www.301833.com:2015高考数学(理)快速提分(每日一练)3

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成都极致教育(数学教研组)

2015 高考数学(理)提分每日一练 3
一、选择题
1.复数 z ? (3 ? 2i )i 的共轭复数 z 等于( A. ?2 ? 3i B. ?2 ? 3i ) C. 2 ? 3i C. 2 ? 3i

? y?x ? 2.若变量 x , y 满足约束条件 ? x ? y ? 1 且 z ? 2 x ? y 的最大值和最小值分别为 M 和 m ,则 M ? m ? y ? ?1 ?
( A. 8 3.若二项式 ( 2 x ? ) B. 7 C. 6 D. 5

a 7 1 ) 的展开式中 3 的系数是 84 ,则实数 a ? ( x x
B. 5 4 C. 1



A. 2

D.

2 4

4.已知 f ( x) ,g ( x) 分别是定义在 R 上的偶函数和奇函数,且 f ( x) ? g ( x) ? x ? x ?1 ,则 f (1) ? g (1) ?
3 2

( A. ?3

) B. ?1 C. 1 D. 3

5.对任意 x, y ? R , x ? 1 ? x ? y ? 1 ? y ? 1 的最小值为( A. 1 B. 2 C. 3

) D. 4

二、填空题
6.在 ?ABC 中,已知 AB ? AC ? tan A ,当 A ?

??? ? ????

?
6

时, ?ABC 的面积为

.

7.设无穷等比数列 {an } 的公比为 q ,若 a1 ?

lim (a
n ??

3

? a4 ? ? ? an ) , 则 q ?

.

8.已知椭圆 C :

x2 y 2 ? ? 1 ,点 M 与 C 的焦点不重合,若 M 关于 C 的焦点的对称点分别为 A , B ,线 9 4
.

段 MN 的中点在 C 上,则 | AN | ? | BN |?

成都极致教育(数学教研组) 三、解答题
9.已知函数 f ( x ) ? sin(3 x ?

?
4

).

(1)求 f ( x ) 的单调递增区间; (2)若 ? 是第二象限角, f ( ) ?

?

3

4 ? cos(? ? ) cos 2? ,求 cos ? ? sin ? 的值. 5 4

10.某大学志愿者协会有 6 名男同学, 4 名女同学.在这 10 名同学中,3 名同学来自数学学院,其余 7 名同 学来自物理、化学等其他互不相同的七个学院. 现从这 10 名同学中随机选取 3 名同学,到希望小学进行 支教活动(每位同学被选到的可能性相同). (Ⅰ)求选出的 3 名同学是来自互不相同学院的概率; (Ⅱ)设 X 为选出的 3 名同学中女同学的人数,求随机变量 X 的分布列和数学期望.


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