2011-2012学年卢湾区高三一模考试(文2012-01)

上海市卢湾区2012届第一学期高三期末考试英语试题第I卷（共105分）I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. At a bank. B. At a hotel. C. At a restaurant. D. At a bus stop.2. A. $13. B. $30. C. $23. D. $40.3. A. Teacher and student. B. Boss and secretary.C. Waiter and guest.D. Policeman and driver.4. A. She agrees with the man. B. She prefers to go shopping.C. She dislikes raining days.D. She thinks it won’t rain.5. A. The air is fresh. B. It’s hot inside.C. The window is open.D. It’s noisy outside.6. A. A postman. B. A shop assistant. C. A cashier. D. A waiter.7. A. The size. B. The price. C. The location. D. The facilities.8. A. She is fond of pizza very much. B. She disagrees with the man.C. She doesn’t understand what the man says.D. She doesn’t like pizza very much.9. A. She doesn’t want a new hairstyle. B. She has no time to try a new hairstyle.C. She wants to try a new hairstyle at once.D. She accepts the man’s advice.10. A. Jack is the better student. B. Jack and his brother are both pretty.C. Jack’s brother is cleverer.D. Jack’s brother is more hardworking.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. Deciding on the stories. B. Checking the language.C. Finding mistakes.D. Writing headlines.12. A. Reporters. B. Cartoonists. C. Foreign editors. D.Page designers.13. A. The importance of reading newspapers.B. The steps of reading a newspaper.C. The process of making a newspaper.D. The similarity between Teens and daily newspapers.Questions 14 through 16 are based on the following passage.14. A. It’s a place for people to gamble at card.B. It’s a place where everyone makes a fortune.C. It’s a place to exchange shares of a factory or company.D. It’s a place where people exchange a factory or company.15. A. To earn more money. B. To try their luck.C. To save money.D. To buy a bigger flat.16. A. The fastest way of getting more money.B. The different purposes of buying stocks.C. The common knowledge of stock markets.D. The advantages of investing money in the stock.Section CDirections: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.Telephone MessageCase reported A car foundLocation of the car Near No. 8 Bridge along the __17__ RoadCar number BWF __18__Colour of the car It’s __19__ and nearly new.Informer’s name Henry RobertsDay of reporting__20__ 5th .Complete the form. Write ONE WORD for each answer.Blanks 21 through 24 are based on the following conversation.What is displayed in the next room?__21__How long is the duration of the__22__exhibition here?10 am-5 pm, __23__What is the time for the gallery?10 am-4 pm, SundayWhat will the woman do? Stay and __24__ the old pictures.Complete the form. Write NO MORE THAN THREE WORDS for each answer.II. Grammar and VocabularySection ADirections: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best completes the sentence.25. During the next 10 years, China will have 100,000 new yachts and the market will be worth______ 50 billion and 100 billion yuan.A. atB. betweenC. withD. from26. A minibus carrying 14 students rolled over on a Friday afternoon, two students killed and six______ badly injured.A. anotherB. the otherC. othersD. the others27. David apologized for ______ to inform me of the change in the plan.A. his being not ableB. him not to be ableC. his not being ableD. him to he not able28. It’s important to talk about your problems with your friends or your parents and they ______really help a lot.A. canB. mustC. shouldD. need29. “People are better-paid, better-educated and attach ______ attention to quality of life,” saidMichelle Liao, Pegasus.A. a lot ofB. much moreC. as muchD. the most30. As we all know, it is what you do rather than what you say ______ matters.A. whichB. whatC. thisD. that31. Tower Bridge, one of Britain’s most famous landmarks, ______ at the end of the 19th Century.A. builtB. was builtC. has builtD. had been built32. Outdoor Film Festival, held in December, is the first festival in Asia ______ on cyclingmountain bike documentaries and environmental protection movies.A. focusedB. focusingC. to be focusedD. had focused33. Medical experts say the most effective way to prevent the spread of disease is for people______ their hands with soap and water.A. to washB. washedC. washingD. being washed34. The number of children who contracted colds and visited the hospital ______ in the countysince last fall.A. increasedB. would increasedC. has increasedD. had increased35. ______ the coming Olympic Park’s architects have in mind is to build the largest urban park inEurope in 150 years.A. WhatB. HowC. ThatD. Which36. I failed in the final examination last term and only then ______ the importance of regular andproper revision.A. did I realizeB. I realizedC. had I realizedD. I had realized37. If you want to do the experiment again, you’d better be more careful ______ you make amistake.A. only ifB. as ifC. so thatD. in case38. ______, the kidnapped girl told the police all the suffering she had gone through.A. Having rescuedB. Having been rescuedC. To be rescuedD. To have been rescued39. The country is now the world’s largest exporter of goods and the second largest importer,______ has created millions of job opportunities in export industries and related areas.A. thisB. thatC. whichD. what40. Standing on the top of the hill, I would not do anything but ______ the flowing of the cloudsaround me.A. enjoyB. enjoyingC. enjoyedD. to enjoySection BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.A. includedB. promisingC. achievementsD. provedE. transferF. outstandingG. signH. appearancesI. scoringJ. referredRonaldo Luiz Nazario de Lima1 was born on 22 September 1976 in apoor suburb of Rio de Janeiro. Like most of his childhood friends, Ronaldobegan his soccer career playing barefoot in the streets of his neighborhood.At the age of 14, he joined Saint Cristov soccer club and only two years laterbecame the star of Cruzeiro Belo Horizonte __41__ a total of 58 goals in 60matches and earning himself a reputation for his explosive pace and __42__finishing skills. His goal-scoring record and unusual quickness led him to be__43__ in the Brazilian World Cup winning team the following year. After the World Cup, many top European football clubs were trying to __44__ him. Many people, including Brazilian football legend Pelé, considered him as the most __45__ footballer of his generation.Since his __46__ to Dutch team PSV Eindhoven, Ronaldo’s biography is one of success after success. Two Copa América’s, a UEFA Cup, a Dutch Cup, a Spanish League Cup, and two awards as best player in the world, all in the space of two years, are some of Ronaldo’s impressive __47__. On arrival to Inter-Milan in 1997, Ronaldo became the idol of the local fans who refer to him as “il Fenomeno(奇才).”Since the 98 World Cup he has suffered two serious knee injuries that have severely limited his __48__. Just when people began to wonder whether Ronaldo would be able to continue with his football career, he __49__ to the world that he still could play. In the World Cup held in Korea and Japan, the magical striker won the Golden Shoe award and tied Pele’s Brazilian record for career World Cup goals with 12. He helped Brazil capture its fifth World Cup championship onJune 30 with a 2-0 win over Germany. It was the third time that Ronaldo had ever played in the World Cup.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Welcome to the Bourton-on-the-Water Website. The content of the site has been produced by local people __50__ you, as a visitor, can enjoy at your leisure some of the delightful __51__ of our lovely village and the countryside around it.The Cotswolds have always been looked upon as the Heart of England. It is one of the few regions with an __52__ style all of its own and the steeply pitched roofs, stone mullions and dormer windows are typical. Built almost exclusively（仅仅）in warm yellow Cotswold stone, this delightful village has such a unique __53__ to visitors and residents alike.Regularly voted one of the prettiest villages in England, Bourton-on-the-Water has __54__ its share of Cotswold houses and cottages, many of them 300 years old, some __55__ to Elizabethan times 400 years ago. There is plenty to see and do here and we hope this __56__ and also our Visitor Information Centre can help to make your __57__ as enjoyable as possible.Bourton-on-the-Water Visitor Information Centre is independently owned, and __58__ next to the Cotswold Perfumery in Victoria Street. Bed and breakfast accommodation and hotels can be __59__ before you arrive by using our telephone booking service (01451 822583). As agents for National Express Coaches, we are __60__ to book tickets both in Britain and Europe.For locals and visitors alike we hold a wide range of information and leaflets for __61__ and events throughout the area. We also sell discounted entry tickets to Blenheim Palace. Theatre tokens can be purchased here __62__. Locally produced rapeseed oil, honey, lavender products and maps, guide books, postcards, souvenirs are amongst our range of saleable goods.We look forward to __63__ you when you come to Bourton-on-the-Water and answering any question that you may have. We are here to help you make the most of your time in __64__.50. A. such that B. now that C. so that D. as well as51. A. leaflets B. features C. service D. hobbies52. A. architectural B. artificial C. available D. appropriate53. A. building B. material C. appeal D. roof54. A. more than B. less than C. other than D. rather than55. A. looking forward B. adding up C. dating back D. standing up56. A. house B. site C. cottage D. region57. A. study B. play C. life D. stay58. A. located B. based C. closed D. existed59. A. cancelled B. called C. bought D. arranged60. A. eager B. anxious C. able D. lucky61. A. websites B. residents C. visitors D. attractions62. A. and so on B. so far C. as well D. as usual63. A. telling B. meeting C. answering D. showing64. A. Britain B. Europe C. Blenheim Palace D. the CotswoldsSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)When having an interview, it’s not just words you have to think about, but also how you express them. Avoid a flat monotone(单调的) voice that people sometimes get when they are nervous. And it can add so much if you show your excitement and your eagerness to work for that company, and that is where past performance will indicate future performance. So good interviewers will ask you very detailed questions where they’ll put you on the spot and they’ll want to know specifically your role in what you did for a particular project. And so the key to giving a good answer to a behavioral interview question is to do what I call a STAR, S-T-A-R. The S and T stand for explaining a situation or a task that you were given, the A is the action you took and the R is the results.In addition, you need to be prepared before you walk in the door. Go through some mock interviews, if you can have friends ask you questions. Practice in the mirror, answering questions. Go in with three or four things you really want to stress about yourself. And then you can bring those out no matter what question is asked.To follow up after the interview, you can send a thank-you letter. And you can do it by e-mail. In that thank-you letter you do a couple of things. You make sure that you show sincere appreciation for the time that they spent interviewing you. You have another chance to make that case as to how your skills match their needs.65. What should you think about when having an interview?A. How to express what you want to say.B. How to use a flat monotone voice.C. How to ask very detailed questions.D. How to hide your excitement and eagerness.66. To give a good answer to a behavioral interview question you needn’t explain _________.A. the action you tookB. the results you gotC. your eagerness to carry out the projectD. a situation or a task that you were given67. What’s the main purpose of this passage?A. To give suggestions on having an interview.B. To introduce some keys to being a successful interviewer.C. To encourage people to send a thank-letter before interview.D. To advise people to ask friends some questions before interview.(B)68. Linda uses the word children to describe her pets because ________.A. she believes her pets possess childlike qualitiesB. the pets have taken the place of her childrenC. she dresses them in children’s clothingD. the pets all have a lovely girlish figure69. If the pet sitter doesn’t supervise her, ________.A. Regina will play with the catB. Regina will spend an hour wanderingC. Regina will solve her problem herselfD. Regina will damage her owner’s furniture70. The pet sitter is advised to tell Regina “good girl” ________.A. after Regina finds the ballB. after Regina drops the ballC. when Regina brings the ball backD. every time Regina goes after the ball71. What are the three animals mentioned in the letter?A. Two cats and a dog.B. A cat, a dog and a parrot.C. Two dogs and an unspecified animal.D. A dog, a cat, and an unspecified animal.(C)The requisite visit happened typically on every Saturday, when my child spirits were at their highest as it was sunny and could be most weakened by the narrow inner part of my grandmother’s house. My mother, accustomed to the bright, spacious farmhouse that was Grandma’s, seemed no less sensitive to the darkness. She would set her jaw and listened when Grandma described how many small illnesses appeared as she grew older and would check her watch—an hour being the minimum she expected herself to endure. Her barely contained impatience and my grandmother’s disabled age radiated out around me.I would sit at the white and red metal table with the pull-out and built-in silverware drawer, cracking almonds(杏仁). This was the one good thing at Grandma’s house, the almonds, which she kept in a green glass bowl. I would lift the lid carefully and try to set it down on the metal table quietly, then attempt to crack the nuts without scattering the shell crumbs（碎屑）. It was not good to draw attention to myself at Grandma Carlson’s. Sounding angry, she would call to me in her long drawl(长调). When I failed to understand her, she would reach out to me with her trembling and wrinkled hand and shout, “Here!” She would be offering some of her handmade candy, which tasted a little bitter.There was this painful air in the dim house with its old furniture and its dark colours, an awareness that Grandma’s age scared her grandkids. I would long during the dutiful visit to get outside into the yard, where Grandma had transplanted a few flowers when she moved from the farm. But even the yard, with its overgrown hedges(篱笆) and rusted metal lawn chairs, seemed dull. When I came back inside, light and air bursting in with me, Grandma, her hair up, would rock a little and smile. I would lean then against my mother’s chair, Grandma’s fond eyes staring at me, and whisper out of the corner of my mouth, “Mom, can we go?”72. From the overall context of the passage, it is most likely that the word requisite means___________.A. essentialB. recreationalC. happyD. expected73. My mother ___________.A. owned a bright, spacious farmhouseB. listened to grandma carefully and patientlyC. described her small illnesses to meD. would listen to grandma for at least one hour74. Which of the following statements is NOT true according to the passage?A. I would sit at the white and red metal table, cracking almonds.B. I would lift the lid quickly enough to set it down on the metal table.C. It was impolite to draw attention to myself at Grandma Carlson’s.D. Grandma had transplanted a few flowers in the yard.75. Which of the following might be the best title of the passage?A. The Weekly VisitB. The Grandma’s LoveC. A Family ReunionD. My joyful SaturdaysSection CDirections: Read the following text and choose the most suitable heading from A-F for each paragraph. There is one extra heading which you do not need.A. Break it upB. Have a listC. Sleep on itD. Create Visual AidsE. Take Small Bites of TimeF. Do it Out LoudThere are many ways to help you improve your memory.76.Most people memorize information best when they study in short periods over a long period of time. Memorizing facts from index cards that can be carried with you and pulled out for a few ten-minute sessions each day will yield better results than sitting down with a text book for an hour straight. Index card notes can be pulled out in odd moments: while you are sitting in the car waiting to pick up your friend, during the 15 minutes you spend on the bus in the morning, while you wait to be picked up from school or work, and so on. You’ll find these short but regular practices will greatly aid your recall of lots of information. They’re a great way to add more study time to your schedule.77.When you have a list to memorize, divide the list into groups of seven or any other number. People seem to remember best when they divide long lists into shorter ones—and, for some reasons, shorter ones that have an odd number of items. So instead of trying to memorize ten vocabulary or spelling words, split your list into smaller lists of seven and three, or five and five, to help you remember them.78.Give yourself visual assistance in memorizing. If there’s a tricky combination of letters in a word you need to spell, for example, circle or underline it in red or highlight it in the text. Your eye will recall what the word looks like. With some information, you can even draw a map or picture to help you remember.79.Give yourself auditory assistance in memorizing. Many people learn best if they hear the information. Sit by yourself in a quiet room and say aloud what you need to learn. Or give your notes to someone else and let that person ask you or quiz you on the material.80.When you study right before going to bed and don’t allow any interference—such as conversation, radio, television, or music—to come between study and sleep, you remember material better. This is especially true if you review first thing after waking as well. A rested and relaxed brain seems to hang on to information better than a tired and stressed-out brain.Section DDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.It is foolish to dream of reversing history. We cannot pass laws forbidding science and technology. The computing machines are here, and they will not merely stay, they will grow smarter, faster, and more useful every year. They will continue growing because engineers want to build them, scientists want to use them, industrialists want to employ them, scientists want to enlist them in new weapons systems, politicians want their help in the processes of government. In short, they will flourish（兴旺）because they enable us to finish tasks that could never before have been undertaken, no matter how many unskilled laborers we might have set to work. Computers will continue to improve our intelligence for the same reason that engines continue to strengthen our muscles. The question we must ask is not whether we shall have computers or not, but rather, since we are going to have them, how can we make the most intelligent use of them?Obviously, there would be no point in investing in a computer if you had to check all its answers, but people should also rely on their own internal computers and check the machine when they have the feeling that something has gone wrong.Questioning and routine double-checks must continue to be as much a part of good business as they were in pre-computer days. Maybe each computer should come with the warning: For all the help this computer may provide, it should not be seen as a substitute for fundamental thinking and reasoning skills.(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)81. How will the computing machines change every year?82. Why will the computing machines keep growing?83. The question we must ask mentioned in Para. 1 is _____________.84. From the warning at the end of the passage, we can conclude computers should not be used to_____________.第Ⅱ卷（共45分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 在公共场所吸烟是违法的。

2011年卢湾区高三语文第一学期期末质量抽查试卷（满分：150分考试时间：100分钟）考生注意：1．答卷前，考生务必在答题纸上将自己的姓名等填写清楚。

2．本考试设试卷和答题纸两部分，所有试题的答案必须全部写在答题纸上，写在试卷上一律不给分；答题时应注意试置题号和答题纸题号一一对应，不能错位。

一、阅读80分（一）阅读下文，完成第1-6题。

(16分)①人类之所以有今天这样的文明，文学在其中的力量和功德是不言而喻的。

难道文学要中断这样的责任了吗？让生活向下还是向上，向善还是向恶，难道文学就完全没有必要对这样最起码的问题进行拷问吗？“如果川端康成与大江健三两人生活的年代颠倒一下，大江在川端时代写大江式的作品，川端在大江的时代写川端式的作品，这两个日本人还会获得诺贝尔文学奖吗？”回答几乎是肯定的：不会。

因为川端时代的文学的标准还不只是“深刻”一维。

而大江时代，却将川端文学的命根子——美——彻底抛弃了。

②这个时代，是一个横着心要将“美”搞成矫情字眼、一提及就自觉浅薄的时代。

这个时代是讲思想神话的时代，悠悠万事，唯有思想——思想宝贝。

文学企图使人相信，在这个世界上，唯一值得人们尊重的就是思想：思想是高于一切的；谁在思想的峰巅，谁就是英雄，谁就应当名利双收。

正是在这样的语境中，我们患上了“恋思癖”的毛病。

对思想的变态追求，已使我们脱离了常识。

当我们穷凶极恶地在追求思想深度的时候，我们忘记一个常识：获得石油必须钻井，因为石油蕴藏在具有一定深度的地下，但如果以为钻得越深就越有石油那就错了，因为再无止境地钻下去，就是泥浆和岩浆了。

思想崇拜，会导致思想迷信，而思想迷信则一定会导致思想的变态，其结果就是我们放弃常识，进入云山雾罩的思想幻觉。

其实，一旦背离真实，一个看上去再深刻的思想，也是无意义的。

( )，这世界上有力量的并不只有思想。

我还是愿意重复我的老话：美的力量丝毫也不亚于思想的力量，有时甚至比思想的力量更加强大。

③“一种牺牲民族甚至人类体面的文学境界，是值得我们赞美和崇尚的境界吗？”斯洛文尼亚的齐泽克在谈到前南斯拉夫时代萨拉热窝被围困的情状时说，那些闻风而来的西方记者争先恐后寻找的只是：残缺不全的儿童尸体、被强奸的妇女、饥饿不堪的战俘。

2011年高三文科综合试题24、在右图中，当某商品的价格停留在A点或B点时，下列说法正确的是①在A点时是卖方市场，在B点时是买方市场②在A点时是通货膨胀，在B点时是通货紧缩③在A点时商品生产者会获利，在B点时会亏本④在C、D点，生产者需提高劳动生产率，降低成本A．①③ B.②④ C.①④ D.②③25、如果A国的年利率为2.54%，B国的年利率为1.54%，B国货币对A国货币呈现升值趋势，预期一年后升值5%。

那么，在其他条件不变的情况下，可能带来的影响有①A国会出现债务危机②B国可能出现通胀压力③短期内会有更多资金流向B国④A国出口商品价格上升A．①④B．②③ C．①② D．③④26、国家发展改革委2011年9月28日宣布，为保护农民种粮积极性，促进粮食生产，2012年生产的白小麦、红小麦和混合麦最低收购价均提高到每50公斤102元。

该决定A．表明市场是实现资源配置的手段B．是国家运用行政手段对生产实施宏观调控C．表明价格形成以政府定价为主 D．是利用价值规律的调节作用27、有人这样比喻政府机构中的分工和职责：蝗虫飞在天上，农业部门要管；落在树上，林业部门要管；趴在草丛里，畜牧部门要管；飞到公园，城建部门要管。

针对多头管理造成管理成本加大、人力资源浪费的现象，政府机构改革应该A．科学划分职能，提高宏观管理效率 B．坚持依法治国，建设法治型政府C．强化政府职责，推行行政问责制 D．取消职能交叉，增设宏观管理机构28、2011年9月29日，东莞市聘50名监督员，从单位外部加强对官员的监督，盯紧官员“八小时”之外的“生活圈”、“社交圈”。

围绕重点工程项目、大额资金的使用、重要公务、人事安排等，加强对领导干部运用权力环节的监督。

这一举措A．说明行政外部监督的广泛性 B．扩大了公民依法行政的权利C．强化了政府公共服务的职能D．加强了民主监督的力度29、有人认为，现在中国对外表现的越来越强硬。

而坚持原则立场同是否强硬是两码事。

卢湾区2011年高考模拟考试数学试题（文科）参考答案与评分标准一、选择题：（每小题4分）1. [1,3]2.2log (1)y x =+3. {|,}Ζx x k k =π∈4. 25. 2i6. 24-7. 5 8．60 9.725- 10.(0,4) 11．14.14 12. 32pk pk -- 13． 14.1006二．选择题（每小题5分）15．A 16．D 17．C 18． B19．解：设圆柱下底面圆O 的半径为r ，连AC ，由矩形ABCD 内接于圆O ，可知AC 是圆O 的直径，……2分于是210r AC ==，得5r =， ……………4分由AB ∥CD ，可知PBA ∠就是异面直线PB 与CD 所成的角，即arctan 2PBA ∠=，故tan 2PBA ∠=． ………………7分在直角三角形PAB 中，tan 12PA AB PBA =∠=，…………9分故圆柱的体积22512300V r PA =π⋅=π⨯⨯=π．……………12分20．解：（1）在参加活动次数为1,2,3的三组学生中各取一个人，则选法种数为111348C C C 96=． 故3人参加活动次数各不相同的选法共有96种． ……………………………5分（2）2人参加活动次数之和不大于3的概率为2113341215C +C C 1C 7P ==， ……………………………10分 故他们参加活动次数之和大于3的概率为21161177P P =-=-=． 所以，2人参加活动次数之和大于3的概率67． ……………………………13分 （另法：（2）中可用直接法来求解） 21．解：（1）设点12,F F 的坐标分别为(,0),(,0)(0)c c c ->，则12(3,1),(3,1),F P c F P c =+=-故212(3)(3)1106F P F P c c c ⋅=+-+=-=- ，可得4c =， …………………2分所以122||||a PF PF =+= ………………4分故22218162a b a c ==-=-=，所以椭圆E 的方程为221182x y +=． ……………………………6分（2）设,M N 的坐标分别为(5,),(5,)m n ，则12(9,),(1,)F M m F N n == ，又12F M F N ⊥ ， 可得1290F M F N mn ⋅=+= ，即9mn =-， ……………………8分又||||||||6MN m n m n =-=+≥=， ……………………10分 （当且仅当||||m n =时取等号） 故2min 6π()9π2S ==，且当S 取最小值时， ……………………11分 有3,3m n ==-或3,3m n =-=，此时圆C 的方程为22(5)9x y -+=． ……………………13分 （另法：（1）中也可以直接将点P 坐标代入椭圆方程来进行求解）22．解：（1）由题意知2n c q a +=，2c a d =+， 又0,0a d >>，可得2211n c d q a a+==+>， ………………………………2分 即2||1n q +>，故2||1n q +>，又2n +是正数，故||1q >．………………………………4分（2）由,,a b c 是首项为1、公差为d 的等差数列，故d c d b 21,1+=+=，若插入的这一个数位于,a b 之间，则21q d =+，321q d =+，消去q 可得32)1()21(d d +=+，即320d d d --=，其正根为251+=d ．………7分 若插入的这一个数位于,b c 之间，则q d =+1，321q d =+，消去q 可得3)1(21d d +=+，即3230d d d ++=，此方程无正根． 故所求公差251+=d ． ………………………………………9分 （3）由题意得1s b a d q a a ++==，12t c a d q b a d++==+，又0,0a d >>， 故220()a d a d d a a d a a d ++-=>++， ………………………………………11分 可得2a d a d a a d ++>+，又20a d a d+>+， 故110s t q q ++>>，即11||||s t q q ++>又||1q >，故有11s t +>+，即s t >． ………………………………………13分 设3n +个数所构成的等比数列为}{n a ，则123,,2t n a c a a a b a c +++====， 由413(2,3,4,k n k n a a a a ac k +-+===…，2)n +，可得 32(a a …222231)()()n n n a a a a a +++=…11322()()()n n n a a a a ac +++=， …………………16分又10s b q a +=>，01>=+bc q t ， 由,s t 不都为奇数，可得1,1s t ++不都为偶数，所以q 必为正数，从而}{n a 中的项也都为正数，故23a a …2n a +12()n ac +=，可得所插入n 个数的乘积为122()n ac a c++．………………18分 （另法：由又10s b q a +=>，01>=+b c q t ， 由,s t 不都为奇数，可知1,1s t ++不都为偶数，所以q 必为正数，又20n c q a +=>， …………………15分 故23a a …2n a +23()()()aq aq aq =…(1)(2)112()n n n n aq a q ++++=111121222()()()n n n n n n c a q a ac a++++++===， 所以插入n 个数的乘积为122()n ac a c ++． …………………18分） 23．解：（1）对任意的1[1,1]x ∈-，有1[1,1]x -∈-，当且仅当21x x =-时，有121212()()22022f x f x x x x x ++==+=， 故存在唯一2[1,1]x ∈-，满足12()()02f x f x +=， ……………………2分 所以0是函数()2(11)f x x x =-≤≤的“均值”． ……………………4分 (另法：对任意的1[1,1]x ∈-，有1[1,1]x -∈-，令21x x =-，则2[1,1]x ∈-，且1212()()22022f x f x x x ++==， 若2[1,1]x '∈-，且12()()02f x f x '+=，则有22()()f x f x '=，可得22x x '=， 故存在唯一2[1,1]x ∈-，满足12()()02f x f x +=， ……………………2分 所以0是函数()2(11)f x x x =-≤≤的“均值”． ……………………4分）（2）当0a =时，()2(12)f x x x =-<<存在“均值”，且“均值”为3-；…………5分 当0a ≠时，由2()2(12)f x ax x x =-<<存在均值，可知对任意的1x ，都有唯一的2x 与之对应，从而有2()2(12)f x ax x x =-<<单调， 故有11a ≤或12a ≥，解得1a ≥或0a <或102a <≤， ……………………9分 综上，a 的取值范围是12a ≤或1a ≥． ……………………10分 （另法：分0,a =1111,12,2a a a ≤<<≥四种情形进行讨论） （3）①当I (,)a b =或[,]a b 时，函数()f x 存在唯一的“均值”．这时函数()f x 的“均值”为2a b +； …………………12分 ②当I 为(,)-∞+∞时，函数()f x 存在无数多个“均值”．这时任意实数均为函数()f x 的“均值”； ……………………14分③当I (,)a =+∞或(,)a -∞或[,)a +∞或(,]a -∞或[,)a b 或(,]a b 时，函数()f x 不存在“均值”． ……………………16分[评分说明：若三种情况讨论完整且正确，但未用等价形式进行叙述，至多得6分；若三种情况讨论不完整，且未用等价形式叙述，至多得5分]①当且仅当I 形如(,)a b 、[,]a b 其中之一时，函数()f x 存在唯一的“均值”．这时函数()f x 的“均值”为2a b +； ……………………13分 ②当且仅当I 为(,)-∞+∞时，函数()f x 存在无数多个“均值”．这时任意实数均为函数()f x 的“均值”； ……………………16分③当且仅当I 形如(,)a +∞、(,)a -∞、[,)a +∞、(,]a -∞、[,)a b 、(,]a b 其中之一时，函数()f x 不存在“均值”． ……………………18分 （另法：①当且仅当I 为开区间或闭区间时，函数()f x 存在唯一的“均值”．这时函数()f x 的均值为区间I 两端点的算术平均数； ……………………13分②当且仅当I 为(,)-∞+∞时，函数()f x 存在无数多个“均值”．这时任意实数均为函数()f x 的“均值”； ……………………16分③当且仅当I 为除去开区间、闭区间与(,)-∞+∞之外的其它区间时，函数()f x 不存在“均值”． ……………………18分）[评分说明：在情形①与②中，等价关系叙述正确但未正确求出函数“均值”，各扣1分]。

2012学年高三第一次六校联考(2012.12)语文试卷（东昌中学、卢湾中学、光明中学、北虹中学、六十中学、同济二附中）一、阅读下文，完成1——6题。

（17分）怀疑和想象是创新的前提葛剑雄①人类认识世界——无论是精神的还是物质的——是一个漫长而无限的过程，在此过程中积累了极其丰富的知识，形成了错综复杂的观念和理论。

稍有哲学常识的人都明白，这些知识、观念和理论绝不是完美无缺的，其中一部分本身就是谬误，有的是建立在谬误的基础上的。

（）至今仍被认为无懈可击的，（）只是相对真理，只能在一定的时间和空间中保持其正确性。

如果没有人对它们提出怀疑和挑战，是不会进步和完善的。

怀疑不一定正确，但排除怀疑的过程却必不可少。

如果怀疑被证明为错误，实际上是更巩固了原来的知识、观念或理论。

反之，如果怀疑被证实为正确，那就意味着原来的知识、观念或理论存在局部或整体的谬误，或者需要修正或完善，或者必须完全否定或清除。

无论如何，都为新的知识、观念或理论的出现提供了条件。

我们称某一真理为“颠扑不破”或“战无不胜”，就表明它不害怕被怀疑，经得起怀疑，并且能在不断的怀疑中坚持其主体部分，同时在局部得到经常性的修正与完善。

任何不允许怀疑的事物，并不能表明它的正确，恰恰显示了它的虚弱．．。

实际上连它的持有者和拥护者心里都明白，它是经不起怀疑的，更害怕受到挑战。

②创新的途径很多，但无非是两个方面：一是否定或破坏旧有的，一是在空白的基础上建立新的。

前者不能完全脱离旧有的，后者却能凭空产生崭新的。

所谓凭空，并非没有实际基础，或者不符合客观条件，只是人们此前尚未认识或拥有。

这就需要想象，想象力越丰富越好。

想象力可以来自个人的天赋和灵感，也可以出于对被当作天经地义的规律或真理的突破或颠覆。

多数想象一时无法成为现实，甚至永远无法证实，但在想象和求证的过程中形成了大量新的成果。

一部分想象纯属胡思乱想，或者被证实是谬误。

但只要有一小部分想象产生效果，就能带来人类社会的飞跃。

上海市卢湾区2012届高三上学期期末考试英语试题(一模)参考答案第I卷（共105分）第一大题第1至10小题，每题1分；第11至16小题，每题2分；第17至24小题，每题1分。

共30分。

I. Listening comprehension (30分)Part A Short ConversationsDirections: In Part A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard. (10分)1. M: Waitress, we’d like a menu, please.W: Yes, sir. Would you care for a drink before you order?Q: Where does the conversation probably take place?2. M: Excuse me. Did you say that sweater is thirteen dollars?W: Sorry, I said thirty dollars, that is “three-zero”, 30 dollars. Let me show you the price tag.Q: How much does the sweater cost?3. M: Why didn’t you wear your seat belt, madam?W: I’m sorry, sir. Will I have to pay a fine?Q: What is the probable relationship between the two speakers?4. M: It’s starting to rain now. It must be cold outside. Let’s just stay at home.W: Well, I think raining days are good days for shopping.Q: What does the woman mean?5. M: Would you mind if I open the window? We need some fresh air.W: We also need to keep it quiet in here.Q: What does the woman mean?6. M: Here is your express mail from New York. Could you please sign your name here?W: Sure, thanks.Q: What is the man’s probable occupation?7. M: What sort of apartment do you want to have? Something big? Or somethingcheap?W: The size and the price are not so important, but it must be in a convenient location.Q: What is the woman’s first concern when she considers buying an apartment?8. M: I don’t understand why so many people are crazy about pizza.W: Neither do I.Q: What does the woman mean?9. M: Do you want to try a new hairstyle today?W: Er, not this time. I’m in a hurry.Q: What can we learn from the conversation?10.W: Who do you think is a better student, Jack or his brother?M: Both are pretty good. Jack is cleverer while his brother works harder.Q: What do we learn from the conversation?Keys:1. C 2. B 3. D 4. B 5. D 6. A 7.C 8.D 9. B 10. DPart B Short PassagesDirections: In Part B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard. (12分)Questions 11 through 13 are based on the following passage.Reading newspapers is an important part of our daily life. But do you know how a newspaper is made?There are many steps to making a newspaper. Take Teens for example. On Monday, editors and reporters hold a meeting to decide on the stories for the week’s paper. On Tuesday and Wednesday, reporters write news stories. Cartoonists draw cartoons and photographers take pictures to match the stories. Foreign editors check the language.On Thursday, page designers put the stories, cartoons and pictures on the pages. Editors read through the stories to find mistakes and write headlines and captions.Friday is a busy day. Page designers print the page drafts. Editors read pages and check them again. At night, Teens comes out in the printing house.Teens is a weekly newspaper. Daily newspapers have all the same steps, but do them all in a day instead of a week.Questions:11. What’s editors’ task on Monday?12. Who are probably not busy on Tuesday and Wednesday?13. What is the passage mainly about?Keys: 11. A 12. D 13. CQuestions 14 through 16 are based on the following passage.There are stock markets in large cities in many countries. Stock markets in Paris, London, Tokyo, Shanghai and New York are among the largest and most well-known. The stock market, also called stock exchange, is a place where people can buy or sell shares of a factory or company. And each share means certain ownership of a factory or company.Different people go to stock markets. Some are rich, who want to get more money than they have. Others are not very rich, who buy stocks and want to try their luck and become rich enough to buy a larger flat. Still others buy stocks as part of their plan to save money.Of course, investing money in the stock market is not the safest way to make money. No one can tell exactly whether the shares will be doing well. The factory or company may do badly. Then the stocks will go down, and investors will lose money. The stocks may go up, but sometimes even if a factory or company does a good job, the stock may still go down.No wonder going to the stock market is often compared to gambling. Indeed, the stock market is an attractive and complex part of the business world.Questions:14. What is a stock market?15. Why do rich people go to stock markets?16. What does the passage mainly tell us?Keys: 14. C 15. A 16. CPart C Longer ConversationDirections:In Part C, you will hear two longer conversations. The conver sations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on the answer sheet. (8分)Blanks 17 through 20 are based on the following conversation.W: Police station. Can I help you?M: Yes. I’m calling to tell you I found a car near a bridge. I thought it might be a stolen car.W: I see. Where exactly did you find it?M: Near the No. 8 Bridge al ong the London Road.W: Can you recall the number of the car?M: Yes, the number was BWF 3586.W: What kind of car is i t?M: A Mini. It’s brown and nearly new.W: When did you find the car?M: Yesterday, January 5th.W: Your name and address, please.M: Henry Roberts. I live at 51 Eaton Road.W: Well, thank you very much, Mr. Roberts. We’ll investigate it.Keys: 17. London 18. 3586 19. brown 20. JanuaryBlanks 21 through 24 are based on the following conversation.M: Please come this way, ladies and gentlemen. In the next room we have a special showing of modern paintings.W: I didn’t know about the modern paintings. How long have they been here?M: We’ve had them for three weeks. They’re part of a special art exhibit. One more week here it will be sent to Paris.W: I hope I can come back again while it’s here. How late does the gallery stay open?M: During the week it’s open till five.W: Isn’t it open on Sundays?M: It’s open till four on Sundays. It opens every day at ten am.W: Thank you.M: Now come this way, please.W: I’d rather stay here and look at these old pictures. I don’t like modern art. I think modern painters make people square, and they paint faces green.M: You don’t understand modern art, I’m afraid.Keys: 21. Modern paintings. 22. (About) Four weeks.23. Monday to Saturday 24. look at/appreciate第二大题每小题1分。

卢湾区2012届一模语文试卷及参考答案卢湾2011学年第一学期高三年级期末考试语文试卷考生注意：1．答卷前，考生务必在答题纸上将自己的姓名等填写清楚。

2．本考试设试卷和答题纸两部分，所有试题的答案必须全部涂写在答题纸上，写在试卷上一律不给分；答题时应注意试题题号和答题纸题号一一对应，不能错位。

3．考试时间150分钟，试卷满分150分。

一阅读80分（一）阅读下文，完成第1—6题。

（18分）机器的神话南帆①现在，机器已经如此密集地介入了生活，甚至参与每一天的开始与结束。

人类与自然的搏斗，这个阶段占据了大部分的历史时光；人与人的社会关系压倒了人与自然的关系之后，一个重要的转折开始了。

现在，如此之多的机器嵌入了我们的生活——又一个历史的拐点来了吗？②我们进入了一个机器装配的世界。

我们的行程是由汽车和飞机设计的，我们的休闲是由电视频道和节目表设计的，我们的午餐欲望由钟表批准，我们脸上的表情竭力取悦照相机。

机器为我们提供了种种知识。

可以上互联网查询一个典故，一个机构的地址，一个学科的前沿问题；甚至可以在身体不适的时候查找各种病症的解释。

钱锺书由于博闻强记而成为神话google之曲软件被装入计算机之后，那些艺术家还有多少事情可以干？现在，机器是我们的教师，保姆，工程师，工作同事，娱乐伙伴，机器设置我们的居住环境，出行步骤，聚会空间以及艺术享受的形式。

换句话说，机器如同我们新的上帝。

③人与机器长期磨合之中，我们总是认为自己占据了上风。

充当主人的幻觉隐瞒了一个意味深长的事实，机器正在将我们调教成它的附属零件。

我们说得出各个频道节目主持人的近期绯闻以及何时曾经整容，但是，我们对于一墙之隔的邻居一无所知。

寄宿学校的孩子周末回家，扔下了书包直扑计算机。

他认为三天不上网就会成为傻瓜，而拨出半小时陪伴父母聊天简直是活受罪。

④我们不清楚是否已经越过临界点。

人类的许多传统坐标正在失效，例如“真实”。

那一幢房子是真的吗？水里游动的热带鱼、一个人脸上惊恐的表情是真的吗？炮火、高高溅起的水柱与燃烧的炮舰真的是一场海战吗？通常，我们对于这一类问题的判断不会发生错误。

卢湾2011学年第一学期高三年级期末考试 数学试卷（文科） 2012.1（本卷完成时间为120分钟，满分为150分）一、填空题（本大题满分56分）本大题共有14小题，考生应在答题纸相应编号的空格内直接写结果，每个空格填对得4分，否则一律得零分．1．不等式210x x ++<的解集为 ．2．若1sin 3θ=，则cos 2θ= ． 3．函数1ln 2y x =(0)x >的反函数为 ． 4．若集合{|05,}A x x x =∈Z ≤≤，{|,}2k B x x k A ==∈，则A B = （用列举法表示）．5．若函数()f x ax b =+的零点为2x =，则函数2()g x bx ax =-的零点是0x =和x = ．6．已知二元一次方程组111222,a x b y c a x b y c +=⎧⎨+=⎩，若记12a a a ⎛⎫= ⎪⎝⎭ ，12b b b ⎛⎫= ⎪⎝⎭ ，12c c c ⎛⎫= ⎪⎝⎭ ，则该方程组存在唯一解的条件为 （用a 、b 、c 表示）．7．若5255(1)110ax x bx a x +=++++ ，则b = ．8．若常数t 满足||1t >，则211lim n nn t t t t -→∞++++= ． 9．已知数列{}n a ，若114a =，123n n a a +=-（*n ∈N ），则使20n n a a +⋅<成立的n 的值是 ．10．甲、乙、丙三人同在某公司上班，若该公司规定，每位职工可以在每周七天中任选两天休息（如选定星期一、星期三），以后不再改动，则他们选定的两个休息日相同的概率是 （结果用数值表示）．11．在平面直角坐标系中，若不等式组10,10,10x y x ax y +-⎧⎪-⎨⎪-+⎩≥≤≥（a 为常数）所表示的平面区域内的面积等于2，则a 的值为 ．12．为了解某校高三学生的视力情况，随机地抽查了该校100名高三学生的视力情况，得到频率分布直方图，如右图，由于不慎将部分数据丢失，但知道前4组的频数成等比数列，后6组的频数成等差数列，那么最大频率为 ，视力在4.6到5.0之间的学生数为 ． 13．已知函数()x f x ab c =+(0,1)b b >≠，[0,)x ∈+∞，若其值域为[2,3)-，则该函数的一个解析式可以为()f x = ．14．若对于满足13t -≤≤的一切实数t ，不等式222(3)(3)0x t t x t t -+-+->恒成立，则x 的取值范围为 ．二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分．15．在复平面内，复数(1i)i z =+（i 为虚数单位）对应的点位于（ ）．A ．第一象限B ．第二象限C ．第三象限D ．第四象限16．“2k αβ=π+()k ∈Z ”是“tan tan αβ=”成立的（ ）．A ．充分非必要条件B ．必要非充分条件C ．充要条件D ．既非充分又非必要条件17．若函数()f x 同时满足下列三个条件：①有反函数 ②是奇函数 ③其定义域与值域相同，则函数()f x 可以是（ ）．A ．()sin f x x =（22x ππ-≤≤）B ．2)(x x e e x f -+=C ．3)(x x f -=D ．xx x f -+=11ln )( 18．已知函数2()|1|f x x =-，若0x y <<，且()()f x f y =，则（ ）．A．y（0x < B．y （02x <<）C．y（0x < D．y （01x <<）三、解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸相应的编号规定区域内写出必要的步骤．19．（本题满分12分）在△ABC 中，角,,A B C 的对边分别为,,a b c ，且2cos a b C =，3b c a +=． 求sin A 的值．20．（本题满分14分）本题共有2个小题，第1小题满分4分，第2小题满分10分．已知函数()||f x x a =-，2()21g x x ax =++（a 为正常数），且函数()f x 与()g x 的图像在y 轴上的截距相等．（1）求a 的值；（2）若()()h x f x =+b 为常数），试讨论函数()h x 的奇偶性．21．（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分． 已知a 、b 是两个不共线的非零向量．（1）设a OA =，OB tb = （t ∈R ），)(31+=，当A 、B 、C 三点共线时，求t 的值． （2）如图，若a OD = ，b OE = ，a 与b 夹角为120︒，||||1a b == ，点P 是以O 为圆心的圆弧 DE 上一动点，设OP xOD yOE =+ （,x y ∈R ），求x y +的最大值．22．（本题满分16分）本题共有3个小题，第1小题满分3分，第2小题满分6分，第3小题满分7分．已知数列{}n b ，若存在正整数T ，对一切*n ∈N 都有n T n b b +=，则称数列{}n b 为周期数列，T 是它的一个周期．例如：数列a ，a ，a ，a ，… ① 可看作周期为1的数列；数列a ，b ，a ，b ，… ② 可看作周期为2的数列；数列a ，b ，c ，a ，b ，c ，… ③ 可看作周期为3的数列…（1）对于数列②，它的一个通项公式可以是n a n a b n ⎧=⎨⎩为正奇数，为正偶数.试再写出该数列的一个通项公式；（2）求数列③的前n 项和n S ；（3）在数列③中，若12,,12a b c ===-，且它有一个形如sin()n b A n ωϕ=+B +的通项公式，其中A 、B 、ω、ϕ均为实数，0A >，0ω>，||2ϕπ<，求该数列的一个通项公式n b ．第（2）小题23．（本题满分18分）本题共有3个小题，第1小题满分6分，第2小题满分6分，第3小题满分6分． 已知函数1()x t f x t x +-=-（t 为常数）． （1）当1t =时，在图中的直角坐标系内作出函数()y f x =的大致图像，并指出该函数所具备的基本性质中的两个（只需写两个）．（2）设()n a f n =（*n ∈N ），当10t >，且*t ∉N 时，试判断数列{}n a 的单调性并由此写出该数列中最大项和最小项（可用[]t 来表示不超过t 的最大整数）． （3）利用函数()y f x =构造一个数列{}n x ，方法如下：对于给定的定义域中的1x ，令21()x f x =，32()x f x =，…，1()n n x f x -=（2n ≥，*n ∈N ），…在上述构造过程中，若i x （*i ∈N ）在定义域中，则构造数列的过程继续下去；若i x 不在定义域中，则构造数列的过程停止．若可用上述方法构造出一个常数列{}n x ，求t 的取值范围．。

2012年上海市卢湾区高考数学一模试卷（文科）一、填空题：（本大题56分）1．（4分）不等式x2+x+1＜0的解集为．2．（4分）若，则cos2α=．3．（4分）函数（x＞0）的反函数为．4．（4分）若集合A={x|0≤x≤5，x∈Z}，B={x|}，则A∩B=（用列举法表示）．5．（4分）若函数f（x）=ax+b的零点为x=2，则函数g（x）=bx2﹣ax的零点是x=0和x=．6．（4分）已知二元一次方程组，若记，，，则该方程组存在唯一解的条件为（用、、表示）．7．（4分）若（1+ax）5=1+10x+bx2+…+a5x5，则b=．8．（4分）若常数b满足|b|＞1，则=．9．（4分）已知数列{a n}，若a1=14，（n∈N*），则使a n•a n+2＜0成立的n的值是．10．（4分）甲、乙、丙三人同在某公司上班，若该公司规定，每位职工可以在每周七天中任选两天休息（如选定星期一、星期三），以后不再改动，则他们选定的两个休息日相同的概率是（结果用数值表示）．11．（4分）在平面直角坐标系中，不等式组所表示的平面区域的面积为2，则实数a的值为．12．（4分）为了解某校高三学生的视力情况，随机地抽查了该校100名高三学生的视力情况，得到的频率分布直方图如下，由于不幸将部分数据丢失，但知道前4组的频率成等比数列，后6组的频率成等差数列，设最大的频率为a，视力在4.6到达5.0之间的学生数为b，则a，b的值分别为、．13．（4分）已知函数f（x）=ab x+c（b＞0，b≠1），x∈[0，+∞），若其值域为[﹣2，3），则该函数的一个解析式可以为f（x）=．14．（4分）若对于满足﹣1≤t≤3的一切实数t，不等式x2﹣（t2+t﹣3）x+t2（t ﹣3）＞0恒成立，则x的取值范围为．二、选择题：（本大题满分20分）15．（5分）设复数z=i⋅（1+i）（其中i是虚数单位），则复数z对应的点位于（）A．第一象限B．第二象限C．第三象限D．第四象限16．（5分）“α=2kπ+β（k∈Z）”是“tanα=tanβ”成立的（）A．充分非必要条件B．必要非充分条件C．充要条件D．既非充分又非必要条件17．（5分）若函数f（x）同时满足下列三个条件：①有反函数②是奇函数③其定义域与值域相同，则函数f（x）可以是（）A．f（x）=sinx（）B．f（x）=C．f（x）=﹣x3D．f（x）=ln18．（5分）设函数f（x）=|x2﹣1|，若0＜x＜y，且f（x）=f（y），则（）A．y=（0＜x＜）B．（0＜x＜2）C．（0＜x＜）D．（0＜x＜1）三、解答题：（本大题满分74分）19．（12分）在△ABC中，角A，B，C的对边分别为a，b，c，且a=2bcosC，b+c=3a．求sinA的值．20．（14分）已知函数f（x）=|x﹣a|，g（x）=x2+2ax+1（a为正常数），且函数f（x）与g（x）的图象在y轴上的截距相等．（1）求a的值；（2）若h（x）=f（x）+b（b为常数），试讨论函数h（x）的奇偶性．21．（14分）已知、是两个不共线的非零向量，（1）设=，=t（t∈R），=（+），当A，B，C三点共线时，求t 的值；（2）如图，若=，=，、的夹角为120°，且||=||=1，点P是以O 为圆心的圆弧上的一个动点，设=x+2y（x，y∈R），求x+y的最大值．22．（16分）已知数列{b n}，若存在正整数T，对一切n∈N*都有b n+r=b n，则称数列{b n}为周期数列，T是它的一个周期．例如：数列a，a，a，a，…①可看作周期为1的数列；数列a，b，a，b，…②可看作周期为2的数列；数列a，b，c，a，b，c，…③可看作周期为3的数列…（1）对于数列②，它的一个通项公式可以是，试再写出该数列的一个通项公式；（2）求数列③的前n项和S n；（3）在数列③中，若a=2，b=，c=﹣1，且它有一个形如b n=Asin（ωn+φ）+B的通项公式，其中A、B、ω、φ均为实数，A＞0，ω＞0，|φ|＜，求该数列的一个通项公式b n．23．（18分）已知函数f（x）=（t为常数）．（1）当t=1时，在图中的直角坐标系内作出函数y=f（x）的大致图象，并指出该函数所具备的基本性质中的两个（只需写两个）．（2）设a n=f（n）（n∈N*），当t＞10，且t∉N*时，试判断数列{a n}的单调性并由此写出该数列中最大项和最小项（可用[t]来表示不超过t的最大整数）．（3）利用函数y=f（x）构造一个数列{x n}，方法如下：对于给定的定义域中的x1，令x2=f（x1），x3=f（x2），…，x n=f（x n﹣1）（n≥2，n∈N*），…在上述构造过程中，若x i（i∈N*）在定义域中，则构造数列的过程继续下去；若x i不在定义域中，则构造数列的过程停止．若可用上述方法构造出一个常数列{x n}，求t的取值范围．2012年上海市卢湾区高考数学一模试卷（文科）参考答案与试题解析一、填空题：（本大题56分）1．（4分）不等式x2+x+1＜0的解集为∅．【考点】73：一元二次不等式及其应用．【专题】11：计算题．【分析】原不等式即+＜0，不等式显然无解，由此得到不等式x2+x+1＜0的解集．【解答】解：不等式x2+x+1＜0 即+＜0，故不等式无解，故答案为∅．【点评】本题主要考查二元一次不等式的解法，属于基础题．2．（4分）若，则cos2α=．【考点】GS：二倍角的三角函数．【专题】11：计算题．【分析】把所求的式子利用二倍角的余弦函数公式化为关于sinα的式子，将sin α的值代入即可求出值．【解答】解：因为sinα=，所以cos2α=1﹣2sin2α=1﹣2×=．故答案为：．【点评】通常，在高考题中，三角函数多会以解答题的形式出现在第一个解答题的位置，是基础分值的题目，学生在解答三角函数问题时，往往会出现，会而不对的状况．所以，在平时练习时，既要熟练掌握相关知识点，又要在解答时考虑更为全面．这样才能熟练驾驭三角函数题．3．（4分）函数（x＞0）的反函数为y=e2x（x∈R）．【考点】4R：反函数．【专题】11：计算题．【分析】根据反函数的定义，只要从y=lnx，反解出x，互换x，y即得．【解答】解：∵f（x）=lnx，∴y=lnx，∴x=e2y，互换x，y得y=e2x，∴函数f（x）=lnx（x＞0）的反函数是y=e2x，故答案为：y=e2x（x∈R）．【点评】本题主要考查了反函数的求法，求解时，一定要注意指数式与对数的互化，属于基础题．4．（4分）若集合A={x|0≤x≤5，x∈Z}，B={x|}，则A∩B={0，1，2}（用列举法表示）．【考点】1E：交集及其运算．【专题】11：计算题．【分析】根据题意，用列举法表示集合A，进而可得集合B；由交集的定义，计算可得答案．【解答】解：根据题意，A=集合A={x|0≤x≤5，x∈Z}={0，1，2，3，4，5}，则B={0，，1，，2，}，则A∩B={0，1，2}；故答案为{0，1，2}．【点评】本题考查集合的交集运算，关键是用列举法得到集合B．5．（4分）若函数f（x）=ax+b的零点为x=2，则函数g（x）=bx2﹣ax的零点是x=0和x=﹣．【考点】52：函数零点的判定定理．【专题】51：函数的性质及应用．【分析】由函数f（x）=ax+b的零点为x=2，可得2a+b=0，令g（x）=0，可得x=0，或x=﹣，由此得出结论．【解答】解：∵函数f（x）=ax+b的零点为x=2，∴2a+b=0，即b=﹣2a．∴函数g（x）=bx2﹣ax=﹣2ax2﹣ax=ax（﹣2x﹣1），令g（x）=0，可得x=0，或x=﹣．故它的零点为x=0和x=﹣，故答案为﹣．【点评】本题主要考查函数的零点的定义，求得2a+b=0，是解题的关键，属于基础题．6．（4分）已知二元一次方程组，若记，，，则该方程组存在唯一解的条件为与不平行（用、、表示）．【考点】OQ：系数矩阵的逆矩阵解方程组．【专题】29：规律型．【分析】二元一次方程组，存在唯一解时，系数行列式≠0，由此可得结论．【解答】解：二元一次方程组，存在唯一解时，系数行列式≠0∴a1b2﹣a2b1≠0∵，，∴与不平行故答案为：与不平行【点评】本题考查二元一次方程组的解，解题的关键是利用二元一次方程组存在唯一解时，系数行列式不等于0．7．（4分）若（1+ax）5=1+10x+bx2+…+a5x5，则b=40．【考点】DA：二项式定理．【专题】11：计算题．【分析】由二项式定理，可得（1+ax）5的展开式的通项，写出含x的项，结合题意可得5a=10，即可得a=2，再根据通项可得b=C52a2，计算可得答案．【解答】解：（1+ax）5的展开式的通项为T r+1=C5r a r x r，则含x的项为C51ax=5ax，又由题意，可得5a=10，即a=2，则b=C52a2=10×4=40；故答案为40．【点评】本题考查二项式定理的应用，关键是求出a的值．8．（4分）若常数b满足|b|＞1，则=．【考点】6F：极限及其运算．【专题】11：计算题；16：压轴题．【分析】先由等比数列的求和公式把原式转化为，再由|b|＞1可知，由此能够求出的值．【解答】解：∵|b|＞1，∴===．答案：．【点评】本题考查等比数列的求和公式和数列极限的求法，解题时要注意合理地进行等价转化．9．（4分）已知数列{a n}，若a1=14，（n∈N*），则使a n•a n+2＜0成立的n的值是21．【考点】8H：数列递推式．【专题】11：计算题．【分析】由题设知数列{a n}是首项为14，公差为﹣的等差数列，故=﹣+，由此推导出a n•a n+2=，由此能求出使a n•a n+2＜0成立的n的值．【解答】解：∵a1=14，（n∈N*），∴数列{a n}是首项为14，公差为﹣的等差数列，∴=﹣+，∴a n•a n+2=（﹣+）[﹣]=，∵a n•a n+2＜0，∴＜0，整理，得n2﹣42n+440＜0，解得20＜n＜22，∵n∈N*，∴n=21．故答案为：21．【点评】本题考查数列的递推公式的应用，解题时要熟练掌握等差数列的性质和应用，注意合理地进行等价转化．10．（4分）甲、乙、丙三人同在某公司上班，若该公司规定，每位职工可以在每周七天中任选两天休息（如选定星期一、星期三），以后不再改动，则他们选定的两个休息日相同的概率是（结果用数值表示）．【考点】C6：等可能事件和等可能事件的概率．【专题】11：计算题．【分析】根据题意，由组合数公式可得甲在每周七天中任选两天休息的情况数目，同理可得乙、丙的选法数目，由分步计数原理可得三人选择休息日的情况数目，进而由等可能事件的概率公式，计算可得答案．【解答】解：根据题意，甲在每周七天中任选两天，有C72=21种选法，同理乙、丙也有21种选法，则三人共有21×21×21种选法；其中三人选定的两个休息日相同的情况有C72=21种，则他们选定的两个休息日相同的概率为=；故答案为．【点评】本题考查等可能事件的概率，注意灵活应用组合数公式和分步计数原理．11．（4分）在平面直角坐标系中，不等式组所表示的平面区域的面积为2，则实数a的值为3．【考点】7C：简单线性规划．【分析】先根据约束条件（a为常数），画出可行域，求出可行域顶点的坐标，再利用几何意义求关于面积的等式求出a值即可．【解答】解：当a＜0时，不等式组所表示的平面区域，如图中的M，一个无限的角形区域，面积不可能为2，故只能a≥0，此时不等式组所表示的平面区域如图中的N，区域为三角形区域，若这个三角形的面积为2，则AB=4，即点B的坐标为（1，4），代入y=ax+1得a=3．故答案为：3．【点评】本题主要考查了用平面区域二元一次不等式组，以及简单的转化思想和数形结合的思想，属中档题．12．（4分）为了解某校高三学生的视力情况，随机地抽查了该校100名高三学生的视力情况，得到的频率分布直方图如下，由于不幸将部分数据丢失，但知道前4组的频率成等比数列，后6组的频率成等差数列，设最大的频率为a，视力在 4.6到达 5.0之间的学生数为b，则a，b的值分别为a=0.27、b=78．【考点】B8：频率分布直方图．【专题】11：计算题．【分析】先根据直方图求出前2组的频数，根据前4组成等比数列求出第3和第4组的人数，从而求出后6组的人数，根据直方图可知4.6～4.7间的频数最大，即可求出频率a，根据等差数列的性质可求出公差d，从而求出在4.6到5.0之间的学生数为b．【解答】解：由频率分布直方图知组矩为0.1，4.3～4.4间的频数为100×0.1×0.1=1．4.4～4.5间的频数为100×0.1×0.3=3．又前4组的频数成等比数列，∴公比为3．根据后6组频数成等差数列，且共有100﹣13=87人．从而4.6～4.7间的频数最大，且为1×33=27，∴a=0.27，设公差为d，则6×27+d=87．∴d=﹣5，从而b=4×27+（﹣5）=78．故答案为：0.27，78．【点评】本题考查频率分布直方图的相关知识，以及等差数列和等比数列的应用等有关知识，直方图中的各个矩形的面积代表了频率，所以各个矩形面积之和为1，同时考查分析问题的能力，属于基础题．13．（4分）已知函数f（x）=ab x+c（b＞0，b≠1），x∈[0，+∞），若其值域为[﹣2，3），则该函数的一个解析式可以为f（x）=﹣5（满足0＜b＜1的b均可）．【考点】48：指数函数的定义、解析式、定义域和值域．【专题】11：计算题．【分析】由题设条件知：当x=0时，f（0）=a+c=﹣2，当x→+∞时，b x→0，f （x）→c=3，解得a=﹣5，c=3，0＜b＜1．【解答】解：∵f（x）=ab x+c（b＞0，b≠1），x∈[0，+∞），其值域为[﹣2，3），∴当x=0时，f（0）=a+c=﹣2，当x→+∞时，b x→0，f（x）→c=3，解得a=﹣5，c=3，0＜b＜1，∴f（x）=﹣5（满足0＜b＜1的b均可）．故答案为：﹣5（满足0＜b＜1的b均可）．【点评】本题考查指数函数的性质和应用，是基础题．解题时要认真审题，仔细解答．14．（4分）若对于满足﹣1≤t≤3的一切实数t，不等式x2﹣（t2+t﹣3）x+t2（t ﹣3）＞0恒成立，则x的取值范围为（﹣∞，﹣4）∪（9，+∞）．【考点】3R：函数恒成立问题．【专题】11：计算题．【分析】不等式x2﹣（t2+t﹣3）x+t2（t﹣3）＞0可化为（x﹣t2）（x﹣t+3）＞0，求出不等式的解集，再求出函数的最值，即可确定x的取值范围．【解答】解：不等式x2﹣（t2+t﹣3）x+t2（t﹣3）＞0可化为（x﹣t2）（x﹣t+3）＞0∵﹣1≤t≤3，∴t2＞t﹣3∴x＞t2或x＜t﹣3∵y=t2在﹣1≤t≤3时，最大值为9；y=t﹣3在﹣1≤t≤3时，最小值为﹣4，∴x＞9或x＜﹣4故答案为（﹣∞，﹣4）∪（9，+∞）【点评】本题考查恒成立问题，解题的关键是求出不等式的解集，确定函数的最值，属于中档题．二、选择题：（本大题满分20分）15．（5分）设复数z=i⋅（1+i）（其中i是虚数单位），则复数z对应的点位于（）A．第一象限B．第二象限C．第三象限D．第四象限【考点】A1：虚数单位i、复数；A5：复数的运算．【专题】11：计算题．【分析】利用虚数单位i的幂运算性质，复数Z=i（1+i）=﹣1+i，在复平面内对应点为（﹣1，1）．【解答】解：复数Z=i（1+i）=i+i2=﹣1+i，在复平面内对应点为（﹣1，1），在第二象限，故选：B．【点评】本题考查虚数单位i的幂运算性质，复数与复平面内对应点之间的关系．16．（5分）“α=2kπ+β（k∈Z）”是“tanα=tanβ”成立的（）A．充分非必要条件B．必要非充分条件C．充要条件D．既非充分又非必要条件【考点】29：充分条件、必要条件、充要条件．【专题】11：计算题．【分析】当a=k，k∈Z时，tanα和tanβ不存在，“α=2kπ+β（k∈Z）”推不出“tanα=tanβ”，“tanα=tanβ”⇒“α=kπ+β（k∈Z）”．【解答】解：∵“α=2kπ+β（k∈Z）”推不出“tanα=tanβ”，例如当a=k，k∈Z时，tanα和tanβ不存在，“tanα=tanβ”⇒“α=kπ+β（k∈Z）”，∴“α=2kπ+β（k∈Z）”是“tanα=tanβ”成立的既非充分又非必要条件故选：D．【点评】本题考查必要条件、充分条件、充要条件的判断与应用，是基础题．解题时要认真审题，仔细解答．17．（5分）若函数f（x）同时满足下列三个条件：①有反函数②是奇函数③其定义域与值域相同，则函数f（x）可以是（）A．f（x）=sinx（）B．f（x）=C．f（x）=﹣x3D．f（x）=ln【考点】34：函数的值域；3K：函数奇偶性的性质与判断；4R：反函数．【专题】11：计算题．【分析】先依据奇函数排除一选项，再根据定义域与值域是否相同，又排除一些选项，最后根据是否有反函数，即可得出答案．【解答】解：由于f（x）=是偶函数，即B不是奇函数，又A：f（x）=sinx（）的定义域为，值域为[﹣1，1]，D：f（x）=ln的定义域为（﹣1，1），值域不是（﹣1，1），故选项A、D定义域与值域不同，对于C：同时满足下列三个条件：①有反函数②是奇函数③其定义域与值域相同，故只有C正确．故选：C．【点评】本题主要考查了函数奇偶性的判断．设函数y=f（x）的定义域为D，如果对D内的任意一个x，都有x∈D，且f（﹣x）=﹣f（x），则这个函数叫做奇函数．灵活利用题目的条件解好数学问题是一种能力．18．（5分）设函数f（x）=|x2﹣1|，若0＜x＜y，且f（x）=f（y），则（）A．y=（0＜x＜）B．（0＜x＜2）C．（0＜x＜）D．（0＜x＜1）【考点】36：函数解析式的求解及常用方法．【专题】11：计算题．【分析】利用题设条件，得到|x2﹣1|=|y2﹣1|，再由绝对值的含义能够求出函数的解析式．【解答】解：∵函数f（x）=|x2﹣1|，且f（x）=f（y），∴|x2﹣1|=|y2﹣1|，∵0＜x＜y，∴x2﹣1＜0，y2﹣1＞0|x2﹣1|=1﹣x2=y2﹣1，所以y=，0＜x＜1．故选：D．【点评】本题考查函数的解析式的求法，是基础题．解题时要认真审题，仔细解答．三、解答题：（本大题满分74分）19．（12分）在△ABC中，角A，B，C的对边分别为a，b，c，且a=2bcosC，b+c=3a．求sinA的值．【考点】HU：解三角形．【专题】11：计算题．【分析】由a=2bcosC及正弦定理，得sinA=2sinB cosC，展开整理得sin（B﹣C）=0，可得b=c．由b+c=3a，求得cosC==，再求得sinC，由sinA=sin（π﹣2C）=2sinCcosC 求得结果．【解答】解：由a=2bcosC及正弦定理，得sinA=2sinB cosC，又A=π﹣B﹣C，可化为sin（B+C）=2sinB cosC，展开整理得sin（B﹣C）=0，（4分）在三角形中得B﹣C=0，即B=C，可得b=c．（6分）于是由b+c=3a，得2b=3a，因此cosC==，（8分）可得sinC=，（10分）故sinA=sin（π﹣2C）=2sinCcosC=．（12分）【点评】本题主要考查正弦定理的应用，三角形的内角和公式，判断三角形的形状的方法，属于中档题．20．（14分）已知函数f（x）=|x﹣a|，g（x）=x2+2ax+1（a为正常数），且函数f（x）与g（x）的图象在y轴上的截距相等．（1）求a的值；（2）若h（x）=f（x）+b（b为常数），试讨论函数h（x）的奇偶性．【考点】&2：带绝对值的函数；3V：二次函数的性质与图象．【专题】2A：探究型．【分析】（1）利用函数f（x）与g（x）的图象在y轴上的截距相等，建立方程，可求a的值；（2）利用奇偶函数的定义，确定b的值，进而可得函数的奇偶性．【解答】解：（1）由题意，∵函数f（x）与g（x）的图象在y轴上的截距相等，∴f（0）=g（0），即|a|=1，又a＞0，故a=1．（4分）（2）h（x）=f（x）+b=|x﹣1|+b|x+1|，其定义域为R，（8分）∴h（﹣x）=|x+1|+b|x﹣1|．若h（x）为偶函数，即h（x）=h（﹣x），则有b=1，此时h（2）=4，h（﹣2）=4，故h（2）≠﹣h（﹣2），即h（x）不为奇函数；若h（x）为奇函数，即h（x）=﹣h（﹣x），则b=﹣1，此时h（2）=2，h（﹣2）=﹣2，故h（2）≠h（﹣2），即h（x）不为偶函数；综上，当且仅当b=1时，函数h（x）为偶函数，且不为奇函数，（10分）当且仅当b=﹣1时，函数h（x）为奇函数，且不为偶函数，（12分）当b≠±1时，函数h（x）既非奇函数又非偶函数．（14分）【点评】本题考查函数的性质，考查函数的奇偶性，正确运用函数奇偶性的定义是关键．21．（14分）已知、是两个不共线的非零向量，（1）设=，=t（t∈R），=（+），当A，B，C三点共线时，求t 的值；（2）如图，若=，=，、的夹角为120°，且||=||=1，点P是以O 为圆心的圆弧上的一个动点，设=x+2y（x，y∈R），求x+y的最大值．【考点】9Y：平面向量的综合题．【专题】15：综合题．【分析】（1）利用向量共线定理，及已知向量建立等式，利用平面向量基本定理，即可得到结论；（2）建立坐标系，用三角函数确定x+y，再利用辅助角公式，即可得到结论．【解答】解：（1）由题意，A、B、C三点共线，可设，（2分）∵，（t∈R），，∴，，∴=∴k=﹣3，t=．（6分）（2）以O为原点，OD为x轴建立直角坐标系，则D（1，0），E（﹣，）．设∠POD=α（0≤α），则P（cosα，sinα），由，得cosα=x﹣y，sinα=，于是y=，x=cosα+，（10分）于是x+y=cosα+=2sin（α+），故当α=时，x+y的最大值为2．（14分）【点评】本题考查向量知识的综合运用，考查三角函数知识，解题的关键是掌握向量共线定理，正确运用三角函数知识，属于中档题．22．（16分）已知数列{b n}，若存在正整数T，对一切n∈N*都有b n+r=b n，则称数列{b n}为周期数列，T是它的一个周期．例如：数列a，a，a，a，…①可看作周期为1的数列；数列a，b，a，b，…②可看作周期为2的数列；数列a，b，c，a，b，c，…③可看作周期为3的数列…（1）对于数列②，它的一个通项公式可以是，试再写出该数列的一个通项公式；（2）求数列③的前n项和S n；（3）在数列③中，若a=2，b=，c=﹣1，且它有一个形如b n=Asin（ωn+φ）+B的通项公式，其中A、B、ω、φ均为实数，A＞0，ω＞0，|φ|＜，求该数列的一个通项公式b n．【考点】82：数列的函数特性；8E：数列的求和；8N：数列与三角函数的综合．【专题】15：综合题．【分析】（1）根据数列a，b，a，b，…可看作周期为2的数列，可写出数列的通项；（2）数列a，b，c，a，b，c，…可看作周期为3的数列，故可分类得出结论；（3）由题意，ω＞0，应有，得ω=，于是b n=Asin（n+φ）+B，把b1=2，b2=，b3=﹣1，代入上式，即可得出结论．【解答】解：（1）∵数列a，b，a，b，…可看作周期为2的数列；∴a n=等．（3分）（2）数列a，b，c，a，b，c，…可看作周期为3的数列，所以当n=3k+1时，；（5分）当n=3k+2时，；（7分）当n=3k+3时，（k∈N）．（9分）（3）由题意，ω＞0，应有，得ω=，（10分）于是b n=Asin（n+φ）+B，把b1=2，b2=，b3=﹣1，代入上式得（12分）由（1）（2）可得Acosφ=，再代入（1）的展开式，可得﹣φ+B=，与（3）联立得B=，（13分）Asinφ=﹣，于是tanφ=﹣因为|φ|＜，所以φ=﹣，（14分）于是可求得A=．（15分）故b n=sin（）+（16分）【点评】本题考查数列与三角函数的综合，考查学生分析解决问题的能力，考查分类讨论的数学思想，有一定难度．23．（18分）已知函数f（x）=（t为常数）．（1）当t=1时，在图中的直角坐标系内作出函数y=f（x）的大致图象，并指出该函数所具备的基本性质中的两个（只需写两个）．（2）设a n=f（n）（n∈N*），当t＞10，且t∉N*时，试判断数列{a n}的单调性并由此写出该数列中最大项和最小项（可用[t]来表示不超过t的最大整数）．（3）利用函数y=f（x）构造一个数列{x n}，方法如下：对于给定的定义域中的x1，令x2=f（x1），x3=f（x2），…，x n=f（x n﹣1）（n≥2，n∈N*），…在上述构造过程中，若x i（i∈N*）在定义域中，则构造数列的过程继续下去；若x i不在定义域中，则构造数列的过程停止．若可用上述方法构造出一个常数列{x n}，求t的取值范围．【考点】82：数列的函数特性；8I：数列与函数的综合．【专题】15：综合题．【分析】（1）当t=1时，f（x）==﹣1+，画出函数的图象，利用图象可得函数的性质；（2）a n==﹣1+，确定1≤n≤[t]，n∈N*时，数列单调递增，且此时a n 均大于﹣1；n≥[t]+1，n∈N*时，数列单调递增，且此时a n均小于﹣1，由此可得结论（3）只需当x≠t时，方程f（x）=x有解，亦即方程x2+（1﹣t）x+1﹣t=0有不等于t的解，由△≥0，可得实数t的取值范围．【解答】解：（1）当t=1时，f（x）==﹣1+．图象如图（2分）基本性质：（每个2分）奇偶性：既非奇函数又非偶函数；单调性：在（﹣∞，1）和（1，+∞）上分别递增；零点：x=0；最值：无最大、小值．（6分）（2）a n==﹣1+，当1≤n≤[t]，n∈N*时，数列单调递增，且此时a n均大于﹣1，当n≥[t]+1，n∈N*时，数列单调递增，且此时a n均小于﹣1，（8分）因此，数列中的最大项为a[t}=，（10分）最小项为a[t}+1=．（12分）（3）根据题意，只需当x≠t时，方程f（x）=x有解，亦即方程x2+（1﹣t）x+1﹣t=0有不等于t的解，（14分）将x=t代入方程左边，得左边为1≠0，故方程不可能有x=t的解．（16分）由△=（1﹣t）2﹣4（1﹣t）≥0，解得t≤﹣3或t≥1，即实数t的取值范围是（﹣∞，﹣3]∪[1，+∞）．（18分）【点评】本题考查函数的图象与性质，考查函数的单调性，考查数列与函数的关系，考查方程解的研究，确定函数的单调性是关键．。