2016年江西省三校生高等职业院校招生统一考试高考数学试题

江西省2016年高等职业院校招生统一考试

数学试题

一．是非选择题，

１、若集合{},2,1,0=A {},4,2,0=B 则{}.2=B A ( ) 2、直线032=+-y x 的斜率为2.

( ) 3、若向量).1,1(),3,2(),2,1(-=+-=-=→

→

b a b a 则 ( ) 4、不等式12

(

)

5、2

25sin 35cos 25cos 35sin =??+?? ( )

6、.33310

( ) 7、设等差数列{}n a 的公差为d ，,6,5425=+=a a a 则.1=d ( ) 8、若8)1(x -的展开式的第6项的系数为56.

(

) 9、若圆柱的轴截面是边长为2的正方形，则该圆柱的全面积为.6π (

) 10、直线01:1=++y ax l 与01:2=-+ay x l 平行的充要条件是.1=a (

)

二.单项选择题：

11.双曲线19

2=-y x 的虚轴长为( ) A 、2

B 、4

C 、6

D 、9

12.函数)2ln()(2x x f -=的定义域为() A 、[]2,2-

B 、()2,2-

C 、[]

2,2-

D 、()

2,2-

13.已知集合{}

,sin x y y A ==那么( ) A 、A ∈2

B 、A ∈1

C 、φ=A

D 、A ?-1

14.已知函数)10(log )(≠>=a a x x f a 且，若)3()2(f f >，则此函数在定义域内( )

A 、单调递增

B 、单调递减

C 、有最大值

D 、有最小值

15.已知l 是一条直线，βα,是两个不同的平面，那么下列命题中正确的是(

)

A 、若ββαα//,,l l 则⊥⊥

B 、若ββαα//,//,//l l 则

C 、若βαβα//,,则⊥⊥l l

D 、若βαβα⊥⊥⊥则,,l l

16.若实数d c b a ,,,满足d c b a >>>,0，则下列命题中正确的是(

) A 、bc ac >

B 、3

d c >

C 、d b c a ->-

D 、

c 11< 17.若函数322+-=x x y 在区间[)+∞,m 上的最小值为2，则实数m 的取值范围是() A 、(]1,∞-

B 、()+∞,1

C 、[)+∞,2

D 、()+∞,2

18.某校高三年级500名学生的数学月考成绩(满分150分) 的频率分布直方图如右图所示，则分数不．低于130分的人数为() A 、75

B 、110

C 、125

D 、150

三．填空题：

19.函数x y 2cos =的最小正周期为 .

20.椭圆

120

362

2=+y x 的右焦点坐标为 . 21.圆心坐标为)1,2(-，直径为2的圆的方程为

22.不等式283<-x 的整数解为=x . 23.在ABC ?中，若,2,1,4

===

∠BC AC B π

则ABC ?的面积为 .

24.

2S 甲，2S 乙分别表示甲、乙两人比赛成绩的方差，则2S 甲2

S 乙

的大小关系是

.（用>=<,, 连接）

距

29、如图，已知长方体1AC 中，11==AA AD ，E 为11C D 的中点，

（Ⅰ）证明：//1BD 平面EC B 1；（Ⅱ）求平面1ABD 与平面ABCD 所成二面角的大小．

30、已知抛物线)0(2:2

>=p px y C 的焦点为)0,1(F ，直线0434:=--y x l 与抛物线相交于B A ,两点。

（Ⅰ）求抛物线C 的方程；（Ⅱ）求AB 的长．

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