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云南省会泽县茚旺高级中学2011-2012学年高二5月月考数学(文)试题(无答案)_图文


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考生注意:本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分,共 22 个小题,满分 150 分,考试用时 120 分钟.请在答题卡上作答.
第Ⅰ卷(选择题,共 60 分)

一、选择题(本题共 12 小题,每小题 5 分,共计 60 分) 1.已知集合 M ? {x | x ? 3}, N ? {x | 2x ? 1},则 M N 等于( )
2

A. ?

B. {x | ?1 ? x ? 3} C. {x | 0 ? x ? 3} D.

{x |1 ? x ? 3}

2.如果复数 2 ? bi (b ? R,i为虚数单位) 的实部和虚部互为相反 1? i

数,则 b 的值等于( )

A.0

B.1

C.2

D.3

3.“ lg x, lg y, lg z 成等差数列”是“ y2 ? xz ”成立的( )

A.充分非必要条件; B.必要非充分条件;

C.充要条件;

D.既非充分也非必要条件.

4.已知向量 p ? (2, ?3), q ? (x, 6),且 p // q ,则| p ? q | 的值为( )

A. 5

B. 13

C. 5

D.13

5、函数 y ? ln x 在点 P(1,0)处的切线方程是( ) x

A. y ? x ?1 B. y ? 0 C. y ? ?x ? 1 D. y ? 2x ? 2

6.已知某个几何体的三视图如下图,根据图中标出的尺寸(单位:cm),

可得这个几何体的体积是( ) A.错误!未找到引用源。cm3 C.错误!未找到引用源。 cm3

B.错误!未找到引用源。cm3 D.2 cm3

7.已知函数 f (x) ? a ? 1 满足 f (?x) ? f (x) ? 0 ,则 a 的值为( ) 4x ?1

A. 1

B. 1 4

C. ? 1 2

D. ? 1

8.某程序框图如图所示,则该程序运行后输出的 s 值为( )

A. 8 13

B. 13 21

C. 21 34

D. 34 55

9.函数 y ? ax , y ? sin ax (a>0 且 a≠1)在同一个直角坐标系中的图象可

以是( )

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10.已知 f (x) ? 2x3 ? 6x2 ? m ( m 为常数)在[-2,2]上有最大值 3,那么此函数在[-2,2]

上的最小值是( )

A.-37

B.-29

C.-5

D.以上都不对

11.数列 {an}满足 a1 ? 2 ,且 an ? an?1 ? 2n ? 2n?1(n ? 2) , Sn 为{an}前 n 项和,

则 log2 (S2012 ? 2) ? ( ) A.2013

B.2012

C.2011 D.2010

12.二次函数 f (x) ? ax2 ? 2x ? c(x ? R) 的值域为[0, ??) ,则 a ?1 ? c ?1 的 ca
最小值为( )

A.2

B. 2 ? 2

C.4

D. 2 ? 2 2

第Ⅱ卷(非选择题,共 90 分)

二.填空题(本题共 4 小题,每小题 5 分,共 20 分)

13.若直线 y ? kx ?1和圆 O :x2 ? y2 ? 1相交于 A 、B 两点(其中 O 为坐标原点),且 ?AOB ? 60 , 则实数 k 的值为________.

?x ? y ? 4 ? 0

14.已知不等式组

? ?

y

?

x

确定的区域为 D,若 M(x,y)

??x ? 0

为区域 D 上的动点,点 A 的坐标为(2,1),则 OA?OM 的 最大值为_____________.

15. 如 图 , 在 平 面 直 角 坐 标 系 xoy 中 , 已 知 椭 圆

x2 a2

?

y2 b2

? 1 (a

?b

? 0) 的左顶点为

A ,左焦点为 F

,上顶点

为B,

若 ?BAO ? ?BFO ? 900 ,则椭圆的离心率是

.

16.某地区为了解中学生的日平均睡眠时间(单位:h),

随机选择了 n 位中学生进行调查,根据所得数据

画出样本的频率分布直方图如图所示,且从左到

右的第 1 个、第 4 个、第 2 个、第 3 个小长方形

的面积依次构成公差为 0.1 的等差数列,

又第一小组的频数是 10,则 n ?



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三.解答题(本大题共 6 题,共计 70 分) 17.(12 分)数列{ an }的前 n 项和记为 Sn , a1 ? t, 点( Sn , an?1 )
线 y=2x +1 上, n ? N * . (I)若数列{ an }是等比数列,求实数 t 的值.

在直

(Ⅱ)在(I)的结论下,设 bn

?

log3

an?1

,

Tn

是数列

{ bn

1 bn?1

}

的前

n

项和,求

T2012 的值.

18.(12 分)如图,在四棱锥 P-ABCD 中,底面 ABCD 为矩形,PD⊥底面 ABCD, E 是 AB 上一点.已知 PD= 2,CD=4,AD= 3.
(1)若∠ADE=π6 ,求证:CE⊥平面 PDE; (2)若 AE=2,求三棱锥 E-PBC 的体积.
19.(12 分) 为了解某居住小区住户的年收入和年饮食支出的关系,抽取了其中 5 户家庭的调 查数据如下表:
(I)根据表中数据用最小二乘法求得回归直线方程 y =bx +a 中的 b=0.31,请预测年收入为 9 万元家庭的年饮食支出;
(Ⅱ)从 5 户家庭中任选 2 户,求“恰有一户家庭年饮食支出小于 1.6 万元”的概率.
▃ ▄ ▅ ▆ ▇ █ █ ■ ▓点亮心灯 ~~~///(^v^)\\\~~~ 照亮人生 ▃ ▄ ▅ ▆ ▇ █ █ ■ ▓

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20. (12 分)已知抛物线 C1 : y2 ? 4 px( p ? 0) ,焦点为 F2 ,其准线与 x 轴交点为 F1 ,椭圆 C2 分别

以为 F1, F2

为左右焦点,其离心率 e

?

1 2

,且抛物线 C1 与椭圆 C2

的一个交点记为

M



(Ⅰ)当 p ? 1时,求椭圆 C2 的方程。

(Ⅱ)在(Ⅰ)条件下,若直线 l 过椭圆 C2 的右焦点 F2 ,且与抛物线 C1 相交于 A, B 两点,若弦

长| AB | 等于 ?MF1F2 的周长,求直线 l 的方程。

21.

(12 分)已知函数

f (x) ?

x2 ? a ex

(x ? R) ( e 是自然对数的底数, e ? 2.71).

(Ⅰ)当 a ? ?15时,求 f (x) 的单调区间; (Ⅱ)若 f (x) 在区间[1 , e] 上是减函数,求实数 a 的取值范围;
e

请考生在 22,23,24 三题中任选一题作答,如果多做,则按所做的第一题记分. 22.(10 分) 在极坐标系中,若直线 l : ? cos? ? 3? sin? ? 0 ,

与曲线

C

:

?? ?

x

?

a

?

2 cos? (? 为参数,a>0)有两个公共点 A、B,且|AB| =2,

?? y ? 2 sin?

(Ⅰ)将直线化为直角坐标方程,曲线 C 化为普通方程。

(Ⅱ)求实数 a 的值。

▃ ▄ ▅ ▆ ▇ █ █ ■ ▓点亮心灯 ~~~///(^v^)\\\~~~ 照亮人生 ▃ ▄ ▅ ▆ ▇ █ █ ■ ▓

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23.(10 分) 已知直线 l 经过点 P(2,3) ,倾斜角? ? ? , 6
(Ⅰ)写出直线 l 的参数方程. (Ⅱ)设 l 与圆 x2 ? y 2 ? 4 相交与两点 A 、 B ,求点 P 到 A 、 B 两点的距离之积.

24. (10 分) 已知极坐标的极点在平面直角坐标系的原点 O 处,极轴与 x 轴的正半轴重合,且

长度单位相同.直线 l 的极坐标方程为:

2? sin(? ? ? ) ? 10 ,点 P 在曲线 C: 4

? ? ?

x y

? ?

4 cos?,(? 3 sin ? .

为参数)上,

(Ⅰ)求直线 l 的直角坐标方程;

(Ⅱ)求点 P 到直线 l 距离的最大值.

▃ ▄ ▅ ▆ ▇ █ █ ■ ▓点亮心灯 ~~~///(^v^)\\\~~~ 照亮人生 ▃ ▄ ▅ ▆ ▇ █ █ ■ ▓


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