数学20分钟专题突破09解三角形一.选择题1.△ABC的内角A.B.C所对的边分别为a.b.c.若sinA=.b=sinB.则a等于 A. B. C. ——青夏教育精英家教网—

数学20分钟专题突破09

解三角形

一.选择题

1.△ABC的内角A、B、C所对的边分别为a、b、c，若sinA=，b=sinB，则a等于（）
A. B. C. D.

2.在△ABC中,A=，b=1，面积为，则=（）

A． B． C．2 D．4

3.在△ABC中，tanA＝，cosB＝．若最长边为1，则最短边的长为（）

A． B． C． D．

4．在△ABC中，角A，B，C的对边为a,b,c，若，，，则角A=（）

A．30° B．30°或105° C．60° D．60°或120°

二.填空题

1.已知为的三个内角的对边，

向量，．若，且，则角．

2.在中，角所对的边分别为，则．

三.解答题

（2008年高考全国二17）．在中，，．

（Ⅰ）求的值；

（Ⅱ）设的面积，求的长．

答案：

一.选择题

1.〖解析〗由得．

〖答案〗D．

2. 〖解析〗在△ABC中，，；又，

．

〖答案〗C．

3. 〖解析〗由条件知A、B都是小于，所以角C最大，又，B最小，

由得，，所以最短边长为．

4. 〖解析〗，即，又，所以或．

〖答案〗D．

二.填空题

1. 〖解析〗，

由正弦定理得：，

．

〖答案〗．

2. 〖解析〗由及正弦定理得：，又，

两式平方相加得：．

〖答案〗13．

三.解答题

〖解析〗（Ⅰ）由，得，由，得．

所以．

（Ⅱ）由得，

由（Ⅰ）知，故，

又，故，．

所以．

试题详情

数学20分钟专题突破08

三角恒等变换

一.选择题

1．若，则的值为（　　）

Ａ．Ｂ．Ｃ．Ｄ．

2.=（）

A. B. C. 2 D.

3.函数是（）

A．周期为的奇函数 B．周期为的偶函数

C．周期为的奇函数 D．周期为的偶函数

4．求值（）A． B． C． D．

二.填空题

1．求值：_____________。

2．若则。

3．函数的最小正周期是___________。

4．的三个内角为、、，当为时，取得最大值，且这个最大值为。

三.解答题

6.已知函数 6ec8aac122bd4f6e ．

（Ⅰ）若，，求的值；

（Ⅱ）求函数在上最大值和最小值．

答案：

一.选择题：

1.〖解析〗由,

∴sinα+cosα=．

2. 〖解析〗．

〖答案〗C．

3. ．选C ，为奇函数，

4.C

二.填空题

1.

2．

3．，

4．

当，即时，得

三.解答题

〖解析〗（Ⅰ）

由题意知：，即．

∵，即，

∴，．

（Ⅱ）∵ ，即，

∴，．

试题详情

数学20分钟专题突破07

平面向量

一.选择题

1.在平行四边形ABCD中，AC为一条对角线，若，,则（）

A．（－2，－4） B．（－3，－5） C．（3，5） D．（2，4）

2.已知向量，若与垂直，则（Ｃ）

A． B． C． D．4

3.已知是平面上的三个点,直线上有一点,满足,则等于( )

A. B. C. D.

4.已知，是平面内两个互相垂直的单位向量，若向量满足，则的最大值是( )

A. 1 B. 2 C. D.

二.填空题

1.如图，在平行四边形中，，

则．

6ec8aac122bd4f6e 2.如图，在中，，是边上一点，，则　　　　　．

三.解答题

已知ΔABC三个顶点的直角坐标分别为A(3，4)、B(0，0)、C(，0)．

(1)若，求的值；

(2)若，求sin∠A的值

答案：

一.选择题

1.〖解析〗因为，选B．

〖答案〗B．

2. 〖解析〗∵2－与垂直. ∴(2－)?=0, 而2－= (3 , n) , ∴－3+n²=0 , 而||²== 4 即 ||=2 . 两个非零向量⊥?=0x₁x₂+y₁y₂=0 , ||²=² = x² +y²．

〖答案〗C．

3. 〖解析〗依题∴

〖答案〗A．

4. 〖解析〗

∴，则的最大值是；

∴，对应的点A,B在圆上,对应的点C在圆上即可.

〖答案〗C．

二.填空题

1.〖解析〗令，，则

所以.

〖答案〗3．

2. 〖解析〗在中，有余弦定理得，，

由正弦定理得，则，在中，由余弦定理求得，则，

由余弦定理得，

_．

〖答案〗．

三.解答题

〖解析〗 (1) ，，

由得．

(2) ，，，

．

试题详情

数学20分钟专题突破06

三角函数

一.选择题

1.函数y＝sin(x＋)(0≤x≤)是R上的偶函数，则＝( )　

(A) 0 (B) (C) (D)

2.已知如图是函数y＝2sin(ωx＋)的图象(其中｜｜＜)，那么

6ec8aac122bd4f6e Aω＝，＝； Bω＝，＝－；

Cω＝2，＝； Dω＝2，＝－．

3.点P从（1，0）出发，沿单位圆逆时针方向运动弧长到达Q点，则Q点的坐标为（）

（A）（B）（C）（D）

4.下列与的值相等的式子为

A. B. C. D.

5. 设，如果且，那么的取值范围是

A. B. C. D.

二.填空题

1. .圆的一段弧长等于该圆外切正三角形的边长,则这段弧所对圆心角的弧度数是 .

2.. 已知，sin()=－ sin则cos= .

3.已知,其单调递增区间为 .

4.在△中，已知，三角形面积为12，则 .

三.解答题：

已知函数f(x)=2cos²x+sin2x+m(mR)．若x[0，]，且f(x)的最小值是2，求m的值．

答案：

一.选择题

1.解：把＝0，，，分别代入原函数验证，可知仅当＝时为偶函数，故选(C)．

2.解：观察各选择答案可知，应有ω＞0，观察图象可看出，应有T＝＜2π，

∴ω＞1 ，故可排除A与B，由图象还可看出，函数y＝2sin(ωx＋)的图象是由函数y＝2sinωx的图象向左移而得到的，∴＞0，又可排除D，故选C

3. 解：记，由三角函数定义可知Q点的坐标满足，故选（A）．

4. 选D

5 选C.

二.填空题：

1.

2.

3.

4.

解答题：解：由已知得f(x)=1+cos2x+sin2x+m=2sin(2x+)+m+1．当x[0,]时， 2x+[，]，此时当2x+=时，f(x)的最小值是+m+1=2，∴m=2．

试题详情

河北省石家庄市2009年高中毕业班一模

理综

可能用到的相对原子质量：

As―75 C―12 N―14 O―16 Na―23 Mg―24 Al―27 S―32 Cl―35.5

试题详情

山东省潍坊市2009年高考一模

基本能力测试

试卷类型：A

说明：本试题分第Ⅰ卷和第Ⅱ卷两部分，共12页，满分100分。以考生实际得分

的60％计人总分。用时120分钟。答题前，考生务必用O.5毫米的黑色签字笔将自己

的姓名、座号、准考证号、考试科目涂写在答题卡和试卷规定的位置。考试结束后，将

本卷、答题卡一并交回。

第Ⅰ卷选择题(共30分)

注意事项：

1．每小题选出答案后。用2B铅笔把答题卡对应题目的答案标号涂黑。(特别强

调：鉴于还没有阅“基本能力”答题卡的配套设备，为方便本次闲卷，每位考生在认

真填涂“基本能力”答题卡的前提下，再将I卷选择题答案重涂在另一答题卡上。)

如需改动，用橡皮擦干净后，再选涂其它答案标号。不涂答题卡，只答在试卷上的不得

分。

2．第Ⅰ卷共30小题，全部为单项选择题，每小题1分，共30分。

3．答题卡科目涂写要求：文科和艺术文考生在科目处涂物理，理科、艺术理和体

育考生在科目处涂政治。

试题详情

平遥中学08-09学年高二下学期三月质检

英语试题

满分150分，时间120分钟；命题人：王晓玮

第一卷

第一部分：单项填空（共15小题；每小题1分，满分15分）

从A、B、C、 D四个选项中，选出可以填入空白处的最佳选项.

1． person like him won’t be satisfied with little progress that he has made.

A．The；a B．The；／ C．A：／ D．A：the

2．-----You just think of yourself! You kept me waiting for at least three hours．

----- I am sorry that you ________ think so．

A．should B．would C．migh t D．could

3．----- What do you think of the furniture on exhibition?

----- Well，great! But I don’t think much of__________ you bought．

A．the one B．it C．that D．which

4．------Did Alice enjoy the concert held in Xi Yuan Theater yesterday?

------Yes．she did．She ________ such an excellent concert for a long time．

A．didn’t take part in B．wouldn’t take in

C．hasn’t been in D．hadn’t been in

5．I’m sorry，but I didn’t see how we can get all this work you assigned_______ by next Tuesday．

A．having done B．done C．being done D．to do

6．They have _____ most carefully the time and money needed to complete the project.

A．picked out B．left out C．figured out D．taken out

7.This kind of cloth _______ well. I think it is worthy ________.

A. washes; buying B. is washed; buying

C. washes; to be bought D. is washed; to be bought

8．Have you got any explanation to the question________ he came here for the day before yesterday?

A．why B．what C．how D．which

9. Christmas is a holiday usually celebrated on December 25th ____ the birth of Jesus Christ.

A. in charge of B. in terms of C. in favor of D. in honor of

10. These problems,____ will seriously affect the growth of teenagers and even the nation's future.

A. not if solved properly B. if solved properly

C. not if properly solved D. if not solved properly

11. --- “I’m afraid I can’t finish the magazine within the required time.”

--- “ .”

A．Please go ahead B．That’s right

C．Not at all D．Take your time

12. It’s _____ me why Alice, aged 28, gave up her job and got married to a man of 62.

A. under B. above C. beyond D. over

13. ------The English exam is not difficult, is it?

------ ______, even Tom ______ to the top students failed in it.

A. Yes, belongs B. No, belonged C. Yes, belonging D. No, belonging

14．$100 a month could hardly the cost of his life in such a big city in this country.

A．cover B．afford C．include D．contain

15. -----How ____feel to be home again after 20 years abroad ?

------Exciting .

A . do you B. does that C. did you D. does it

第二部分：完形填空 (共20小题；每小题2分，满分40分)

阅读下列短文，掌握其大意，从短文后每题所给的A、B、C、D四个选项中，选出可以填入空白处的最佳答案。

第二节：完形填空（共20小题；每小题1.5分，满分30分）

阅读下面短文，掌握其大意，然后从16-36 各题所给的四个选项（A、B、C和D）中，选出最佳选项，并在答题纸上将该选项标号涂黑。

That which cometh from the heart goes to the heart.-------- Jeremiah Burroughs

I was working as a consultant(someone whose job is to give advice on a particular subject) in a beer company, helping the president and senior vice-presidents formulate(develop something) and implement(take action) their new strategic vision. It was a big 16 .

At the same time, my mother was in the final stages of cancer.

I worked during the day and drove 40 miles home to be with her every night. It was 17 and stressful, but it was 18 I wanted to do. My promise was to continue to do excellent consulting during the day, 19 my evenings were very hard. I didn’t want to 20 the president with my situation, yet I felt someone at the company needed to know what was 21 on. So I told the vice-president of Human Resources, asking him not to share the information 22 anyone.

A few days 23 , the president called me into his office. I 24 he wanted to talk to me about one of the many issues we were 25 . When I entered, he asked me to 26 . He faced me from across his large desk, 27 me in the eye and said, “I hear your mother is very ill.”

I was 28 caught by surprise and burst into 29 He just looked at me, let my crying die down, and then 30 said a sentence I will never forget: “ 31 you need.”

That was it. His 32 and his willingness to both let me be in my pain 33 to offer me everything were 34 of compassion（同情）that I carry with me 35 this day.

16. A. work

B. challenge

C. employment

D. career

17. A. interesting

B. exciting

C. tiring

D. annoying

18. A. that

B. what

C. which

D. where

19. A. even though

B. even if

C. what’s more

D. as if

20. A. worry

B. disappoint

C. bother

D. excuse

21. A. happening

B. doing

C. keeping

D. going

22. A. with

B. in

C. on

D. at

23. A. after

B. later

C. in

D. before

24. A. hoped

B. expected

C. figured

D. wished

25. A. working on

B. studying

C. engaging

D. involving

26. A. stand up

B. sit down

C. go away

D. settle down

27. A. watched

B. stared at

C. glared at

D. looked

28. A. directly

B. slightly

C. totally

D. carefully

29. A. tears

B. laughing

C. crying

D. laughter

30. A. angrily

B. gently

C. gladly

D. hurriedly

31. A. However

B. What

C. Nothing

D. Whatever

32. A. understanding

B. courage

C. bravery

D. appreciation

33. A. or

B. and

C. but

D. so

34. A. spirits

B. strength

C. encouragement

D. qualities

35. A. by

B. until

C. to

D. till

第三部分：阅读理解（每题3分, 满分60分）

阅读下面的短文，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

218 Chestnut Street　
　　Philadelphia, PA28774
　　May 7th, 2002
　　Social Security Administration
　　2119 Main Street
　　Philadelphia, PA28000

Dear Social Security,
　　I am applying for a new Social Security Card.
　　I lost my old one last week. I was walking home from the subway station, and I pulled a tissue （纸巾）out of my pocket and lost my wallet at the same time. My card was in my wallet. Please send me a new card. If you can get the card to me within two weeks, please sent it to the address at the top of the page. If it will take longer than this, then you will have to send it to my new address. I am moving on May 23rd to:
　　103 Walnut Street
　　Philadelphia, PA28445
　　If you can send my new card within two weeks, I would be very pleased. I am applying for a new job at Ventura Savings Bank, and I know they will want to have my Social Security Number. Unfortunately I have forgotten it, so I will need my card to find out. On my old card I was called Victoria Matthews. Since then I have gotten married. Please issue my new card in my married name: Victoria Villata. In case you need more information about me to hunt down my old number, my date of birth was September 11, 1985. Thank you very much.
　　Sincerely
　　Victoria Villata n

36.Why does Mrs. Villata need a new Social Security Card?
　　A. She is moving.
　　B. She lost the old one.
　　C. She has just gotten married.
　　D. She doesn’t remember her Social Security Number.
37.Why does Mrs. Villata give the Social Security Administration her date of birth?
　　A. She wants them to know how old she is.
　　B. She is afraid they may have lost her Social Security Card.
　　C. She thinks it will help them track down her Social Security Number.
　　D. She thinks that the older she is, the more Social Security she will get.
　38.Which part of Victoria Villata’s letter is LEAST important to the Social Security Administration?
　　A. The fact that she has changed her name.
　　B. The fact that her card should be mailed to a new address.
　　C. The fact that she needs a replacement Social Security Card.
　　D. The fact that she lost her wallet while pulling a tissue out of her pocket.

　　 B

Dr Wiseman started “the laugh lab” project in September 2001. It is the largest study of humour. Participants（参加者）are invited to log on to the laugh lab website, give a few personal details, tell their favourite jokes and judge the jokes told by other people.
　　The project will last for a year, and the organizers hope to finally discover the world’s funniest joke. But there is also a serious purpose. The researches want to know what people from different nations and cultures find funny. And they want to find out the differences between the male and female sense of humour. The idea is that if we want to understand each other, we have to find out what makes us laugh.
　　This is a subject that has long interested psychologists（心理学家）and philosophers（哲学家）. Most of the time, people are not completely honest. We do things that society expects us to and say things that help us get what we want. But laughing cannot be controlled. When we laugh, we tell the truth about ourselves.
　　By December 2001 over 10, 000 jokes had been submitted. This gave the scientists enough evidence （证据）to make early conclusions. It seems that men and women do have different senses of humour, for instance.
　　“Our findings show the major differences in the ways in which males and females use humour, ” said Dr.　Wiseman. “Males use humour to appear superior（优越）to others, while women are more skilled in languages and prefer word play. ”
　　Researchers also found that there really is such a thing as a national sense of humour. the British enjoy what is usually called “toilet humour”. But the French like their jokes short and sharp: “You’re a high priced lawyer. Will you answer two questions for 500?” “Yes. What’s the second question?”
　　The Germans are famous for not having a sense of humour. But the survey found that German participants were more likely to find submitted jokes funny than any other nationality. Perhaps that proves the point. Is this joke funny? I don’t know, but let’s say yes, just to be safe.
　　Dr Wiseman and his workmates also submitted jokes created by computer. But none of those who took part in the survey found any of them amusing. Perhaps this is relief. Computers already seem like they can do everything. At least they should leave the funny stuff to us.
　　39．Scientist started“ the laugh lab” project________
　　A. to find the funniest joke in European countries
　　B. to know what funny people are from different nations and cultures
　　C. to find out the differences between the male and female sense of humour
　　D. to get more personal details about participants
　　40．We can infer from the passage that________.
　　A. most of the people all over he world are completely honest
　　B. psychologists and philosophers take interest in the “laugh lab” project
　　C. ordinary people are not interested in “the laugh lab” project at all
　　D. people tell the truth about themselves only when they laugh
　　41．What is the main idea of the 4th and 5th paragraph?
　　A. Man and woman have different senses of humour.
　　B. male and female have similar senses of humour.
　　C. About 10, 000 jokes have been submitted from September 2001 to December 2001.
　　D. Scientists have collected enough evidence to make conclusions.
　　42．The writer gave the examples of the British, the French and the Germans________.
　　A. to show that French people have a better sense of humour
　　B. to prove the British people have a sense of “toilet humour”
　　C. to show people from different nations have different senses of humour
　　D. to prove that the Germans have no sense of humour
　　43．Which statement is true according to the passage?
　　A. The jokes by computer are less funny than those by humans.
　　B. The Germans cannot find the submitted jokes amusing.
　　C. Males are better at word play compared with women.
　　D. Females like to use humour to show that they are superior.

Several days ago, a Beijing - based IT company fired about 400 people overnight. No one had expected the job cuts, which broke with traditional ways of letting go of workers in China. Moreover, what was special about this case was that the day before the 400 were fired, they all received from their boss a gift - the book “Who Moved My Cheese?”.
　　The book - a bestseller in the US - is being used by men and women to deal with changes in their lives and work. Some large organizations, including Coca- Cola, Kodak and General Motors, ask their employees to read it in order to encourage them to be active towards changes.
　　Cheese is something related to everyone’s livelihood - our jobs, the industries we work in, relationships and love as well.
　　With China’s official entry into WTO, the whole nation will face up to more changes and challenges. So what should we do once this “cheese” on which we are so dependent is moved?
　　“Whatever challenges and changes we meet, we should face up to them bravely” Jiang Hengwei, a civil servant said after reading the book.
　　Professor Yang in Renmin University of China agrees. “We should change our way of thinking. The coming competitive foreign companies and products provide us with great chances to learn from them and improve our own products to meet international standards and be more competitive.”
　　“With hard work and wisdom, we will create a much larger and better piece of cheese. ”Zhang smiled confidently.
　　44．The whole passage is about________.
　　A. a bestseller in the US
　　B. what people think about China’s entry into the WTO
　　C. people’s attitude toward changes and challenges
　　D. how a book influences the Chinese workers
　　45．The company in Beijing gave each of the 400 fired workers a copy of “Who Moved My Cheese” in order to________.
　　A. be more competitive with foreign firms
　　B. find an excuse for their job cuts
　　C. let the workers make a living on their own
　　D. encourage the fired workers
　　46．The word “cheese”in the passage can refer to________.
　　A. something we depend on for a living
　　B. a most important kind of food
　　C. change or challenge
　　D. way of life
　　47．From what Hengwei and Professor Zhang Yang said, we can know that________.
　　A. they have different opinions on changes and challenges
　　B. people are not afraid of competition from foreign companies
　　C. the Chinese people are ready to face any changes and challenges
　　D. they are both greatly encouraged by the book

D

If you don’t want people to know too much about you, then you had better keep your fridge contents secret according to a British market research document released last week.

Researchers peered (凝视) into the fridges of 400 people in Britain and compared the contents with the owners’ lifestyles. They claim to be able to classify the nation’s people by fridge contents.

They say those people can be separated into five categories："nutrition nerds (no social sense)", "food faddies (whatever’s in style)", "martyr mums", "fast food fanatics" and "restaurant regulars".

"Nutrition nerds" care much about what they put into their bodies. Their fridges are stocked with fruit, vegetables and healthy meat.

People in this category tend to be highly organized and usually work in law or accountancy. The vast majority are single, but if they have a partner, that person will be similar.

A fridge full of vitamins ― enriched juices implies its owner works in media or fashion. They tend not to eat the foods they buy. Known as the "food faddies", they just want to be seen as purchasing the latest important things.

A fridge filled with everything from steak to frozen fish suggests the "martyr mum". Her fridge tends to be stocked with every kind of product, except what she herself would want. This fridge hints at difficulty balancing family and work life.

"Fast food fanatics" always buy mineral water for soda pop; the nearest they will get to fresh fruit is tomato sauce. Their fridges hint at someone who works hard and plays hard. Also, someone who is not into long term planning.

Finally, a fridge filled with nothing more than a bottle of white wine and some sparkling mineral water implies an owner who is single, lives in a big city and enjoys the finer things in life. The fridge is empty because this person regularly eats in restaurants.

48．We can know from the first two paragraphs that ______.

A．some researchers are fond of staring at other people’s fridges

B．people don’t want others to know about their secrets

C．the food you put in the fridge has something to do with your personality

D．there are mainly five kinds of lifestyles among British people

49．According to the passage, people who belong to "food faddies" ______.

A．don’t care much about money when buying things

B．will try their best to stay healthy

C．often stay up late to finish their job

D．prefer to ask others about what to do next

50．What will those who often dine out put in the fridge?

A．All kinds of food they like. B．Only something to drink.

C．Fruit, vegetables and meat. D．Food rich in vitamins.

51．What might be the most suitable title for the text?

A．Keep your fridge a secret B．You are what’s in your fridge

C．What to put in the fridge? D．Be careful about your fridge

E

Botany, the study of plants, plays a strange role in the history of human knowledge. For many thousands of years it was one field about which humans had little knowledge. It is impossible to know today just what our Stone Age Ancestors knew about plants, but from what we can observe of preindustrial societies that still exists, a detailed learning of plants and their properties（特征）must be very ancient. This is reasonable. Plants are the basis of the food pyramid for all living things, even for other plants. They have always been greatly important to the good of peoples, not only for food, but also for clothing, weapons, tools, medicines, housing, and a great many other purposes. Tribes(部落)living today in the woods of the Amazon recognize hundreds of plants and know many properties of each. To them botany, as such, has no name and is probably not even recognized as a special branch of knowledge at all.

Unfortunately, the more industrialized we become the farther away we move from direct relation with plants, and the less clear our knowledge of botany grows. Yet everyone comes unconsciously on a surprising amount of botanical knowledge, and few people will fail to recognize a rose or an apple. When our New Stone Age ancestors, living in the Middle East about 10 000 years ago, discovered that certain grasses could be harvested and their seeds planted for richer production the next season, the first great step in a new connection of plants and humans was taken. Grains were discovered and from them flowed the marvel of agriculture: planted crops. From then on, humans would increasingly take their living from the controlled production of a few plants, rather than getting a little here and a little there from many varieties that grew wild and the collected knowledge of tens of thousands of years of experience and close relations with plants in the wild would begin to disappear.

52. Which of the following assumptions（假设）about early humans is expressed in the passage?

A. They probably had wide knowledge of plants.

B. They clearly divided knowledge into separate fields

C. They did not enjoy the study of botany.

D. They placed great importance on ownership of property.

53.According to the passage, why has general knowledge of botany decreased?

A. People no longer value plants as a useful resource.

B. Botany is not recognized as a special branch of science.

C. Research is unable to keep up with the increasing number of plants.

D. Direct relation with a variety of plants has decreased.

54.In paragraph 2, the underlined word “marvel” is closest in meaning to _____.

A. edge B. sign C. beginning D. wonder

55. According to the passage, what was the first great step toward the practice of agriculture?

A. The invention of agriculture tools and machines.

B. The development of a system of names for plants.

C. The discovery of grasses that could be harvested and replanted.

D. The changing food of early humans.

第II卷（共35分）

第四部分：写作（共两节，满分35分）

第一节 短文改错（共10小题；每小题1分，满分10分）

此题要求改正所给短文中的错误。对标有题号的每一行作出判断：如无错误，在该行右边横线上画一个勾（√）；如有错误（每行只有一个错误），则按下列情况改正：此行多一个词：把多余的词用斜线（\）划掉，在该行右边横线上写出该词，并也用斜线划掉。此行缺一个词；在缺词处加一个漏字符号（∧），在该行右边横线上写出该加的词。

此行错一个词：在错的词下划一横线，在该行右边横线上写出改正后的词。

注意：原行没有错误的不要改。

This city changed a lot in the past five years. First, 56.____________

more high buildings have appeared, that are modem and 57____________

beautiful. Many overpasses have set up, so it is very 58.____________

convenient for people to travel. However, many families 59.____________

have cars of their own. The people's life there has 60.____________

become richly and colorful. People can enjoy themselves 61.____________

travel on holidays. To my delight, I can taste delicious 62.____________

food of different country such as the food of America 63.____________

and Japan. And it's much more easier for me to keep 64.____________

in touch with you, for I can e-mail you in my office. 65.____________

第二节 书面表达（满分25分）

假如你叫李华，是某农村中学的学生。你校打算在教室里面安装空调，让学生讨论。请根据下表中讨论的结果，给校长写封信。

赞成观点

反对观点

你的观点

空调冬暖夏凉

优化学习环境

家庭条件好了

支付得起费用

装空调会污染环境

产生噪音影响学习

增加学生经济负担

有的家庭负担不起

不同意装空调，并给出你的理由：

①……

②……

③……

注意： 1．信的格式已经为你写好，不计人总词数。

2．词数：120词以上。

3．参考词汇：install air-conditioners

Dear headmaster,

With best wishes!

Yours,

Li Hua

英语答题卡

改错

书面表达

总分