广东省深圳外国语学校2008届高三第三次质量检测
2008、2009深圳外国语学校考试真题
2008深圳外国语学校考试真题（英语基础题：60分；综合知识题：40分；共100分）英语部分1．听短文，给5幅图标序号。
A．救灾方面B.宠物C.熊猫D. 放生E.敬礼男孩-朗铮2．听对话的选择题（把A。
B。
C。
D。
的答案读进录音机里）内容是关于出行计划或习惯爱好等。
3．听短文的选择题（把A。
B。
C。
D。
的答案读进录音机里）第一篇关于英语学习方面，第二篇关于长颈鹿或袋鼠方面的知识。
录音只放一遍，每篇文章给5道选择题，每道选择题给4个选项。
综合部分1．4句描述景色的句子，给5个地点，选出一个古诗中没有提到过的一个。
2．国歌《义勇军进行曲》的作词和作曲分别是谁？3．听一段京剧(歌曲：说唱脸谱)，选出脸谱中错误的一项A．蓝脸的多尔礅B.红脸的关公C.黄脸的曹操D.黑脸的张飞4.四川汶川地震发生的时间。
5．一个圆柱体切开横截面有几种形状（说出3种）6.远望微微塔5层，红光点点倍加增。
灯共186盏，请问塔顶几盏灯？2009深圳外国语学校考试真题（英语基础题：65分；综合知识题：35分；共100分）英语部分一、听短文，给5幅图标序号。
（每题4分，共20分）1、（一个小孩在骑自行车）2、（一个孤儿）3、（一个女孩撅着嘴）4、（一个小男孩坐在爸爸的腿上）5、（一只熊猫怀里还有一只小熊猫）二、听对话的选择题（把A.B.C.D.的答案读进录音机里）（每题4分，共20分）三、听短文的选择题（把A.B.C.D.的答案读进录音机里）（每题5分，共25分）综合部分一、今年建国共多少周年？（3分）二、（听一段音乐《白龙马》）问1：这首歌是出自我国四大名著的哪一个？（3分）问2：这个名著的作者是谁？（3分）三、老师给学生一元钱，老师和学生手里的钱一样多;学生给老师一元钱，老师手里的钱是学生手里钱的两倍。
问老师有多少钱，学生有多少钱？四、（把一个成语中的四个字全部拆分成若干个偏旁部首）问这些能组成一个什么成语？（5分）五、“业精于勤荒于嬉，行成于思毁于随。
2008届全国百套高考数学模拟试题分类汇编-022函数填空题
2008届全国百套高考数学模拟试题分类汇编02函数二、填空题1、(广东省广州执信中学、中山纪念中学、深圳外国语学校三校期末联考)三位同学在研究函数 f (x ) = x1 + | x |(x ∈R ) 时，分别给出下面三个结论：① 函数 f (x ) 的值域为 (－1,1)② 若x 1≠x 2，则一定有f (x 1)≠f (x 2)③ 若规定 f 1(x ) = f (x )，f n +1(x ) = f [ f n (x )]，则 f n (x ) = x1 + n | x | 对任意 n ∈N *恒成立. 你认为上述三个结论中正确的个数有 答案：3.2、(江苏省启东中学2008年高三综合测试一)已知函数()3x f x =的反函数是1()f x -且1(18)23a f a -=+则=______________答案：23、(江苏省启东中学高三综合测试二)给出下列图象其中可能为函数f (x )＝x 4＋ax 3＋bx 2＋cx ＋d (a ，b ，c ，d ∈R)的图象的是_____. 答案：①③4、(江苏省启东中学高三综合测试二)已知f (x )=a ｘ（ａ＞1），ｇ（ｘ）＝ｂｘ（ｂ＞1），当f (x 1)＝g (ｘ2)＝2时，有ｘ1＞ｘ2，则a,ｂ的大小关系是 . 答案：a ＜b5、(江苏省启东中学高三综合测试四)已知函数⎩⎨⎧≤>=)0(2)0(log )(3x x x x f x，则 )]91([f f = 答案：146、(江西省五校2008届高三开学联考)设{x }表示离x 最近的整数，即若x m <-21≤21+m (m ∈Z )，则{x } = m ．给出下列关于函数|}{|)(x x x f -=的四个命题： ①函数)(x f y =的定义域是R ，值域是[0，21]； ②函数)(x f y =的图像关于直线2kx =(k ∈Z )对称； ③函数)(x f y =是周期函数，最小正周期是1； ④函数)(x f y =是连续函数，但不可导．其中真命题是 __________ ． 答案：①②③④7、(四川省巴蜀联盟2008届高三年级第二次联考)已知函数y =[0,)+∞，则实数m 的取值范围是 答案：(0,1][9,)+∞8、(陕西长安二中2008届高三第一学期第二次月考)函数)1lg ()(2--=ax x x f 在区间),1(+∞上单调增函数，则a 的取值范围是________。
08年高三年级英语3月份质量检测试题
08年高三年级英语3月份质量检测试题英语试题第一部分:听力(共两节,满分30分)听下面5段对话.每段对话后有一个小题,从题中所给的A.B.C三个选项中选出最佳选项,并标在试卷的相应位置,听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题,每段对话仅读一遍.1. What do you think the man will do at last?A. Help the woman push her car .B. Let the woman push her own car.C. Ask someone to push the car for the woman.2. What time does the second movie start?A. At 9:45.B. At 10:00.C. At 10:153. What can we learn about the man ?A. He works very carefully.B. He drove carelessly and got a traffic ticket.C. He always drives through a lot of traffic.4. What does the man probably do according to the dialogue?A. A teacher.B. A student.C. A meeting organizer.5. Where are the two speakers?A. They are in Britain.B. They are in the U.S.A.C. They are in France.第二节(共15小题; 每小题1.5分满分22.5分)听下面5段对话或独白.每段对话或独白后有几个小题,从题中所给的A.B.C三个选项中选出最佳选项, 并标在试卷的相应位置,.听每段对话或独白前,你将有时间阅读各个小题,每小题5秒钟;听完后,各个小题将给出5秒钟的作答时间.每段对话或独白读两遍.听下面一段对话, 回答第6—7 题.6. What is Susan doing now?A. She is climbing on the plane.B. She is coming from the plane.C. She is standing near the plane.7. Which of the following about Susan is Not true?A. She carries a package under her arm.B. She carries a suitcase under her arm..C. She is the tall one next to the window.听下面一段对话,回答第8—10 题.8. How does the man feel about his interview tomorrow?A. He is worried about it.B. He is looking forward to it.C. He is sure of what to expect.9. What is the job he wants to get?A. A salesman.B. An engineer.C. A translator.10. What impressed the woman most?A. The man’s German.B. The man’s experience.C. The man’s business skills.听下面一段对话,回答第11—13 题.11. Why does the man want to get a car?A. Because it is useful for his work.B. Because he has got a lot of money.C. Because the car is cheap.12. What does the man mainly consider when he chooses the car?A. Price.B. Quality.C. Ways of payment.13. How much should the man pay for the remaining part?A. $2,500.B. $ 13,800.C. $30,000.听下面一段对话,回答第14—17 题.14. What is the main topic of this conversation?A. The man’s graduation.B. The couple’s engagement.C. The man’s smoking.15. What does the woman suggest?A. The man rethink their plans.B. The man see a family doctor.C. The man concentrate on his studies.16. How does the man feel about the woman’s decision?A. Patient.B. Surprised.C. Worried .17. What can we infer about the woman?A. She has stopped smoking.B. She does not want to marry the man.C. She has asked the man to quit smoking many times.听下面一段独白,回答第18—20 题.18. When did the incident happen?A. When the young people were waiting outside.B. When top group were giving a concert.C. When the young people rushed to get tickets.19. Why were the organizers blamed for the incident?A. Because they hadn’t sold all the tickets beforehand.B. Because they hadn’t stopped the concert immediately.C. Because they hadn’t opened the door earlier.20. What do we learn about the British pop group?A. They had planned to give several concerts in the United States.B. They knew about the incident before the concert started.C. They decided to continue their concert to avoid further trouble.第二部分:语言知识运用(共两节,满分55分)第一节: 多项选择(共10小题; 每小题1分,满分10分)21. The captain showed great perseverance and never __________ to disappointment, even when the ship sank.A. gave offB. gave awayC. gave wayD. gave up22. As economy was declining, jobs _________to the laid-off workers continued to be scarce.A. valuableB. convenientC. comfortableD. available23. As more and more nations put satellites into space, the risk of ________ can only increase asa result.A. collisionB. discoveryC. crashD. invention24. When I ______ my senses, I found myself wrapped up in bed in my little room, with Grandma bending over me.A. woke upB. took toC. picked upD. came to25. We were told that keys should never be hidden around the house since thieves _______ know where to find them.A. especiallyB. generallyC. originallyD. basically26. The husband and wife run their own business near the entrance to the park. They do a(n) _____trade in souvenirs and gifts.A. lovelyB. livelyC. activeD. busy27. Our newspaper is national. Imperfect articles are _____ by our quality control.A. dismissedB. ignoredC. neglectedD. rejected28. –My dog can speak seven languages.--No, you are _____ me on .A. takingB. puttingC. lettingD. depending29. The company was _______ willing to provide us with what we need, which made us excided.A. no more thanB. no other thanC. more thanD. not more than30. Students, who are better at class, always _______ more attention on what the teachers teach them than those who are not good at it.A. payB. drawC. fixD. attract第二节:完成句子(共0小题;每小题1.5分,满分15分)31. It is reported that the United States _______________________( 两倍的能源) the whole of Europe. ( as, energy)32. ___________________________________(他一下飞机) he was met and surrounded by his fans.(than )33. I look on it as _____________________________ (获得新技能的一个机会) . ( opportunity).34. Love and patience _____________________ ( 所需要的东西) look after children. (what)35. He _____________________ ( 不可能在看) TV at 8:00 last night. He has gone to New York. (watch)36. More and more people are signing up for Yoga classes nowadays, ______________________________(考虑到健康和放松的原因) . (advantage)37. _________________________ ( 他的钱用完了), the lazy middle-aged man began to steal others’ money in the city. (run )38. She needed some help but there ___________________ (碰巧连一个人都没看见) . (happen )39. All the food and clothes must be sent immediately ________________ ( 以便那儿的人及时收到) . (receive )40. The suggestion __________________ ( 换一个大马力的发动机) is worth considering. (powerful)第三节: 完形填空(共20小题;每小题1.5分,满分30分)阅读下面短文,从所给的四个选项中,选出可以填入空白处的最佳选项,并在答题卡上将该项涂黑.Some people who find themselves unable to solve a problem react by just giving up. But it is not good to 41 from problems by giving up or by making 42 for failure. You may be sure that all young people go through the same 43 process that you are going through; 44 new situations, developing new skills , and testing their abilities.In many cases, we only “think” there is no 45 to a particular. But 46 we can overcome the problem and achieve the goal by making a direct attack.47 , a boy wanted to be a debater. When he 48 for the debating team as a freshman, the coach thought he was 49 . He as shy; he had a high pitched( 音调) voice; and his posture (体态) was poor. By his junior year, he 50 the school debating team, and in his senior year he was 51 the team in his state. He achieved his goal because he had made a direct attack upon his problem.52 attack is often the beat way to meet problems, we have to be realistic in judging situations.53 it is necessary to 54 either tactics (策略) or the goal.A boy who wants to be a great football player may be too light and not quite 55 for football. In this situation, becoming a great player may be an 56 goal for him. 57 , he may become outstanding in tennis or golf, and 58 his desire to take part in sports.So, although direct attack is often the best way to 59 problems, it is important to study the 60 and make a wise decision about what to do.41. A. ignore B. escape C. free D. neglect42. A. excuses B. apologies C. stories D. decisions43. A different B. difficult C. easy D. unpleasant44. A. overcoming B. facing C. meeting D. judging45. A. key B. answer C. way D. solution46. A. often B. possibly C. fortunately D. ever47. A. In fact B. For example C. After all D. In other words48. A. tried out B. went in C. went all out D. joined in49. A. useless B. hopeless C. helpless D. priceless50. A. became B. made C. entered D. got51. A. at B. in C. on D. of52. A. When B. As though C. While D. As if53. A. Seldom B. Sometimes C. Frequently D. Usually54. A. change B. rebuild C. start D. renew55. A. smart B. strong C. confident D. fast56. A. impossible B. unreasonable C. unfair D. unacceptable57. A. Though B. However C. Fortunately D. Thus58. A. satisfy B. complete C. achieve D. win59. A. meet B. deal C. handle D. treat60. A. causes B. phenomenon C. situation D. difficulties第三部分:阅读理解(共20小题;每小题2分,满分40分)阅读下面短文,从每篇短文后所给的四个选项中,选出可以填入最佳选项,并在答题卡上将该项涂黑.A.“Penn Station,” I told the cab driver and got in. The young , heavy-set man looked friendly and we naturally started a conversation, which went from the weather and quickly varied into the struggles of a cab driver’s life.“What do you do besides your job?”he asked curiously. “I help a nonprofit organization trying to bring some goodness in the world,” I responded. “Do they pay you well?”“Well, no, but I get by. I don’t have many material things in life, but I’ve realized that I don’t need all that to keep me happy. If I die tomorrow, I want to go out knowing that I’ve made a few people smile.”The young cab driver, perhaps in his late thirties, looked back through the sliding glass as if extending his hand for a hand shake--- “Man, it is nice to meet you.”Although we were strangers, both of us felt deeply connected as human beings. And by now, 7 minutes into our ride, we were on a first-name basis. He even spelled his name for me: H—a—k—e—e—m. Hakeem and I talked a bit about simple acts of generosity, the power of a pay—it—forward mindset and now that can promote trust and connection in our communities. He understood the idea, but it seemed very abstract and foreign to him.We arrived at Penn station and traded e—mail addresses after I paid my ride fare. As I was heading out, I turned to him and said, “ Hakeem, here’s a $20. Whenever you feel like it, you give a ride to people and tell them that someone before them has paid for their fare. See what happens.Hearing this, Hakeem was visibly moved. “ Really? Are you sure?”61. The phrase “get by” In Paragraph Two probably means “ ____________”?A. receive some profits by helping the organizationB. receive no profit by helping the organizationC. gain some fame by helping the organizationD. gain some happiness by helping the organization62. From the decription that Hakeem looked back through the sliding glass, the author expects to indicate that__________.A. Hakeem was inspired by his wordsB. Hakeem didn’t believe what he had saidC. Hakeem was carefully driving while talking with the authorD. Hakeem felt a little tried and wanted to shake his hand63. Hakeem understand the idea of a pay-it-forward act__________.A. as soon as the author had told him about it.B. after the author set an example to himC. after he made some further explanationsD. after he saw a scene of it acted out64. We can learn from the passage that the author’s goal of an act of kindness was ________.A. to help people in troubleB. to strengthen friendship among friendsC. to make people happyD. to contribute to people’s trust and connectionB.February 24, 2008 saw thieves break into the showroom of an Italian jeweler favored by Hollywood stars and stole items worth up to 10 million dollars while its owners were in Los Angeles hosting a party to celebrate the Oscars.The robbery, which took place at the Damiani showroom in Milan’s fashion district that morning, was compared later with the “perfect scenes” in films such as Ocean’s Eleven and The Italian Job.The gang had spent more than a month digging a tunnel from a disused cellar in an adjoining building. The drilling had been heard for weeks but was thought to be part of continuing building works next door. The four thieves, dressed in balaclavas, sunglasses and fake uniforms of the Guardia di Finanza, used an internal staircase to reach the first floor, thus avoiding alarms and video surveillance cameras.The showroom had been opened for a private viewing by wealthy clients and there were five employees inside, including a cleaning lady and a member of the catering staff, as well as the manager. The thieves said they were there to check the accounts, then overpowered the staff, tied them up with electrical cable, sealed their mouths with tape and locked them in the washroom. They then helped themselves to jewelry from the safe-deposit boxes and left the way they had come.The entire operation had taken little more than 40 minutes. The employees managed to free themselves and raise the alarm, but by then the gang was long gone. The police said that they were looked into whether the robbers had “inside assistance” that had helped them to avoid the alarms and surveillance cameras.65. Which of the following is the best title of this passage?A. A perfect robberyB. 10 million of Jewelry StolenC. The Smart ThievesD. Thieves Breaking into an Italian Jeweler66. Why didn’t the thieves appear in the cameras? Perhaps because _______________.A. there was something wrong with the cameras thenB. the thieves entered the showroom through an internal staircaseC. the employees were too frightened to open the cameras thenD. the cameras didn’t work with the uniforms of the finance guards67. which of the following is true according to the passage?A. The Italian jeweler was popular with some famous American film stars.B. The thieves went into a disused tunnel into an adjoining building.C. The robbery took place in the morning and there was no one in the showroom.D. One of the jeweler employees must have helped the robbery secretly.68. We can from the passage that ____________.A. The items were so dear that few people could afford to buy one.B. The thieves left the jewels from where they came into it.C. The most valuable jewels couldn’t have survived the robbery.D. The jeweler had to close down because of the showroom robbery.CMicrosoft is developing Big Brother –L--style software capable of remotely monitoring a worker’s productivity, physical wellbeing and ability.The times has seen a patient application filed by the company for a computer system that links workers to their computers via wireless sensor that measure their metabolism ( 新陈代谢) . The system would allow managers to monitor employees’ performance by measuring their heart rate, body temperature, movement ,facial expression and blood pressure.Technology allowing constant monitoring of workers was previously limited to pilots, firefighters and Nasa astronauts. This is believed to be the first time a company has proposed developing such software for mainstream workplaces.Microsoft applied a patent application in the US for a “unique monitoring system” that could link workers to their computers. Wireless sensors could read “ heart rate, skin response, EMG, brain signals, breath rate, body temperatures, movement, facial movements, facial expressions and blood pressure”, the application states.The system could also “automatically detect frustration(失意) or stress in the user” and “ offer and provide assistance accordingly”. Physical changes to an employee would be matched to an individual psychological profile based on a worker’s weight, age and health. If the system picked up an increase in heart rate or facial expressions suggestive of stress or frustration, it would tell management that he needed help.Unions said they fear that employees could be dismissed on the basis of a computer’s watching. The Information Commissioner, civil liberties groups and privacy lawyers strongly criticized (批评) the potential of the system for” raising very serious privacy issues.”69. Microsoft is developing Big Brother—style software____________.A. to monitor a worker’s health conditionB. to apply for a patentC. to watch a worker’s workD. to compete with other companies70. The computer system knows whether a worker is feeling well or not because ______.A. the cameras can take a close look at the workerB. the computer can measure the worker’s metabolism via sensorsC. the sensors can measure his heart rate, body temperature and blood pressureD. the sensors have been placed on the workers in advance71. It can be inferred from the passage that____________.A. the Big Brother—style software can monitor from far awayB. the Big Brother—style software has gained a patentC. no other similar software is being developed by other companiesD. some of the workers will express their objections to the monitoring72. The main idea of this passage may be ______________.A. Microsoft is seeking a patent for an office “spy” softwareB. Microsoft is developing a software to competeC. Microsoft is developing a software against some willsD. Microsoft is the first with a way to monitor workersDParents risk discouraging children from reading by dragging them around bookstores and force-feeding them literary classics, leading children’s writer Anthony Horowitz has suggested. Horowitz, author of the best—selling Alex Rider series of action adventure books ,said the current public concern about children’s reading had been fuelled (激起) and hijacked “( 控制)”by the overanxious middle class.“Reading is not an issue we should keep banging children over the head with,’ he told The Times. Horowitz’s comments followed publication yesterday of a major review of literacy in primary schools by Cambridge University, which suggested that gains in reading skills at school through the national literacy strategy had been achieved at the expense of pupils enjoyment of reading. He also called on schools to set aside more time for children to read for pleasure and less time for analyzing texts line by line.“At home parents should not force their children to read books they read as a child as children literature was now in a golden period,” he said. “As children, my generation was given the books that our parents read. Now children can discover their own books. There have never been so many good living young writers.”Horowitz was speaking at the opening of the annual Starbucks Bookdrive, a Starbucks campaign in partnership with the National Literacy Trust to promote reading by encouraging donations to school libraries.He suggested that the best way that parents could encourage a child to read was to set aside 15 minutes a day to read to them. “As adults we are all so busy that we tend to forget the great value of spending 15 minutes a day reading with our child. There is no better way to get to know your child than to share their books with them. It’s not going to be for ever and they may not thank you for it by the time they are teenagers, so that makes it more valuable,” he said.73. The underlined sentence in Paragraph 3 means _________.A. children should not be forced to readB. parents should not hit the children’s head to force them to readC. children should not be forced to know that reading is a serious issueD. parents should not keep banging their children’s head74. We can infer that the national literacy strategy ___________.A. is welcomed by childrenB. is supported by teachersC. is perhaps not successfulD. is popular in Cambridge University75. What kind of books was Horowitz probably given to read when he was a child?A. The kind of books he enjoyed muchB. Books about adventuresC. Books for pleasure.D. Books of literacy classics.76. The best title of this passage is _____________.A. How to encourage children to readB. Don’t force young to read classicsC. Children’s writer Anthony HorowitzD. Spend time reading with childrenE.A is for always getting to work on time.B is for being extremely busy.C. is for the diligent way you do your job.You may be all these things at the office , and more. But when it comes to getting ahead, experts say, the ABCs of business should include a P, for politics, as in office politics.Dale Carnegie suggested as much more than 50 years ago: hard work alone doesn’t make sure career advancement. You have to be able to sell yourself and your ideas, both publicly and behind the scenes. Yet, despite the obvious rewards of engaging in office politics—a better job, a raise, praise –many people are still unable or unwilling to “play the game”.“People think that office politics involves some manipulative ( 工于心计的) behavior” says Deborah Comer, an assistant professor of management at Hofstra University. “But politics comes from the word ‘polite’ . It can mean persuading and forming small personal groups . It can mean being kind and helpful, or even trying to please your superior, and then expecting something in return.”In fact, today, expects say office politics as proper behavior used to seek for one’s own self—interest in the workplace. In many cases, this involves some form of socializing within the office environment—not just in large companies, but in small workplaces as well.“This first people are usually judged on is their ability to perform well on an unchanging basis,” says Neil P.I.ewis, a management psychologist. “But if two or three candidates(候选人) are up for being raised to a higher position, each of whom has reasonably similar ability, a manager is going to promote the person he or she likes best. It’s simple human nature.”Yet, psychologists say, many employees and employers have trouble with the meaning of politics in the office. Some people, they say, have a proper knowledge of work and what it takes to succeed. Still others connect politics with flattery (奉承) ,fearful that, if they speak up for themselves, they may appear to be flattering their boss for favors.Experts suggest changing this negative (负面的) picture by recognizing the need for some self—promotion.77. “Office politics” is used in the passage to refer to _______________.A. the political views and beliefs of office workersB. the interpersonal relationships within a companyC. the various qualities required for a successful careerD. the rules of behavior for company staff78. To get promoted, one must not only have the necessary ability but ________.A. avoid being too outstandingB. get along well with his colleaguesC. honest and loyal to his companyD. give his boss a good impression79. Why are many people unwilling to “play the game”?A. They are not good at controlling colleagues.B. They feel that such behavior is dishonest.C. They think the effort will get them nowhere.D. They believe that doing so is impractical.80. It is the author’s view that ____________.A. self—promotion does not necessarily mean flatteryB. hard work contributes very little to one’s promotionC. many employees fail to recognize the need of flatteryD. speaking up for oneself is part of human nature第四部分:书面表达(满分25 )你的笔友Sara从电视上看到今年我国南方部分省份遭受冰雪灾害的报道,特来信询问.请你简要介绍此次雪灾的情况.注意:1. 短文字数100左右.2. 开头已写好,不计入总词数.This late January and early February,…参考答案1—5 AABAB 6—10 BBABA 11—15 ABCCB 16—20 BCCAA 21—25 CDADB 26—30 BDBCC31. twice as much energy as32. No sooner had he got off the plane than33. an opportunity to acquire/ get fresh/ new skills34. are what it takes to35. can/ could not have been watching36. taking advantage of health and relaxation benefits37. With his money running out/ His money running out38. happened to be nobody/ not a single person in sight39. so as to be received in time by people there/ so that people there can receive them in time40. that a powerful engine should be used/ of the use of a powerful engine41—45 BABCD 46—50 ABABB 51—55 CCBAD 56—60 BBACC61—65 DCBDA 66—70 BABCC 71—75 DAACD 76—80 BBDBAWritingOne possible version:This late January and early February, unusual snowstorms continuously hit southern provinces of China. Railways, highways and even the airports were covered by thick snow and ice, which also struck electricity supply seriously in some provinces, causing the breaking –off of Jingguang Railway and an extreme jam in Jingzhu Expressway. Tens of thousands of passengers were blocked on their way home. People’s life in these areas was seriously affected.At this urgent moment, the government called on the whole nation to help those in trouble. Soldiers were sent to the snow-stricken areas to clear the ways, policemen were on the roads to help the drivers to fix the tyre chains, and fire engines were used to carry water for people.With great efforts, things have now gradually become normal.。
高考数学不等式典型综合题型 含详解
全国名校高考专题训练06不等式一、选择题1、(江苏省启东中学高三综合测试二)在R 上定义运算).1(:y x y x -=⊗⊗若不等式1)()(<+⊗-a x a x 对任意实数x 成立，则A.11<<-aB.20<<aC.2321<<-a D.2123<<-a 答案：C2、(江苏省启东中学高三综合测试二)已知a ，b ，c ，d 均为实数，有下列命题：0,0,0)2(;0,00)1(>->->>->->ad bc bda c ab b d dc ad bc ab 则若则，若其中正确命题的个数是则若,0,,0)3(>>->-ab bda c ad bcA. 0B. 1C. 2D. 3 答案：D3、(江苏省启东中学高三综合测试二) ab>ac 是b>c 的A.充分不必要条件B. 必要不充分条件C.充要条件D.即不充分也不必要条件 答案：D4、(江苏省启东中学高三综合测试三)当x>1时，不等式x+11-x ≥a 恒成立，则实数a 的取值范围是A ．(－∞,2]B ．[2,+∞)C ．[3,+∞)D ．(－∞,3]答案：D5、(江苏省启东中学高三综合测试四)不等式xx 1log 2-≥1的解集为 ( ) A ．(]1,-∞- B ．[)∞+-,1 C ．[)0,1- D ．(]()∞+-∞-,01, 答案：C6、(江西省五校2008届高三开学联考)已知正整数b a ,满足304＝＋b a ，使得ba 11+取最小值时，则实数对（),b a 是（ ）A ．(5，10）B ．（6，6）C ．（10，5）D ．（7，2）答案：A7、(江西省五校2008届高三开学联考)设2sin1sin 2sin 222n n na =++⋅⋅⋅+ , 则对任意正整数,()m n m n > , 都成立的是A ．||2n m m n a a ⋅-<B ．||2n m m n a a -->C ．1||2n m n a a -<D ．1||2n m n a a -> 答案：C12sin(1)sin(2)sin ||||222n m n n mn n ma a ++++-=++⋅⋅⋅+ 12sin(1)sin(2)sin ||||||222n n mn n m ++++≤++⋅⋅⋅+ 1112111111122||||||12222212n m n n m n m ++++-<++⋅⋅⋅+==--12n < . 故应选C . 8、(陕西长安二中2008届高三第一学期第二次月考)设1212121<⎪⎭⎫⎝⎛<⎪⎭⎫ ⎝⎛<ab，那么( )A.ab a b a a <<B.b a a a b a << C 。
深圳外国语学校2008届高三第三次质量检测(数学文)
广东省深圳外国语学校2008届高三年级第三次质量检测文科数学试题本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分， 第Ⅰ卷为1－10题，共50分，第Ⅱ卷为11－21题，共100分.全卷共计150分。
考试时间为120分钟. 注意事项：参考公式：如果事件A 、B 互斥，那么()()()P A B P A P B +=+如果事件A 、B 相互独立，那么()()()P A B P A P B ⋅=⋅球的表面积公式 24πS R = 球的体积公式 34π3V R =其中R 表示球的半径 第Ⅰ卷（选择题，共50分）一、选择题：本大题共10小题，每小题5分，满分50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．Ｍ＝{}4|2<x x ，Ｎ＝{}032|2<--x x x ，则集合Ｍ Ｎ＝( ). A.{2|-<x x } B.{3|>x x } C.{21|<<-x x } D. {32|<<x x }2. 复数2(2)(1)12i i i+--的值是( ).A ．2 B. 2- C. 2i D. 2i -3. 已知||3a = ，||5b =，12a b = ，则向量a 在向量b 上的投影为（ ）.A 12BCD4. 方程2sin 2sin 0x x a --=x R ∈在上有解，则a 的取值范围是（ ）.A ．[)+∞-,1B ．),1(+∞-C ．]3,1[-D ．[)3,1-5．“12m =”是“直线(2)310m x my +++=与直线(2)(2)30m x m y -++-=相互垂直”的（ ）A 充分必要条件B 充分而不必要条件C 必要而不充分条件D 既不充分也不必要条件6. 等差数列{}n a 中，n S 是前n 项和，且k S S S S ==783,，则k 的值为( ).A.4 B 11 C.2 D 127. 为了得到函数)62sin(π-=x y 的图象，可以将函数x y 2cos =的图象( ).A.向右平移6π个单位 B.向右平移3π个单位C.向左平移6π个单位 D.向左平移3π个单位8.若椭圆2215x y m +=的离心率e =,则m 的值为( ). A.13或2539. 在棱长为2的正方体1111ABCD A BC D -中，点E ，F 分别是棱AB ，BC 的中点，则点1C 到平面1B EF 的距离是( ).A.332 B.322 C.32D.3410．10.定义A D D C C B B A ****,,,的运算分别对应下图中的(1)、(2)、(3)、(4)，A ）、（B（1） （2） （3） （4） （A ） （B ） A.D A D B **, B.C A D B **, C.D A C B **, D.D A D C **,第Ⅱ部分（非选择题，共100分）二、填空题：本大题共5小题，每小题5分，满分20分，其中14，15题是选做题，考生只能选做一题,，若两题全都做的，只计算前一题的得分． 11. 函数()212log 2y x x =-的单调递减区间是 .12.甲、乙两人独立的解决一个问题，甲能解决这个问题的概率为0.6，乙能解决这个问题的概率为0.7，那么甲乙两人中至少有一人解决这个问题的概率是 .13．设x 、y 满足条件310x y y x y +≤⎧⎪≤-⎨⎪≥⎩，则22(1)z x y =++的最.14．(坐标系与参数方程选做题)自极点O 向直线l 做垂线，垂足为(2,)3H π，则直线l 的极坐标方程是 . 15．(几何证明选讲选做题)已知圆的直径13AB =，C 为圆上一点，过C 作CD AB ⊥于D（AD BD >），若6CD =，则AD 的长为 . 三、解答题：本大题共6小题，满分80分．解答须写出文字说明、证明过程或演算步骤． 16．(本小题满分12分) 在ABC △中，1tan 4A =，3tan 5B = （Ⅰ）求角C 的大小；（Ⅱ）若AB ，求BC 边的长A B 1BC 17．（本小题满分13分）如图,在直三棱柱111ABC A B C -中, 3AC =, 4BC =, 5AB =,14AA =, 点D 是AB 的中点.(1)求证:1AC BC ⊥; (2)求证:1AC ∥平面1CDB .18.(本小题满分13分)设数列{}n a 的前n 项和为n S ，点(,)()nS n n N n*∈均在函数32y x =-的图像上.（Ⅰ）求数列{}n a 的通项公式；（Ⅱ）设13+=n n n a a b ，n T 是数列{}n b 的前n 项和，求使得20n m T <对所有n N *∈都成立的最小正整数m .19.(本小题满分14分)已知圆C 过点(0,)A a (0)a >, 且在x 轴上截得的弦MN 的长为2a .(1) 求圆C 的圆心的轨迹方程； (2) 若45MAN ∠=, 求圆C 的方程. 20.(本小题满分14分）已知函数2()(0,0)f x ax bx c a bc =++>≠,()0,,()()0.f x x F x f x x >⎧=⎨-<⎩ （Ⅰ）若函数)(x f 的最小值是(1)0f -=，且(0)1f =，求(2)(2)F F +-的值； （Ⅱ）在（Ⅰ）的条件下，k x x f +>)(在区间[3,1]--恒成立，试求k 的取值范围；（Ⅲ）令()2g x ax b =+,若(1)0g =,又()f x 的图象在x 轴上截得的弦的长度为m ，且02m <≤，试确定c b -的符号.21.(本小题满分14分）已知函数2221()()1ax a f x x x -+=∈+R ，其中a ∈R ． （Ⅰ）当1a =时，求曲线()y f x =在点(2(2))f ，处的切线方程； （Ⅱ）当0a ≠时，求函数()f x 的单调区间与极值．A B 1BC 08届高三第三次质量检测文科数学参考答案:二、填空题：本大题共5小题，每小题5分，满分20分，其中14，15题是选做题，考生只能选做一题,，若两题全都做的，只计算前一题的得分． 11.(2,+∞) 12.0.88 13. 4 14.cos()23πρθ-= 15. 9三、解答题：本大题共6小题，满分80分．解答须写出文字说明、证明过程或演算步骤． 16．(本小题满分12分)解：（Ⅰ）∵ π()C A B =-+， ………………1分∴ 1345tan tan()113145C A B +=-+=-=--………………4分 又 ∵ 0πC <<， ∴ 3π4C = …………………5分（Ⅱ）由22sin 1tan cos 4sin cos 1A A A A A ⎧==⎪⎨⎪+=⎩，，且π02A ⎛⎫∈ ⎪⎝⎭，，…………………7分得sin A =…………………………9分 由正弦定理sin sin AB BC C A =， 得sin sin ABC AB C== ……………………12分 17．（本小题满分13分）证明: (1) ∵ 三棱柱111ABC A B C -为直三棱柱, ∴ 1C C ⊥平面ABC , ∴1C C AC ⊥, ∵ 3AC =, 4BC =, 5AB =, ∴ 222AC BC AB +=,∴ AC BC ⊥, 又 1CC BC C ⋂=, ∴ AC ⊥平面11CC B B ,∴ 1AC BC ⊥ ……………………………………7分(2) 令1BC 与1CB 的交点为E , 连结DE .∵ D 是AB 的中点, E 为1BC 的中点, ∴ DE ∥1AC . 又 ∵1AC ⊄平面1CDB , DE ⊂平面1CDB , ∴1AC ∥平面1CDB . ………………………13分 18.(本小题满分13分) 解: (1) 由题意得 32nS n n=- , 即 232n S n n =-,…………………1分 当2n ≥时,22132[3(1)2(1)]65n n n a S S n n n n n -=-=-----=-,…………4分当1n =时, 111615a S ===⨯-, ………………5分 ∴ 165()n n n a S S n n N *-=-=-∈, ……………………6分 (2) 由(1)得133111()(65)(61)26561n n n b a a n n n n +===--+-+,…………………8分∴ 111111[(1)()()]277136561n T n n =-+-++--+ 11(1)261n =-+ . ……………………11分 因此,使得11(1)()26120m n N n *-<∈+成立的m 必须且只需满足1220m≤, 即10m ≥,故满足要求的的最小正整数10m =………………13分19.(本小题满分14分)解: (1)设圆C 的圆心为,)(y C x ,依题意圆的半径r =……………… 2分∵ 圆C 在x 轴上截得的弦MN 的长为2a . ∴ 222||y a r +=故 2222()||x y a y a +-=+ ………………………… 4分 ∴ 22x ay =∴ 圆C 的圆心的轨迹方程为22x ay = ………………… 6分(2) ∵ 45MAN ∠= , ∴ 90MCN ∠=……………………… 9分令圆C 的圆心为00(,)x y , 则有2002x ay = (00y ≥) ,…………… 10分又 ∵ 01||2y MN a == …………………… 11分∴ 0x = ……………………… 12分∴ r == ……………………… 13分∴ 圆C 的方程为 222()()2x y a a +-= …………………… 14分 21.(本小题满分14分)解：（Ⅰ）由已知.12,0,1-=-=+-=abc b a c 且 解得1a =，2b =， …………………2分 ∴2()(1)f x x =+ ,∴22(1),(0)()(1),(0),x x F x x x ⎧+>⎪=⎨-+<⎪⎩ …………4分∴ 22(2)(2)(21)[(21)]8F F +-=++--+=. ……………………5分（Ⅱ）在（Ⅰ）条件下，k x x f +>)(在区间[3,1]--恒成立,即210x x k ++->在区间[3,1]--恒成立,从而12++<x x k 在区间[3,1]--上恒成立，…………………8分 令函数2()1p x x x =++,则函数2()1p x x x =++在区间[3,1]--上是减函数，且其最小值min ()(1)1p x p =-=，∴ k 的取值范围为(,1)-∞…………………………10分（Ⅲ）由(1)0g =，得20a b +=，∵ 0a > ∴20b a =-<,………………11分 设方程0)(=x f 的两根为21,x x ，则122bx x a+=-=,12c x x a =,∴12||m x x =-=∵ 02m <≤， ∴ 01<≤, ∴01c a ≤<，∵ 0a >且0bc ≠， ∴ 0c >，∴ 0c b ->……………14分 21.(本小题满分14分)解: （Ⅰ）解：当1a =时，22()1x f x x =+，4(2)5f =，……………1分又22222222(1)422()(1)(1)x x x f x x x +--'==++，则6(2)25f '=-．…………………3分 所以，曲线()y f x =在点(2(2))f ，处的切线方程为46(2)525y x -=--， 即625320x y +-=．……………4分（Ⅱ）解：2222222(1)2(21)2()(1)()(1)(1)a x x ax a x a ax f x x x +--+--+'==++．…………6分 由于0a ≠，以下分两种情况讨论．（1）当0a >时，令()0f x '=，得到11x a=-，2x a =,当x 变化时，()()f x f x '，的变化情况如下表：所以()f x 在区间a ⎛⎫-- ⎪⎝⎭，∞,()a +，∞内为减函数，在区间a a ⎛⎫- ⎪⎝⎭，内为增函数 故函数()f x 在点11x a =-处取得极小值1f a ⎛⎫- ⎪⎝⎭，且21f a a ⎛⎫-=- ⎪⎝⎭，函数()f x 在点2x a =处取得极大值()f a ，且()1f a =．…………………10分（2）当0a <时，令()0f x '=，得到121x a x a==-，，当x 变化时，()()f x f x '，的变化情况如下表：所以()f x 在区间()a -，∞,a ⎛⎫- ⎪⎝⎭，+∞内为增函数，在区间a a ⎛⎫- ⎪⎝⎭，内为减函数．函数()f x 在1x a =处取得极大值()f a ，且()1f a =．函数()f x 在21x a=-处取得极小值1f a ⎛⎫- ⎪⎝⎭，且21f a a ⎛⎫-=- ⎪⎝⎭．………………14分。
函数与导数选择题题库 含答案
14、(河北省正定中学2008年高三第五次月考)定义在R上的函数y＝f（x）满足：f（－x）＝－f（x），f（1＋x）＝f（1－x），当x∈[－1,1]时，f（x）＝x3，则f（2 007）的值是（）
(A)－1(B)0(C)1(D)2
15、(河南省濮阳市2008年高三摸底考试)设函数f(x)＝ax2＋bx－c (a≠0)对任意实数t都有f(2＋t)＝f(2－t)成立，在函数值f(－1)，f(1)，f(2)，f(5)中最小的一个不可能是( )
A．a>1B．1<a<12C．1<a≤12D．1<a≤4
6、(陕西长安二中2008届高三第一学期第二次月考)定义在R上的偶函数 满足 ，且在[-1，0]上单调递增，设 ， ， ，则 大小关系是
A． B． C． D．
7、(陕西长安二中2008届高三第一学期第二次月考)函数 值域为
A．（-∞，1）B．（ ，1）C．[ ，1）D．[ ，+∞）
A．11 B．6 C． D．
7、(北京市宣武区2008年高三综合练习一)给出定义：若 （其中m为整数），则m叫做离实数x最近的整数，记作 = m.在此基础上给出下列关于函数 的四个命题：
①函数y= 的定义域为R，值域为 ；
②函数y= 的图像关于直线 （ ）对称；
③函数y= 是周期函数，最小正周期为1；
A. B. C. D.
16、(甘肃省兰州一中2008届高三上期期末考试)如果函数 对任意的实数x，都有 ，那么（）
A． B．
C． D．
17、(四川省乐山市2008届第一次调研考试)若函数 在R上既是奇函数，又是减函数，则 的图象是（ ）
18、(四川省成都市一诊)对任意的实数a、b，记 ．若 ，其中奇函数y=f(x)在x=l时有极小值-2，y=g(x)是正比例函数，函数 与函数y=g(x)的图象如图所示．则下列关于函数 的说法中，正确的是
数列的通项公式与求和的常用方法
数列的通项公式与求和的常用方法高考要求数列是函数概念的继续和延伸，数列的通项公式及前n 项和公式都可以看作项数n 的函数，是函数思想在数列中的应用 数列以通项为纲，数列的问题，最终归结为对数列通项的研究，而数列的前n 项和S n 可视为数列{S n }的通项 通项及求和是数列中最基本也是最重要的问题之一，与数列极限及数学归纳法有着密切的联系，是高考对数列问题考查中的热点，本点的动态函数观点解决有关问题，为其提供行之有效的方法 一、重难点1．数列通项的求法： ⑴定义法（利用AP,GP 的定义）；⑵累加法（n n n c a a =-+1型）；⑶⑷累乘法（n nn c a a =+1型）；⑸构造法:若一阶线性递归数列a n =ka n －1+b （k ≠形式:)1(11-+=-+-k b a k k b a n n (n ≥2)，于是可依据等比数列的定义求出其通项公式；⑹间接法（例如：4114111=-⇒=----n n n n n n a a a a a a ）；⑺（理科）数学归纳法。
2．前n 项和的求法：⑴分组求和法；⑵裂项法；⑶错位相减法；(4)倒序相加法。
3．等差数列前n 项和最值的求法：⑴⎪⎪⎭⎫ ⎝⎛⎩⎨⎧≥≤⎩⎨⎧≤≥++000011n n n n a a a a 或 ；⑵利用二次函数的图象与性质。
数列单调递增1<n n a a +⇔。
二、例题例1已知数列{a n }是公差为d 的等差数列，数列{b n }是公比为q 的(q ∈R 且q ≠1)的等比数列，若函数f (x )=(x －1)2，且a 1=f (d －1)，a 3=f (d +1)，b 1=f (q +1)，b 3=f (q －1)，(1)求数列{a n }和{b n }的通项公式；(2)设数列{c n }的前n 项和为S n ，对一切n ∈N *，都有n n c c b c b c +++ 2111=a n +1成立，求lim ∞→n nn S S212+命题意图 本题主要考查等差、等比数列的通项公式及前n 项和公式、数列的极限，以及运算能力和综合分析问题的能力知识依托 本题利用函数思想把题设条件转化为方程问题非常明显，而(2)中条件等式的左边可视为某数列前n 项和，实质上是该数列前n 项和与数列{a n }的关系，借助通项与前n 项和的关系求解c n 是该条件转化的突破口错解分析 本题两问环环相扣，(1)问是基础，但解方程求基本量a 1、b 1、d 、q ，计算不准易出错；(2)问中对条件的正确认识和转化是关键技巧与方法 本题(1)问运用函数思想转化为方程问题，思路较为自然，(2)问“借鸡生蛋”构造新数列{d n }运用和与通项的关系求出d n ，丝丝入扣解 (1)∵a 1=f (d －1)=(d －2)2，a 3=f (d +1)=d 2， ∴a 3－a 1=d 2－(d －2)2=2d ，∵d =2，∴a n =a 1+(n －1)d =2(n －1)； 又b 1=f (q +1)=q 2，b 3=f (q －1)=(q －2)2，∴2213)2(qq b b -==q 2，由q ∈R ，且q ≠1，得q =－2， ∴b n =b ·q n －1=4·(－2)n －1(2)令nn b c=d n ，则d 1+d 2+…+d n =a n +1,(n ∈N *),∴d n =a n +1－a n =2, ∴n n b c =2,即c n =2·b n =8·(－2)n －1；∴S n =38［1－(－2)n ］ ∴2lim ,1)21(2)21()2(1)2(121222212212-=--+-=----=+∞→++n n n n n n n n n S S S S 例2设A n 为数列{a n }的前n 项和，A n =23(a n －1)，数列{b n }的通项公式为b n =4n +3;(1)求数列{a n }的通项公式；(2)把数列{a n }与{b n }的公共项按从小到大的顺序排成一个新的数列，证明 数列{d n }的通项公式为d n =32n +1;(3)设数列{d n }的第n 项是数列{b n }中的第r 项，B r 为数列{b n }的前r 项的和；D n 为数列{d n }的前n 项和，T n =B r －D n ，求lim ∞→n 4)(n na T 命题意图 本题考查数列的通项公式及前n 项和公式及其相互关系；集合的相关概念，数列极限，以及逻辑推理能力知识依托 利用项与和的关系求a n 是本题的先决；(2)问中探寻{a n }与{b n }的相通之处，须借助于二项式定理；而(3)问中利用求和公式求和则是最基本的知识点错解分析 待证通项d n =32n +1与a n 的共同点易被忽视而寸步难行；注意不到r 与n 的关系，使T n 中既含有n ，又含有r ，会使所求的极限模糊不清技巧与方法 (1)问中项与和的关系为常规方法，(2)问中把3拆解为4－1，再利用二项式定理，寻找数列通项在形式上相通之处堪称妙笔；(3)问中挖掘出n 与r 的关系，正确表示B r ，问题便可迎刃而解解 (1)由A n =23(a n －1)，可知A n +1=23(a n +1－1)， ∴a n +1－a n =23 (a n +1－a n )，即n n a a 1+=3，而a 1=A 1=23(a 1－1)，得a 1=3，所以数列是以3为首项，公比为3的等比数列，数列{a n }的通项公式a n =3n(2)∵32n +1=3·32n =3·(4－1)2n=3·［42n +C 12n ·42n －1(－1)+…+C 122-n n ·4·(－1)+(－1)2n ］=4n +3， ∴32n +1∈{b n } 而数32n =(4－1)2n=42n +C 12n ·42n －1·(－1)+…+C 122-n n ·4·(－1)+(－1)2n =(4k +1)， ∴32n ∉{b n }，而数列{a n }={a 2n +1}∪{a 2n }，∴d n =32n +1(3)由32n +1=4·r +3，可知r =43312-+n ，∴B r =)19(827)91(9127,273433)52(2)347(1212-=-⋅-=+⋅-=+=++++n n n n n D r r r r ， 89)(lim ,3)(,433811389)19(827821349444241212=∴=+⋅-⋅=---⋅+=-=∴∞→++n n n n n n n nn n n r n a T a D B T 例3 设{a n }是正数组成的数列，其前n 项和为S n ，并且对于所有的自然数n ，a n 与2的等差中项等于S n 与2的等比中项(1)写出数列{a n }的前3项(2)求数列{a n }的通项公式(写出推证过程)(3)令b n =)(2111+++n n n n a a a a(n ∈N *)，求lim ∞→n (b 1+b 2+b 3+…+b n －n )解析 (1)由题意，当n =1时，有11222S a =+，S 1=a 1， ∴11222a a =+，解得a 1=2 当n =2时，有22222S a =+，S 2=a 1+a 2，将a 1=2代入，整理得(a 2－2)2=16，由a 2＞0，解得a 2=6当n =3时，有33222S a =+，S 3=a 1+a 2+a 3， 将a 1=2，a 2=6代入，整理得(a 3－2)2=64，由a 3＞0，解得a 3=10 故该数列的前3项为2，6，10(2）解法一 由(1）猜想数列{a n } 有通项公式a n =4n －2 下面用数学归纳法证明{a n }的通项公式是a n =4n －2，(n ∈N *） ①当n =1时，因为4×1－2=2，，又在(1)中已求出a 1=2，所以上述结论成立②假设当n =k 时，结论成立，即有a k =4k －2，由题意，有k k S a 222=+，将a k =4k －2 代入上式，解得2k =k S 2，得S k =2k 2，由题意，有11222++=+k k S a ，S k +1=S k +a k +1， 将S k =2k 2代入得(221++k a )2=2(a k +1+2k 2)，整理得a k +12－4a k +1+4－16k 2=0，由a k +1＞0，解得a k +1=2+4k ， 所以a k +1=2+4k =4(k +1)－2，即当n =k +1时，上述结论成立根据①②，上述结论对所有的自然数n ∈N *成立解法二 由题意知n n S a 222=+，(n ∈N *) 整理得，S n =81(a n +2)2, 由此得S n +1=81(a n +1+2)2，∴a n +1=S n +1－S n =81［(a n +1+2)2－(a n +2)2］整理得(a n +1+a n ）(a n +1－a n －4)=0， 由题意知a n +1+a n ≠0，∴a n +1－a n =4，即数列{a n }为等差数列，其中a 1=2，公差d =4∴a n =a 1+(n －1)d =2+4(n －1)，即通项公式为a n =4n －2解法三 由已知得n n S a 222=+,(n ∈N *) ①， 所以有11222++=+n n S a ②， 由②式得11222++=+-n n n S S S ，整理得S n +1－22·1+n S +2－S n =0，解得n n S S ±=+21，由于数列{a n }为正项数列，而2,211>+∴=+n n S S S ， 因而n n S S +=+21，即{S n }是以21=S 为首项，以2为公差的等差数列所以n S = 2+(n －1) 2=2n ,S n =2n 2，故a n =⎩⎨⎧≥-=-=-)2(,24)1(,21n n S S n n n 即a n =4n －2(n ∈N *)(3)令c n =b n －1，则c n =)2(2111-+++n n n n a a a a1212111[(1)(1)],221212121n n n n n n +-=-+-=--+-+ 1212n n b b b n c c c +++-=+++111111(1)()()1,335212121n n n =-+-++-=--++121()(1) 1.lim lim 21n n n b b b n n →∞→∞∴+++-=-=+ 三、练习1 作边长为a 的正三角形的内切圆，在这个圆内作新的内接正三角形，在新的正三角形内再作内切圆，如此继续下去，所有这些圆的周长之和及面积之和分别为_________2 数列{a n }满足a 1=2，对于任意的n ∈N *都有a n ＞0,且(n +1)a n 2+a n ·a n +1－na n +12=0，又知数列{b n }的通项为b n =2n－1+1(1)求数列{a n }的通项a n 及它的前n 项和S n ； (2)求数列{b n }的前n 项和T n ；(3)猜想S n 与T n 的大小关系，并说明理由3 数列{a n }中，a 1=8,a 4=2且满足a n +2=2a n +1－a n ,(n ∈N *)(1)求数列{a n }的通项公式；(2)设S n =｜a 1｜+｜a 2｜+…+｜a n ｜,求S n ;(3)设b n =)12(1n a n -(n ∈N *),T n =b 1+b 2+……+b n (n ∈N *),是否存在最大的整数m ，使得对任意n ∈N *均有T n ＞32m成立？若存在，求出m 的值；若不存在，说明理由4 设数列{a n }的前n 项和为S n ，且S n =(m +1)－ma n 对任意正整数n 都成立，其中m 为常数，且m ＜－1 (1)求证 {a n }是等比数列；(2)设数列{a n }的公比q =f (m )，数列{b n }满足 b 1=31a 1,b n =f (b n －1)(n ≥2,n ∈N *) 试问当m 为何值时，)(3lim )lg (lim 13221n n n n n n b b b b b b a b -∞→∞→+++=⋅ 成立？5 已知数列{b n }是等差数列，b 1=1,b 1+b 2+…+b 10=145 (1)求数列{b n }的通项b n ；(2)设数列{a n }的通项a n =log a (1+n b 1)(其中a ＞0且a ≠1),记S n 是数列{a n }的前n 项和，试比较S n 与31log a b n +1的大小，并证明你的结论6 设数列{a n }的首项a 1=1，前n 项和S n 满足关系式 3tS n －(2t +3)S n －1=3t (t ＞0,n =2,3,4…) (1)求证 数列{a n }是等比数列；(2)设数列{a n }的公比为f (t )，作数列{b n }，使b 1=1,b n =f (11-n b )(n =2,3,4…)，求数列{b n }的通项b n ；(3)求和 b 1b 2－b 2b 3+b 3b 4－…+b 2n －1b 2n －b 2n b 2n +1 参考答案1 解析 由题意所有正三角形的边长构成等比数列{a n }，可得a n =12-n a ，正三角形的内切圆构成等比数列{r n }，可得r n =12163-n a ,∴这些圆的周长之和c =lim ∞→n 2π(r 1+r 2+…+r n )=233π a 2， 面积之和S =lim ∞→n π(n 2+r 22+…+r n 2)=9πa 2答案 周长之和233πa ，面积之和9πa 22 解 (1）可解得11+=+n na a n n ，从而a n =2n ，有S n =n 2+n ，(2)T n =2n +n －1(3)T n －S n =2n －n 2－1，验证可知，n =1时，T 1=S 1，n =2时T 2＜S 2；n =3时，T 3＜S 3;n =4时，T 4＜S 4；n =5时，T 5＞S 5；n =6时T 6＞S 6猜想当n ≥5时，T n ＞S n ，即2n ＞n 2+1可用数学归纳法证明(略）3 解 (1）由a n +2=2a n +1－a n ⇒a n +2－a n +1=a n +1－a n 可知{a n }成等差数列，d =1414--a a =－2,∴a n =10－2n (2)由a n =10－2n ≥0可得n ≤5，当n ≤5时，S n =－n 2+9n ，当n ＞5时，S n =n 2－9n +40，故S n =⎪⎩⎪⎨⎧>+-≤≤+-540951922n n n n n n(3)b n =)111(21)22(1)12(1+-=+=-n n n n a n n )1(2)]111()3121()211[(2121+=+-++-+-=+++=∴n n n n b b b T n n ；要使T n ＞32m 总成立，需32m＜T 1=41成立，即m ＜8且m ∈Z ，故适合条件的m 的最大值为74 解 (1）由已知S n +1=(m +1)－ma n +1 ①， S n =(m +1)－ma n ②, 由①－②，得a n +1=ma n －ma n +1，即(m +1)a n +1=ma n 对任意正整数n 都成立∵m 为常数，且m ＜－1 ∴11+=+m m a a n n ，即{1+n n a a }为等比数列(2)当n =1时，a 1=m +1－ma 1，∴a 1=1，从而b 11 由(1)知q =f (m )=1+m m，∴b n =f (b n －1)=111+--n n b b (n ∈N *,且n ≥2)∴1111-+=n n b b ，即1111=--n n b b ， ∴{n b 1}为等差数列 ∴nb 1=3+(n －1)=n +2，21+=∴n b n (n ∈N *) 11(),(lg )[lg ]lg ,lim lim 1211n n n n n n m n m m a b a m n m m -→∞→∞-=∴⋅==++++122311111113()3()1lim lim 344512n n n n b b b b b b n n -→∞→∞+++=-+-++-=++ 而10lg 1,10,119m m m m m =∴=∴=++由题意知5 解 (1)设数列{b n }的公差为d ，由题意得 ⎪⎩⎪⎨⎧=-+=1452)110(1010111d b b 解得b 1=1,d =3,∴b n =3n －2(2)由b n =3n －2,知S n =log a (1+1)+log a (1+41)+…+log a (1+231-n )=log a ［(1+1)(1+41)…(1+231-n )］，31log a b n +1=log a因此要比较S n 与31log a b n +1的大小，可先比较(1+1)(1+41)…(1+231-n )与313+n 的大小，取n =1时，有(1+1)＞3113+⋅取n =2时，有(1+1)(1+41)＞3123+⋅…由此推测(1+1)(1+41)…(1+231-n )＞313+n ①若①式成立，则由对数函数性质可判定当a ＞1时，S n ＞31log a b n +1， ②当0＜a ＜1时，S n ＜31log a b n +1， ③下面用数学归纳法证明①式(ⅰ)当n =1时，已验证①式成立 (ⅱ)假设当n =k 时(k ≥1），①式成立，即313)2311()411)(11(+>-+++k k那么当n =k +1时，1111(11)(1)(1)(1))2).4323(1)23131k k k k k++++>+=+-+-++ 22232(32)(34)(31)[(32)]31(31)k k k k k k +-+++-=++2940,2)(31)31k k k k +=>+>=++111(11)(1)(1)(1)43231k k ++++>-+ 因而这就是说①式当n =k +1时也成立由(ⅰ）(ⅱ）可知①式对任何正整数n 都成立由此证得 当a ＞1时，S n ＞31log a b n +1；当0＜a ＜1时，S n ＜31log a b n +1 6 解 (1)由S 1=a 1=1,S 2=1+a 2，得3t (1+a 2)－(2t +3)=3t∴a 2=tt a a t t 332,33212+=+ 又3tS n －(2t +3)S n －1=3t ， ① 3tS n －1－(2t +3)S n －2=3t ②①－②得3ta n －(2t +3)a n －1=0∴tt a a n n 3321+=-,n =2,3,4…, 所以{a n }是一个首项为1公比为t t 332+的等比数列； (2)由f (t )= t t 332+=t132+,得b n =f (11-n b )=32+b n －1可见{b n }是一个首项为1，公差为32的等差数列于是b n =1+32(n －1)=312+n ;(3)由b n =312+n ,可知{b 2n －1}和{b 2n }是首项分别为1和35，公差均为34的等差数列，于是b 2n =314+n ,∴b 1b 2－b 2b 3+b 3b 4－b 4b 5+…+b 2n －1b 2n －b 2n b 2n +1 =b 2(b 1－b 3)+b 4(b 3－b 5)+…+b 2n (b 2n －1－b 2n +1) =－34 (b 2+b 4+…+b 2n )=－34·21n (35+314+n )=－94 (2n 2+3n )四、易错题 1、(广东省韶关市2008届高三第一次调研考试)已知等差数列{}n a 的前n 项和为n S ，且2510,55S S ==，则过点(,)n P n a 和2(2,)n Q n a ++(n ÎN *)的直线的斜率是 A ．4 B ．3 C ．2 D ．1 答案：A2、(广东省深圳外国语学校2008届第三次质检)设等比数列{}n a 的公比为q ，前n 项和为s n ，若s n+1，s n ，s n +2成等差数列，则公比q 为 （ ） A ．2-=q B ．1=q C ．12=-=q q 或 D ．12-==q q 或 答案：A3、(广东实验中学2008届高三第三次段考)等差数列}{n a 的前n 项和为30,,1182=++a a a S n 若，那么下列S 13值的是 （ ） A ．130 B ．65 C ．70 D ．以上都不对 答案：A4、(广东省五校2008年高三上期末联考)已知数列{}n a 、{}n b 都是公差为1的等差数列，其首项分别为1a 、1b ，且11a +b =5，11a >b ，++11a b N (n N )、∈∈，则数列nb {a }前10项的和等于A.55B.70C.85D.100答案：C ．解析：本题考查了等差数列的通项及前n 项和计算．11111111,11(1)12523n n n b n a a n b b n a a b a b n a b n n n =+-=+-=+-=++--=++-=+-=+ 因此，数列{}nba 也是等差数列，并且前10项和等于：10(413)852+= 5、(河北省正定中学高2008届一模)在正项等差数列{a n }中，前n 项和为n S ，在正项等比数列{b n }中，前n 项和为T n ，若a 15＝b 5，a 30＝b 20，则S 30－S 15T 20－T 5∈( )A ．(0，1)B ．(12，1)C ．[1，＋∞]D ．[12，2]答案：C6、(河北省正定中学2008年高三第五次月考)在等差数列{n a }中，a 1>0, 95175a a =, 则数列{n a }前n 项和n S 取最大值时，n 的值等（ ）A 12B 11C 10D 9 答案：C7、(黑龙江省哈尔滨九中2008年第三次模拟考试)设n S 是等差数列}{n a 的前n 项和，若3184=S S ，则168S S等于（ ）A ．103 B ．13 C ．91 D ．81答案：A8、(黑龙江省哈师大附中2008届高三上期末)设等比数列{a n }的前n 项和为S n ，若S 10：S 5=1：2，则S 15：S 5=（ ） A ．3：4 B ．2：3 C ．1：2 D ．1：3 答案：A 9、(黑龙江省哈师大附中2008届高三上期末)已知数列}{n a 的前三项依次是—2，2，6，前n 项的和S n 是n 的二次函数，则a 100等于（ ） A ．3900 B ．392C ．394D ．396答案：C 10、(湖北省鄂州市2008年高考模拟)设数列}{n a 的前n 项和为)(*N n S n ∈，关于数列}{n a 有下列三个命题：①若数列}{n a 既是等差数列又是等比数列，则1+=n n a a ； ②若),(2R b a bn an S n ∈+=，则数列}{n a 是等差数列； ③若n n S )1(1--=，则数列}{n a 是等比数列. 这些命题中，真命题的个数是（ ）A ．0B ．1C ．2D ．3答案：D ①不妨设数列}{n a 的前三项为d a a d a +-,,，则其又成等比数列，故222d a a -=，∴0=d ，即1+=n n a a ；②由n S 的公式，可求出b a n a n +-=)12(，故}{n a 是等差数列；③由n S 可求由1)1(2--=n n a ，故数列}{n a 是等比数列. 故选D .【总结点评】本题主要考查等差、等比数列的概念，n S 与n a 的关系，思维的灵活性. 11、(湖北省黄冈市麻城博达学校2008届三月综合测试)}{n a 为等差数列，若11101a a <-，且它的前n 项和S n 有最小值，那么当S n 取得最小正值时，n = A ．11 B ．17 C ．19 D ．21答案：C12、(湖北省黄冈市麻城博达学校2008届三月综合测试)在正项等差数列{a n }中，前n 项和为Sn ，在正项等比数列{b n }中，前n 项和为Tn ，若a 15＝b 5，a 30＝b 20，则S 30－S 15T 20－T 5∈( )A ．(0，1)B ．(12，1)C ．[1，＋∞]D ．[12，2]答案：C13、(湖北省黄冈中学2008届高三第一次模拟考试)各项均为正数的等比数列{a n }的前n 项和为n S ，若32,14n n S S ==，则4n S 等于（ ） A ．16 B ．26 C ．30 D ．80答案：C14、(湖北省黄冈市2007年秋季高三年级期末考试)数列{}n a 中，0n a ≠，且满足113(2)32n n n a a n a --=≥+，则数列1{}na 是：A 递增等差数列B 递增等比数列C 递减数列D 以上都不是 答案：A15、(湖北省随州市2008年高三五月模拟)数列{}n a 满足2113,1()2n n n a a a a n N ++==-+∈，则122008111m a a a =+++ 的整数部分是 A. 0 B. 1 C. 2 D. 3 答案：B16、(湖南省长沙市一中2008届高三第六次月考)数列{a n }满足=+-==+200811a ,11,2则n n a a aA ．2B ．－31 C ．－23 D ．1答案：A17、(湖南省株洲市2008届高三第二次质检)已知数列{a n }满足a 1＝0，a n ＋1＝a n －33a n ＋1( n ∈N *)，则a 2007＝ （ ）A ．0B ．－ 3C ． 3D ．32答案：C18、(黄家中学高08级十二月月考)在等比数列{}()n a n N *∈中，若1411,8a a ==，则该数列的前10项的和为 A ． 8122-B. 9122-C. 10122-D. 11122-【解】：由21813314=⇒===q q q a a ，所以()1010110911()112211212a q S q -⋅-===---故选B ； 19、(江苏省盐城市2008届高三六校联考)数列1，1+2，1+2+22，1+2+22+23，…，1+2+22+…+2n －1，…的前n 项和S n >1020，那么n 的最小值是( ) A 、7 B 、8 C 、9 D 、10答案：D20、(江西省鹰潭市2008届高三第一次模拟)若数列{a n }满足112,0;2121, 1.2n n n nn a a a a a +⎧≤<⎪⎪=⎨⎪-≤<⎪⎩若167a =，则20a 的值为（ ） A .67 B. 57 C. 37 D. 17答案：B21、(宁夏区银川一中2008届第六次月考)已知f(x)=bx+1为关于x 的一次函数，b 为不等于1的常数，且满足g(n)=⎩⎨⎧≥-=)1( )]1([)0(1n n g f n 设a n =g(n)－g(n －1)(n ∈N 8),则数列{a n }为（ ）A ．等差数列B ．等比数列C ．递增数列D ．递减数列答案：B22、(山东省实验中学2008届高三第三次诊断性测试)设5021,,,a a a 是以1,0,1-这三个整数中取值的数列，若：95021=+++a a a 且107)1()1()1(2502221=++++++a a a ,则5021,,,a a a 当中取零的项共有（ ）A ．11个B ．12个C ．15个D ．25个答案：A23、(山东省郓城一中2007-2008学年第一学期期末考试)在等差数列{}n a 中，若181006100510041003=+++a a a a ，则该数列的前2008项的和是（ ）A ．18072B ．3012C ．9036D ．12048答案：C24、(山东省郓城一中2007-2008学年第一学期期末考试)已知*,7980N n n n a n ∈--=，则在数列{a n }的前50项中最小项和最大项分别是（ ）A ．1a ，50aB ．9a ，50aC ．8a ，9aD ．9a ，8a 答案：D25、(山西大学附中2008届二月月考)二次函数2(1)(21)1y n n x n x =+-++，当n 依次取1，2，3，4，…，n ，…时，图象在x 轴上截得的线段的长度的总和为 A ．1 B ．2 C ．3 D ．4答案：A。
2008年广东省高三三校联考语文试卷
2008年广东省高三三校联考语文试卷本试卷分必考和选考两部分，满分为150分。
考试用时150分钟。
注意事项：1．答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名和考生号填写在答题卡上，用2B铅笔将试卷类型(A)填涂在答题卡上。
并在答题卡右上角的“试室号”和“座位号”栏填写试室号、座位号，将相应的试室号、座位号信息点涂黑。
2．选择题每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑；如需改动，用橡皮擦干净后，再选涂其他答案；答案不能答在试卷上。
3．非选择题必须用黑色字迹钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内的相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔和涂改液。
不按以上要求作答的答案无效。
4．考生必须保持答题卡的整洁，考试结束后，将本试卷和答题卡一并交回。
必考题1．下列词语中加点的字，读音全都不相同的一组是（）（3分）A．模．棱摹．拟落寞．莫．逆之交顶礼膜．拜B．扉．页菲．薄斐．然匪．夷所思蜚．短流长C．诋．毁底．蕴邸．所低．首下心砥．柱中流D．搁．浅奶酪．贿赂．洛．阳纸贵一丘之貉．2.下列加点词语使用正确的一项是：（）（3分）A.我们虽然缺乏管理经验，但可以向先进企业学习，起初可能是邯郸学步．．．．，但终究会走出自己的路来。
B.运动会上，他借的一身衣服很不合身，真是捉襟见肘．．．．。
C.他就静悄悄地看下去，看到把各种责难都驳斥得体无完肤．．．．之后，他又低声念起来。
D.听说这位气功大师能够功发疾消，今天会了他一下，果不其然．．．．，他没有那么大的能耐。
3.依次填入句中横线上的词语，最恰当的一组是（）（3分）①国家有关部门的结果表明，广东大亚湾核电站运行一年，废液、废气排放量均大大低于国家标准。
②事发当日，看守所民警值班期间未认真履行看管职责，离岗，外出吃饭，造成在押人员脱管。
③像孩童第一次睁开眼睛看见阳光，作者目光是那样惊喜，着饱满的生气。
广东省深圳市外国语学校高三上学期第三次调研考试(理综化学).doc
高三第三次调研考试理科综合能力测试试题说明：本试卷共12页，36小题，满分300分。
考试用时150分钟．答案须做在答题卷和答题卡上；须用黑色字迹的钢笔或签字笔作答主观题，答题卡的填涂须用2B 铅笔，考试结束后只交答题卷和答题卡。
一、单项选择题（本题共16个小题。
每小题4分，共64分。
每小题给出的四个选项中，只有一个选项量符合题目要求。
多选、错选均不得分。
）7．“毒奶粉”事件提醒我们要注意食品安全，下列食品加工方法安全的是A ．用工业盐(含2NaNO )做食品添加剂 B. 用小苏打作糕点的发酵粉C ．用塑料颗粒制作珍珠奶茶中的“珍珠”D ．用工业酒精勾兑白酒8．2ClO 是一种常用的预防“禽流感”的消毒剂，可通过以下反应制得（未配平）：O H CO SO K ClO SO H O C H KClO 22422424223+↑++↑→++下列说法正确的是A ．42SO H 做氧化剂 B. 2ClO 是氧化产物C ．422O C H 被氧化D ．每消耗lmol 3KClO 就有2mol 电子转移9．x 、y 、z 是三种短周期的主族元素，在周期表中的位置如图，x 原子的最外层电子数是其次外层电子数的3倍，下列说法正确的是A ．原子半径：X<Y<ZB. 气态氢化物的热稳定性：X>ZC ．Y 和Z 的最高价氧化物对应水化物均为强酸D ．若Z 的最高正价为+m ，则X 的最高正价也一定为+m10.如图A ～D 四种物质均含有同一种元素，A 可以是单质也可以是气态氢化物，D 是最高价氧化物对应的水化物，则A 、B 、C 、D 中共含有的元素是A. ClB. FeC. CD. N11．下列关于离子键、共价键的各种叙述中正确的是A ．在离子化合物里，只存在离子键，没有共价键B ．非极性键只存在于双原子的单质分子中C ．在共价化合物分子内，一定不存在离子键D ．由不同元素组成的多原子分子里，一定只存在极性键12.除杂时加入的试剂须稍加过量，最后过量的物质可用物理或化学方法除去。
08年高三语文第三次教学质量检测.doc
08年高三语文第三次教学质量检测语文试题本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，第Ⅰ卷（第1题至10题），第Ⅱ卷（第11题至21题），共300分，考试时间150分钟。
第Ⅰ卷（选择题共30分）注意事项：1．选择题用答题卡的考生，答第Ⅰ卷前，考生务必将自己的姓名、准考证号、试题科目用2B铅笔涂写在答题卡上。
2．选择题用答题卡的考生，每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案，不能答在试题卷和答题卷的选择题栏中；不用答题卡的考生，每小题选出答案后，填在答题卷相应的选择题栏中。
3．考试结束，监考人将答题卷和答题卡一并收回，第Ⅰ、Ⅱ卷不收回。
一、（12分，每小题3分）1．下列各组词语中，有错别字．．．．的一组是A．淹没湮没无闻代劳以逸待劳B．退化蜕化变质题纲提纲挈领C．谋取牟取暴利截至截止日期D．报复抱负远大正规步入正轨2．下列各句中，加点的成语使用恰当．．．．的一句是A．在几千年的中华文明中，孝道文化代代相传，不绝如缕．．．．，是我们共同的精神财富，因此在青少年中进行孝道教育是非常必要的。
B．一种偏激的观点认为，而今，文学萧条了，音乐冷清了，话剧玩不转了，小品平庸了，而影视却成了众星捧月．．．．的主流消费品。
C．为充分满足奥运用水需求，北京市自来水集团领导亲自抓水质，上行下效．．．．，涌现出许多干部职工争相重视水质的感人事迹。
D．中国人民银行、中国银监会近日联合下发了关于加强商业性房地产信贷管理的通知，要求加强贷款管理．杜绝久假不归．．．．的现象。
3．下列各句中，没有语病．．．．的一句是A．为进一步保障我省成品油市场，我们将密切关注市场动态，加快成品油资源的调进，在油品供应上切实保证质量。
B．如果将废旧电池丢弃到荒郊野外，就会对地下水发生严重污染，而这些污染又会通过不同的途径影响人类的健康。
C．近日，东航云南分公司18个航班的飞行员，因劳资纠纷在驾机到达目的地机场上空后，相继强行返航。
深圳外国语学校2008届高三第三次质量检测(数学理)
广东省深圳外国语学校2008届高三年级第三次质量检测数学（理科）试卷本试卷分为第I 卷（选择题）和第II 卷（非选择题）两部分，第I 卷为1—8题，共40分，第II 卷为9—21题，共110分。
全卷共计150分。
考试用时120分钟．一、选择题：本大题共8小题，每小题5分，满分40分，在每小题给出的四个选项中，只有一项是符合要求的．1．已知集合A={}4,3,2,1，那么A 的真子集的个数是（ ） A ．3 B ．16 C ．15 D ．42．已知向量)3,(),2,4(x b a ==向量，且a ∥b ，则x = （ ）A ．9B ．6C ．5D ．13．函数12sin cos y x x=++的最大值是 （ ）A 1-B 1C ．1D ． 1- 4． 若5522105)1(...)1()1()1(-++-+-+=+x a x a x a a x ，则0a = （ ） A ．32 B ．1 C ．-1 D ．-325．若函数ln y x ax =-的减区间为(1,0)-，则a 的值是 （ ）A.01a <<B.01<<-aC. 1a =-D. 1a = 6． 在ABC ∆中，“A>B ”是“sin sin A B >”成立的 （ ）A ．充要条件B ．2充分部必要条件C ．必要不充分条件D ．既不充分也不必要条件7．设等比数列{}n a 的公比为q ，前n 项和为s n ，若s n+1，s n ，s n +2成等差数列，则公比q 为 （ ）A ．2-=qB ．1=qC．12=-=q q 或D ．12-==q q 或8．已知函数()d cx bx ax x f +++=23的图象如右图，则 （ ）A ． ()0,∞-∈bB ．()1,0∈bC ．()2,1∈bD ．()+∞∈,2b二、填空题：本大题共7小题，每小题5分，满分30分．其中13~15题是选做题，考生只能选做二题，三题全答的，只计算前两题得分． 9．计算2111333324()3a ba b ---÷-= （其中0,0a b >>） ；10．曲线sin y x =在点（3π）处的切线方程为 ； 11．从10名女生和5名男生中选出6名组成课外学习小组，如果按性别比例分层抽样，则组成此课外学习小组的概率是 ；12．在的面积则中，若ABC BC AB A ABC ∆===∠∆,7,5,1200＝ ；13．（坐标系与参数方程选做题）以极坐标系中的点 1 , 6π⎛⎫ ⎪⎝⎭为圆心，1为半径的圆的方程是 ；14．（不等式选讲选做题）不等式|4||3|2x x -+-<的解集是 ； 15．（几何证明选讲选做题）,,,D EF AD C O EF O AB 于于切圆的直径是圆⊥2,6,AD AB ==则AC 长为_______.三、解答题：本大题共6小题，满分80分．解答须写出文字说明、证明过程和演算步骤． 16．（本小题满分12分）在△ABC 中，角A 、B 、C 所对边分别为a ，b ，c ，已知11tan ,tan 23A B ==，且最长边的边长为l.求：（I ）角C 的大小；（II ）△ABC 最短边的长.17. （本小题满分12分）在一次抗洪抢险中，准备用射击的方法引爆从桥上游漂流而下的一巨大汽油罐.已知只有5发子弹备用，且首次命中只能使汽油流出，再次命中才能引爆成功，每次射击命中率都是32.，每次命中与否互相独立. (Ⅰ) 求油罐被引爆的概率.(Ⅱ) 如果引爆或子弹打光则停止射击，设射击次数为ξ，求ξ的分布列及ξ的数学期望；18. (本小题满分14分）设S n 是正项数列}{n a 的前n 项和，且4321412-+=n n n a a S ， （Ⅰ）求数列}{n a 的通项公式；（Ⅱ）n n n nn b a b a b a T b +++== 2211,2求已知的值AOFCED第15题19． (本小题满分14分）据调查，某地区100万从事传统农业的农民，人均收入3000元，为了增加农民的收入，当地政府积极引进资本，建立各种加工企业，对当地的农产品进行深加工，同时吸收当地部分农民进入加工企业工作，据估计，如果有x (x ＞0)万人进企业工作，那么剩下从事传统农业的农民的人均收入有望提高2x %，而进入企业工作的农民的人均收入为3000a 元（a ＞0）。
广东省广州执信中学、中山纪念中学、深圳外国语学校2008届高三三校期末联考
广东省广州执信中学、中山纪念中学、深圳外国语学校三校2008届高三期末联考生物科第一部分选择题（共70 分）一、单项选择题：本题包括20个小题，每题2分，共40分。
每小题给出的四个选项中，只有一个选项最符合题目要求。
1．当绿色植物缺磷时，光合作用明显受阻。
其原因是A．磷是叶绿素的重要组成部分B．磷是酶的重要组成部分C．光合作用的产物在植物体内的运输需要磷D．磷对维持叶绿体膜的结构和功能起重要作用2．有一位科学家分离到一种动物细胞的细胞膜，他将膜放在特制的仪器中，分隔两边装蒸馏水的槽。
当他将稀释的乙酸放入一侧时，发现另一侧槽中的pH没有变化。
于是它将动物细胞匀浆磨碎，过滤出细胞器和膜的碎片，然后再将滤液加到膜的一侧，这时发现另外一侧的pH下降了。
造成这种变化的最合理的解释是：A．质子通过主动运输跨膜B．质子通过扩散跨膜运动C．质子通过协助扩散跨膜D．细胞滤液能溶解膜中的脂3．如果使用基因工程的手段将变形虫溶酶体膜上的质子通道改造成只在低于16℃的温度下才能发挥作用，那么，变形虫在20℃的环境中将发生：A．饥饿而死B．pH过低死亡C．膨胀直至破裂D．溶酶体破裂4．左下图为某植物根示意图，右下图是左下图中的P、Q、R的放大示意图。
表面积最大、吸收水和无机盐功能最强的、生长速率最快、分裂能力最强的细胞依次是A．7；1；7；4或7 B．2或3；1；2或3；5或6C．7；1；7；2或3 D．1；1；2或3；5或65．给一只小白鼠吸入18O2，则这只小白鼠体内最先含有18O2的物质可能存在于A．小白鼠的尿液中B．呼出的CO2气体中C．细胞内的C6H12O6中D．细胞质基质中的丙酮酸中6．光照强度和CO2浓度是影响光合作用强度的两个主要外界因素。
下面是北方夏季的一天中，棉花叶片光合作用强度的变化曲线。
请指出正确的图解是7．关于人体癌细胞的叙述，不正确的是A．癌变主要是因为人体细胞的原癌基因和抑癌基因发生突变B．癌细胞比所有正常细胞分裂周期长、生长速度快C．有些病毒能将其基因整合到人的基因组中，从而诱发人的细胞癌变D．癌细胞的形态结构和表面的物质都发生明显的变化8．某一动物的体细胞内有6对染色体。
集合与函数
答案：A
11、(四川省巴蜀联盟2008届高三年级第二次联考)已知集合A={x|x-m<0}，B={y|y=x2+2x，x∈N}，若A∩B=Φ，则实数m的范围为
A．m≤-1B．m<-1C．m≤0D．m<0
答案：C
12、(陕西长安二中2008届高三第一学期第二次月考)已知集合 = ， = ，
A. 20B. 30C. 42D. 56
答案：B
17、(安徽省巢湖市2008届高三第二次教学质量检测)设全集 ，集合 ， ，则 等于()
A.{2}B.
C. D.
答案：C
18、(北京市朝阳区2008年高三数学一模)已知集合 ， ，则集合 等于
A． B．
C． D．
答案：C
19、(北京市朝阳区2008年高三数学一模)已知 且 ，则“ ”是“ >1”的
A．充分而不必要条件B．必要而不充分条件
C．充要条件D．既不充分也不必要条件
答案：B
26、(北京市西城区2008年4月高三抽样测试)若集合 ， ，则“ ”是“ ”的（）
A.充分但不必要条件B.必要但不充分条件
C.充要条件D.既不充分又不必要条件
答案：A
27、(北京市西城区2008年5月高三抽样测试)设A，B是全集I的两个子集，且 ，则下列结论一定正确的是（）
A．3B．7C．15D．31
答案：B
43、(甘肃省兰州一中2008届高三上期期末考试) 的（）
A．充要条件B．充分非必要条件
C．必要非充分条件D．非充分非必要条件
答案：D
44、(广东省2008届六校第二次联考)已知 ,若 ,则实数 的取值范围是( )
A. B. C. D.
高中英语2008年高三第三次质量检测试卷试题4300
高中英语2008年高三第三次质量检测试卷试题2019.091,The once “Badly-off” boy bought a car for his teacher______ gratitude.A. withB. forC. out ofD. by2,You should put the money to____ the moment you gain it. A. being used B. use C. usingD. using it3,Rachel resisted the enquiries to the degree_____ it seemed she didn’t want the mystery of the Moon Stone_________.A. that, to be solvedB. which, to solveC. as, to be solvedD. which, to be solved4,Chimpanzees’feet and hands are similar to Man’s______ they still have opposable toes.A. althoughB. except forC. except thatD. except5,It usually takes a species quite long to______ a new environment and survive there.Which of the following can’t be used to fill in the blank?A. fit in withB. get used toC. go ahead withD. agree with6,____ improving the situation for the poorest, China isperforming a great many government programs.A. Aiming atB. Aiming toC. Aimed atD. Aimed to7,Many schools are exchanging programs_____ various academic levels____ a reasonable cost.A. with, atB. at, forC. at, withD. at, at8,Can you imagine the problem the war widows had_____ their kids?A. raisingB. to raiseC. raisedD. to rise9, Dedication is which of the characteristics of an applicant_____ counts.A. whichB. thatC. whoD. /10,---- Do you believe what he says? ----Yes! __________!A. AnythingB. Much moreC. WhateverD. He’s my boyfriend11, Our plant is_____ due to a material shortage, while theirs is______ as a result of heavy pollution.A. closed down, closed upB. closed up, shut upC. shut down, closed downD. closed up, closed down12,Buildings were destroyed, and paintings and statues _____on the ground.A. lay in piecesB. lay in pieceC. lay into piecesD. laid in pieces13,“Open the box yourself, Della, and you will know…..”“My Dear!” Della cried, hugged the box to her breast, and______ it open, threw herself down on the shabby sofa.A. tearingB. toreC. to tearD. torn14,Every culture has its heroes. The heroes are the people the nation, especially the young 1 . If you get a list of heroes of a nation,2 will tell you the potential of that nation.If today in China, you ask the high school students to 3 their heroes, their4 would probably 5 into three groups. The first group would be the pop stars-the people 6 with pop songs. There is no doubt that such people do have talent but one 7 if one should hold up pop stars as a model. The pop stars too often are mixed with drugs and their personal life is not all that 8 . They are rich and wear the latest fashion styles. However, one should 9 more in a hero than such things as money and fine clothes.A 10 type of heroes for the Chinese youth are the sports stars. Again you have a person who has a gift in one area- 11 . However, too often the personal life of the sports star is 12 disorder. Too frequently drugs and drinking are a part of life of these stars.A third group of heroes are TV and movie stars. These people may have lots of 13 talent and are quite handsome. 14 , the personal life of too many actors is quite sad and confused and15 be held up as a model for young people.Today, the pop singers, the sportsmen and the actors all have become the models of the youth in China. Really, do you hear a young man say that his hero is a doctor, a teacher or a scientist? These people are not rich and do not wear fashionable clothes. However they are 16 people who work hard to make the world a better place for everyone. 17 is really sad is that the young try to 18 their heroes. They like to wear the same clothes as theirs. If the heroes of today for the Chinese youth are 19only to pop stars, sportsmen and actors, the future does not look too 20 .1.A. addicted to B. admire C. hate D. satisfy2.A. they B. which C. who D. it3.A. listB. giveC. call D. love4.A.conclusion B. questionC. choiceD. majority5.A. getB. enterC. fill D. fall6.A. interested B. connected C. excitedD. pleased7.A. wants B. puzzles C. wonders D. expects8.A. badB. simple C. silentD. good9.A. putB. gather C. spendD. look10.A. anotherB. other C. secondD. different11.A. musicB. sports C. movie D. songs12.A. littleB. a few C. a bit of D. very13.A. singing B. runningC. pretending D. acting14.A. Nevertheless B. What’s worseC. BesidesD. And15.A. shouldB. should not C. mustD. may not16.A. kind-hearted B. weak C. talentedD. terrible17.A. WhichB. WhetherC. WhateverD. What18.A. rememberB. follow C. praise D. persuade19.A. limited B. enoughC. powerfulD. great20.A. usualB. necessary C. bright D. important15,Sena was unusually busy in his grocery shop and restaurant. It was two days after tsunami struck his motherland, Sri Lanka. In addition to answering questions from customers when his family would start off back to Sri Lanka, Sena was taking in clothes and other items donated by generous locals. There were no sign boards to indicate he was collecting aid for the tsunami survivors, but people were giving whatever they could to anyone who had collections to a tsunami-hit country. During a break in the customers flow, Sena noticed a woman standing to one side. Dressed in a dark coat, she appeared to be in her sixties. The woman stepped forward and passed an envelope to Sena, telling him its contents should be sent to the victims in Sri Lanka. She was about to leave when Sena opened the envelope. Seeing a bundle of $ 50 notes inside, he asked her to wait until he wrote her a receipt. He counted the money--$ 1500!When Sena told the woman he was hesitant to take her money, shesaid she was horrified and saddened to see the tsunami in Sri Lanka. “Why are you giving it to me?”Sena asked, “Why not give it to some charity organization?”“You are from Sri Lanka,”she said, “I trust you and know you will use it to help your people”Then she explained how, several months earlier, she was walking past and was drawn into the shop by a good smell. “You told me it came from cooking Sri Lanka food and invited me to have lunch,” she said, “I didn’t have enough money on me to pay for a meal, but you served me a meal in a box to be taken away. You did not take any money. That’s why I know you have a good heart.”The woman then removed her coat to also send to the tsunami victims. She also gave Sena a matchbox full of trinkets.Sena could not recall the particular incident. However, he knew full well the age-old custom he had picked up from his parents. In most villages in Sri Lanka, it was the practice to cook a little bit of extra food when preparing a meal. It ensured that if a stranger dropped by during meal times, he or she would not go away hungry. Sena’s hospitable gesture could ensure that a family who lost everything in the tsunami may gain a roof over its head.1. What did the woman donate to the victims in Sri Lanka?A. $ 1500B. $ 1500 and a coatC. $ 1500 , a coat, a matchboxD. $ 1500, a coat, some trinkets2. The woman donated money to Sri Lanka for the reason that______.A.she had once been to Sri Lanka and was moved by their hospitalityB.she was sure Sena would help people in Sri Lanka with her moneyC.in order to pay back the lunch given by SenaD.all the local people were appealed to donate3. Why did many locals donate to Sri Lanka through Sena?A.There were no organizations which collected aid for the tsunami victimsB.Sena’s family was lost in the tsunamiC.Sri Lanka, Sena’s motherland, was struck by the tsunamiD.Sena managed a shop which collected aid4. ______, most villagers in Sri Lanka prefer to cook a little more when preparing a meal.A.In case a dropper-in at dining time would need something to eatB.For they were all hospitable to visitors in time of hungerC.Because their kids would probably eat more than neededD.Passing from generation to generation5. We can conclude the story with the saying “_________.”A. No pain, no gainB. where there is a will, there is a wayC. Great minds think alikeD. To be virtuous is to do good16, ●Argosy Christmas Ship FestivalSeattleDecember 1-December 23, 2007The Argosy Christmas Ship Festival is a ship-to-shore holiday celebration that has become a local Northwest tradition. Aboardthe Christmas Ship, some of the finest Northwest choirs sing holiday greetings. These performances are broadcast via speakers to bonfire sites and to other boats participating in the parade.●Holiday Island Lights Festival Friday Harbor, Sand Juan Island December 1-December 31, 2007An island-wide holiday tradition including local businesses decorating contest, a tree lighting ceremony on Dec. 4 with shops staying open until 7:00 pm. On Dec. 11 a Lighted Boat Parade starts the evening, to be followed by the Santa Ship into Friday Harbor for the children, ships staying open until 7:00 pm. Dec. 18―19 Roche Harbor’s Christmas Festival begins at 3:00 pm and will include artists booths, Victorian carol singing, story telling, theater and dining.●Christmas Lighting Festival Leaven WorthDecember 4-December 19This old-fashioned Lighted Farm Implement parade, which expressed its admiration for the Yakima Valley’s agricultural heritage, including entries with up to 35,000 lights decorating the tractor or plow. Pre-parade activities include a Christmas Tree Ceremony and other special entertainment before the parade. Join us and you’re sure to enjoy the carolers dressed in traditional attire.●Holiday With LightsFederal WayDecember 10,2007-January 1, 2008With over a million twinkling lights displayed throughout the park,your heart will be filled with cheer and spirit of the season! Holiday light displays,festive music and strolling carolers, visit with Santa, enchanted village rides, and much more.1. Which of the following festivals lasts the longest?A.Argosy Christmas Ship FestivalB.Holiday Island Lights FestivalC.Christmas Lighting FestivalD.Holiday With Lights2. The purpose of writing the passage is to_________.A.Offer advice on how to enjoy the holidayspare the advantages and disadvantages of different festivalsC.attract visitorsD. introduce different festivals3.If you want to attend a lighted Boat Parade, you should go to_______.A. SeattleB. Leaven WorthC. Friday HarborD. Federal Way4. How will people feel when they are spending Holiday with Lights?A. AstonishedB. TiredC. FreshD. Happy5. Christmas Lighting Festival has been fashioned long to_________.A. hold a paradeB. serve as a Christmas Tree CeremonyC. show adoration for agricultural heritageD. allow people to be dressed in traditional attire17,For 65 years Binyamin Shilon believed his sister was among the 6 million Jews killed by the Nazis during the Second World war. Now he holds her in his arms and cries with joy.November was a child when her family broke apart and she spent many of her earliest years in an orphanage. When the Nazis invaded Poland in 1939, her father was shot dead and soon she found herself in the Jewish camp in Krakow in the care of a stepmother. The little girl escaped the death camps for a time, and nearly died in 1943 when she was sent to Auschwitz. She was saved when a stranger pushed her into the line of those allowed to live. November soon found herself back in the care of her stepmother. She survived the war in work camps. Shilon meanwhile spent the first years in the Soviet-occupied sector of eastern Poland, and then was sent to the city of Minsk in 1941. He joined Soviet leader Josef Stalin’s army and headed west. In 1943 he was sent to the Ukrainian front. In early 1945 he returned to Poland with new orders to liberate Auschwitz. There was no chance of an immediate postwar reunion. Shilon accepted the fact he would never see his mother, sister or two brothers again.The siblings came to Israel for different reasons. November moved to Palestine on the eve of Israel’s 1948 independence to avoid following her stepmother to Canada. Shilon immigrated in 1957 to Israel. The two continued their lives, married and raised children.In 1999 Shilon finally filled forms for his mother and all the siblings he believed had been killed by the Nazis including his little sister Ruja. Then on Dec. 19, 2003 an American cousin brought November to check the records left by other survivors. She learned Shilon was alive and just a 90-minute drive from her own house. That night she spoke to her brother for the first time since 1938.The siblings spoke twice that night and on Saturday saw each other for the first time since 1938. They traded stories. November learned she was two years older than she thought. “It’s hard to explain that feeling we have…It’s hard to measure in terms of gain. It’s all inside.” Shilon said, “You cannot explain it”1. The story is mainly about_____________.A.the Jews’ terrible life under Hitler’s controlB.how a brother looked for his missing sisterC.siblings separated by Nazis reunited after 65 yearsD.the survivors during World War Ⅱ2. “The siblings in Para” 3 refer to________.A. Shilon’s mother and brothersB. Shilon and his sisterC. survivors after the warD. November and her stepmother3. Which of the below shows the right order of what happened to the family?a. shilon and his sister met again in Israelb. Their father was killedc. November came to settle in Israeld. Shilon returned to his motherlande. Shilon left the information about his mother and sister A. b, d, c, e, aB. b, c, e, d, aC. b, e, c, d, a D. d, b, c, e, a4. From the text, we learn that___________.A.Shilon came to Israel in order to find his missing sisterB.after the war November believed his brother was still aliveC.November’s cousin had known Shilon beforeD.Shilon and November were very excited about their reunion18,The policeman on the beat moved up the avenue. The time was about ten at night, but freezing wind with a taste of rain had almost emptied the streets. Trying doors as he went, swinging his club with many clever movements, he turned now and then to set his watchful eye down the peaceful street. When about midway of a certain block, he suddenly slowed his walk. In the doorway of a closed store a man leaned, with an unlighted cigar in his mouth. As the policeman walked up to him, the man spoke up quickly. “It’s all right, officer,”he said confidently, “I’m just waiting for a friend. It’s an appointment made twenty years ago. Sounds a little funny to you, doesn’t it? Well, I’ll explain. About that long ago there used to be a restaurant where this store stands-BigJoe Brady’s restaurant”“Until five years ago.”said the policeman. “It was torn down then”The man in the doorway struck a match and lit his cigar. “I came a thousand miles to stand in the door tonight, and it’s worth.”Said the man, “Twenty years ago tonight, I dined here at Big Joe Brady’s with Jimmy Wells, my best friend. He and I were brought up here in New York, just like two brothers, together. I was eighteen and Jimmy was twenty. The next morning I was to start for the West to make my fortune. You couldn’t have dragged Jimmy out of New York, he thought it was the only place on earth. Well, we agreed that we would meet here again exactly twenty years from that date and time, no matter what our conditions might be or from what distance we might have to come from. We figured that in twenty years each of us ought to have our fortunes made, whatever there were going to be.”“It sounds pretty interesting.” said the policeman.1. At the beginning of the story, the policeman was “on the beat”. He was most probably_________.A. walking down the street on dutyB. swinging his club following a beatC. experiencing a fast heart-beatingD. on the point of beatinga wrong doer2. The writer’s description about the weather at the beginning of the story is meant__________.A.to sing the praises of the greatness of friendshipB.to create an atmosphere for the coming appointmentC.to praise the office for his willing awareness of his dutyD.to inform us the situations about the appointment made 20 years ago3. Which of the following can NOT be a reasonable guess?A.Jimmy may have come to the appointment as he had promisedB.The man from the West might have made a lot of fortunesC.The man may have been to “Big Joe” several times in the past20 yearsD.The office might be Jimmy Wells himself19,With only about 1,000 pandas left in the world, China is desperately trying to clone the animal and save the endangered species. That’s a move similar to what a Texas A & M University researchers have been undertaking for the past five years in a project called “Noah’s Ark”. Noah’s Ark is aimed at collecting eggs, embryos(胚胎), semen and DNA of endangered animals and storing them in liquid nitrogen. If certain species should become extinct, DR. Duane, a professor in Texas A & M College of Veterinary Medicine, says there would be enough of the basic building blocks to reintroduce the species in the future.It is estimated that as many as 2,000 species of mammals, birds and reptiles will become extinct in over 100 years. The panda,native only to China, is in danger of becoming extinct in the next 25 years. This week, Chinese scientists said they grew an embryo by introducing cells from a dead female panda into the egg cells of a Japanese white rabbit. They are now trying to implant the embryo into a host animal.“The nuclear transfer(核子移植) of one species to another is not easy, and the lack of available panda eggs could be a major problem.”Kraemer believes, “They will probably have to do several hundred transfers to result in one pregnancy. It takes a long time and it’s difficult, but this could be goundbreaking science if it works. They are certainly not putting any live pandas at risk, so it is worth the effort.”Adds Kraemer, who is one of the leaders of the project in Texas A & M, the first--ever attempt at cloning a dog.“They are trying to do something that’s pioneering, and this is very similar to our work in Noah’s Ark. We’re both trying to save animals that faces extinction. I certainly appreciate their effort and there’s a lot we can learn from what they are attempting to do. It’s a research that is very much needed. ”1. Find a word in the passage closest to the meaning to the underlined word “goundbreaking”_______________________________2. Why are some of the scientists trying to clone some animals?(回答字数不超过5个)___________________________________________________3. What can we know about the nuclear transfer of one species to another?(回答字数不超过9个)_____________________________________________________________ _20,Packaging is an important form of advertising. A package can sometimes motivate someone to buy a product. For example, a small child might ask for a breakfast food that comes to a box with a picture of a TV character. The child is more interested in the picture than in the breakfast food. Pictures for children to color or cut out, games printed on a package, or a small gift inside a box also motivate children to buy the products or to ask their parents to buy for them.Some packages suggest that a buyer will get something for nothing. Food products sold in reusable containers are examples of this. Although a similar product in a plain container might cost less, people often prefer to buy the product in a reusable glass or dish, because they believe the container is free. However, the cost of the container is added to the coat of the product. The size of a package also motivate the buyers. Maybe the package has “Economy Size”or “Family Size”printed on it. This suggests that the larger size has the largest amount for the least money. But that is notalways true. To find out, the buyers have to know how the product is sold and the price of the basic unit.The information on the package should provide some answers. But the important thing for any buyer to remember is that a package is often an advertisement. The words and pictures do not tell the whole story. Only the product inside can do that.Title 1试题答案1, C2, B3, A4, C5, C6, A7, D8, A9, B10, C11, A12, A13, A14, 1-5：B、D、A、C、D 6-10：B、C、D、A、C11-15：B、C、D、A、B 16-20：C、D、B、A、C15, D、B、C、A、D16, B、C、C、D、C17, C、B、A、D18, A、B、C19, 1:pioneering 2: To save the endangered species3: It is not easy/ It will take a long time and it’s difficult20, 1. Packaging Advertising/Advertisement 2. Package Size3. Small gifts4. Dishes5. Economy Size6. Free7. the least money8. Selling food9. Not always true 10. Basic unit prices。
广东省深圳市外国语学校2024届高三第三次月考语文试卷及答案
广东省深圳市外国语学校2024届高三第三次月考语文试卷及答案一、现代文阅读（35分）（一）现代文阅读I（本题共5小题，19分）阅读下面的文字，完成1~5题。
材料一：最近火热的ChatGPT，是美国人工智能研究实验室OpenAI开发的一种全新聊天机器人模型，它能够通过学习和理解人类的语言来进行对话，还能根据聊天的上下文进行互动，并协助人类完成一系列任务。
这款AI语言模型，让撰写邮件、论文、脚本，制订商业提案，创作诗歌、故事，甚至敲代码、检查程序错误都变得易如反掌。
ChatGPT的迅速普及有可能颠覆许多行业。
纽约大学计算机科学与电气工程系副教授ChinmayHegde认为，新闻、高等教育、图形和软件设计等行业的某些工作——这些工作有被AI代替的风险。
以新闻媒体为例，卫报早在2020年就让ChatGPT软件撰写了一篇文章——结果喜忧参半。
“复制编辑当然是它非常擅长的事情。
总结一下，使文章简洁明了，这确实做得很好，”Hegde说，“但一个主要缺点是该工具无法有效地进行事实核查。
”在教育领域，《纽约邮报》则指出，教授和教师可能被人工智能课程取代。
英国牛津互联网研究所的学者Sandra Wachte担心，如果学生们开始使用ChatGPT，这不仅是“外包”了他们的论文写作，还会“外包”他们的思维。
AI面试、AI聊天、AI绘画……随着AIGC（利用人工智能技术生成内容）作为工具在工作生活中高效应用，难道面试官、作家、设计师……就要失业了吗？我们应当秉持怎样的态度看待这种技术革新？——选自央广网《火爆全网的ChatGPT到底是个啥？》材料二：似乎在一夜之间，周围不少朋友都在讨论一款名为ChatGPT的人工智能聊天程序。
有人用它即兴创作诗歌，有人试图用它设计小说大纲，还有程序员用它解决工作问题……根据多家媒体引述的调查结果，89%的美国大学生在用ChatGPT 写作业——这个数据恐怕是言过其实了，但至少说明该程序在解答问题方面具有显著优势。
广东省广州执信中学、中山纪念中学、深圳外国语学校2008届高三三校期末联考(历史)
广东省广州执信中学、中山纪念中学、深圳外国语学校三校2008届高三期末联考历史科本试卷分选择题和非选择题两部分，共16页，满分为150分。
考试用时120分钟。
注意事项：1、答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名和学号填写在答题卡和答卷密封线内相应的位置上，用2B铅笔将自己的学号填涂在答题卡上。
2、选择题每小题选出答案后，有2B铅笔把答题卡上对应题目的答案标号涂黑；如需改动，用橡皮擦干净后，再选涂其他答案；不能答在试卷上。
3、非选择题必须用黑色字迹的钢笔或签字笔在答卷纸上作答，答案必须写在答卷纸各题目指定区域内的相应位置上，超出指定区域的答案无效；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔和涂改液。
不按以上要求作答的答案无效。
4、考生必须保持答题卡的整洁和平整。
第一部分选择题(共75 分)1．我国古代的农业是一种典型的精耕细作农业，推动精耕细作技术发展的主要动力是：A．农具的改进B．技术的提高C．小农经济的发展D．国家政策的推动2．唐•骆宾王《讨武氏檄》：“伪临朝武氏者，性非和顺，地实寒微。
”这从本质上反映了：A．武则天不得人心B．武则天代唐建周，违背历史潮流C．武则天政敌对她进行人身攻击D．庶族地主与士族地主的斗争3．据分析统计，《孟子》一书中关于水利的谈话有11次，都涉及黄河洪水泛滥殃及邻国。
从当时历史发展的趋势来看，解决的根本之道在于：A．各国减少战争，专力治黄B．各国加强协调，统一治黄C．统一中原，由中央政府治理D．各自为政，加强治理41975年12月，考古工作者在湖北省云梦县发掘了12座战国至秦汉的古墓。
在第11．号墓中出土了大量秦代竹简，其中一些竹简上刻着内容具体的《田律》。
《田律》的颁布，证实了下列那句史料记载的正确性：A．“（商鞅）为田开阡陌封疆，而赋税平”B．《史记》：“明法度，定律令，皆以始皇始。
”C．《诗经》：“七月亨葵及菽。
八月剥枣，十月获稻。
08届高三年级英语第三次质量检测.doc
08届高三年级英语第三次质量检测英语试题本试卷分第一卷(选择题)和第二卷(非选择题)两部分；第一卷1至9页，第二卷9至11页。
考试时间120分钟。
满分150分。
第一卷(三部分，共115分)注意事项：1．答第一卷前，考生务必将自己的姓名、准考证号、考试科目用铅笔涂写在答题卡上。
2．每小题选出答案后，用铅笔把答题卡上对应题目的答案标号涂黑。
如需改动，用橡皮擦干净后，再选涂其他答案标号。
不能答在试卷上。
3．考试结束，考生将第二卷和答题卡一并交回。
第一部分：听力(共两节，满分30分)做题时，先将答案划在试卷上。
录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。
第一节：(共5小题；每小题1．5分，满分7．5分)听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. When will there be a birthday party?A. Next Sunday.B. Next Monday.C. This Sunday.2. What address is given by the woman?A. 1120, East 32nd Street.B. 1120, East 42nd Street.C. 1220, East 32nd Street.3. What did the man buy when he was in Paris?A. A large leather suitcase.B. A large leather briefcase.C. A large leather cigarette case.4. What does the man want to know?A. How to pronounce the word.B. The meaning of the word.C. How to spell the word.5. Why did the woman stop the man from whistling?A. She was trying to go to sleep.B. She was working on a problem.C. She was writing a paper.第二节：(共15小题；每小题1．5分，满分22．5分)听下面5段对话或独自。
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广东省深圳外国语学校2008届高三第三次质量检测数学(文科)试题本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分， 第Ⅰ卷为1－10题，共50分，第Ⅱ卷为11－21题，共100分.全卷共计150分。
考试时间为120分钟. 注意事项：参考公式：如果事件A 、B 互斥，那么()()()P A B P A P B +=+如果事件A 、B 相互独立，那么()()()P A B P A P B ⋅=⋅球的表面积公式 24πS R = 球的体积公式 34π3V R =其中R 表示球的半径 第Ⅰ卷（选择题，共50分）一、选择题：本大题共10小题，每小题5分，满分50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．Ｍ＝{}4|2<x x ，Ｎ＝{}032|2<--x x x ，则集合Ｍ Ｎ＝( ). A.{2|-<x x } B.{3|>x x } C.{21|<<-x x } D. {32|<<x x }2. 复数2(2)(1)12i i i+--的值是( ).A ．2 B. 2- C. 2i D. 2i - 3. 已知||3a =，||5b =，12a b =，则向量在向量上的投影为（ ）.A 12BC D4. 方程2sin 2sin 0x x a --=x R ∈在上有解，则a 的取值范围是（ ）.A ．[)+∞-,1B ．),1(+∞-C ．]3,1[-D ．[)3,1-5．“12m =”是“直线(2)310m x my +++=与直线(2)(2)30m x m y -++-=相互垂直”的（ ）A 充分必要条件B 充分而不必要条件C 必要而不充分条件D 既不充分也不必要条件6. 等差数列{}n a 中，n S 是前n 项和，且k S S S S ==783,，则k 的值为( ).A.4 B 11 C.2 D 127. 为了得到函数)62sin(π-=x y 的图象，可以将函数x y 2cos =的图象( ).A.向右平移6π个单位 B.向右平移3π个单位 C.向左平移6π个单位 D.向左平移3π个单位8.若椭圆2215x y m +=的离心率5e =,则m 的值为( ). A.13或2539. 在棱长为2的正方体1111ABCD A BC D -中，点E ，F 分别是棱AB ，BC 的中点，则点1C 到平面1B EF 的距离是( ).A.332 B.322 C.32D.3410．10.定义A D D C C B B A ****,,,的运算分别对应下图中的(1)、(2)、(3)、(4)，那么下图中的（A ）、（B ）所对应的运算结果可能是（1） （2） （3） （4） （A ） （B ） A.D A D B **, B.C A D B **, C.D A C B **, D.D A D C **,第Ⅱ部分（非选择题，共100分）二、填空题：本大题共5小题，每小题5分，满分20分，其中14，15题是选做题，考生只能选做一题,，若两题全都做的，只计算前一题的得分． 11. 函数()212log 2y x x =-的单调递减区间是 .12.甲、乙两人独立的解决一个问题，甲能解决这个问题的概率为0.6，乙能解决这个问题的概率为0.7，那么甲乙两人中至少有一人解决这个问题的概率是 .13．设x 、y 满足条件310x y y x y +≤⎧⎪≤-⎨⎪≥⎩，则22(1)z x y =++的最小值 .14．(坐标系与参数方程选做题)自极点O 向直线l 做垂线，垂足为(2,)3H π，则直线l 的极坐标方程是 .15．(几何证明选讲选做题)已知圆的直径13AB =，C 为圆上一点，过C 作CD AB ⊥于D（AD BD >），若6CD =，则AD 的长为.A B 1BC 三、解答题：本大题共6小题，满分80分．解答须写出文字说明、证明过程或演算步骤． 16．(本小题满分12分) 在ABC △中，1tan 4A =，3tan 5B =（Ⅰ）求角C 的大小；（Ⅱ）若AB ，求BC 边的长17．（本小题满分13分）如图,在直三棱柱111ABC A B C -中, 3AC =, 4BC =, 5AB =,14AA =, 点D 是AB 的中点.(1)求证:1AC BC ⊥; (2)求证:1AC ∥平面1CDB .18.(本小题满分13分)设数列{}n a 的前n 项和为n S ，点(,)()n S n n N n*∈均在函数32y x =-的图像上.（Ⅰ）求数列{}n a 的通项公式；（Ⅱ）设13+=n n n a a b ，n T 是数列{}n b 的前n 项和，求使得20n m T <对所有n N *∈都成立的最小正整数m .19.(本小题满分14分)已知圆C 过点(0,)A a (0)a >, 且在x 轴上截得的弦MN 的长为2a .(1) 求圆C 的圆心的轨迹方程； (2) 若45MAN ∠=, 求圆C 的方程. 20.(本小题满分14分）已知函数2()(0,0)f x ax bx c a bc =++>≠,()0,,()()0.f x x F x f x x >⎧=⎨-<⎩ （Ⅰ）若函数)(x f 的最小值是(1)0f -=，且(0)1f =，求(2)(2)F F +-的值； （Ⅱ）在（Ⅰ）的条件下，k x x f +>)(在区间[3,1]--恒成立，试求k 的取值范围；（Ⅲ）令()2g x ax b =+,若(1)0g =,又()f x 的图象在x 轴上截得的弦的长度为m ，且02m <≤，试确定c b -的符号.21.(本小题满分14分）已知函数2221()()1ax a f x x x -+=∈+R ，其中a ∈R ． （Ⅰ）当1a =时，求曲线()y f x =在点(2(2))f ，处的切线方程； （Ⅱ）当0a ≠时，求函数()f x 的单调区间与极值．A B 1BC 广东省深圳外国语学校2008届高三第三次质量检测数学(文科)试题参考答案二、填空题：本大题共5小题，每小题5分，满分20分，其中14，15题是选做题，考生只能选做一题,，若两题全都做的，只计算前一题的得分． 11.(2,+∞) 12.0.88 13. 4 14.cos()23πρθ-= 15. 9三、解答题：本大题共6小题，满分80分．解答须写出文字说明、证明过程或演算步骤． 16．(本小题满分12分)解：（Ⅰ）∵ π()C A B =-+， ………………1分∴ 1345tan tan()113145C A B +=-+=-=--………………4分 又 ∵ 0πC <<， ∴ 3π4C = …………………5分（Ⅱ）由22sin 1tan cos 4sin cos 1A A A A A ⎧==⎪⎨⎪+=⎩，，且π02A ⎛⎫∈ ⎪⎝⎭，，…………………7分得sin A =…………………………9分 由正弦定理sin sin AB BC C A =， 得sin 2sin ABC AB C==……………………12分 17．（本小题满分13分）证明: (1) ∵ 三棱柱111ABC A B C -为直三棱柱, ∴ 1C C ⊥平面ABC , ∴1C C AC ⊥, ∵ 3AC =, 4BC =, 5AB =, ∴ 222AC BC AB +=,∴ AC BC ⊥, 又 1CC BC C ⋂=,∴ AC ⊥平面11CC B B ,∴ 1AC BC ⊥ ……………………………………7分(2) 令1BC 与1CB 的交点为E , 连结DE .∵ D 是AB 的中点, E 为1BC 的中点, ∴ DE ∥1AC . 又 ∵1AC ⊄平面1CDB , DE ⊂平面1CDB , ∴1AC ∥平面1CDB . ………………………13分 18.(本小题满分13分) 解: (1) 由题意得 32nS n n=- , 即 232n S n n =-,…………………1分 当2n ≥时,22132[3(1)2(1)]65n n n a S S n n n n n -=-=-----=-,…………4分当1n =时, 111615a S ===⨯-, ………………5分 ∴ 165()n n n a S S n n N *-=-=-∈, ……………………6分 (2) 由(1)得133111()(65)(61)26561n n n b a a n n n n +===--+-+,…………………8分 ∴ 111111[(1)()()]277136561n T n n =-+-++--+ 11(1)261n =-+ . ……………………11分 因此,使得11(1)()26120m n N n *-<∈+成立的m 必须且只需满足1220m≤, 即10m ≥,故满足要求的的最小正整数10m=………………13分19.(本小题满分14分)解: (1)设圆C 的圆心为,)(y C x ,依题意圆的半径 r =……………… 2分∵ 圆C 在x 轴上截得的弦MN 的长为2a . ∴ 222||y a r +=故 2222()||x y a y a +-=+ ………………………… 4分 ∴ 22x ay =∴ 圆C 的圆心的轨迹方程为22x ay = ………………… 6分 (2) ∵ 45MAN ∠= , ∴ 90MCN ∠= ……………………… 9分令圆C 的圆心为00(,)x y , 则有2002x ay = (00y ≥) ,…………… 10分又 ∵ 01||2y MN a == …………………… 11分∴ 0x = ……………………… 12分∴ r == ……………………… 13分∴ 圆C 的方程为 222()()2x y a a +-= …………………… 14分 21.(本小题满分14分)解：（Ⅰ）由已知.12,0,1-=-=+-=abc b a c 且 解得1a =，2b =， …………………2分∴ 2()(1)f x x =+ , ∴ 22(1),(0)()(1),(0),x x F x x x ⎧+>⎪=⎨-+<⎪⎩ (4)分∴ 22(2)(2)(21)[(21)]8F F +-=++--+=. ……………………5分（Ⅱ）在（Ⅰ）条件下，k x x f +>)(在区间[3,1]--恒成立,即210x x k ++->在区间[3,1]--恒成立,从而12++<x x k 在区间[3,1]--上恒成立，…………………8分 令函数2()1p x x x =++,则函数2()1p x x x =++在区间[3,1]--上是减函数，且其最小值min ()(1)1p x p =-=，∴ k 的取值范围为(,1)-∞…………………………10分（Ⅲ）由(1)0g =，得20a b +=，∵ 0a > ∴20b a =-<,………………11分 设方程0)(=x f 的两根为21,x x ，则122bx x a+=-=,12c x x a =,∴12||m x x =-=∵ 02m <≤， ∴ 01<≤, ∴01c a ≤<，∵ 0a >且0bc ≠， ∴ 0c >，∴ 0c b ->……………14分 21.(本小题满分14分)解: （Ⅰ）解：当1a =时，22()1x f x x =+，4(2)5f =，……………1分又22222222(1)422()(1)(1)x x x f x x x +--'==++，则6(2)25f '=-．…………………3分 所以，曲线()y f x =在点(2(2))f ，处的切线方程为46(2)525y x -=--， 即625320x y +-=．……………4分（Ⅱ）解：2222222(1)2(21)2()(1)()(1)(1)a x x ax a x a ax f x x x +--+--+'==++．…………6分 由于0a ≠，以下分两种情况讨论．（1）当0a >时，令()0f x '=，得到11x a=-，2x a =,当x 变化时，()()f x f x '，的变化情况如下表：所以()f x 在区间a ⎛⎫--⎪⎝⎭，∞,()a +，∞内为减函数，在区间a a ⎛⎫- ⎪⎝⎭，内为增函数 故函数()f x 在点11x a =-处取得极小值1f a ⎛⎫- ⎪⎝⎭，且21f a a ⎛⎫-=- ⎪⎝⎭，函数()f x 在点2x a =处取得极大值()f a ，且()1f a =．…………………10分（2）当0a <时，令()0f x '=，得到121x a x a==-，，当x 变化时，()()f x f x '，的变化情况如下表：所以()f x 在区间()a -，∞,a ⎛⎫- ⎪⎝⎭，+∞内为增函数，在区间a a ⎛⎫- ⎪⎝⎭，内为减函数． 函数()f x 在1x a =处取得极大值()f a ，且()1f a =． 函数()f x 在21x a=-处取得极小值1f a ⎛⎫- ⎪⎝⎭，且21f a a ⎛⎫-=- ⎪⎝⎭．………………14分。