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2017年高考模拟试卷(9)

2017年高考模拟试卷(9)
2017年高考模拟试卷(9)

(第3题)

开始输入x y ←5

x <4

y ←x 2-2x +2

输出y 结束

Y N (第6题)频率组距

0.004

0.0080.0120.0160

50751001251502017年高考模拟试卷(9)

南通市数学学科基地命题

第Ⅰ卷(必做题,共160分)

一、填空题:本大题共14小题,每小题5分,共70分.1.全集{}1,2,3,4,5U =,集合{}1,3,4A =,则U C A =▲.2.设复数i z a b =+(a b ∈,R ,i 是虚数单位),若()2i i z -=,

则a b +的值为

3.在如图所示的算法流程图中,若输出的y 的值为26,

则输入的x 的值为

4.甲、乙两人下棋,结果是一人获胜或下成和棋.已知甲不输的

概率为0.8,乙不输的概率为0.7,则两人下成和棋的概率为

5.顶点在原点且以双曲线13

22=-y x 的右准线为准线的抛物线

方程是

6.为了解学生课外阅读的情况,随机统计了n 名学

生的课外阅读时间,所得数据都在[50,150]中,其频率分布直方图如图所示.已知在[50 100)

,中的频数为24,则n 的值为

7.甲,乙两种食物的维生素含量如下表:

分别取这两种食物若干并混合,且使混合物中维生素A ,B 的含量分别不低于100,120单位,则混合物重量的最小值为

kg .

8.,侧棱与底面所成的角为60°,则该棱锥的体积

9.在平面直角坐标系xOy 中,已知圆C :22(3)2x y +-=,点A 是x 轴上的一个动点,AP ,AQ 分别切圆C 于P ,Q 两点,则线段PQ 长的取值范围为▲.10.若函数0,2,()0ln ,≤x x x f x x ax x ?+=?>-?

在其定义域上恰有两个零点,则正实数a 的值为

▲.

11.设直线l 是曲线343ln y x x =+的切线,则直线l 的斜率的最小值为

▲.

维生素A (单位/kg )

维生素B (单位/kg )

甲35乙

4

2

12.扇形AOB 中,弦1AB =,C 为劣弧 AB 上的动点,AB 与OC 交于点P ,则OP BP ?

的最小

值是▲.

13.在平面直角坐标系xOy 中,已知(cos sin )A αα,,(cos sin )B ββ,

是直线y =+上的两点,则tan()αβ+的值为

14.已知函数3()2f x x a a x

=--+-有且仅有三个零点,且它们成等差数列,则实数a 的

取值集合为

二、解答题:本大题共6小题,共90分.15.(本小题满分14分)

已知tan α=2,cos β=-72

10

,且α,β∈(0,π),(1)求cos2α的值;(2)求2α-β的值.16.(本小题满分14分)

如图,在四棱锥P ABCD -中,△ACD 是正三角形,BD 垂直平分AC ,垂足为M ,ABC ∠=120°,=1PA AB =,2PD =,N 为PD 的中点.

(1)求证:AD ⊥平面PAB ;(2)求证:CN ∥平面PAB .

17.(本小题满分14分)

在平面直角坐标系xOy 中,已知A B ,分别是椭圆2

2

221(0)y

x a b a b

+=>>的上、下顶点,

点()

102M ,

为线段AO 的中点,AB =.

(1)求椭圆的方程;

(2)设(2)N t ,(0t ≠),直线NA ,NB 分别

交椭圆于点P Q ,,直线NA ,NB ,PQ 的斜率分别为1k ,2k ,3k .①求证:P M Q ,,三点共线;②求证:132312k k k k k k +-为定值.

D

(第16题)

P

A

P

B

P

C

M

N

x

y O M N A (第17题)

B

P

Q

18.(本小题满分16分)

如图,一个角形海湾AOB ,∠AOB =2θ(常数θ为锐角).拟用长度为l (l 为常数)的围网围成一个养殖区,有以下两种方案可供选择:方案一:如图1,围成扇形养殖区OPQ ,其中⌒

PQ =l ;方案二:如图2,围成三角形养殖区OCD ,其中CD =l ;

(1)求方案一中养殖区的面积S 1;

(2)求证:方案二中养殖区的最大面积S 2=l 2

4tan θ

(3)为使养殖区的面积最大,应选择何种方案?并说明理由.19.(本小题满分16分)

已知数列{}n a 的首项为2,前n 项的和为n S ,且111241n n n a a S +-=(*n ∈N ).

(1)求2a 的值;(2)设1n

n n n

a b a a +=

-,求数列{}n b 的通项公式;

(3)若m p r a a a ,,(*m p r ∈,,N ,m p r <<,)成等比数列,试比较2p 与

mr 的大小,并证明.

20.(本小题满分16分)

已知函数2

()ln )x

f x e a x b x

=+

+(,其中,a b R ∈. 2.71828e =是自然对数的底数.(1)若曲线()y f x =在1x =处的切线方程为(1)y e x =-.求实数,a b 的值;

(2)①若2a =-时,函数()y f x =既有极大值,又有极小值,求实数b 的取值范围;

②若2a =,2b ≥-.若()f x kx ≥对一切正实数x 恒成立,求实数k 的最大值(用b 表示).

l

l

A

O

B

A

O

B 图1

Q

A

O

B

C D 图2

(第18题)

1O 2O B P

Q

D

C 第II 卷(附加题,共40分)

21.【选做题】本题包括A,B,C,D 四小题,每小题10分,请选定其中两小题,并在相应的答题.......

区域内作答.....

.A ,(选修4-1;几何证明选讲)

如图,1O ,2O 交于两点P Q ,,直线AB 过点P ,与1O ,2O 分别交于点A B ,,

直线CD 过点Q ,与1O ,2O 分别交于点C D ,.求证:AC ∥BD .

B .(选修4-2:矩阵与变换)

若二阶矩阵M 满足:12583446M ????

= ? ?????

.

(1)求二阶矩阵M ;

(2)若曲线2

2

:221C x xy y ++=在矩阵M 所对应的变换作用下得到曲线C ',求曲线

C '

的方程.

C

(选修4-4:坐标系与参数方程)已知点(1)P αα-(其中[)0,2)απ∈,点P

的轨迹记为曲线1C ,以坐标原点为极点,x 轴的正半轴为极轴建立极坐标系,点Q 在曲线21

:)

4

C ρπ

θ=

+上.

(1)求曲线1C 的极坐标方程和曲线2C 的直角坐标方程;

(2)当0,02ρθπ≥≤<时,求曲线1C 与曲线2C 的公共点的极坐标.

D .(选修4-5:不等式选讲)

已知实数0x >,0y >,0z >,证明:1239()()2462

y

x z x y z ++++≥.

【选做题】第22题、23题,每题10分,共计20分.

22.已知正六棱锥S ABCDEF -的底面边长为2,高为1.现从该棱锥的7个顶点中随机

选取3个点构成三角形,设随机变量X 表示所得三角形的面积.

(1)求概率(P X =的值;

(2)求X 的分布列,并求其数学期望()E X .

23.已知数列{a n }满足:a 1=1,对任意的n ∈N *,都有a n +1=(1+

1n 2+n

)a n +12n .

(1)求证:当n ≥2时,a n ≥2;

(2)利用“?x >0,ln(1+x )<x ”,证明:a n <2e 3

4(其中e 是自然对数的底数).

湖北省2017年高考英语试题及答案

湖北省2017年高考英语试题及答案 (考试时间:120分钟试卷满分:150分) 第一部分听力(共两节,满分30分) 做题时,先将答案标在试卷上。录音内容结束后,你将有两分钟的时间将试卷上的答案转涂到答题卡上。 第一节(共5小题;每小题1.5分,满分7.5分) 听下面5段对话。每段对话后有一个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。 例:How much is the shirt? A. £ 19. 15. B. £ 9. 18. C. £ 9. 15. 答案是C。 1. What does the woman think of the movie? A.It’s amusing B.It’s exciting C.It’s disappointing 2. How will Susan spend most of her time in France? A. Traveling around B.Studying at a school C.Looking after her aunt 3. What are the speakers talking about? A. Going out B.Ordering drinks C.Preparing for a party 4. Where are the speakers? A.In a classroom B.In a library C.In a bookstore 5. What is the man going to do ? A.Go on the Internet B.Make a phone call C.Take a train trip 第二节(共15小题;每小题1.5分,满分22.5分) 听下面5段对话或独白。每段对话或独白后有几个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。听每段对话或独白前,你将有时间阅读各个小题,每小题5秒钟;听完后,各小题将给出5秒钟的作答时间。每段对话或独白读两遍。 听第6段材料,回答第6、7题。 6. What is the woman looking for? A. An information office B.A police station C.A shoe repair shop 1

2017年高考英语全国卷3-答案

2017年普通高等学校招生全国统一考试(全国卷Ⅲ) 英语答案解析 第一部分:阅读理解 第一节 1.【答案】A 【解析】题干问的是三月份可参加的旅行,而第一个项目San Francisco Winery Tour的时间是从2月1日到4月30日。故选A。 【考点】冠词,细节理解。 2.【答案】C 【解析】第二个项目Back to the Fifties Tour中提到在San Francisco你能免费品尝冰淇淋。而其他选项在这个旅行中没有被提到。故选C。 【考点】介词辨析,细节理解。 3.【答案】D 【解析】第四个项目Holiday Lights Tour的最后一句话提到”Advance reservations required”,由此可知,该旅行需要提前预定。故选D。 【考点】代词,细节理解。 4.【答案】B 【解析】根据第一段的最后一句”As one group of workers carried out the rubbish,another group began removing seats and other theater equipment in preparation for the buildings end”可推断出工人们清理垃圾和清除座位及其他剧院设备是在为剧院的关闭做准备。故选B。 【考点】副词辨析,推理判断。 5.【答案】D 【解析】根据第二段中的”Theater owner Ed Bradford said he chose the movie because it seemed appropriate”可知,剧院的老板亲自选定了The Last picture Show这部电影,因为他认为这部电影很合适。原文中的“appropriate”和D选项的“suitable都表示“合适的”。故选D。 【考点】细节理解。 6.【答案】C 【解析】第四段最后一句说剧院被卖给了当地的开发公司,该公司计划在剧院所在地建综合购物大楼,因此可推断出剧院将被推倒拆除。故选C。 【考点】动词的时态,推理判断。

2017年江苏高考数学真题及答案

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5.若tan 1 -= 4 6 π α ?? ? ?? ,则tanα= . 6.如图,在圆柱O1 O2内有一个球O,该球与圆柱的上、下底面及母线均相切。记圆柱O1O2 的体积为V1 ,球O的体积为V2,则1 2 V V 的值是 7.记函数2 ()6 f x x x +-的定义域为D.在区间[-4,5]上随机取一个数x,则x∈ D的 概率是 8.在平面直角坐标系xoy中 ,双曲线 2 21 3 x y -=的右准线与它的两条渐近线分别交于点P,Q,其焦点是F1 , F2 ,则四边形F1 P F2 Q的面积是 9.等比数列{}n a的各项均为实数,其前n项的和为S n,已知36 763 , 44 S S ==, 则 8 a= 10.某公司一年购买某种货物600吨,每次购买x吨,运费为6万元/次,一年的总存储费用

2017年湖北高考英语真题

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2017年高考英语全国卷1

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D. The merchant of Venice. 22.What is special about Deafinnitely Theatre? A. It has two groups of actors. B. It is the leading theatre in London. C. It performs plays in BSL. D. It is good at producing comedies. 23.When can you see a play in Hebrew? A. On Saturday 28Apil. B. On Sunday 29 April. C. On Tuesday 22 May. D. On Tuesday 29 May. B I first met Paul Newman in 1968, when George Roy Hill, the director of Butch Cassidy and the Sundance Kid, introduced us in New York City. When the studio didn’t want me for the film— it wanted somebody as well known as Paul — he stood up for me. I don’t know how many people would have done that; they would hav e listened to their agents or the studio powers. The friendship that grew out of the experience of making that film and The Sting four years later had its root in the fact that although there was an age difference, we both came from a tradition of theater and live TV. We were respectful of craft (技艺)and focused on digging into the characters we were going to play. Both of us had the qualities and virtues that are typical of American actors: humorous, aggressive, and making fun of each other— but always with an underlying affection. Those were also at the core(核心)of our relationship off the screen. We shared the bel ief that if you’re fortunate enough to have success, you should put something back—he with his Newman’s Own food and his Hole in the Wall camps fo r kids who are seriously ill, and me with Sundance and the institute and the festival. Paul and I didn’t see each other all that regularly, but sharing that brought us together. We supported each other financially and by showing up at events. I last saw him a few months ago. He’d been in and out of the hospital. He and I both knew what the deal was, and we didn’t talk about it. Ours was a relationship that didn’t need a lot of words. 24.Why was the studio unwilling to give the role to author at first? A. Paul Newman wanted it. B. The studio powers didn’t like his agent. C. He wasn’t famous enough. D. The director recommended someone else. 25.Why did Paul and the author have a lasting friendship? A. They were of the same age. B. They worked in the same theater. C. They were both good actors. D. They have similar characteristics. 26.What does the underlined word “that” in paragraph 3 refer to? A. Their belief. B. Their care for children. C. Their success. D. Their support for each other. 27.What is the author’s purpose in writing the text? A. To show his love of films. B. To remember a friend. C. To introduce a new movie. D. To share his acting experience. C Terrafugia Inc. said Monday that its new flying car has completed its first flight, bringing the company closer to its goal of selling the flying car within the next year. The vehicle —named the Transition – has two seats, four wheels and wings that fold up so it can be driven like a car. The Transition, which flew at 1,400 feet for eight minutes last month, can reach around 70 miles per hour on the road and 115 in the air. It flies using a 23-gallon tank of gas and burns 5 gallons per hour in the air. On the ground, it gets 35 miles per gallon. Around 100 people have already put down a $10,000 deposit to get a Transition when they go on sale, and those numbers will likely rise after Terrafugia introduces the Transition to the public later this week at the New York Auto Show. But don’t expect it to show up in too many driveways. It’s expected to cost $279,000. And it won’t help if you’re stuck in traffic. The car needs a runway. Inventors have been trying to make flying cars since the 1930s, according to Robert Mann, an airline industry expert. But Mann thinks Terrafugia has come closer than anyone to making the flying car a reality. The government has already permitted the company to use special materials to make it easier for the vehicle to fly. The Transition is now going through crash tests to make sure it meets federal safety standards. Mann said Terraf ugia was helped by the Federal Aviation Administration’s decision five years ago to create a separate set of standards for light sport aircraft, which are lower than those for pilots of larger planes. Terrafugia says an owner would need to pass a test and complete 20 hours of flying time to be able to fly the Transition, a requirement

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