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2013届35中高三综合提高测试(1)

2012-2013北京三十五中高三数学综合提高测试一 (理)

一、选择题

1、设直线x m =与函数3()f x x =,()ln g x x =的图象分别交于点M 、N ,则||

M N 的最小值

A .1

(1ln 3)3

+ B .1

ln 33

C .1

(1ln 3)3

- D .ln 31-

2、在A B C ?中,,,a b c 为C B A ∠∠∠,,的对边,且1)cos(cos 2cos =-++C A B B ,则( )

A .c b a ,,成等差数列

B .b c a ,,成等差数列

C .b c a ,,成等比数列

D .c b a ,,成等比数列

3、函数32()393,f x x x x =--+若函数()()[2,5]g x f x m x =-∈-在上有3个零点,

则m 的取值 范围为 ( )

A .()-24,8

B .(]-24,1

C .[1,8]

D . [)1,8

4.已知321,,a a a 为一等差数列,321,,b b b 为一等比数列,且这6个数都为实数,

则下面四个结 论:

①21a a <与32a a >可能同时成立; ②21b b <与32b b >可能同时成立; ③若021<+a a ,则032<+a a ;

④若021

二、填空题

5.设

,x y 满足约束条件3

123

x y x y x y +??

--??-?

≥≥≤,若目标函数(0,0)x y z a b a b =+>>的最大值为

10,则54a b +

的最小值为 . 6.已知椭圆2

2

:

12

x

C y +=的两焦点为12,F F ,点00(,)P x y 满足2

2

00012

x y <

+<,则

|1PF |+2P F |的取值范围为 ,直线0012x x y y +=与椭圆

C 的公共点个

数 .

7.已知数列{}n a 满足1133,2,n n a a a n +=-=则

n a n

的最小值为 .

8.已知以F 为焦点的抛物线2

4y x =上的两点,A B 满足3AF FB =

,则弦A B 的中

点到准线的距离为 . 三、解答题

9.若1212()x x x x ≠、是函数)0()(223>-+=a x a bx ax x f 的两个极值点. (Ⅰ)若121

,13x x =-=,求函数)(x f 的解析式;

(Ⅱ)若12x x +=b 的最大值;

(Ⅲ)若13

-

为函数()f x 的一个极值点,设函数()()1

3

g x f x ax a '=--,当

1,3x a ??∈-??

??

时求()g x 的最大值.

宣武一模20

已知数列}{n a 满足11=a ,点),(1+n n a a 在直线12+=x y 上. (I )求数列}{n a 的通项公式;

(II )若数列}{n b 满足),2(111,

*

1

2

1

11N n n a a a a b a b n n

n ∈≥+

++==-且

求11)1(+++-n n n n a b a b 的值;

(III )对于(II )中的数列}{n b ,求证:n n b b b b b b 21213

10)1()1)(1(<

+++

10.抛物线2:C y x =,过定点()0,0A x 01

()8

x ≥,作直线l 交抛物线于,P Q (点P 在

第一象限).

(Ⅰ)当点A 是抛物线C 的焦点,且弦长2PQ =时,求直线l 的方程;

(Ⅱ)设点Q 关于x 轴的对称点为M ,直线PM 交x 轴于点B ,且BQ BP ⊥.求证:点B 的坐标是0(,0)x -并求点B 到直线l 的距离d 的取值范围.

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