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内蒙古包头第九中学2015届高三下学期第一次周考数学(理)试题 (Word版含答案)

一、选择题(每小题5分)

1.已知集合{}

ln(12)A x y x ==-,{

}

2

B x x x =≤,则()=A

B

C A B ( )

A .(,0)-∞

B .1(,1]2-

C .(,0)

-∞1[,1]2 D .1(,0]2

- 2. 在复平面内,复数z

满足(1)1z i +=,则z 的共轭复数对应的点位于() A .第一象限 B.第二象限 C .第三象限 D.第四象限

3. 将5名教师分配到高一年级的3个班实习,每班至少1名,最多2名,则不同的分配方案有()

A .30种

B .90种

C .180种

D .270种 4.在平面直角坐标系内,已知角α的终边经过点(3,4)-,将角α的终边按顺时针方向旋转

450后,与角β的终边重合,则sin 2β的值是()

A.2425-

B.725

C.7

25

- D.2425

5. 设,x y 满足约束条件0,

230,230x x y x y ≥??

+-≥??+-≤?

(,)a y m x =+,(2,1)b =-,且a b ⊥,则m 的最小

值为()

A .2

B .1

C .

1

2

D .13

6.已知数列}{},{n n b a 满足n n a b 2log =,*

N n ∈,其中}{n b 是等差数列,且820081

4

a a ?=

,则1232015b b b b ++++=()

A .2015-

B .2015

C .2log 2015

D .1008

7.从某高中随机选取5名高三男生,其身高和体重的数据如下表所示:

根据上表可得回归直线方程^

^

0.56y x a =+,据此模型预报身高为172cm 的高三男生的体重为 ( )

A .70.09kg

B .70.55kg

C . 70.12kg

D .71.05kg

8.一个几何体的三视图如图.该几何体的各个顶点都在球O 的球面上,球O 的体积为()

A .

B

C D

9.已知ABC ?外接圆O 的半径为1,且向量OA 在向量OB 上的投影为1

2

-,3C π∠=,从圆O

内随机取一个点M ,若点M 取自ABC ?ABC ?的形状为( ) A. 等边三角形B.直角三角形C.钝角三角形D.等腰直角三角形 10.以下四个命题中:

①设随机变量ξ服从正态分布()2,9N ,若()()2P C P C ξξ>=<-,则c 的值是2;

②若命题0",x R ?∈使得2

0010x ax ++≤成立”为真命题,则a 的取值范围为

(][),22,-∞-+∞;

③设函数())cos(2)f x x x ??+++(||)2

π

?<,且其图像关于直线0x =对称,

则()y f x =的最小正周期为π,且在(0,)2

π

上为增函数;

④已知11

3

:

:<+≥x q k x p ,,如果p 是q 的充分不必要条件,则实数k 的取值范围是()2,+∞.其中真命题的个数为(

)

A .1

B .2

C .3

D .4

11.如图,

12,F F 是分别是双曲线22

221x y a b

-=(0,0)a b >>的

左、右焦点,P 为双曲线右支上的一点,圆M 与12PF F ?三边所在的直线都相切,切点为,,A B C ,若P B a =,则双曲线的离心率为()

A B .2D .3

12. 形如)0,0(||>>-=

b c c

x b

y 的函数因其图像类似于汉字中的“囧”字,故我们把其生动

地称为“囧函数”.若函数()()

2

log 1a f x x x =++)1,0(≠>a a 有最小值,则当,c b 的

值分别为方程222220x y x y +--+=中的,x y 时的“囧函数”与函数||log x y a =的图像交点个数为( ). A .6 B .4C .2 D .1

二、填空题(每小题5分)

13. 设2

[0,1]()1

(1,]

x x f x x e x

?∈?

=?∈??(其中e 为自然对数的底数),则()y f x =的图像与0x =,

x e =以及x 轴所围成图形的面积为_____.

14.阅读如图所示的程序框图,若输入a

的值为二项9

4119x ??? 展开式的常数项,则输出的k 值为______.

15. 抛物线x 4y 2=的焦点为F ,点P 为抛物线上的动点,若

)01(,-A ,则

PA

PF 的最小值为.

16.式子),,(c b a σ满足),,(),,(),,(b a c a c b c b a σσσ==,则称),,(c b a σ为轮换对称式.给

出如下三个式子:①abc c b a =),,(σ;②

222),,(c b a c b a +-=σ;③

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