当前位置:文档之家› 伊宁县第一中学2013届高三年级第十次模拟考试

伊宁县第一中学2013届高三年级第十次模拟考试

伊宁县第一中学2013届高三年级第十次模拟考试
伊宁县第一中学2013届高三年级第十次模拟考试

伊宁县第一中学2013届高三年级第9次作业

理 科 数 学

第I 卷(选择题 共60分)

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,只有一项符合题目要求。

1.已知全集{12345}U =,,,,,集合{1,3}A =,{3,4,5}B =,则集合()U C A

B = ( )

A .{2}

B .{4,5}

C .{3,4,5}

D .{1245},,,

2.已知{}n a 为等差数列,13524618,24a a a a a a ++=++=,则20a 等于 ( )

A. 10

B. 20

C. 40

D.80

3.平面向量a 与b 的夹角为0

60,a = 2, |b | = 1,则 |a +2b |= ( )

4.下列命题中是假命题的是 ( )

A .R ∈?βα,,使sin (+)=sin +sin αβαβ;

B . ,R ∈??函数)2sin()(?+=x x f 都不是偶函数

C .R ∈?m ,使3

42

)1(+-?-=m m

x m x f ()是幂函数,且在),0(+∞上递减

D .>0a ?函数a x x x f -+=ln ln )(2有零点.

5.已知函数(+1)

23log ,>3

()2+1,3

x x x f x x -??=?≤??,满足()=3f a ,则(5)f a -的值为 ( )

A .2log 3

B . 1716

C .3

2

D .1

6.在斜三角形ABC

中,sin = cos A B C ?

,且tan tan =1B C ?A ∠的值为 ( )

A .

4π B .3π C .2π D .34

π

7.已知函数

()f x 是定义在(0,+)∞上的单调函数,且对任意的正数,x y 都有()=()+(),f x y f x f y ?若数列

{}n a 的前n 项和为n S ,且满足(+2) ()=(3) (n ),n n f S f a f N *-∈则n a 为 ( )

A . -1

2

n B . n C .21n - D . 13 ()2

n -

8.已知m 、n 是两条不同的直线,α、β、γ是三个不同的平面,下列命题中错误的是( ) A. 若,m m αβ⊥⊥则α∥β B. 若α∥γ,β∥γ则α∥β C. 若,,m n m αβ??∥n 则α∥β

D. 若m 、n 是异面直线,,,m n m αβ??∥β,n ∥α则α∥β 9.已知数列{}n a 是等差数列,0n a ≠若2142lg lg lg a a a =+,则78

89

a a a a ++的值是( ) A .

1517 B .1或1517 C.1315 D .1或13

15

10.已知函数()f x 的导函数为'()5cos ,(1,1)f x x x =+∈-且(0)0f =若2(1)(1)0f x f x -+-<,则x 的取值范围为( )思路:1.判断奇偶性,2。单调性

A (0,1)

B (1,

C (2,-

∪(1)- 11.函数()1log (0,1)a f x x a a =+>≠的图像恒过定点A ,若点A 在直线20mx ny +-=上,

其中m ,n>0,则

11

m n

+的最小值为( ) A1 B2 C3 D4

12.在三角形ABC 中,B=600,AC=3, 则AB+2BC 的最大值为( )

A .3 B. 3 C. 7 D. 27

第II 卷(非选择题 共90分)

二、填空题:本大题共4小题,每小题5分,共20分。

13.如图所示是一个几何体的三视图(单位:cm ),主视图和左视图是底边长为4cm ,腰

长为俯视图是边长为4的正方形,则这个几何体的表面积是__________ 14.执行下图所示的程序框图,输出结果是______

15.设向量()21,a a a =,()21,b b b =,定义一种向量积()2211,b a b a b a =?,已知???

??=21,2m ,

??

?

??=0,3πn ,点P ()y x ,在x y sin =的图像上运动。Q 是函数()x f y =图像上的点,且满足

+?=(其中O 为坐标原点)

,函数()x f y =的值域是 16.已知函数bx x x f +=2

)(的图象在点))1(,1(f A 处的切线l 与直线023=+-y x 平行,若数列})

(1

{

n f 的前n 项和为n S ,则2013S 的值为

三、解答题:解答题写出文字说明、证明过程或演算步骤。

17.(本小题满分12分)已知数列{}n a 的相邻两项1,n n a a +是关于x 的方程220,()

n n x x b n N *-+=∈的两根,且11a = 。 (1)求证:数列123n n a ??

-?????

是等比数列;

(2)求数列{}n a 的前n 项和n S ;

18. (本小题满分6分)已知函数21

()(1)ln(1)2

f x x x x x =+-++(1)判断()f x 的单调性;

19. (本小题满分12分)在四棱锥P ABCD -中,底面ABCD 是直角梯形,A B ∥CD ,

∠ABC=090,AB=PB=PC=BC=2CD ,平面PBC ⊥平面ABCD

(1)求证:A B ⊥平面PBC

(2)求平面PAD 和平面BCP 所成的二面角(小于090)的大小。

(3)在棱PB 上是否存在点M 使C M ∥平面PAD ?

若存在,求PM

PB

的值。若不存在,请说明理由。

20.(本小题满分6分)设a ≥0,函数x a x x x f ln 2ln 1)(2+--=。

(Ⅰ)令)()(x f x x F '=,讨论)(x F 在(0,+∞)内的单调性并求极值;

21.(本小题满分10分)已知函数

2()ln ,a

f x x a x =+

∈R .(1)若1a =,求函数()f x 的极值;

(2)若函数()f x 在[2,)+∞上是增函数,求实数a 的取值范围;

22.(本小题满分12分)已知向量33(cos

,sin )22a x x =,(cos ,sin )22

x x

b =-,且0,2x π??

∈????

.(Ⅰ)求||a b +;

(Ⅱ)设函数()||f x a b a b =++?,求函数()f x 的最值及相应的x 的值.

23.(本小题满分12分)

设数列{}n a 的前n 项和为n S ,且满足n S =2-n a ,n =1,2,3,…. (1)求数列{}n a 的通项公式;

(2)若数列{}n b 满足1b =1,且1n b +=n b +n a ,求数列{}n b 的通项公式; (3)设n c =n (3-n b ),求数列{}n c 的前n 项和为n T .

俯视图

第14题

江苏赣榆县海头高级中学14-15学年高二下学期周末训练数学(理)试题(15) (Word版含答案)

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