高一 人教课标 必修3 unit 5 测试题
Unit 5 检测题
第一卷
第一部分：听力(略)
第二部分：英语知识运用
第一节单项填空
21. —Shall we go for a walk ________ watch TV?
—That’s a good idea.
A. instead of
B. rather than
C. in place of
D. in the place of
22. After Yang Liwei succeeded in circling the earth, ________ our astronauts desire to do is walk
in space.
A. where
B. how
C. that
D. what
23. A table made of steel costs more than ________ made of wood.
A. one
B. it
C. those
D. which
24. The launch pad from which Shenzhou VI is launched can be seen from a ________ of 10
miles.
A. length
B. distance
C. way
D. space
25. I can go anywhere if I ________ how to use the subway.
A. work out
B. make out
C. point out
D. figure out
26. —________ for the fire!
—It's OK. I’ll be careful enough.
A. Look out
B. Look around
C. Look through
D. Look up
27. Word came ________ China's second manned spacecraft Shenzhou VI blasted off into the sky
Wednesday morning October 12, 2005.
A. which
B. that
C. /
D. what
28. —Where do they live?
—________ I know, they live in the same town.
A. As long as
B. As far as
C. As well as
D. As often as
29. It’s getting dark. We’d better ________ in a hotel for the night.
A. set up
B. settle down
C. set out
D. settle up
30. It’s always difficult being in a forging country, ________ if you don’t speak the language.
A. especially
B. specially
C. extremely
D. obviously
31. They live in a beautiful village, with many trees and flowers ________ it.
A. surrounded
B. surrounds
C. surrounding
D. to surround
32. Poisonous things mustn’t be put ________ children’s reach so that they can’t cause unexpected
troubles.
A. into
B. out
C. within
D. near
33. The news ________ is spreading around China is that the bird-flu broke out in Anhui
Province.
A. that
B. what
C.／
D. whether
34. —Why is it hot in summer while cold in winter?
—It’s because we are ________ the sun while farther from it in winter.
A. close to
B. farther from
C. closer from
D. farther to
35. —I wonder what I should learn in the future?
—You may learn art since you ________ painting and drawing.
A. benefit from
B. have a gift for
C. look forward to
D. are tired of
第二节完形填空
Two men, both seriously ill, occupied the same hospital room. One man was allowed to 36 in his bed for an hour each afternoon for treatment. His 37 was next to the room's only window. The other man 38 spend all his time flat on his back. Every 39 when the man in the bed by the window could sit up, he 40 pass the time by describing to his 41 all the things he could see outside the window. The window overlooked a 42 with a lovely lake. Ducks and swans played on the water while children 43 their model boats. Young lovers walked 44 among flowers. As the man by the window described all this beautifully, the other man would close his eyes and 45 the scene.
One morning, the day nurse arrived to bring water for their baths only to find the 46 body of the man by the window, who had died 47 in his sleep. She was saddened and 48 the hospital attendants (服务员) to take the body away. 49 it seemed appropriate (合适的), the other man asked if he could 50 next to the window. The nurse was happy to make the switch, and after 51 he was comfortable, she left him alone. Slowly and painfully, he sat up to take his 52 look at the world outside. Finally, he would have the 53 of seeing it for himself. He strained (紧张地) to slowly turn to 54 the window beside the bed. It faced a blank wall.
The man asked the nurse what could have forced his dead roommate to 55 those wonderful things outside this window. The nurse answered that the man was blind and could not even see the wall. She said, “Perhaps he just wanted to encourage you.”
36. A. stand up B. lie down C. sit up D. sit down
37. A. room B. table C. seat D. bed
38. A. had to B. would rather C. prefer to D. rather than
39. A. morning B. evening C. afternoon D. dawn
40. A. will B. would C. should D. might
41. A. nurse B. workmate C. roommate D. doctor
42. A. park B. street C. garden D. field
43. A. played B. made C. started D. sailed
44. A. face to face B. shoulder to shoulder
C. arm in arm
D. back to back
45. A. describe B. tell C. hear D. imagine
46. A. strong B. warm C. sick D. lifeless
47. A. peacefully B. sadly C. secretly D. completely
48. A. looked B. found C. called D. ordered
49. A. Before B. As soon as C. When D. As far as
50. A. changed B. sit C. be moved D. be taken
51. A. making sure B. depending on C. making up D. accounting for
52. A. next B. first C. last D. another
53. A. surprise B. feeling C. try D. joy
54. A. look out B. look at C. glare at D. stare at
55. A. remember B. describe C. write D. talk
第三部分：阅读理解
A
Much has happened since July 3, 1608, when French explorer Samuel de Champlain established a settlement in a place called Kébec —an Algonquin word meaning where the River
narrows. He might not have realized at the time that this day marked the beginning of a permanent French presence in North America, after several unsuccessful attempts.
For people of French descent (血统), all over America, everything points back to Quebec City, recognized as the founding site of French civilization in North America. At one point, Quebec City was at the centre of an empire, New France, which covered all of Eastern Canada and almost half of the current US territory. French possessions (领地) in North America then reached from the Gulf of St Lawrence to the Great Lakes and from Hudson Bay to the Gulf of Mexico.
After having been the capital of France’s colonies in America, and then of Lower Canada, Quebec City became the capital of the province of Quebec in 1867, when the Canadian Confederation came into being. Quebec City has kept growing and prospering continuously until today. And this is why it remains known as the founding site of French North America.
However, this does not mean that Quebec City is a museum town, focused only on its heritage (遗产) and history. On the contrary, it is a modern, people-friendly city that is resolutely turned towards the future.
56. Which of the following statements is TRUE?
A. The empire of New France once controlled almost all of the America.
B. Quebec City is not only a museum town, but also the capital of France’s colonies.
C. July 3, 2008 will mark the 400th anniversary of the founding of Quebec City.
D. Samuel de Champlain established the empire of New France.
57. From this passage, we can infer that Quebec City ________.
A. was, is and will be an important and growing city
B. is the biggest French enclave (飞地) in Canada
C. belonged to France before the Canadian Confederation came into being
D. is located in the centre of Canada
58. The main purpose of the passage is to ________.
A. show us that in history Quebec City was once an important city
B. show us how Quebec City was established
C. tell us that Quebec City is a modern, people-friendly city
D. tell us a brief introduction of Quebec City
B
School is a place that is familiar to everyone. Let’s find out what American students do in school.
An official dance party is held about twice a year in high schools in the United States. When the final football game is over for the season there is a homecoming party. Sometimes, students select a king from among the football players, and a queen from among the girls. Every student can attend and have fun with the help of their teachers. Sometimes, students, called bookworms, to the surprise of the other students, come to the party in a beautiful dress.
The most exciting party that students can go to would have to be a dance party. Students attend it in dresses similar to those of Hollywood stars and the atmosphere is comparable to an Oscar Award party. Since such a party is for seniors, students usually stay up the night trying to enjoy their last year in high school.
In American schools, instead of the teachers going to different rooms, students have their own class schedules (课程表) and go to different classrooms. When a student is away from school, they must have an explanation for being away along with the signature(签名) of a parent. The
signed paper is then handed in to the school office. High school drop outs and students being expelled (除名) are not that uncommon in the States. High absences without excuses are one of the reasons why students are expelled from school. American students also enjoy a number of activities out of school like cheerleading (拉拉队), student government and a host of different sports.
59. Whose presence at the homecoming party can make others amazed?
A. The king and the queen acted by students.
B. The laziest student in study.
C. The teacher who offers advice.
D. Students who study hardest.
60. Why do students hold the dance party till the next morning?
A. Because they would like to dance and sang madly.
B. Because this is the only chance that they get dressed like film stars.
C. Because students make it as exciting as an awarding party of Oscar.
D. Because this perhaps is the last chance that they can enjoy their school life.
61. According to the passage, American students in school ________.
A. study in the same classroom
B. have the same class with each other
C. attend different classes in different places
D. wait for their teachers in their class
62. What is this passage mainly about?
A. The organizing of dance parties.
B. Homecoming party.
C. How to ask for a leave.
D. School life in America.
C
Vancouver is located in the southwest corner of Canada in the province of British Columbia. Vancouver is the largest city in the province and the third largest in Canada. It covers an area of 113 sq km. It is surrounded by water on three sides and overlooked by the Coast Range. Its climate is one of the mildest in Canada. Temperatures average 3°C in January and 18°C in July. Vancouver's most rainfall occurs in winter.
Archaeological evidence shows that coastal Indians had settled the Vancouver area by 500 BC. British naval (海军的) captain George Vancouver explored the area in 1792. Vancouver was founded as a sawmill settlement called Granville in the 1870s. The city was united in 1886 and renamed after Captain Vancouver.
As the main western terminus of Canada's transcontinental highway and rail routes, Vancouver is the primary city of western Canada, as well as one of the nation's largest industrial centres.
The Port of Vancouver is Canada’s largest and most various port, trading more than $43 billion in goods with more than 90 trading economies annually. Port activities generate 69,200 jobs in total with $4 billion in gross domestic product (GDP) and $8.9 billion in economic output.
Vancouver is a major tourist place. In addition to the city's scenic location, visitors enjoy beautiful gardens and world-famous Stanley Park, one of more than 180 city parks, and a combination of natural forest and parklands near the city centre.
63. Which of the following description about Vancouver is NOT true, according to the passage?
A. Vancouver is the third largest city in Canada.
B. Vancouver is a city located on water.
C. Vancouver is not far from the Coast Range.
D. The largest industrial centre in Canada lies in Vancouver.
64. According to the passage, originally Vancouver is the name of ________.
A. a British man who explored the city
B. a sawmill settlement called Granville
C. the leader who controlled the area
D. a transcontinental highway
65. The passage mainly tells us ________.
A. the Port of Vancouver, the largest one in Canada
B. how Vancouver got its name
C. Vancouver’s history
D. a brief introduction of the city of Vancouver
第二卷
第四部分：
第一节短文改错
In Canada you can find dogs, cats, horses and so
on in almost every family. People who love these pets 66. ________
and have them as their good friends. After they keep 67. ________
them in its houses, they take them to animal hospitals 68. ________
to give them injections (注射) so they will not carry 69. ________ disease. They have specially animal food stores, though 70. ________
they can get animal food in almost every store. Some 71. ________
people spend around two hundreds Canadian dollars a 72. ________
month on animal food. They have a law for killing wild 73. ________ animals. If you killed an animal, you would be published. 74. ________
If an animal happened to get run by a car, people would 75. ________
be very sad about it.
第二节书面表达
Smith先生是一位加拿大籍教师，今天他给你们做了一个讲座，介绍了有关加拿大的情况。请你根据Smith先生的讲座，写一篇报告，向全校同学介绍加拿大的有关情况。词数100左右。要点包括：
1. 加拿大约占世界四分之一陆地面积，是世界第二大国；
2. 人口稀少，全国人口约3200万，居民主要讲法语和英语；
3. 气候区域差别很大；
4. 多湖泊，淡水资源丰富；
5. 丰富的森林资源，是世界最大纸张出口国。
选做题：
阅读下面短文，根据文章内容回答下列问题。（
Since young I had been thinking about all the suffering in the world, wondering why this was so. As a child I was quiet, hardly spoke and thought too much in my own world.
In kindergarten (幼儿园) I had no one to turn to. My dad was always away for business so it was just my mom, my brother and me. My brother was often sick as a child and required a lot of
attention. One day after kindergarten I had an accident. A big kid on a bicycle sped by as I was walking home with a friend and hit me. The big kid hurriedly got back onto his bike and fled. I was bleeding from the knees where I fell hard on the sand. My walking friend was scared, but I was feeling more of something else than pain from the injury. I got up and then started crying.
I couldn’t stop crying. I still don’t und erstand why I cried so hard then, although I knew it was not from the pain of my knees. My friend begged me to stop crying and that he would take me home. I wouldn’t move. I didn’t want to go home because that was not where I found comfort.
After a long time, I finally moved away from the lamp post. We walked to where I lived. When my mother answered the door, my friend told her that I was hurt from the accident with a bicycle. That wound slowly healed too.
1. Why did the writer keep everything in his mind?
2. What made him always think about the suffering in the world?
3. What did he think about when the big kid rode away after knocking him down?
4. What does home mean in his mind?
5. What do you think of the writer’s character? Can you give any advice?
Unit 5检测题参考答案及重点解析
参考答案
1-5 CBCAB 6-10 ABCBC 11-15 CBABB 16- 20 CACCA
21-25 BDABD 26-30 ABBBA 31-35 CCAAB
36-40 CDACB 41-45 CADCD 46-50 DACBC 51-55 ABDAB
56-60 CADDD 61-65 CDBAD
66. 去掉who 67. After→Before 68. its→their 69. will后加not
70. specially→special 71. √72. hundreds→hundred
73. for→against 74. Whether→If 75. run后加over
书面表达
One possible version:
Today Mr Smith, from Canada gave us a lecture about his country. As the second largest country in the world, Canada covers about a quarter of the world’s land area. But its population is very small, about 32 million. People in Canada mainly speak French and English. The weather in Canada is quite different from area to area. There are many lakes in Canada, which supply it with one third of the world’s fresh water. Canada also has many forests, which make it the biggest producer of paper in the world. Besides, Canada also has lots of beautiful scenery.
选做题：
1. Because his parents were too busy to take care of him and he had no one to turn to.
2. It seems that he lacked of love and happiness in his boyhood, so he felt lonely and his heart was always dim.
3. He might think that he was so unlucky and so wea k that he couldn’t do anything to the kid. He also felt he was helpless not only at home but also outside.
4. He thought home was just a place where he might had his stomach filled or a place to sleep in but not a place to get love and justice.
5. I don’t think it a good way to face his life. He should have an active attitude towards life. He’d better learn to make friends and try to share his thought with them and try to help and understand his parents. So he can find his value and become light-hearted.
重点解析
21. B。句意为：我们是要去散步而不是去看电视么？答语是“我喜欢散步”。rather than意
为“而不是”。
22. D。这是一个主语从句，连接代词what在主语从句中作do的宾语。
23. A。one 指代a table，是泛指。
24. B。a distance of与数字连用，表示“……的距离”。
25. D。figure out的意思是“领悟到；弄明白”。句意为：我要是知道如何换乘地铁线，就可
以到处转一转了。
26. A。look out for sb / sth意为“当心；提防；留心防备”；watch over意为“看守；监视”；
put out可指把火扑灭；light up意为“点燃”。根据答语“没关系，我会很小心的”可知，第一个说话者是提醒要小心点，所以用look out。
27. B。考查同位语从句。在同位语从句中，连接词that不作成分，that引导的从句是word (消
息) 的内容。
28. B。as far as I know意为“就我所知”。
29. B。settle down意为“定居；平静下来”；set off意为“出发；动身”；take part in意为“参
加”；prepare for意为“为……做准备”。本句指“安定下来”。
30. A。句意为：在国外生活常遇到很多困难，特别是当你不会说那个国家的语言时。especially
指“特别；尤其”；specially指“专门地”；extremely指“极端地；非常地”；obviously 指“明显地”。
31. C。这里是with复合结构，trees and flowers与village是动宾关系，所以用动词-ing形式。
32. C。within one’s reach指在某人够得着的范围内。
33. A。用关系代词that引导定语从句，that指代先行词t he news，并在从句中作主语。后面
的that引导表语从句，that为从属连词，在从句中不作成分。
34. A。夏天热是因为离太阳比较近，所以用closer to。
35. B。have a gift for指在某方面有天赋。
听力原文
(Text 1)
W: Could you have my car ready at 5:00, please?
M: Sure, the damage is minor.
(Text 2)
W: Glad to see you again!
M: Me, too. I really enjoyed my trip to Canada.
(Text 3)
W: Louise speaks English as if she were an American.
M: Her family lived in the United States until Louise was 12 years old.
(Text 4)
W: Hello, this is Mary Conners. May I speak to my husband, please?
M: He has just gone out with a customer to show him a new car.
(Text 5)
W: Can you tell me the cheapest way to get to New York City?
M: If you go by bus it’s only $ 25. But if you go by train, it’s almost twice that much.
(Text 6)
M: That was my mother on the phone. She and my father will be here this Friday.
W: Yeah …
M: What’s the matter? Don’t you like them?
W: Sure I do! It’s their smoking I don’t like. I really don’t want them to smoke in the house.
M: They’re just here for the weekend. It’s not a big problem, is it?
W: We can ask them to smoke outside.
M: I guess you’re right. OK, you can tell them when they get here.
W: Me? Are you joking? They’re your parents! You tell them.
(Text 7)
W: Please turn off the light, Harry. If we turn on too many lights, all the electricity in the house will go off.
M: Now who told you that?
W: Our new neighbour Mr Smith. When I turned on the washing machine, all the lights went out.
So I had to go to his home for help today.
M: Well, did he take care of it for you?
W: Yes, but he said it would take a lot of work to do a really good job. He said that we needed new electric wires throughout the house and a lot of other things.
(Text 8)
W: How are you, Jimmy? Have you been to New York recently?
M: Not since we met at the airport. I’ve been busy here working as a guide at the Canyon all summer.
W: Have you seen any bears this summer?
M: There haven’t been any bears for several years. Too many people visit here every year.
W: Aren’t there any wild animals on this side of the Canyon?
M: Yes, there are a lot of deer in the forests. There must be a lot of wolves around. Quite a few people have heard them recently.
W: Have you seen any snakes?
M: Yes, there are a lot of them in the rocks around here.
W: I hope I won’t see any.
(Text 9)
M: Welcome back! I didn’t see you in physics class last Thursday.
W: I wasn’t here that day. I went on a trip to New York and just came back last night.
M: New York! What a beautiful city! I am sure you had lots of fun there.
W: No, not really. I was too busy doing business. It’s very hot there, too.
M: Well, did you visit any places of interest?
W: Yeah, I went to see the Statue of Liberty and that made the trip interesting.
M: I have never been to New York. I would like to go there some day.
W: Try to go during the spring or autumn when the weather is very nice.
(Text 10)
In the past, when people had problems, they went to their families or friends to get advice.
Today it is possible to get advice from radio shows, TV programs and telephone hotlines, too. A telephone hotline is one that offers a direct way of getting in touch with advisers. On most hotlines callers do not have to say their real names and telephone numbers. Most hotlines are usually free, too. Callers do not have to pay for the advice or the phone calls —even if they are long distance calls. On some hotlines, the advisers are volunteers. Other hotlines pay their advisers for their work. Usually the advisers are professionals with years of education and experience, but sometimes, the advisers take a short class before starting to work on the hotline. All the advisers listen to people and help them solve their problems.
高一英语人教版必修三Unit 5 课文内容
Unit 5 CANADA- “THE TRUE NORTH” A TRIP ON “THE TRUE NORTH” Li Daiyu and her cousin Liu Qian were on a trip to Canada to visit their cousins in Montreal on the Atlantic coast. Rather than take the aeroplane all the way, they decided to fly to Vancouver and then take the train from west to east across Canada. The thought that they could cross the whole continent was exciting. Their friend, Danny Lin, was waiting at the airport. He was going to take them and their baggage to catch “The True North”, the cross-Canada train. On the way to the station, he chatted about their trip. “You’re going to see some great scenery. Going eastward, you’ll pass mountains and thousands of lakes and forests, as well as wide rivers and large cities. Some people have the idea that you can cross Canada in less than five days, but they forget the fact that Canada is 5,500 kilometres from coast to coast. Here in Vancouver, you’re in Canada’s warmest part. People say it is Canada’s most popular cities to live in. Its population is increasing rapidly. The coast north of Vancouver has some of the oldest and most beautiful forests in the world. It is so wet there that the trees are extremely tall, some measuring over 90 metres.” That afternoon aboard the train, the cousins settled down in their seats. Earlier that day, when they crossed the Rocky Mountains, they managed to catch sight of some mountain goats and even a grizzly bear and an eagle. Their next stop was Calgary, which is famous for the Calgary Stampede. Cowboys from all over the world come to compete in the Stampede. Many of them have a gift for riding wild horses and can win thousands of dollars in prizes. After two days’ travel, the girls began to realize that Canada is quite empty. At school, they had learned that most Canadians live within a few hundred kilometres of the USA border, and Canada’s population is only slightly over thirty million, but now they were amazed to see such an empty country. They went through a wheat-growing province and saw farms that covered thousands of acres. After dinner, they were back in an urban area, the busy port city of Thunder Bay at the top of the Great Lakes. The girls were surprised at the fact that ocean ships can sail up the Great Lakes. Because of the Great Lakes, they learned, Canada has more fresh water than any other country in the world. In fact, it has one-third of the world’s total fresh water, and much of it is in the Great Lakes. That night as they slept, the train rushed across the top of Lake Superior, through the great forests and southward towards Toronto. “THE TRUE NORTH” FROM TORONTO TO MONTREAL The next morning the bushes and maple trees outside their windows were red, gold and orange, and there was frost on the ground, confirming that fall had arrived in Canada. Around noon they arrived in Toronto, the biggest and most wealthy city in Canada. They were not leaving for Montreal until later, so they went on a tour of the city. They went up the tall CN Tower and looked across the lake. In the distance, they could see the misty cloud that rose from the great Niagara Falls, which is on the south side of the lake. The water flows into the Niagara River and over the falls on its way to the sea. They saw the covered stadium, home of several famous basketball teams. As they walked north from the harbour area, Li Daiyu said, “Lin Fei, one of my mother’s old schoolmates, lives here. I should phone her from a telephone booth.”
高中数学必修五数列单元综合测试(含答案)
数列单元测试题 命题人：张晓光 一、选择题(本大题共10个小题，每小题5分，共50分，在每小题给出的四个选项中，只有 一项是符号题目要求的。) 1．已知等差数列{a n }的前n 项和为S n ，且满足S 33－S 2 2 ＝1，则数列{a n }的公差是( ) A.1 2 B ．1 C ．2 D ．3 2．设等比数列{a n }的前n 项和为S n ，若8a 2＋a 5＝0，则下列式子中数值不能确定的是( ) A.a 5a 3 B.S 5 S 3 C.a n ＋1a n D.S n ＋1S n 3．设数列{a n }满足a 1＝0，a n ＋a n ＋1＝2，则a 2011的值为( ) A ．2 B ．1 C ．0 D ．－2 4．已知数列{a n }满足log 3a n ＋1＝log 3a n ＋1(n ∈N *)且a 2＋a 4＋a 6＝9，则log 13 (a 5＋a 7＋a 9)的值是 ( ) A ．－5 B ．－15 C ．5 D.15 5．已知两个等差数列{a n }和{b n }的前n 项和分别为A n 和B n ，且A n B n ＝7n ＋45n ＋3，则使得a n b n 为正偶数 时，n 的值可以是( ) A ．1 B ．2 C ．5 D ．3或11 6．各项都是正数的等比数列{a n }的公比q ≠1，且a 2，1 2a 3，a 1成等差数列，则a 3＋a 4a 4＋a 5 的值为( ) A.1－52 B.5＋12 C.5－12 D.5＋12或5－12 7．已知数列{a n }为等差数列，若a 11 a 10 <－1，且它们的前n 项和S n 有最大值，则使得S n >0的最大 值n 为( ) A ．11 B ．19 C ．20 D ．21 8．等比数列{a n }中，a 1＝512，公比q ＝－1 2 ，用Πn 表示它的前n 项之积：Πn ＝a 1·a 2·…·a n ， 则Πn 中最大的是( ) A ．Π11 B ．Π10 C ．Π9 D ．Π8 9．已知等差数列{a n }的前n 项和为S n ，若a 1＝1，S 3＝a 5，a m ＝2011，则m ＝( ) A ．1004 B ．1005 C ．1006 D ．1007 10．已知数列{a n }的通项公式为a n ＝6n －4，数列{b n }的通项公式为b n ＝2n ，则在数列{a n }的前 100项中与数列{b n }中相同的项有( ) A ．50项 B ．34项 C ．6项 D ．5项 二、填空题(本大题共5个小题，每小题5分，共25分，把正确答案填在题中横线上) 11．已知数列{a n }满足：a n ＋1＝1－1 a n ，a 1 ＝2，记数列{a n }的前n 项之积为P n ，则P 2011＝________. 12．秋末冬初，流感盛行，荆门市某医院近30天每天入院治疗流感的人数依次构成数列{a n }， 已知a 1＝1，a 2＝2，且a n ＋2－a n ＝1＋(－1)n (n ∈N *)，则该医院30天入院治疗流感的人数共有________人．
高中数学必修五综合测试题(卷) 含答案解析
绝密★启用前 高中数学必修五综合考试卷 第I卷（选择题） 一、单选题 1．数列的一个通项公式是（） A．B． C．D． 2．不等式的解集是（） A．B．C．D． 3．若变量满足，则的最小值是（） A．B．C．D．4 4．在实数等比数列{a n}中，a2，a6是方程x2－34x＋64＝0的两根，则a4等于( ) A．8B．－8C．±8D．以上都不对 5．己知数列为正项等比数列，且，则（）A．1B．2C．3D．4 6．数列 1111 1,2,3,4, 24816 L前n项的和为（） A． 2 1 22 n n n + +B． 2 1 1 22 n n n + -++C． 2 1 22 n n n + -+D． 2 1 1 22 n n n + - -+ 7．若的三边长成公差为的等差数列，最大角的正弦值为，则这个三角形的面积为（） A．B．C．D． 8．在△ABC中，已知,则B等于( ) A．30°B．60°C．30°或150°D．60°或120° 9．下列命题中正确的是( ) A．a＞b?ac2＞bc2B．a＞b?a2＞b2 C．a＞b?a3＞b3D．a2＞b2?a＞b 10．满足条件，的的个数是( ) A．1个B．2个C．无数个D．不存在
11．已知函数满足：则应满足（）A．B．C．D． 12．已知数列{a n}是公差为2的等差数列，且成等比数列，则为（）A．-2B．-3C．2D．3 13．等差数列的前10项和，则等于（） A．3 B．6 C．9 D．10 14．等差数列的前项和分别为，若，则的值为（）A．B．C．D． 第II卷（非选择题） 二、填空题 15．已知为等差数列，且－2＝－1,＝0,则公差= 16．在中，，，面积为，则边长=_________. 17．已知中，，，，则面积为_________. 18．若数列的前n项和，则的通项公式____________ 19．直线下方的平面区域用不等式表示为________________． 20．函数的最小值是_____________． 21．已知，且，则的最小值是______． 三、解答题 22．解一元二次不等式 （1）（2） 23．△的角、、的对边分别是、、。 （1）求边上的中线的长；
高中数学必修五知识点详细解答附答案
姓名____________ 20XX 年____月_____日 第___次课 正、余弦定理 一。知识回顾：在初中我们知道：（1）在三角形中，大边对大角、大角对大边的边角关系； （2）在直角三角形中，sinA= a c ,sinB= b c ?c=sin a A ,c=sin b B ? sin a A =sin b B ,又Q sinC=1?sin a A =sin b B =sin c C 二。学习提纲： <一>.正弦定理： （1）概念：在一个三角形中，各边与它所对应角的正弦比相等，即： sin a A =sin b B =sin c C （2）证明： j r C ①几何证明法：（略，同学们自己证明） ②向量证明： 证明：（如图）当?ABC 为锐角三角形时， A B 过A 作单位向量j r ⊥AB u u u r ,则j r 与AB u u u r 的夹角为2π，j r 与BC uuu r 的夹角为2π-B ，j r 与CA u u u r 的夹角为2π +A ； 设AB=a,BC=c,AC=b. Q AB u u u r +BC uuu r +CA u u u r =0r ,∴j r g (AB u u u r +BC uuu r +CA u u u r )=j r g 0r ∴j r g AB u u u r +j r g BC uuu r +j r g CA u u u r =0 ∴|j r |g |AB u u u r |g cos 2π+|j r |g |BC uuu r |g cos(2π-B )+|j r |g |CA u u u r |g cos 2 π +A )=0 ∴asinB=bsinA,即：sin a A =sin b B 同理可得：sin b B =sin c C ，故：sin a A =sin b B =sin c C 当?ABC 为钝角三角形或直角三角形时，同样可证明得到：sin a A =sin b B =sin c C （3）正弦定理的变形： ①asinB=bsinA; csinB=bsinC; asinC=csinA; ②a ：b:c=sinA:sinB:sinC ③ sin a A =sin b B =sin c C =2R （R 为?ABC 外接圆的半径） ?a=2RsinA; b=2RsinB; c=2RsinC ? sinA=2a R sinB=2b R sinC=2c R （二）余弦定理： （1）概念：三角形中任何一边的平方等于其他两边的平方的和减去这两边与他们的夹角的余弦的积的两倍，即： 2 a =2 b +2 c -2bccosA; 2 b =2 a +2 c -2accosB; 2 c =2 a +2 b -2abcosC 变形：2 sin A=2 sin B+2 sin C-2sinBsinCcosA 2 sin B=2 sin A+2 sin C-2sinAsinCcosB 2 sin C=2 sin A+2 sin B-2sinAsinBcosC 求角：cosA=2222bc b c a +- , cosB=2222c a c b a +-, cosC=222b 2a c ab +- 变形:cosA=222sin sin sin 2sin sin A B C A B +-,cosB=222sin sin sin 2sin sin A C B A C +-,cosC=222sin sin sin 2sin sin A B C A B +- (2)勾股定理：2 c =2a +2b 推广：A 为锐角→222a b c <+；A 为直角→222a b c =+；A 为钝角→222 a b c >+ （3）三角形的面积公式： ①ABC S ?=12ah ②ABC S ?=12absinC=12bcsinA=1 2 acsinB ③ABC S ?(p=12(a+b+c) ④ABC S ?=4abc R (4)对于任意的三角形，都有：sinA>0
必修三 unit5 课文
Li Daiyu and her cousin Liu Qian were on a trip to Canada to visit their cousins in Montreal on the Atlantic coast. Rather than take the aeroplane all the way, they decided to fly to Vancouver and then take the train west to east across Canada. The thought that they could cross the whole continent was exciting. Their friend, Danny Lin, was waiting at the airport. He was going to take them and their baggage to catch "The True North", the cross-Canada train. On the way to the station, he chatted about their trip. "You're going to see some great scenery. Going eastward, you'll pass mountains and thousands of lakes and forests, as well as wide rivers and large cities. Some people have the idea that you can cross Canada in less than five days, but they forget the fact that Canada is 5,500 kilometres from coast to coast. Here in Vancouver, you're in Canada's warmest part. People say it is Canada's most beautiful city, surrounded by mountains and the Pacific Ocean. Skiing in the Rocky Mountains and sailing in the harbour make Vancouver one of Canada's most popular cities to live in. Its population is increasing rapidly. The coast north of Vancouver has some of the oldest and most beautiful forests in the world. It is so wet there that the trees are extremely tall, some measuring over 90 metres." That afternoon aboard the train, the cousins settled down in their seats. Earlier that day, when they crossed the Rocky Mountains, they managed to catch sight of some mountain goats and even a grizzly bear and an eagle. Their next stop was Calgary, which is famous for the Calgary Stampede. Cowboys from all over the world come to compete in the Stampede. Many of them have a gift for riding wild horses and can win thousands of dollars in prizes. After two days' travel, the girls began to realize that Canada is quite empty. At school, they had learned that most Canadians live within a few hundred kilometres of the USA border, and Canada's population is only slightly over thirty million, but now they were
必修五数列单元测试
必修五数列复习综合练习题 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） 1.2011是等差数列：1，4，7，10,…的第几项( ) （A ）669 （B ）670 （C ）671 （D ）672 2.数列{a n }满足a n =4a n-1+3,a 1=0，则此数列的第5项是（ ） （A ）15 （B ）255 （C ）20 （D ）8 3.等比数列{a n }中，如果a 6=6,a 9=9,那么a 3为（ ） （A ）4 （B ）2 3 （C ） 9 16 （D ）2 4.在等差数列{a n }中，a 1+a 3+a 5=105,a 2+a 4+a 6=99,则a 20=( ) （A ）-1 （B ）1 （C ）3 （D ）7 5.在等差数列{a n }中，已知a 1=2,a 2+a 3=13,则a 4+a 5+a 6=( ) （A ）40 （B ）42 （C ）43 （D ）45 6.记等差数列的前n 项和为S n ，若S 2=4，S 4=20，则该数列的公差d=（ ） (A)2 (B)3 (C)6 (D)7 7.等差数列{a n }的公差不为零，首项a 1=1，a 2是a 1和a 5的等比中项，则数列的前10项之和是（ ） （A ）90 （B ）100 （C ）145 （D ）190 8.在数列{a n }中，a 1=2,2a n+1-2a n =1,则a 101的值为（ ） （A ）49 （B ）50 （C ）51 （D ）52
9.计算机是将信息转化成二进制数进行处理的，二进制即“逢二进一”，如 （1101）2表示二进制的数，将它转化成十进制的形式是1×23+1×22+0×21+1×20=13，那么将二进制数16111???位 转换成十进制数的形式是（ ） （A ）217-2 （B ）216-1 （C ）216-2 （D ）215-1 10.在等差数列{a n }中，若a 1+a 2+a 3=32,a 11+a 12+a 13=118,则a 4+a 10=（ ） （A ）45 （B ）50 （C ）75 （D ）60 11.（2011·江西高考）已知数列{a n }的前n 项和S n 满足：S n +S m =S n+m ,且a 1=1,那么a 10=（ ） （A ）1 （B ）9 （C ）10 （D ）55 12.等比数列{a n }满足a n >0,n=1,2,…，且a 5·a 2n-5=22n (n ≥3),则当n ≥1时，log 2a 1+log 2a 3+…+log 2a 2n-1=（ ） （A ）n(2n-1) （B ）(n+1)2 （C ）n 2 （D ）(n-1)2 二、填空题（本大题共4小题，每小题5分，共20分，请把正确的答案填在题中的横线上） 13.等差数列{a n }前m 项的和为30，前2m 项的和为100，则它的前3m 项的和 为______. 14.（2011·广东高考）已知{a n }是递增等比数列，a 2=2,a 4-a 3=4,则此数列的公比q=______. 15.两个等差数列{a n },{b n }, 12n 12n a a a 7n 2 b b b n 3 ++?++= ++?++,则55a b =______. 16.设数列{a n }中,a 1=2,a n+1=a n +n+1，则通项a n =_____.
(完整版)高中数学必修五第二章数列测试题
高中数学必修5 第二章数列测试题 一、选择题(每题5分,共50分) 1、{a n }是首项a 1＝1，公差为d ＝3的等差数列，如果a n ＝2 005，则序号n 等于( )． A 、667 B 、668 C 、669 D 、670 2、在各项都为正数的等比数列{a n }中，首项a 1＝3，前三项和为21，则a 3＋a 4＋a 5＝( )． A 、33 B 、72 C 、84 D 、189 3、如果a 1，a 2，…，a 8为各项都大于零的等差数列，公差d ≠0，则( ) A 、a 1a 8＞a 4a 5 B 、a 1a 8＜a 4a 5 C 、a 1＋a 8＜a 4＋a 5 D 、a 1a 8＝a 4a 5 4、已知方程(x 2－2x ＋m )(x 2－2x ＋n )＝0的四个根组成一个首项为 41的等差数列，则｜m －n ｜等于( ) A 、1 B 、43 C 、2 1 D 、83 5、等比数列{a n }中，a 2＝9，a 5＝243，则{a n }的前4项和为( ). A 、81 B 、120 C 、168 D 、192 6、若数列{a n }是等差数列，首项a 1＞0，a 2 003＋a 2 004＞0，a 2 003·a 2 004＜0，则使前n 项和S n ＞0成立的最大自然数n 是( ) A 、4 005 B 、4 006 C 、4 007 D 、4 008 7、已知等差数列{a n }的公差为2，若a 1，a 3，a 4成等比数列, 则a 2＝( )． A 、－4 B 、－6 C 、－8 D 、－10 8、设S n 是等差数列{a n }的前n 项和，若35a a ＝9 5，则59S S ＝( )． A 、1 B 、－1 C 、2 D 、2 1 9、已知数列－1，a 1，a 2，－4成等差数列，－1，b 1，b 2，b 3，－4成等比数列，则 212b a a -的值是( )． A 、21 B 、－21 C 、－21或2 1 D 、41 10、在等差数列{a n }中，a n ≠0，a n －1－2n a ＋a n ＋1＝0(n ≥2)，若S 2n －1＝38，则n ＝( )． A 、38 B 、20 C 、10 D 、9 二、填空题(每题6分,12题15分,16题10分,共49分) 11、设f (x )＝221 +x ，利用课本中推导等差数列前n 项和公式的方法，可求得f (－5)＋f (－4)＋…＋f (0) ＋…＋f (5)＋f (6)的值为 .
高中数学必修五 知识点总结【经典】
《必修五 知识点总结》 第一章：解三角形知识要点 一、正弦定理和余弦定理 1、正弦定理：在C ?AB 中，a 、b 、c 分别为角A 、B 、C 的对边，，则有 2sin sin sin a b c R C ===A B (R 为C ?AB 的外接圆的半径) 2、正弦定理的变形公式： ①2sin a R =A ，2sin b R =B ，2sin c R C =； ②sin 2a R A = ，sin 2b R B =，sin 2c C R =； ③::sin :sin :sin a b c C =A B ； 3、三角形面积公式：111 sin sin sin 222 C S bc ab C ac ?AB = A == B ． 4、余弦定理：在 C ?AB 中，有2 2 2 2cos a b c bc =+-A ，推论：bc a c b A 2cos 2 22-+= B ac c a b cos 2222-+=，推论： C ab b a c cos 22 2 2 -+=，推论：ab c b a C 2cos 2 22-+= 二、解三角形 处理三角形问题，必须结合三角形全等的判定定理理解斜三角形的四类基本可解型，特别要多角度（几何作图，三角函数定义，正、余弦定理，勾股定理等角度）去理解“边边角”型问题可能有两解、一解、无解的三种情况，根据已知条件判断解的情况，并能正确求解 1、三角形中的边角关系 （1）三角形内角和等于180°； （2）三角形中任意两边之和大于第三边，任意两边之差小于第三边； ac b c a B 2cos 2 22-+=
（3）三角形中大边对大角，小边对小角； （4）正弦定理中,a =2R ·sin A , b =2R ·sin B , c =2R ·sin C ，其中R 是△ABC 外接圆半径. （5）在余弦定理中:2bc cos A =222a c b -+. （6）三角形的面积公式有:S = 21ah , S =21ab sin C=21bc sin A=2 1 ac sinB , S =))(()(c P b P a P P --?-其中，h 是BC 边上高，P 是半周长. 2、利用正、余弦定理及三角形面积公式等解任意三角形 （1）已知两角及一边，求其它边角，常选用正弦定理. （2）已知两边及其中一边的对角，求另一边的对角，常选用正弦定理. （3）已知三边，求三个角，常选用余弦定理. （4）已知两边和它们的夹角，求第三边和其他两个角，常选用余弦定理. （5）已知两边和其中一边的对角，求第三边和其他两个角，常选用正弦定理. 3、利用正、余弦定理判断三角形的形状 常用方法是：①化边为角；②化角为边. 4、三角形中的三角变换 （1）角的变换 因为在△ABC 中，A+B+C=π，所以sin(A+B)=sinC ；cos(A+B)=－cosC ；tan(A+B)=－tanC 。 2 sin 2cos ,2cos 2sin C B A C B A =+=+； （2）三角形边、角关系定理及面积公式，正弦定理，余弦定理。 r 为三角形内切圆半径，p 为周长之半 （3）在△ABC 中，熟记并会证明：∠A ，∠B ，∠C 成等差数列的充分必要条件是∠B=60°；△ABC 是正三角形的充分必要条件是∠A ，∠B ，∠C 成等差数列且a ，b ，c 成等比数列.
高中英语新课标必修四Unit5课文原文
Book 4 Unit 5 Theme Parks . There are v arious kinds of theme parks, with a different park for almost everything: food, culture, science, c artoons, movies or history. . Some parks are famous for having the biggest or longest r oller coasters, others for showing the famous sights and sounds of a culture. . Whichever and whatever you like, there is a theme park for you! . It will bring you into a magical world and make your dreams come true, whether traveling through space, visiting a pirate ship or meeting your favourite fairy tale or Disney cartoon character. 8. As you wander around the fantasy amusement park, you may see Snow White or Mickey Mouse in a parade or on the street. 9. Of course Disneyland also has many exciting rides, from giant swinging ships to terrifying free-fall drops. 10. With all these attractions, no wonder tourism is increasing w herever there is a Disneyland. 12. Dollywood, in the beautiful Smoky Mountains in the southeastern USA, is one of the most unique theme parks in the world. Dollywood shows and celebrates America's traditional southeastern culture. Although Dollywood has rides, the park's main a ttraction is its culture. People come from all over America to see carpenters and other craftsmen make wood, glass and iron objects in the old-fashioned way. Visit the candy shop to try the same kind of candy that American southerners made 150 years ago, or take a ride on the only steam- engine train still working in the southeast USA. preserve. You can even see beautiful bald eagles in the world's largest bald eagle And for those who like rides, Dollywood has one of the best old wooden roller coasters, Thunderhead. It is world-famous for having the most length in the smallest space. Come to Dollywood to have fun learning all about America's historical southeastern culture! If you want to experience the ancient days and great deeds o f English knights and ladies, princes and queens, then England's Camelot Park is the place for you.
高二数学必修5数列单元测试.doc
________ 高二数学必修 5 数列单元测试 一、选择题： 时间 120 分钟 满分 100 分 3 分，共 30 分 . ） （本大题共 10 小题，每小题 1. 在数列－ 1， 0， 1 ， 1 ， ， n 2 中，是它的 9 8 n 2 A ．第 100 项 B ．第 12 项 C ．第 10项 D ．第 8项 2. 在数列 { a n } 中， a 1 2 ， 2a n 1 2a n 1，则 a 101 的值为 A ． 49 B ． 50 C ． 51 D ．52 3. 等差数列 { a n } 中， a 1 a 4 a 7 39 ， a 3 a 6 a 9 27 ，则数列 { a n } 的前 9 项的和等于 A ． 66 B ． 99 C ． 144 D ． 297 4. 设数列 {a n } 、 {b n } 都是等差数列，且 a 1=25,b 1=75,a 2+b 2=100，那么 a n +b n 所组成的数列的第 37 项的值是 ( ) .37 C 5．已知－ 7， a 1， a 2，－ 1 四个实数成等差数列，－ 4， b 1， b 2， b 3，－ 1 五个实数成等比数列，则 a 2a 1 = b 2 A ． 1 B ．－ 1 C ． 2 D ．± 1 6. 等比数列 {a n } 中，前 n 项和 S n =3n +r ，则 r 等于 ( ) .0 C 7．已知数列 { a n } 的前 n 项和为 S 1 5 9 13 17 21 ( 1) n 1 (4n 3) , n 则 S 15 S 22 S 31 的值是（ ） A. -76 B. 76 C. 46 D. 13 8． 6．已知等差数列 {a n } 的公差 d ≠0, 若 a 5、a 9、 a 15 成等比数列 , 那么公比为 A ． 3 B ． 2 C ． 3 D ． 4 4 3 2 3 9．若数列 { a } 是等比数列 , 则数列 { a +a } n n n+1 A ．一定是等比数列 C ．一定是等差数列 10．等比数列 {a n } 中， a 1 =512，公比 q= 1 2 B ．可能是等比数列 , 也可能是等差数列 D ．一定不是等比数列 ，用Ⅱ n 表示它的前 n 项之积：Ⅱ n =a 1 · a 2 a n 则Ⅱ 1 ，Ⅱ 2 ， ，中最大的是 A ．Ⅱ 11 B ．Ⅱ 10 C ．Ⅱ 9 D ．Ⅱ 8 题号 1 2 3 4 5 6 7 8 9 10 答案 二、填空题 ：( 本大题共 5 小题，每小题 4 分，共 20分。) 11．在数 {a n } 中，其前 n 项和 S n =4n 2－ n － 8，则 a 4= 。 12. 设 S n 是等差数列 a 5 5 S 9 的值为 ________. a n 的前 n 项和，若 ，则 S 5 13．在等差数列 { a } 中，当 a ＝ a a 3 9 { a } 中，对某些正整数 r 、s ( r ≠ s ) ，当 a ( r ≠ s ) 时， { a } 必定是常数数列。然而在等比数列 r n r s n n ＝a s 时，非常数数列 { a n } 的一个例子是 ____________． 14. 已知数列 1, ，则其前 n 项的和等于 。 15. 观察下列的图形中小正方形的个数，则第 n 个图中有 个小正方形 . 三、解答题：（本大题共 5 小题，共 50 分。解答应写出文字说明，或演算步骤） 16. （本小题满分 8 分）已知 a n 是等差数列，其中 a 1 25, a 4 16
高中数学必修五测试题含答案
高一数学月考试题 1．选择题（本大题共 12 小题，每小题 5 分，共 60 分） 1．已知数列{a n }中， a 1 2 ， a n 1 a n 1 2 (n N ) ， 则 a 101 的值为 （ ） A ．49 B ．50 C ．51 D ．52 2． 2 + 1 与 2 - 1，两数的等比中项是（ ） A ．1 B ． - 1 C ． ± 1 D ． 1 2 3．在三角形 ABC 中，如果 a b c b c a 3bc ，那么 A 等于（ ） A ． 30 B ． 60 C ．120 0 D ．150 0 4．在⊿ABC 中， c cos C b cos B ，则此三角形为 （ ） A ． 直角三角形； B. 等腰直角三角形 C. 等腰三角形 D. 等腰或直角三角形 5.已知 { a n } 是等差数列，且 a 2+ a 3+ a 10 + a 11 =48，则 a 6+ a 7= ( ) A ．12 B ．16 C ．20 D ．24 6．在各项均为正数的等比数列b n 中，若b 7b 83， 则 log 3 b 2 …… log 3 b 14 等于（ ） (A) 5 (B) 6 (C) 7 (D)8 7．已知 a , b 满足： a =3， b =2， a b =4，则 a b =( ) A ． 3 B ． 5 C ．3 D 10 8.一个等比数列{a n } 的前 n 项和为 48，前 2n 项和为 60，则前 3n 项和为（ ） A 、63 B 、108 C 、75 D 、83 9．数列{a n }满足 a 1＝1，a n ＋1 ＝2a n ＋1(n ∈N + )，那么 a 4 的值为( )． A ．4 B ．8 C ．15 D ．31 10．已知△ABC 中，∠A ＝60°，a ＝ 6 ，b ＝4，那么满足条件的△ABC 的形状大 小 ( )． * 0 r r r r r r r r
人教版高中英语必修三Unit5课文翻译
第二天早上，在她们的车窗外到处是灌木丛和枫树，挂满朱红、赤金和橘黄色的叶子，地面覆盖上一层薄霜，表明秋天已经来到了加拿大。中午时分，她们来到多伦多—加拿大最大、最富有的城市。她们要晚些时候才动身去蒙特利尔，因此就在多伦多市内游览了一番。她们登上了高高的加拿大国家电视塔，俯瞰着下面的湖水。远处，她们可以看到湖的南边尼亚加拉大瀑布上方升腾着的雾霭。湖水流入尼亚加拉河，再经过大瀑布，流向大海。 她们看到了加顶的大型运动场，那是几支著名的篮球队的驻地。当她们从港口区向北走的时候，李黛予说：“我妈妈的老同学林菲住在这里，我该到电话亭去给她打个电话。” 大约黄昏时分，她们在市区的中国城遇到了林菲，这时多伦多三个中国城中的一个。在一个名叫“海珠酒楼”的餐馆里用餐时，表姐妹和许多年前就移居加拿大的林菲闲聊了起来。林菲告诉她们：“我们在这里可以吃到很好的广东菜，因为这里的大多数中国人来自中国南方，尤其是香港。很可惜你们不能一只走到建安大的首都渥太华。它在多伦多东北方约400公里，要去那儿花时间就太多了。” 火车在那夜晚些时候起程了，第二天黎明到达了蒙特利尔。火车站里，人们到处说的是法语。指示牌和广告也都是法文的，但有些标注了小字体的英文。刘倩说：“我们要到傍晚才动身，不如到市区去走走。”整个下午她们穿梭于布局可爱的商店，还摆放了水边工作坊里的艺术家。当她们坐在咖啡馆里眺望广阔的圣劳伦斯河时，一个年轻人坐在了她们的身边。 “你们好，我叫亨利，是这里的大学生。”他说：“请问你们从哪里来？”姑娘们告诉他，她们是坐火车来旅游的，要横穿加拿大，在蒙特利尔只待一天。他说：“这太糟糕了，蒙特利尔这个城市有极好的餐馆和俱乐部。我们大多数人既说英语也说法语，但是这座城市具有法国文化和传统。我们喜欢好咖啡，好面包和好音乐。” 那天晚上，火车沿着圣劳伦斯河疾驰，朝圣劳伦斯湾驶去，一直开到远方的东海岸，姐妹两个做梦都在想着法国餐馆和红色枫叶。 The next morning the bushes and maple trees outside their windows were red, gold and orange, and there was frost on the ground, confirming that fall had arrived in Canada. Around noon they arrived in Toronto, the biggest and most wealthy city in Canada. They were not leaving for Montreal until later, so they went on a tour of the city. They went up the tall CN Tower and looked across the lake. In the distance, they could see the misty cloud that rose from the great Niagara Falls, which is on the south side of the lake. The water flows into the Niagara River and over the falls on its way to the sea. They saw the covered stadium, home of several famous basketball teams. As they walked north from the harbour area, Li Daiyu said, "Lin Fei, one of my mother's old schoolmates, lives here. I should phone her