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山东省潍坊市2015届高三下学期二模考试数学(文)试题 Word版含答案

山东省潍坊市2015届高三下学期二模考试数学(文)试题 Word版含答案
山东省潍坊市2015届高三下学期二模考试数学(文)试题 Word版含答案

潍坊市2015届高三第二次模拟 数学(文史类) 2015.04

本试卷共4页,分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分,共150分。考试时间120分钟。

第Ⅰ卷 选择题(共50分)

一、选择题:本大题共10小题.每小题5分,共50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. 设全集R U =,集合}1|||{≤=x x A ,}1log |{2≤=x x B ,则B A U

等于

A .]1,0(

B .]1,1[-

C .]2,1(

D .]2,1[)1,( --∞ 2. 设i 是虚数单位,若复数)(310

R a i

a ∈--

是纯虚数,则a 的值为 A .-3 B .-1 C .1 D .3 3. 已知命题44,0:≥+

>?x x x p ;命题2

1

2),,0(:00=+∞∈?x x q ,则下列判断正确的是 A .p 是假命题 B .q 是真命题 C .)(q p ?∧是真命题 D .q p ∧?)(是真命题

4. 设n m ,是不同的直线,βα,是不同的平面,下列命题中正确的是

A .若n m n m ⊥⊥,,//βα,则βα⊥;

B .若n m n m //,,//βα⊥,则βα⊥;

C .若n m n m ⊥⊥,,//βα,则βα//;

D .若n m n m //,,//βα⊥,则βα//;

5.若)2

,0(π

α∈,且103

)22cos(

cos 2=

++απ

α,则=αtan

A .

2

1

B .

3

1

C .41

D .5

1

6. 已知定义在R 上的函数)(x f y =满足)(2)2(x f x f =+,当]2,0[∈x 时,

???∈+-∈=]2,1[,2)1.0[,

)(2

x x x x x x f ,则函数)(x f y =在]4,2[上的大致图像是

7. 已知三棱锥S —ABC 的所有顶点都在球O 的球面上,底面△ABC 是边长为1的正三角形,棱SC 是球O 的直径且SC=2,则此三棱锥的体积为 A .

62 B .63 C .32 D .2

2 8.设实数y x ,满足约束条件??

?

??≤-+≤-+≥+-04040

423ay x y x y x ,已知y x z +=2的最大值是

8,最小值是-5,则实数a 的值是 A .6 B .-6 C .-

61 D .6

1 9. 已知两点M (0,1-),N )0,1(,若直线)2(-=x k y 上存在点P ,使得PN PM ⊥,则实数k 的取值范围是

A.]31,0()0,31

[ - B. ]3

3

,0()0,33[ -

C. ]31,31[-

D. ]5,5[- 10. 定义在),0(+∞上的函数)(x f 满足:对),0(+∞∈?x ,都有)(2)2(x f x f =;当]

2,1(∈x 时,x x f -=2)(,给出如下结论: ①对Z m ∈?,有0)2(=m

f ; ②函数)(x f 的值域为),0[+∞; ③存在Z n ∈,使得9)12(=+n

f ; ④函数)(x f 在区间),(b a 单调递减的充分条件是“存在Z k ∈,使得)2,2(),(1

+?k k b a ,

其中所有正确结论的序号是: .

A.①②④

B. ①②

C. ①③④

D. ①②③

第Ⅱ卷(非选择题 共100分) 二、填空题:本大题共5小题,每小题5分,共25分.

11.某校对高三年级1600名男女学生的视力状况进行调查,现用分层抽样的方法抽取一个容量是200的样本,已知样本中女生比男生少10人,则该校高三年级的女生人数是 ;

12. 当输入的实数]3,2[∈x 时,执行如图所示的程序框图,则输出的x 不小于103

的概率是 ;

13. 已知G 为△ABC 的重心,令=,=,过点G 的直线分别交AB 、AC 于P 、Q 两点,且m =,n =,则

n

m 1

1+=__________. 14. 抛物线)0(2:2>=p px y C 的焦点为F ,点O 是坐标原点,M 是抛物线C 的一点,且|MF|=4|OF|,△MFO 的面积为34,则抛物线的方程为 ;

15. 已知函数201520144321)(2015

2014432x x x x x x x f +-+-+-+= ,若函数)(x f 的零点都在),,](,[Z b a b a b a ∈<内,则a b -的最小值是 。

三、解答题:本大题共6小题,共75分,解答时应写出必要的文字说明、证明过程或演算步骤. 16. (本小题满分12分)

已知向量)0)(1,(cos ),cos ,sin 3(2>=-=ωωωωx x x ,把函数2

1

)(+

?=n m x f 化简为B tx A x f ++=)sin()(?的形式后,利用“五点法”画)(x f y =在某一个周期内的图像时,

列表并填入的部分数据如下表所示:

(Ⅰ)请直接写出①处应填的值,并求ω的值及函数)(x f y =在区间]6

,2[π

π-上的值域; (Ⅱ)设ABC ?的内角,,A B C 所对的边分别为,,a b c ,已知1)6

2(

=+π

A f ,2=c ,7=a ,求?.

17.(本小题满分12分)

如图,边长为2的正方形ADEF 与梯形ABCD 所在的平面互相垂直,其中AB ∥CD ,AB ⊥BC ,

DC=BC=

2

1

AB=1,点M 在线段EC 上。 (Ⅰ)证明:平面BDM ⊥平面ADEF ;

(Ⅱ)判断点M 的位置,使得三棱锥B —CDM 的体积为18

2

18.(本小题满分12分)

为了了解学生的校园安全意识,某学校在全校抽取部分学生进行了消防知识问卷调查,问

已知被调查的所有女生的平均得分为8.25分,现从所有答卷中抽取一份,抽到男生的答卷且得分是15分的概率为10

1

。 (Ⅰ)求y x ,的值;

(Ⅱ)现要从得分是15分的学生中用分层抽样的方法抽取6人进行消防知识培训,再从这6人中随机抽取2人参加消防知识竞赛,求所抽取的2人中至少有1名男生的概率。 19.(本小题满分12分) 已知等比数列数列{}n a 的前n 项和为n S ,公比0>q ,2222-=a S ,243-=a S . (Ⅰ)求数列{n a }的通项公式;

(Ⅱ)令????

???+=为偶数为奇数n a n n n n a c n

n

n ,,)2(log 22,n T 为数列{n c }的前n 项和,求n T 2.

20.(本小题满分13分)

已知椭圆E 的中心在坐标原点O ,其焦点与双曲线C :12

2

2

=-y x 的焦点重合,且椭圆E 的短轴的两个端点与其一个焦点构成正三角形. (Ⅰ)求椭圆E 的方程;

(Ⅱ)过双曲线C 的右顶点A 作直线l 与椭圆E 交于不同的两点P 、Q 。设点M (4,3),记直线PM 、QM 的斜率分别为21,k k ,求证:21k k +为定值,求出此定值. 21.(本小题满分14分) 设)0(ln )(,2

1)(2

>==

a x a x g x x f . (Ⅰ)求函数)()()(x g x f x F ?=的极值;

(Ⅱ)若函数x a x g x f x G )1()()()(-+-=在区间),1(e e

内有两个零点,求实数a 的取值范围;

(Ⅲ)求证:当0>x 时,0143ln 2>-+x

e x x .

2018年上海高三数学二模分类汇编

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5.已知集合},2,1{m A =,}4,2{=B ,若}4,3,2,1{=B A Y ,则实数=m _______. 【答案】3 【来源】18届长嘉二模1 【难度】集合、基础题 6. 设集合1|,2x M y y x R ?????? ==∈?? ??????? , ()()()1|1112,121N y y x m x x m ????==+-+--≤≤?? ?-???? ,若N M ?,则实数m 的 取值范围是 . 【答案】(1,0)- 【来源】18届普陀二模11 【难度】集合、中档题 7.已知全集R U =,集合{ } 0322 >--=x x x A ,则=A C U . 【答案】]3,1[- 【来源】18届徐汇二模1 【难度】集合、基础题 8. 已知集合{|(1)(3)0}P x x x =+-<,{|||2}Q x x =>,则P Q =I 【答案】(2,3) 【来源】18届金山二模3 【难度】集合、基础题 9.已知集合{1,0,1,2,3}U =-,{1,0,2}A =-,则U C A =

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北京市东城区2015-2016学年第二学期初三统一练习(二) 英语2016.6 一、听对话,从下面各题所给的A、B、C三幅图片中选择与对话内容相符的图片。每 段对话你将听两遍。(共5分,每小题1分) 二、听对话或独白,根据对话或独白的内容,从下面各题所给的A、B、C三个选项中 选择最佳选项。每段对话或独白你将听两遍。(共15分,每小题1.5分) 请听一段对话,完成第6至第7小题。 6. What's the matter with the man? A. He has a fever. B. He has a cough. C. He has a headache. 7. When will the man go to see the doctor? A. Tomorrow morning. B. Tomorrow afternoon. C. Tomorrow evening. 请听一段刘话,完成第8至第9小题。 8. Where does the girl want to go? A. To a university. B. To a hospital. C. To a shopping center. 9. How long does it take to get there?

A. 10 minutes. B. 20 minutes. C. 30 minutes. 请听一段对话,完成第10至第11小题。 10. Why doesn't the woman want to watch a basketball game? A. Because she doesn't like basketball B. Because the ticket is very expensive. C. Because she watched one last weeekend 11. What do they decide to do at last? A. To go out for dinner. B. To watch a movie. C. To go to a concert. 请听一段对话,完成第12至第13小题。 12. What do we know about Pedro? A. His English is improving. B. He hates doing his homework. C. His English is better than his mother's. 13. What does the teacher tell Pedro's mother to do at home? A. To speak English with Pedro. B. To help Pedro with his listening. C. To make sure Pedro reads his book. 请听一段独白,完成第14至第巧小题。 14. Where is the speaker at the moment? A. In a shop. B. On a bus. C. On a river. 15. What's the speaker mainly doing? A. Telling about the tour plan. B. Giving advice on what to do. C. Describing some famous places. 三、听独白,记录关键信息。本段对话你将听两遍。(共10分,每小题2分) 请根据所听到的对话内容和提示词语,将所缺的关键信息填写在答题卡的相应位置上。 知识运用(共25分) 四、单项填空(共10分,每小题1分) 从下面各题所给的A、B、C、D四个选项中,选择可以填入空白处的最佳选项。21.These students always do homework very carefully. A. our B. his C. their D. her 22. Many people like to take a long vacation summer.

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