合肥2016一模调研卷

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合肥2016一模调研卷(一)
2016合肥一模理科数学含答案

合肥市2016年高三第一次教学质量检测

数学试题（理科）

本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分,满分150分,考试时间120分钟,祝各位考生考试顺利！

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,只有一项是符合题目要求的.

1.在复平面内,复数1(其中i是虚数单位,满足i21)对应的点位于 2i

A.第一象限 B.第二象限 C.第三象限 D.第四象限

2.sin18sin78cos162cos78等于

A.11 B.

D. 223.一次数学考试后,某老师从自己带的两个班级中各抽取5人,记录他们的考试成绩,得到如右图所示的茎叶图,已知甲班5名同学成绩的平均数为81,乙班5名同学的中位数为73,则xy的值为

A.2 B.2 C.3 D.3

4.“x1”是“x12”的 x

A.充分而不必要条件 B.必要而不充分条件 C.充要条件 D.既不充分又不必要条件

5.执行如下程序框图,则输出结果为

A.2 B.3 C.4 D.5

6.已知l,m,n为三条不同直线,,,为三个不同平面,则下列判断正确的是

A .若m//,n//,则m//n B.若m,n//,,则mn

C.若l,m//,m//,则m//l D.若m,n,lm,ln,则l

7,ca2,b3,则a等于 8

57 A.2 B. C .3 D. 22

x2y2x2y2

1与双曲线C2:221(a0,b0)的渐近线相同,8.若双曲线C1:28ab

且双曲线C

2的焦距为则b等于 7.ABC的三内角A,B,C所对的边分别是a,b,c,若cosA

A .2 B.4 C.6 D.8

9.某几何体的三视图如图所示,则该几何体的体积为

A.471523 B. C. D.8 623

10.某企业的4名职工参加职业技能考核,每名职工均可从4

个备选考核项目中任意抽取一个

参加考核,则恰有一个项目未被抽中的概率为

A.927817 B. C. D. 166416256

11.在(x1)

k1nk的展开式中含x2项系数与含x10项系数相等,则正整数n的取值为

A.12 B.13 C.14 D.15

12.函数f(x)x23xa,g(x)2xx2,若f[g(x)]0对x[0,1]恒成立,则实数a的取值范围是

A.[e,) B.[ln2,) C.[2,) D.(,0] 1

2

第Ⅱ卷（非选择题 共90分）

本卷包括必考题和选考题两部分,第13题至第21题为必考题,每个考生都必须作答,第22题至第24题为选考题,考生根据要求作答.

二、填空题：本大题共5小题，每小题5分，共25分，把答案填在答题卡的相应位置上.

13.已知集合A{0,1,3},B{x|x23x0},则AB

2xy6014.已知实数x,y满足xy0,则目标函数zxy的最大值是x215.已知等边ABC的边长为2,若BC3BE,ADDC,则BDAE

2216.存在实数,使得圆面xy4恰好覆盖函数ysin(x)图象的最高点或最低k

点共三个,则正数k的取值范围是

三、解答题:本大题共6小题,共75分,解答应写出文字说明,证明过程或演算步骤. 17(本小题满分12分)

在数列{an}中,a1

(Ⅰ)求证:数列1n1,an1an,nN*. 22nan为等比数列; n

(Ⅱ)求数列{an}的前n项和.

18(本小题满分12分)

某医院对治疗支气管肺炎的两种方案A,B进行比较研究,将志愿者分为两组,分别采用方案

(Ⅱ)能否在犯错误的概率不超过0.05的前提下认为治疗是否有效与方案选择有关?

n(adbc)2

附:K,其中nabcd (ab)(cd)(ac)(bd)2

四棱锥EABCD中,AD//BC,ADAE2BC2AB2,ABAD,平面EAD平

面

ABCD,点

F为DE的中点.

(Ⅰ)求证:CF//平面EAB;

(Ⅱ)若CFAD,求二面角DCFB的余弦值.

20(本小题满分12分)

设A,B为抛物线y2x上相异两点,其纵坐标分别为1,2,分别以A,B为切点作抛物线的切线l1,l2,设l1,l2相交于点P.

(Ⅰ)求点P的坐标;

(Ⅱ)M为A,B间抛物线段上任意一点,设PMPAPB,是否为定值

,如果为定值,求出该定值,如果不是定值,请说明理由.【合肥2016一模调研卷】

21(本小题满分12分) 

x,其中e2.71828是自然对数的底数. 4

(Ⅰ)设g(x)(x1)f'(x)(其中f'(x)为f(x)的导函数),判断g(x)在(1,)上的单调已知函数f(x)e性;

(Ⅱ)若F(x)ln(x1)af(x)4无零点,试确定正数a的取值范围.

x2

请考生在第22题,23题,24题中任选一题作答,如果多做,则按所做的第一题计分,作答时请写清题号.

22(本小题满分10分)选修4-1:几何证明选讲

已知AB是圆O的直径,点C在圆O上(异于点A,B),连接BC并延长至点

D,使得BCCD,连接DA交圆O于点E,过点C作圆O的切线交AD于

点F.

(Ⅰ)若DBA60,求证:点E为AD的中点;

1(Ⅱ)若CFR,其中R为圆C的半径,求DBA 2

23(本小题满分10分)选修4-4:坐标系与参数方程

1x1t2(t为参数),以坐标原点为极点,x轴的非负半轴为极轴且两坐标已知直线l:y2

系中具有相同的长度单位,建立极坐标系,曲线C的极坐标方程

为2sina(a3)

(Ⅰ)将曲线C的极坐标方程化为直角坐标方程;

(Ⅱ)若曲线C与直线l有唯一公共点,求实数a的值.

24(本小题满分10分)选修4-5:不等式选讲

已知a0,b0,

记ABab.

(Ⅰ)

B的最大值;

(Ⅱ)若ab4,是否存在a,b,使得AB6?并说明理由.

合肥2016一模调研卷(二)
2016合肥一模文科数学含答案

合肥市2016年高三第一次教学质量检测

数学试题（文科）

本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分,满分150分,考试时间120分钟

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,只有一项是符合题目要求的.

(1)已知集合A={0,l,3},B={x|x2-3x=0}，则A B=

(A)． {0) (B)．){0,1} (C)．{0,3} (D)．{0,1,3}

(2)已知z=2i（i为虚数单位），则复数z= 12i

(A) -1 (B)l (C)i (D) -i

(3)sin18sin78cos162cos78等于

(A.)11 (B).

(D). 22(4)“x>2"是“x2 +2x -8>0"成立的

(A) 必要不充分条件 (B)充分不必要条件 (C)充要条件 (D)既不充分也不必要条件

(5)已知直线x-my -1-m =0与圆x2+y2 =1相切，则实数m的值为

(A)l或0 (B)0 (C) -1或0 (D)l或-1

(6)执行如图所示的程序框图，如果输出的七的值为3，则

输入的a的值可以是

(A) 20 (B) 21 (C)22 (D) 23

(7)△ABC的角A,B,C的对边分别为a，b，c，

7，c-a=2,b=3，则a= 8

75 (A)2 (B) (C)3 (D) 2 2 若cosA=

(8)在一圆柱中挖去一圆锥所得的机械部件的三视图如图所示，则此机械部件的表面积为



 (C) 22

+6 7

x2y2x2y2

1与C2:221(a0,b0)的 (9)若双曲线C1:28ab

渐近线相同，且双曲线C2的焦距为

b=

(A)2 (B)4 (C)6 (D)8

(10)函数y=sin(x

(A)6)在x=2处取得最大值，则正数∞的最小值为 

(B) (C) (D) 2346

(11)已知等边△ABC的边长为2，若BC3BE,ADDC,则BDAE等于

(A) -2 (B)一1010 (C)2 (D) 33

(12)直线x=t分别与函数f(x)=ex+1的图像及g(x)=2x-l的图像相交于点A和

点B，则|AB|的最小值为

(A)2 (B)3 (C)4-21n2 (D) 3-21n2

第Ⅱ卷（非选择题 共90分）

本卷包括必考题和选考题两部分,第13题至第21题为必考题,每个考生都必须作答,第22题至第24题为选考题,考生根据要求作答.

二、填空题：本大题共5小题，每小题5分，共25分，把答案填在答题卡的相应位置上.

____．

2xy6014.已知实数x,y满足xy0,则目标函数zxy的最大值是x213. 函数f(x)=

15. 将2红2白共4个球随机排成一排，则同色球均相邻的概率为16. 已知函数则关于x的不等式f[f(x)]≤3的解集为三、解答题:本大题共6小题,共75分,解答应写出文字说明,证明过程或演算步骤. 17(本小题满分12分)

已知等差数列{an}的前n项和为Sn，S3= -15，且a1+l，a2+1，a4+1成等比数列， 公比不为1．

(I)求数列{an}的通项公式；

(Ⅱ)设bn=1，求数列{bn}的前n项和Tn. Sn

18(本小题满分12分)

某校拟在高一年级开设英语口语选修课，该年级男生600人，女生480人．按性别分层 抽样，抽取90名同学做意向调查．

(I)求抽取的90名同学中的男生人数；

(Ⅱ)将下列2×2列联表补充完整，并判断能否在犯错误的概率不超过0. 025的前提下

(Ⅱ)能否在犯错误的概率不超过0.05的前提下认为治疗是否有效与方案选择有关?

n(adbc)2

附:K,其中nabcd (

a2

19(本小题满分12分)

四棱锥EABCD中,AD//BC,ADAE2BC2AB2,ABAD,平面EAD平面 ABCD,点F为DE的中点.

(Ⅰ)求证:CF//平面EAB;

(Ⅱ)若CFAD,求四棱锥E-ABCD的体积.

20(本小题满分12分)

已知抛物线x22py（p>0),O是坐标原点，点A,B为抛物线C1上异于O点的两点，以OA为直径的圆C2过点B.

(I)若A（-2，1），求p的值以及圆C2的方程；

(Ⅱ)求圆C2的面积S的最小值（用p表示）

21(本小题满分12分)

已知函数f(x)exxlnx,g(x)etxx,(tR),其中e是自然对数的底数. (Ⅰ)求函数 f(x)在点（1，f（1））处切线方程;

(Ⅱ)若g(x)f(x)对任意x(0,)恒成立，求t的取值范围.

x2

请考生在第22题,23题,24题中任选一题作答,如果多做,则按所做的第一题计分,作答时请写清题号.

22(本小题满分10分)选修4-1:几何证明选讲

已知AB是圆O的直径,点C在圆O上(异于点A,B),连接BC并延长至点

D,使得BCCD,连接DA交圆O于点E,过点C作圆O的切线交AD于【合肥2016一模调研卷】

点F.

(Ⅰ)若DBA60,求证:点E为AD的中点;

1(Ⅱ)若CFR,其中R为圆C的半径,求DBA 2

23(本小题满分10分)选修4-4:坐标系与参数方程【合肥2016一模调研卷】

1x1t2(t为参数),以坐标原点为极点,x轴的非负半轴为极轴且两坐标系已知直线l:y2

中具有相同的长度单位,建立极坐标系,曲线C

的极坐标方程为2sina(a3) (Ⅰ)将曲线C的极坐标方程化为直角坐标方程;

(Ⅱ)若曲线C与直线l有唯一公共点,求实数a的值.

24(本小题满分10分)选修4-5:不等式选讲

已知a0,b0,

记ABab.

(Ⅰ)

B的最大值;

(Ⅱ)若ab4,是否存在a,b,使得AB6?并说明理由.

合肥2016一模调研卷(三)
2016合肥一模语文试卷(带答案)

合肥2016一模调研卷(四)
2016合肥一模英语含答案

合肥市2016年高三第一次教学质量检测

英语试题

（考试时间：120分钟满分:150分）

第I卷（三部分，共115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 will Jack do this weekend?

A. Go for a picnic . B. Make some plans. C. Work on his paper.

2. What-s the woman's favorite sport?

A. Basketball. B. Tennis. C. Baseball.

3. What is the weather like now?

A. Rainy. B. Cloudy. C. Windy.

4. What are the speakers talking about？

A. Public transportation.

B．Ways to get to school.

C. Advantages of riding a bike.

5. What was the woman's problem?

A. She got on the wrong train.

B. She got into the wrong carriage.

C. She lost her train ticket.

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 does the man want to do?

A. Buy a T-shirt. B. Exchange a T-shirt. C. Return a T-shirt.

7. What's wrong with the T-shirt?

A. It has a hole in the collar.

B．It-s not a good match.

C．It-s the wrong color.

听第7段材料，回答第8.9题。

8. Why is the woman going to the library?

A．To return some books.

B. To prepare for the exams.

C. To borrow magazines and newspapers.

9. What are the speakers going to do in the afternoon?

A. Go swimming. B. Read in the library. C. Attend a chemistry class.

听第8段材料，回答第10至12题。

10. What did the woman do at the weekend?

A. She hung out with her friends.

B. She attended a board meeting.

C. She prepared a report for a meeting.

11. Why is the woman so tired?

A. Because she has overworked for half a month.

B. Because she has got a serious sleep problem.

C. Because she stayed up all night yesterday.

12. What does the man advise the woman to do?

A. Ask the boss for an extension.

B. Put off the board meeting.

C,. Stick to the scheduled time.

听第 9段材料,回答第 13至 16题。

13. When is the woman leaving for Hawaii?

A. In two weeks. ' B. Next Wednesday. C. In early November.

14. How long will the woman stay there?

A. Two days. B. Twelve days. C. Fourteen days.

15. What festival falls on the day when the woman arrives?

A. Christmas. B. Thanksgiving. C. New Year's Day.

16. Which of the following will the woman probably take as a gift?

A. French wine. B. Italian cheese. C. Chinese tea.

听第 10段材料,回答第 17至 20题。

17. Where does the speaker work? '

A. At a healthcare center. B. At a nursing home. C. At a local hospital.

18. What's the purpose of the lecture?

A. To draw people's attention to hand washing.

B. To introduce the Global Hand Washing Day.

C. To tell people to prevent some common illnesses.

19. How many seconds should we spend washing our hands at least?

A. Two. B. Twelve. C. Twenty.

20. What does the speaker suggest finally?

A. Exercising our fingers gently.

B. Making our hands dry in time.

C. Using some hand cream of good quality.

第二部分：阅读理解（共两节，满分40分）

第一节（共15小题；每小题2分，满分30分）

阅读下列短文，从每题所给的四个选项(A.B.C和D)中，选出最佳选项，并在答题卡上 将该项涂黑。

A

When you're looking forward to taking a holiday in Egypt, you're certainly not short of choices. The country has so many to see that you'll probably not want to limit yourself to just one city.

Hurghada-A Water Sports Paradise

With 250 hotels ranking from comfortable 3-star hotels

Lip to 5-star accommodation, the main attraction of

staying

here is the activities in and on the warm waters. It has

become

an international centre for water sports, allowing visitors

to

take part in surfing, sailing and deep sea fishing. The

waters

are also home to a huge variety of coral and fish, making it a dream spot for diving. If all that isn-t enough, Hurghada is home to some of the world's finest underwater gardens. Luxor-An Open Air Museum of Ancient History

For those with an interest in Egyptian history, Luxor

is an

excellent place to stay and is built upon the site of the

ancient

Egyptian city of Thebes. If you make this the base for your

Egypt holiday, you're basically staying in an open air

museum!

The modern city of Luxor has the ruins of Karnak. Across the

Nile lie many more monuments, temples and tombs including the Valley of the Kings and the Queens. The Nile sailing is necessary for those with an interest in the country's ancient history. Cairo- The Capital City

Finally, of course, there's Cairo. It-s definitely a

starting

point for most of Egypt holiday makers. Cairo offers an

excel-

llent mix of culture, art, cooking and sightseeing chances.

With

the famous pyramids, various temples and some

fascinating

museums, Cairo is a fantastic choice if you can come to the city.

.

A. the funniest botanic gardens

B. choices of water activities

C. a brief history of Egypt D. the mix of culture and art

22. Which of the following cities do most tourists visit first in Egypt?

A. Cairo. B. Luxor. C. Thebes. D. Hurghada.

23. This passage is most probably taken from _ .

A. a historical document B. a science magazine

C. a travel guide D. a book review

B

It-s the universal cry of parents. "Get a job! " Soliman's mother told Soliman on the second day of his college breaks.

After years of delivering furniture for his mother'-s store, he knew many people had things they wanted to get rid of. If he borrowed his mom's truck, he could make a little money by carrying away their garbage.

One night, Soliman came up with a name for his new business - College Hunks Hauling Junk. He advertised the next day, and within hours, his phone rang. He asked his friend Friedman to help. They made $ 220 in three hours by cleaning out a woman-s garage. Soliman and Friedman earned $ 10,000 that summer. But the two weren't ready to become full- time garbage mcn after graduation. "We were trained to finish college and get a good job," says Soliman, who first worked at a research firm. Friedman bccame an economic analyst.

After working for the firm and the company for a while, both of them changed their minds. They quit their jobs and restarted their business, but had trouble finding a bank willing to lend them money. "Within months," says Friedman, "we were pretty upset. " At last, one bank risked lending them $ 50,000. At first, they lost money. One customer asked them to deal with a dozen garbage cans filled with construction garbage. They

measured the job by volume instead of by weight and charged just $ 130. "The cans were so heavy that it took us two and a half hours," says Soliman, "And it cost us more than $ 250 to carry the load. "

However, the tough experience taught them a lesson. They reduced the cost of

unloading by recycling metals and electronics. Just four years later, they ran a nationwide company that earned $ 3 million in 2014. " I figured if Nick and I failed, we'd learn more from failing than from not trying at all," says Soliman.

24. What does Soliman find when helping to deliver furniture?

A. Some parents want their kids to work at college breaks.

B. Many families have things they don't want to keep.

C. His mom's truck works well in carrying heavy furniture.

D. It's hard to make money by carrying away the garbage.

25. What makes Soliman think of starting his new business?

A. His working experience in his mother's store.

B. His strong desire to make use of the garbage.

C. His hatred for people's throwing away things.

D. His much available time at college breaks.

26. How did Soliman and Friedman cut the cost of the company?

A. By filling the cans with more garbage.

B. By measuring the job by volume.

C. By reducing the working hours.

D. By recycling something useful.

27. Which of the following can be learned from the passage?

A. Easier said than done. B. Nothing succeeds like success.

C. Two heads are better than one. D. Nothing is impossible to a willing heart. C

Blue whales are the largest animals ever known to have existed on the planet, and they can grow to a length of 100 feet and weigh more than 330,000 pounds. But recently researchers have found that these whales are on the move and they have migrated from California waters to areas off Canada and Alaska for the first time since commercial

whaling ended in 1965.

The researchers identified 15 blue whales that have appeared off the coast of British Columbia and the Gulf of Alaska since 1997. Four of these whales were recognized as ones that were once sighted off California shores, suggesting that the whales are returning to an old migration pattern between the coasts.

Before commercial whaling began in the early 1900s, blue whales were found widely throughout the North Pacific and California waters. But from the 1920s to the 1960s, whaling severely reduced the whale populations. Blue whales never recovered in the Northern Pacific, making sightings in this area rare. However, much larger groups of whales have been observed close to California since the 1970s.

The scientists had previously thought that the California population was separate from the population that had historically lived in North Pacific waters. But the current study shows that whales off the coast of British Columbia and the Gulf of Alaska are likely part of the California population.

To identify the blue whales, the researchers looked at photos of cetaceans taken in the North Pacific Ocean and compared them with a library of blue whale pictures taken along the West Cost of the United States and Southern Pacific. Up to now, the researchers are not quite sure why the whales are changing their migration patterns, but they suspect that the whales may be following their food moving farther north by the changes in ocean conditions.

28. According to the passage, blue whales are .

A. following a fixed route of migration

B. dying out due to commercial whaling

C. moving from the south to the north

D. rarely found in the Southern Pacific

.

A. is different from the California population

B. is probably part of the California population

C. has become the largest group since the 1970s

D. has lived there since the 1960s

30. The underlined word "cetaceans" in Paragraph 5 probably means .

A. land creatures B. whale species

C. ocean conditions D. migration patterns

31. What might make blue whales migrate according to the researchers?

合肥2016一模调研卷(五)
2016合肥一模地理试卷(带答案)

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