (2)0N x x ??

=+≥????

,则M N ?=( )

A.32x x ??

≤-????

B. {}

1x x ≤- C. 312x x ??

-

≤≤-???? D. 322x x ??

-<≤-???

?

3. 设a R ∈,则“2a =-”是“直线l 1:1:210l ax y +-=与2:(1)20l x a y +++= 直线l 2:x +(a +1)y +4=0平行”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

4. 阅读如图所示的程序框图,运行相应的程序,输出的结果k =( ) A.4 B.5 C.6 D.7

5. 设a 、b 是两条不同的直线,α、β是两个不同的平面,则 下列命题正确的是( ) A .若//,//,a b a α则//b α

B .若,//,a αβα⊥则a β⊥

C .若,,a αββ⊥⊥则//a α

D .若,,,a b a b αβ⊥⊥⊥则α⊥6. 已知双曲线

2

2

22

1 (,0)x y

a b a b

-=>的一条渐近线与圆8)322=+-y x (相交于N M ,两点,且4=MN ,则此双曲线的离心率为( )

A B C D .5

7. 一个空间几何体的三视图如图所示,则该几何体的表面积

为( )

A .48

B .

C .32+8

D .80

8. 已知锐角βα,满足: 5

1

cos sin =

-ββ,3tan tan 3tan tan =?++βαβα,则cos α=( )

A B . C D

9.用分期付款方式(贷款的月利率为1%)购买总价为25万元的汽车,购买当天首付15万元,此后可采用以下方式支付贷款:以后每月的这一天都支付相同数目的还款,20个月还完,则每月应还款约( )元(20

1.01 1.22≈)

A .5545

B .5546

C .5547

D .5548

10. 函数223,0

()2ln ,0x x x f x x x ?--+≤?=?->??

,直线y m =与函数()f x 的图像相交于四个不同的点,

从小到大,交点横坐标依次记为,,,a b c d ,下列说法错误的是( )

A .)4

0,abcd e

?∈? B .5

62112,2a b c d e

e e e ??

+++∈+-+-???

?

C .若关于x 的方程()=f x x m +恰有三个不同实根,则m 必有一个取值为13

4

D .若关于x 的方程()=f x x m +恰有三个不同实根,则m 取值唯一 二、填空题(每小题5分,共25分) 11. 将函数)(x f y =的图像向左平移

4

π

个单位,再向上平移1个单位后得到的函数对应的表达式为2

2cos y x =,则函数)(x f 的表达式是 (写出最简结果).

12. 在4

(1)(1)x x -+的展开式中,含2

x 项的系数是b ,若77

017(2)bx a a x a x -=+++ , 则127a a a +++=

13. 已知a b >,且1ab =,则221

a b a b

++-的最小值是 .

14.

已知函数

()

l o g 1(

0,1)a

f x x a a =->≠,

若123x x x x <<<,且123

()

()

()()f x f x f x f x ===,则1234

1111

x x x x +++=_________________ 15. 己知AOB ∠为锐角,2,1OA OB ==uu r uu u r

,OM 平分AOB ∠,M 在线段AB 上,点N 为线段AB 的中点,OP xOA yOB =+uu u r uu r uu u r

,若点P 在MON ?内(含边界),则在下列关于,x y 的

式子

①0y x -≥; ②01x y ≤+≤; ③20x y -≤; ④120,023

x y ≤≤≤≤ 中,正确的是 (请填写所有正确式子的番号)

理科答卷 姓名________________总分____________

一、选择题(共50分,每题5分)

二、填空题(每题5分,共25分)

11.________ 12.__________ 13._________ 14.__________ 15.__________

三、解答题(共75分)

16.(本小题12分) 已知函数21

()cos()2sin 42

f x x x x πωωω=

?+++,直线

1y =()f x 的图象交点之间的最短距离为2π

(1)求()f x 的解析式及其图象的对称中心;

(2)设ABC ?的内角A B C 、、的对边分别为a b c 、、,若3

(

)282

A f π+=,

4,c a b =+=,求ABC ?的面积.

17.(本小题12分)某绿化队甲组有10名工人,其中有4名女工人;乙组有5名工人,其中有3名女工人,现采用分层抽样方法(层内采用不放回简单随机抽样)从甲、乙两组中共抽取3名工人进行技能考核.

(1)求从甲、乙两组各抽取的人数; (2)求从甲组抽取的工人中至少1名女工人的概率;

(3)记ξ表示抽取的3名工人中男工人数,求ξ的分布列及数学期望.

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