2011江西三校生高考数学

2011江西三校生高考数学
2011江西三校生高考数学

高职数学试卷

第一卷(选择题 共70分)

一、 是非选择题:本大题共10小题,每小题3分,共30分.对每小题的命题作出

选择,对的选A,错的选B.

1.{}0?= (A,B)

2.sin 26y x π??

=+ ???的最小正周期是π (A,B)

3.常数数列既是等差数列也是等比数列 (A,B)

4.0.20.10.80.8--> (A,B)

5.0AB BC CA ++= (A,B)

6.若,a R ∈a =的充要条件是 0a ≥ (A,B)

7.空间的两条直线若不相交就平行 (A,B)

8.函数()23

21f x x =-是偶函数 (A,B)

9.椭圆2211625x y +=的离心率为3

5 (A,B)

10.空间三条直线,,,a b c 若,,a c b c ⊥⊥则//a b (A,B)

二、 单项选择题:本大题共8小题,每小题5分,共40分.

11.与{}21x x =集合相等的集合是( )

A {}1

B {}1-

C {}1,1-

D ?

12.在下列条件中,可以确定一个平面的条件是( )

A 经过两点

B 经过两条直线

C 经过不在通一条直线上的三点

D 以上都不正确 13若向量(1,2),(2,1),a b ==- 则a b ?= 等于( )

A 0

B 3

C 4

D 以上都不正确

14.使不等式220x x a -+>恒成立a 的取值范围是( )

A 1a <

B 1a >

C 2a >

D 2a <

15.从江西省的11个设区市中任意抽取2个设区市进行“创建卫生城”的检查,省会城市南昌被抽取到的概率是( ) A 110 B 111 C 15 D 211

16.已知中心在原点,焦点在x 轴上的双曲线的离心率为5

,3焦距为10,则双曲线的方程

为( ) A 221925x y -= B 22

1916

x y -= C 221916x y += D 22

1925

x y += 17.10

23132x x ??- ??

?的二项展开式中的常数项为( ) A 第三项 B 第四项 C 第五项 D 第六项 18.函数()()()

200x x f x x x ->??=?

第二卷(非选择题 共80分)

三、 填空题:本大题共6小题,每小题5分,共30分.

19.lg 2lg5+=

20.数2与8的等差中项为

21.函数()90y x x x

=+>的最小值为 22.cos80cos 20sin80sin 20+=

23.过点(2,1)-且垂直于的直线的方程是

24.设,,a b c 为非零向量,λ为实数,则命题 (1)//b a a b λ=? (2)若a b a b

==- 则,a b 的夹角为60 (3)若,a b c b ?=? 则a c = .其中真命题的是

四、解答题:本大题共6小题,25-28小题每小题8分,29-30小题每小题9分,共50分.解答应写出过程或步骤

25.已知4

3sin ,cos .55αα=-=

求212sin 4απα??+ ??

?的值 26.某商品现售价100元.(1)若每次降价20元,经过两次降价后的售价是多少元?

(2)若每次降价20

,经过两次降价后的售价是多少? 27.数列{}n a 中,已知1111,2n n a a a +=-=+

(1)求数列{}n a 的前n 项和n S ;

(2)求n S 的最小值

28.已知函数()3,f x ax bx =+且()13,f =又点()2,12在函数的图像上,

(1)求函数()f x 的解析式

(2)若()()0,f x f >求x 的取值范围

29.已知棱长为1正方体1111ABCD A B C D -中,E 为BC 的中点

(1)求证111D C B E ⊥;

(2)求异面直线11C D 与AE 所成的角.

(3)求二面角1B AE B --的大小

30. 已知点(8,0)A ,B C 、两点分别在x 轴和y 轴上的运动,且,AB BP BC CP ⊥=

(1)求P 动点的轨迹方程;

(2)若过点A 的直线l 于P 的轨迹较于不同的两点49M N QM QN ?= 、,,,其中

()10Q -,,求直线l 的方程

历年江西高考数学文科卷

2006高等学校全国统一数学文试题(江西卷) 一、选择题:本大题共12小题,每小题5分,共60分,在每小题给出的四个选项中,只有一项是符合题目要求的. 1.已知集合{}(1)0P x x x =-≥, 101Q x x ??=>?? -??,则P Q 等于( ) A.? B.{}1x x ≥ C. {}1x x > D. {}1x x x <0或≥ 2.函数 4sin 21 y x π? ?=++ ?3??的最小正周期为( ) A.π 2 B.π C.2π D.4π 3.在各项均不为零的等差数列{}n a 中,若2 110(2)n n n a a a n +--+=≥,则214n S n --=( ) A.2- B.0 C.1 D.2 4.下列四个条件中,p 是q 的必要不充分条件的是( ) A.:p a b >,22 :q a b > B.:p a b >,:22a b q > C. 22 :p ax by c +=为双曲线,:0q ab < D.2 :0p ax bx c ++>, 2: 0c b q a x x -+> 5.对于R 上可导的任意函数()f x ,若满足(1)()0x f x '-≥,则必有( ) A.(0)(2)2(1)f f f +< B.(0)(2)2(1)f f f +≤

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