2003年真题详解

2003年国家司法考试试卷三真题解析一、单项选择题，每题所给的选项中只有一个正确答案。

本部分1—30题，每题1分，共30分。

1.甲、乙、丙共有一套房屋，其应有部分各为1／3。

为提高房屋的价值，甲主张将此房的地面铺上木地板，乙表示赞同，但丙反对。

下列选项哪一个是正确的？A.因没有经过全体共有人的同意，甲乙不得铺木地板B.因甲乙的应有部分合计已过半数，故甲乙可以铺木地板C.甲乙只能在自己的应有部分上铺木地板D.若甲乙坚持铺木地板，则需先分割共有房屋【答案】 B【知识点】改良行为【详解】共有物的管理一般应当由全体共有人共同进行，但有两项例外：保存行为和改良行为。

所谓改良行为是指在不改变共有物性质的前提下，对共有物进行的加工、修理等行为，以增加共有物的效用或价值。

改良行为只需要拥有共有份额一半以上的共有人同意即可进行。

本题中，铺木地板的行为正是改良行为，因此只需要一半以上的共有人同意即可。

而现在甲乙已占2／3的份额，因此可以为改良行为。

B项说法正确。

C项的错误在于，共有财产上，无论是按份共有还是共同共有，都不是对物的某一部分享有所有权，所有权及于物的整体，在分割之前不存在物的“应有部分”的说法。

2.小女孩甲（8岁）与小男孩乙（12岁）放学后常结伴回家。

一日，甲对乙讲：“听说我们回家途中的王家昨日买了一条狗，我们能否绕道回家？”乙答：“不要怕！被狗咬了我负责。

”后甲和乙路经王家同时被狗咬伤住院。

该案赔偿责任应如何承担？A.甲和乙明知有恶犬而不绕道，应自行承担责任B.乙自行承担责任，乙的家长和王家共同赔偿甲的损失C.王家承担全部赔偿责任D.甲、乙和王家均有过错，共同分担责任【答案】 C【知识点】动物侵权【详解】《民法通则》第127条：“饲养的动物造成他人损害的，动物饲养人或者管理人应当承担民事责任；由于受害人的过错造成损害的，动物饲养人或者管理人不承担民事责任；由于第三人的过错造成损害的，第三人应当承担民事责任。

河南省2003年普通高等学校选拔优秀专科毕业生进入本科阶段学习考试公共英语Part Ⅰ Vocabulary and Structure (1×30 points)Directions:There are 30 incomplete sentences in this part. For each sentence there are 4 choices marked A,B,C and D. Choose the one that best completes the sentence. Then mark the corresponding letter on the Answer Sheet with a single line through the center.1._______that the trade between the two countries reached its highest point.A. It was the 1990sB. That it was in the 1990sC. It was in the 1990sD. During the 1990s2. Mary said that Hemingway was her_______writer and that she had read nearly all of his novels.A. FamousB. popularC. CommonD. favorite3. She_______English since she was a child.A. LearningB. had learnedC. is learningD. has been learning4. Not until ten o’clock _______it was too late to return.A. they realizedB. they did realizeC. did they realizeD. realized they5. Once a decision is made，it must be_______ firmly.A. carried onB. carried outC. carried awayD. carried off6. _______born in Chicago，the writer is most famous for his stories about New York City.A. AlthoughB. SinceC. WhenD. As7. The pen I am writing my letter with is different from______.A. that oneB. oneC. the oneD. the ones8. Without his wise mother，he______such a successful scientist.A. would not becomeB. should not have becomeC. may not have becomeD. could not have become9. ______，we shall go out for a picnic on Sunday.A. Weather permitsB. Weather permittingC. With weather permitsD. With weather permitting10. The color______ from yellow through green to black.A. RangesB. constitutesC. ComposesD. consists11. Experiments ______that accurate measurements be made.A. ShowB. proveC. DemandD. head12. I tried to catch the ball but it was ______my reach.A. BeyondB. besidesC. in addition toD. as well as13. Those scientists were conducting an experiment and expected a good______ .A. EffectB. resultC. ConsequenceD. affect14. Under heavy gunfire，those cameramen risked their lives to give______battle field reports.A. word-for -wordB. face- to- faceC.down -to- earthD. on- the- spot15. I appreciate ______to your birthday party.A. to be invitedB. to have invitedC. having invitedD. being invited16. The rain was heavy and ______the house was damaged.A. ConsequentlyB. constantlyC. ConsistentlyD. continuously17. When it ______school work，the professor will treat his students equally.A. comes to evaluateB. comes to evaluatingC. will come to evaluateD. will come to evaluating18. _____, you will never convince him.A. However long you argueB. However you argue longC. How you argue longD. How long you argue19. ______new products have been successfully trial produced.A. A great dealB. A large amount ofC. A plenty ofD. A large number of20. He has made a discovery，______of great importance to the progress of science and technology.A. I think which isB. which I think isC. that I think isD. of which I think it is21. Smoking is so harmful to personal health that it kills people ______each year than automobile accidents.A. six more timesB. six times moreC. over six timesD. six times22. What they have done for us can’t be measured in ______of money.A. WayB. meansC. TermsD. place23. Go and get some water，______?A. don’t youB. shall youC. can’t youD. won’t you24. You must pack plenty of food for the journey，______，you’ll need warm clothes，so pack them too.A. on the wholeB. otherwiseC. HoweverD. likewise25. Meat ______easily in hot weather.A. turns badlyB. becomes badlyC. goes badD. changes worse26. I couldn’t find ______，and so I took this one.A. a large coat enoughB. a large enough coatC. an enough large coatD. a coat enough large27. What_____ would happen if he knew you felt that way?A. will you thinkB. do you thinkC. you thinkD. you would think28. It is _____impossible to find a good educational computer program in this city.A. BarelyB. merelyC. HardlyD. nearly29. _____him do this job by himself?A. Why not letB. Why not to letC. Why don’t letD. Why you not to let30. Almost _____of the population of this country is literate.A. Ninth tenthsB. nine tenthC. Nine tenthsD. ninth tenPart Ⅱ Cloze (1×20 points)Directions：In this section，there are 20 blanks in the following. For each blank there are four choices marked A，B，C and D. You should choose the right answer that best fits into the passage.Scientists used to explore 31 the surface of the ocean. Now they 32 below the surface，too. They want to know about the ocean water and the 33 and animal life 34 in the ocean.In 1934 the scientist William Beebe dived 3，000 feet below the surface in a hollow steel ball. In 1935 Auguste Picard dived 10，330 feet. In 1960 his son Jean dived to a 35 of 35，800 feet.All these early dives were deep. But the divers could not stay down for very long. They had to 36 the surface after a few seconds. Scientists needed to stay down longer to study life below the surface. 37 ，they succeeded. Cousteau，a Frenchman，was able to 38 down to a depth of 36 feet for one month and to a depth of 90 feet for a week.Now scientists are developing even 39 equipment. With this new equipment，men can stay 40 the surface for days or 41 weeks. In 1962 Consteau 42 a research station 35 feet below the surface. Then in 1964 he set up another station on the ocean floor of the Red Sea.This was the first undersea station to operate 43 help from the surface.Many countries are now studying undersea 44 . The Soviet Union has an undersea laboratory in the Crimean Sea. The United States has a laboratory 50 feet 45 on the ocean floor 46 the Virgin Islands. In 1970 five men lived there for two weeks. Then a 47 of five women scientists stayed in the laboratory. 48 came other teams of men. All were there to explore the ocean depths and 49 plans for the use of its resources. Scientists hope to find enough 50 ，vegetable，and animal wealth there to provide food for the whole world.31. A. in B. to C. On D. under32. A. explore B. are exploring C. explored D. will explore33. A. plant B. situation C.surroundings D. circumstance34. A. deeply B. normally C. commonly D. deep35. A. depth B. range C. length D. rate36. A. come to B. come over C. come across D. come back up to37. A. However B. Gradually C. moreover D. Though38. A. stay B. remain C. keep D. take39. A. good B. well C. better D. more40. A. below B. on C. in D. to41. A. even B. more C. several D. some42. A. put up B. came up C. made up D. set up43. A. with B. under C. for D. without44. A. living B. situation C. structure D. environment45. A. below B. down C. under D. deep46. A. away B. on C. off D. to47. A. group B. gang C. crowd D. team48. A. after B. next C. later D. then49. A. make B. to make C. making D. made50. A. mineral B. mine C. minefield D. mine layerPart Ⅲ Reading Comprehension(3×20 points)Directions: There are four passages in this part. Each passage is followed by some questions orunfinished statements. For each of them there are four choices marked A, B, C and D, you should decide the best choice.Passage 1With a tremendous roar from its rocket engine，the satellite is sent up into the sky. Minutes later，at an altitude of 300 miles，this tiny electronic moon begins to orbit about the earth. Its radio begins to transmit a staggering amount of information about the satellite’s orbital path，the amount of radiation it detects，and the presence of meteorites. Information of all kinds races back to the earth. No human being could possibly copy down all these facts，much less remember and organize them. But an electronic computer can.The marvel of the machine age，the electronic computer has been in use only since 1946. It can do simple computations—add，subtract，multiply，and divide—with lightning speed and perfect accuracy. It can multiply two 10digit numbers in 1／1，000 second，a problem that would take an average person five minutes to do with pencil and paper. Some computers can work 500，000 times faster than any person can.Once it is given a program，that is，a carefully worked out set of instructions devised by a technician trained in computer language，a computer can gather a wide range of information for many purposes. For the scientist it can get information from outer space or from the depths of the ocean. In business and industry the computer prepares factory inventories，keeps track of sales trends and production needs，mails dividend checks，and makes out company payrolls. It can keep bank accounts up to date and make out electric bills. If you are planning a trip by plane，the computer will find out what route to take and what space is available.51. Why does the author regard the electronic computer as the marvel of the machine age?A. Because electronic computers are rare.B. Because people know little about electronic computers.C. Because electronic computers can do much more kinds of work that human beings can’t.D. Because electronic computers have been widely suspected.52. Electronic computers were given the name in the beginning just for the simple reason that_______ .A. they could do computationsB. they could work much faster than human beingsC. they looked like an abacusD. they could remember data quickly53. According to the passage，which of the following is NOT true?A. Computers began to be used in 1946.B. Computers can add，subtract，multiply and divide.C. Computers were widely used during World War Ⅱ.D. No human being can work as fast as a computer.54. A computer can calculate_______.A. with lightning speedB. accuratelyC. with a speed 500，000 times faster than a personD. all above55. In the first sentence of last paragraph，“program” would probably mean_______.A. a performanceB. a showC. a worked out set of instructionsD. a TV playPassage 2On the old time farm in America there were chickens and turkeys. There were also cows，pigs，and other livestock. But there were very few machines. Most of the work was done by the entire farm family with the h elp of a “hired” man. Sometimes extra labourers were needed in busy seasons. Horses provided 79 percent of the power used，human labor 15 percent，and machines only 6 percent.Today all that has changed. On many modern farms machines now supply 96 percent of the power，human labor 3 percent，and horses 1 percent. Modern farms are enterprising businesses which keep only the livestock that can pay its way. The children go to school by bus every morning，the parents work on the farm or in the house，and hired help is seldom needed. Their work has been replaced by a whole army of farm machines.Farmers in the machine age also use the new fertilizers，new sprays，new feeds，new hybrid seeds，and other helps developed by farm sciences. As a result the farmers are able to produce more food with less labour. This means fewer but larger farms and fewer but moreprosperous farmers.56. In old days，most of the work on a farm was done by_______.A. all the farm familyB. livestockC. farm machinesD. both A and B57. From the first paragraph，we learn that in old days the most important farming power was____.A. LivestockB. farmersC. MachinesD. extra laborers58. On today’s farms，the chief reason why livestock is still raised would probably be____.A. that farmers conventions are difficult to be given upB. that farmers want to gain more profitC. that farmers have to do soD. that farmers work has been replaced by machines59. On modern farms，farmers need mostly all the followings EXCEPT_______.A. farm scienceB. seedsC. FertilizersD. hard work60. In the last sentence of Paragraph 3，“fewer but larger farms and fewer but more prosperous farmers” means_______.A. hired help is seldom neededB. productivity on the farms has been raised greatlyC. productivity on the farms has fallen sharplyD. more food is never neededPassage 3City traffic jam—one of the least wanted effects of the motor vehicle—is something with which we’re all familiar and for which most of us have an answer. But which solution is best?Some people suggest for better roads，others for cars to be banned(禁止) from city centers and yet others say better public transport would attract drivers from their lonely and boring journeys.But the important question is what natural power creates a big city center. We are，after all，in an age of electronic communication; our big shopping areas have moved out of city centers，and our living areas moved out of them long ago.Yet some force causes offices and service industries related to them to gather in London or New York or Tokyo. This suggests that far from the problems of a crowded environment forcing companies and people to move out，there is a critical (重大的) size beyond which more companies are attracted to move in. Nobody seems to know why，yet the answer is important to the way traffic jam is dealt with.61. Which of the following is NOT mentioned in the passage as the cause of the traffic problem?A. The poor public transport.B. The over concentration of shopping centers.C. The great number of cars in the city centers.D. The bad road conditions.62. According to the passage，offices and their associated service industries move to big cities because of_______.A. the convenience of communicationB. the gathering of companiesC. some unknown forceD. the convenience of shopping63. The word “This”(Line 2，Para.4) refers to_______.A. some forceB. traffic jamC. the force that causes offices to move in or outD. the fact that companies gather in big cities64. This passage is most likely taken from_______.A. a novelB. a TV playC. an instructionD. a news report65. The topic of this passage would probably be_______.A. Best Answer to Traffic ProblemB. The Banning of Cars in the City CenterC. The Formation of City CenterD. Searching for Ways to Solve Traffic ProblemPassage 4Mrs. Cox teaches English in a large high school located in the inner area of a big city on the West Coast. Ever since she was a young girl，Mrs. Cox had wanted to become a teacher. She has taught eight years now and hasn’t changed her mind.After she graduated from high school，Mrs. Cox went on to college. Four years later，she received her bachelor’s degree (B.A.) in English and her teaching certificate. Then she was qualified to teach in the secondary schools of her state. In the summers，Mrs. Cox takes more classes. Someday she hopes to get a master’s degree (M.A.).With an M.A.，she will receive a higher salary.The school day at Mrs. Cox’s high school，like that in many high schools in the United States，is divided into six periods of one hour each. Mrs. Cox must teach five of these six periods. During her free period，which for her is from 2 to 3 p.m.，Mrs. Cox must meet with parents，order supplies，make out examinations，check assignments，and take care of many other things. In short，her free period isn’t really free at all. Mrs. Cox works steadily from the time she arrives at school in the morning until the time she leaves for home late in the afternoon.66. Mrs. Cox wants to be a teacher because_______.A. she likes teachingB. she is a young girlC. she has many problems to deal withD. she doesn’t mind what she is doing67. From paragraph two，we can infer_______.A. Mrs. Cox has received a teaching certificateB. Mrs. Cox likes teaching very muchC. Mrs. Cox takes more classesD. Mrs. Cox is a qualified teacher68. She will receive a higher salary if_______.A. she gets a master’s degreeB. she takes more classesC. she has studies normal teachingD. she gets a bachelor’s degree69. According to the passage, all the followings are true EXCEPT_______.A. she graduated from high schoolB. she graduated from collegeC. she has got her bachelor’s degreeD. she teaches five periods for a school day70. The best title for the passage would probably be_______.A. A Typical School DayB. Teacher Mrs. CoxC. Mrs. Cox Likes TeachingD. Mrs. Cox Has Got Her Teaching CertificatePart Ⅳ Translation (2.5×8 points)Section ADirections：There are 4 sentences in this section. You are required to translate them from Chinese into English.71.这口大钟大约有三个人那么高。

2003年12月大学英语六级(CET-6)真题试卷及答案详解试卷一Part I Listening Comprehension (20 minutes)Section ADirections: In this section, you will hear 10 short conversations. At the end of each conversation, a question will be asked about what was said. Both theconversation and the question will be spoken only once. After each question there will be a pause. During the pause, you must read the four choicesmarked A), B), C) and D), and decide which is the best answer. Then markthe corresponding letter on the Answer Sheet with a single line through thecentre.Example:You will hear:You will read:A) 2 hours.B) 3 hours.C) 4 hours.D) 5 hours.From the conversation, we know that the two were talking about some work they will start at 9 o’clock in the morning and have to finish at 2 in the afternoon. Therefore, D) “5 hours” is the correct answer. You should choose [D] on the Answer Sheet and mark it with a single line through the centre.Sample Answer [A] [B] [C] [D]1. A) She knows where Martha has gone.B) Martha will go to the concert by herself.C) It is quite possible for the man to find Martha.D) The man is going to meet Martha at the concert.2. A) The air pollution is caused by the development of industry.B) The city was poor because there wasn’t much industry then.C) The woman’s exaggerating the seriousness of the pollution.D) He might move to another city very soon.3. A) The man should work harder to improve his grades.B) The man will benefit from the effort he’s put in.C) It serves the man right to get a poor grade.D) It was unfair of the teacher to give the man a C.4. A) She can make a reservation at the restaurant.B) The man should decide where to eat.C) She already has plans for Saturday night.D) The man should ask his brother for suggestions.5. A) The man deserved the award.B) The woman helped the man succeed.C) The man is thankful to the woman for her assistance.D) The woman worked hard and was given an award.6. A) V oluntary work can help the man establish connections with the community.B) The man’s voluntary work has left him little room in his schedule.C) V oluntary work with the environment council requires a time commitment.D) A lot of people have signed up for voluntary work with the environment council.7. A) The patient must receive treatment regularly.B) The patient can’t leave the hospital until the bleeding stops.C) The patient’s husband can attend to the business in her place.D) The patient must take a good rest and forget about her business.8. A) Alice does not know much about electronics.B) Alice is unlikely to find a job anywhere.C) Alice is not interested in anything but electronics.D) Alice is likely to find a job in an electronics company.9. A) Jimmy is going to set out tonight.B) Jimmy has not decided on his journey.C) There is no need to have a farewell dinner.D) They may have a dinner when Jimmy’s back.10. A) The woman had been planning for the conference.B) The woman called the man but the line was busy.C) The woman didn’t come back until midnight.D) The woman had guests all evening.Section BDirections: In this section, you will hear 3 short passages. At the end of each passage, you will hear some questions. Both the passage and the questions will bespoken only once. After you hear a question, you must choose the bestanswer from the four choices marked A), B), C) and D). Then mark thecorresponding letter on the Answer Sheet with a single line through thecentre.Passage OneQuestions 11 to 13 are based on the passage you have just heard.11. A) They are delighted because they can enjoy the scenery while driving.B) They are frightened because traffic accidents are frequent.C) They are irritated because the bridge is jammed with cars.D) They are pleased because it saves them much time.12. A) They don’t have their own cars to drive to work.B) Many of them are romantic by temperament.C) Most of them enjoy the drinks on the boat.D) They tend to be more friendly to each other.13. A) Many welcome the idea of having more bars on board.B) Many prefer the ferry to maintain its present speed.C) Some suggest improving the design of the deck.D) Some object to using larger luxury boats.Passage TwoQuestions 14 to 16 are based on the passage you have just heard.14. A) Coca Cola.B) Sausage.C) Milk.D) Fried chicken.15. A) He has had thirteen decayed teeth.B) He doesn’t have a single decayed tooth.C) He has fewer decayed teeth than other people of his age.D) He never had a single tooth pulled out before he was fifty.16. A) Brush your teeth right before you go to bed in the evening.B) Have as few of your teeth pulled out as possible.C) Have your teeth X-rayed at regular intervals.D) Clean your teeth shortly after eating.Passage ThreeQuestions 17 to 20 are based on the passage you have just heard.17. A) A visit to a prison.B) The influence of his father.C) A talk with some miserable slaves.D) His experience in the war between France and Austria.18. A) He sent surgeons to serve in the army.B) He provided soldiers with medical supplies.C) He recruited volunteers to care for the wounded.D) He helped to free the prisoners of war.19. A) All men are created equal.B) The wounded and dying should be treated for free.C) A wounded soldier should surrender before he receives any medical treatment.D) A suffering person is entitled to help regardless of race, religion or politicalbeliefs.20. A) To honor Swiss heroes who died in the war.B) To show Switzerland was neutral.C) To pay tribute to Switzerland.D) To show gratitude to the Swiss government for its financial support.Part II Reading Comprehension (35 minutes)Directions: There are four passages in this part. Each passage is followed by some questions or unfinished statements. For each of them there are four choicesmarked A), B), C) and D). You should decide on the best choice and markthe corresponding letter on the Answer Sheet with a single line through thecentre.Passage OneQuestions 21 to 25 are based on the following passage.For years, doctors advised their patients that the only thing taking multivitaminsdoes is give them extensive urine (尿). After all, true vitamin deficiencies are practically unheard of in industrialized countries. Now it seems those doctors may have been wrong. The results of a growing number of studies suggest that even a modest vitamin shortfall can be harmful to your health. Although proof of the benefits of multivitamins is still far from certain, the few dollars you spend on them is probably a good investment.Or at least that’s the argument put forward in the New England Journal of Medicine. Ideally, say Dr. Walter Willett and Dr. Meir Stampfer of Harvard, all vitamin supplements would be evaluated in scientifically rigorous clinical trials.But those studies can take a long time and often raise more questions than they answer. At some point, while researchers work on figuring out where the truth lies, it just makes sense to say the potential benefit outweighs the cost.The best evidence to date concerns folate, one of the B vitamins. It’s been proved to limit the number of defects in embryos (胚胎), and a recent trial found that folate in combination with vitamin B 12 and a form of B6 also decreases the re-blockage of arteries after surgical repair.The news on vitamin E has been more mixed. Healthy folks who take 400 international units daily for at least two years appear somewhat less likely to develop heart disease. But when doctors give vitamin E to patients who already have he art disease, the vitamin doesn’t seem to help. It may turn out that vitamin E plays a role in prevention but cannot undo serious damage.Despite vitamin C’s great popularity, consuming large amounts of it still has not been positively linked to any great benefit. The body quickly becomes saturated with C and simply excretes (排泄) any excess.The multivitamins question boils down to this: Do you need to wait until all the evidence is in before you take them, or are you willing to accept that there’s enough evidence that they don’t hurt and could help?If the latter, there’s no need to go to extremes and buy the biggest horse pills or the most expensive bottles. Large doses can cause trouble, including excessive bleeding and nervous system problems.Multivitamins are no substitute for exercise and a balanced diet, of course.As long as you understand that any potential benefit is modest and subject to further refinement, taking a daily multivitamin makes a lot of sense.21. At one time doctors discouraged taking multivitamins because they believed thatmultivitamins ________.A) could not easily be absorbed by the human bodyB) were potentially harmful to people’s healthC) were too expensive for daily consumptionD) could not provide any cure for vitamin deficiencies22. According to the author, clinical trials of vitamin supplements ________.A) often result in misleading conclusionsB) take time and will not produce conclusive resultsC) should be conducted by scientists on a larger scaleD) appear to be a sheer waste of time and resources23. It has been found that vitamin E ________.A) should be taken by patients regularly and persistentlyB) can effectively reduce the recurrence of heart diseaseC) has a preventive but not curative effect on heart diseaseD) should be given to patients with heart disease as early as possible24. It can be seen that large doses of multivitamins ________.A) may bring about serious side effectsB) may help prevent excessive bleedingC) are likely to induce the blockage of arteriesD) are advisable for those with vitamin deficiencies25. The author concludes the passage with the advice that ________.A) the benefit of daily multivitamin intake outweighs that of exercise and abalanced dietB) it’s risky to take multivitamins without knowing their specific functionC) the potential benefit of multivitamins can never be overestimatedD) it’s reasonable to take a rational dose of multivitamins dailyPassage TwoQuestions 26 to 30 are based on the following passage.Some futurologists have assumed that the vast upsurge (剧增) of women in the workforce may portend a rejection of marriage. Many women, according to this hypothesis, would rather work than marry. The converse (反面) of this concern is that the prospects of becoming a multi-paycheck household could encourage marriages. In the past, only the earnings and financial prospects of the man counted in the marriage decision. Now, however, the earning ability of a woman can make her more attractive as a marriage partner. Data show that economic downturns tend to postpone marriage because the parties cannot afford to establish a family or are concerned about rainy days ahead. As the economy rebounds, the number of marriages also rises.Coincident with the increase in women working outside the home is the increase in divorce rates. Yet, it may be wrong to jump to any simple cause-and-effect conclusions. The impact of a wife’s work on divorce is no less cloudy than its impact on marriage decisions. The realization that she can be a good provider may increase the chances thata working wife will choose divorce over an unsatisfactory marriage. But the reverse is equally plausible. Tensions grounded in financial problems often play a key role in ending a marriage. Given high unemployment, inflationary problems, and slow growth in real earnings, a working wife can increase household income and relieve some of these pressing financial burdens. By raising a family’s standard of living, a working wife may strengthen her family’s financial and emotional stability.Psychological factors also should be considered. For example, a wife blocked from a career outside the home may feel caged in the house. She may view her only choice as seeking a divorce.On the other hand, if she can find fulfillment through work outside the home, work and marriage can go together to create a stronger and more stable union.Also, a major part of women’s inequality in marriage has been due to the fact that, in most cases, men have remained the main breadwinners. With higher earning capacity and status occupations outside of the home comes the capacity to exercise power within the family. A working wife may rob a husband of being the master of the house. Depending upon how the couple reacts to these new conditions, it could create a stronger equal partnership or it could create new insecurities.26. The word “portend” (Line 2, Para. 1) is closest in meaning to “________”.A) defyB) signalC) suffer fromD) result from27. It is said in the passage that when the economy slides, ________.A) men would choose working women as their marriage partnersB) more women would get married to seek financial securityC) even working women would worry about their marriagesD) more people would prefer to remain single for the time being28. If women find fulfillment through work outside the home, ________.A) they are more likely to dominate their marriage partnersB) their husbands are expected to do more houseworkC) their marriage ties can be strengthenedD) they tend to put their career before marriage29. One reason why women with no career may seek a divorce is that ________.A) they feel that they have been robbed of their freedomB) they are afraid of being bossed around by their husbandsC) they feel that their partners fail to live up to their expectationsD) they tend to suspect their husbands’ loyalty to their marriage30. Which of the following statements can best summarize the author’s view in thepassage?A) The stability of marriage and the divorce rate may reflect the economic situationof the country.B) Even when economically independent, most women have to struggle for realequality in marriage.C) In order to secure their marriage women should work outside the home andremain independent.D) The impact of the growing female workforce on marriage varies from case tocase.Passage ThreeQuestions 31 to 35 are based on the following passage.For most thinkers since the Greek philosophers, it was self-evident that the re is something called human nature, something that constitutes the essence of man. There were various views about what constitutes it, but there was agreement that such an essence exists—that is to say, that there is something by virtue of which man is man. Thus man was defined as a rational being, as a social animal, an animal that can make tools, or a symbol-making animal.More recently, this traditional view has begun to be questioned. One reason for this change was the increasing emphasis given to the historical approach to man. An examination of the history of humanity suggested that man in our epoch is so different from man in previous times that it seemed unrealistic to assume that men in every age have had in common something t hat can be called “human nature.” The historical approach was reinforced, particularly in the United States, by studies in the field of cultural anthropology (人类学). The study of primitive peoples has discovered such a diversity of customs, values, feelings, and thoughts that many anthropologists arrived at the concept that man is born as a blank sheet of paper on which each culture writes its text. Another factor contributing to the tendency to deny the assumption of a fixed human nature was that the concept has so often been abused as a shield behind which the most inhuman acts are committed. In the name of human nature, for example, Aristotle and most thinkers up to the eighteenth century defended slavery. Or in order to prove the rationality and necessity of the capitalist form of society, scholars have tried to make a case for acquisitiveness, competitiveness, and selfishness as innate(天生的) human traits. Popularly, one refers cynically to “human nature” in accepting the inevitability of such undesirable human behavior as greed, murder, cheating and lying.Another reason for skepticism about the concept of human nature probably lies in the influence of evolutionary thinking. Once man came to be seen as developing in the process of evolution, the idea of a substance which is contained in his essence seemed untenable. Yet I believe it is precisely from an evolutionary standpoint that we canexpect new insight into the problem of the nature of man.31. The traditional view of “human nature” was strongly challe nged by ________.A) the emergence of the evolutionary theoryB) the historical approach to manC) new insight into human behaviorD) the philosophical analysis of slavery32. According to the passage, anthropologists believe that human beings ________.A) have some traits in commonB) are born with diverse culturesC) are born without a fixed natureD) change their characters as they grow up33. The author mentioned Aristotle, a great ancient thinker, in order to ________.A) emphasize that he contributed a lot to defining the concept of “human nature”B) show that the concept of “human nature” was used to justify social evilsC) prove that he had a profound influence on the concept of “human nature”D) support the idea that some human traits are acquired34. The word “untenable” (Line 3) in the last paragraph of the passage most probablymeans ________.A) invaluableB) imaginableC) changeableD) indefensible35. Most philosophers believed that human nature ________.A) is the quality distinguishing man from other animalsB) consists of competitiveness and selfishnessC) is something partly innate and partly acquiredD) consists of rationality and undesirable behaviorPassage FourQuestions 36 to 40 are based on the following passage.Richard Satava, program manager for advanced medical technologies, has been a driving force in bringing virtual reality to medicine, where computers create a “virtual” or simulated environment for surgeons and other medical practitioners (从业者).“With virtu al reality we’ll be able to put a surgeon in every trench,” said Satava. He envisaged a time when soldiers who are wounded fighting overseas are put in mobile surgical units equipped with computers.The computers would transmit images of the soldiers to surgeons back in the U.S. The surgeons would look at the soldier through virtual reality helmets (头盔) that contain a small screen displaying the image of the wound. The doctors would guide robotic instruments in the battlefield mobile surgical unit that operate on the soldier.Although Satava’s vision may be years away from standard operating procedure, scientists are progressing toward virtual reality surgery. Engineers at an international organization in California are developing a tele-operating device. As surgeons watch a three-dimensional image of the surgery, they move instruments that are connected to a computer, which passes their movements to robotic instruments that perform the surgery. The computer provides feedback to the surgeon on force, textures, and sound.These technological wonders may not yet be part of the community hospital setting but increasingly some of the machinery is finding its way into civilian medicine. At Wayne State University Medical School, surgeon Lucia Zamorano takes images of the brain from computerized scans and uses a computer program to produce a 3-D image. She can then maneuver the 3-D image on the computer screen to map the shortest, least invasive surgical path to the tumor (肿瘤). Zamorano is also using technology that attaches a probe to surgical instruments so that she can track their positions. While cutting away a tumor deep in the brain, she watches the movement of her surgical tools in a computer graphics image of the patient’s brain taken before surgery.During these procedures—operations that are done through small cuts in the body in which a miniature camera and surgical tools are maneuvered—surgeons are wearing 3-D glasses for a better view. And they are commanding robot surgeons to cut away tissue more accurately than human surgeons can.Satava says, “We are in the midst of a fundamental change in the field of medicine.”36. According to Richard Satava, the application of virtual reality to medicine________.A) will enable surgeons to be physically present on every battlefieldB) can raise the spirits of soldiers wounded on the battlefieldC) will greatly improve medical conditions on the battlefieldD) can shorten the time for operations on soldiers wounded on the battlefield37. Richard Satava has visions of ________.A) using a remote-control technique to treat wounded soldiers fighting overseasB) wounded soldiers being saved by doctors wearing virtual reality helmets on thebattlefieldC) wounded soldiers being operated on by specially trained surgeonsD) setting up mobile surgical units overseas38. How is virtual reality surgery performed?A) It is performed by a computer-designed high precision device.B) Surgeons wear virtual reality helmets to receive feedback provided by acomputer.C) Surgeons move robotic instruments by means of a computer linked to them.D) A 3-D image records the movements of the surgeons during the operation.39. During virtual reality operations, the surgeon can have a better view of the cuts inthe body because ________.A) he is looking at the cuts on a computer screenB) the cuts can be examined from different anglesC) the cuts have been highly magnifiedD) he is wearing 3-D glasses40. Virtual reality operations are an improvement on conventional surgery in that they________.A) cause less pain to the woundedB) allow the patient to recover more quicklyC) will make human surgeons’ work less tediousD) are done by robot surgeons with greater precisionPart III Vocabulary (20 minutes)Directions: There are 30 incomplete sentences in this part. For each sentence there are four choices marked A), B), C) and D). Choose the ONE that bestcompletes the sentence. Then mark the corresponding letter on the AnswerSheet with a single line through the centre.41. He suggested that we put the scheme into effect, for it is quite ________.A) probableB) sustainableC) feasibleD) eligible42. This book is about how these basic beliefs and values affect important ________ ofAmerican life.A) facetsB) formatsC) formulasD) fashions43. It is one thing to locate oil, but it is quite another to ________ and transport it to theindustrial centers.A) permeateB) extractC) distinguishD) concentrate44. Students are expected to be quiet and ________ in an Asian classroom.A) obedientB) overwhelmingC) skepticalD) subsidiary45. Our reporter has just called to say that rescue teams will ________ to bring out thetrapped miners.A) effectB) affectC) conceiveD) endeavour46. The Spanish team, who are not in superb form, will be doing their best next week to________ themselves on the German team for last year’s defeat.A) remedyB) reproachC) reviveD) revenge47. Creating so much confusion, Mason realized he had better make ________ what hewas trying to tell the audience.A) exclusiveB) explicitC) objectiveD) obscure48. One of the examination questions ________ me completely and I couldn’t answer it..A) baffledB) mingledC) provokedD) diverted49. The vision of that big black car hitting the sidewalk a few feet from us will never be________ from my memory.A) ejectedB) escapedC) erasedD) omitted50. At present, it is not possible to confirm or to refute the suggestion that there is acausal relationship between the amount of fat we eat and the ________ of heart attacks.A) incidenceB) impetusC) ruptureD) emergence51. There are many who believe that the use of force ________ political ends can neverbe justified.A) in search ofB) in pursuit ofC) in view ofD) in light of52. Sometimes the bank manager himself is asked to ________ cheques if his clerks arenot sure about them.A) creditB) assureC) certifyD) access53. It is believed that the authorities are thinking of ________ new taxes to raise extrarevenue.A) impairingB) imposingC) invadingD) integrating54. When she heard the bad news, her eyes ________ with tears as she struggled tocontrol her emotions.A) sparkledB) twinkledC) radiatedD) glittered55. There are occasions when giving a gift ________ spoken communication, since themessage it offers can cut through barriers of language and cultural diversity.A) overtakesB) nourishesC) surpassesD) enforces56. In order to keep the line moving, customers with lengthy ________ are required todo their banking inside.A) transitB) transactionsC) turnoverD) tempos57. President Wilson attempted to ________ between the powers to end the war, butneither side was prepared to give in.A) segregateB) whirlC) compromiseD) mediate58. The police have installed cameras at dangerous road ________ to film those whodrive through red traffic lights.A) trenchesB) utilitiesC) pavementsD) junctions59. It is reported that thirty people were killed in a ________ on the railway yesterday.A) collisionB) collaborationC) corrosionD) confrontation60. Since a circle has no beginning or end, the wedding ring is accepted as a symbol of________ love.A) successiveB) consecutiveC) eternalD) insistent61. Executives of the company enjoyed an ________ lifestyle of free gifts, fine winesand high salaries.A) exquisiteB) extravagantC) exoticD) eccentric62. If you want to get into that tunnel, you first have to ________ away all the rocks.A) haulB) repelC) disposeD) snatch63. Some crops are relatively high yielders and could be planted in preference to othersto ________ the food supply.A) enhanceB) curbC) disruptD) heighten64. Astronomers at the University of California discovered one of the most distant________.A) paradoxesB) paradisesC) galaxiesD) shuttles65. Many great scientists ________ their success to hard work.A) portrayB) ascribeC) impartD) acknowledge66. The sign set up by the road ________ drivers to a sharp turn.A) alertsB) refreshesC) pleadsD) diverts67. The doctors don’t ________ that the patient will live much longer.A) monitorB) manifestC) articulateD) anticipate68. Call your doctor for advice if the ________ persist for more than a few days.A) responsesB) signalsC) symptomsD) reflections69. We find it impossible to ________ with the latest safety regulations.A) accordB) unifyC) obeyD) comply70. Professor Smith and Professor Brown will ________ in presenting the series oflectures on American literature.A) alterB) alternateC) substituteD) exchange试卷二Part IV Error Correction (15 minutes)Directions: This part consists of a short passage. In this passage, there are altogether10 mistakes, one in each numbered line. You may have to change a word,。

2003 年全国硕士研究生入学统一考试数学三试题一、填空题：本题共6 小题，每小题 4 分，共 24 分，请将答案写在答题纸指定位置上 .1 若x 0,(1) 设 f ( x)x cos ,其导函数在 x0 处连续，则.0, x若x 0,的取值范围是(2) 已知曲线 yx 3 3a 2 x b 与 x 轴相切，则 b 2 可以通过 a 表示为 b 2.(3) 设 a0 ， f (x)g( x)a,若 0 x 1,0,其他， 而 D 表示全平面，则If ( x) g( y x)dxdy =.D(4) 设 n 维向量( a,0, ,0, a) T ,a0 ； E 为 n 阶单位矩阵，矩阵 AET ，B E1T，其中 A 的逆矩阵为 B ，则 a .a(5) 设随机变量 X 和 Y 的相关系数为 0.9, 若Z X0.4 ，则 Y 与 Z 的相关系数为.(6) 设总体 X 服从参数为2 的指数分布， X 1, X 2 , , X n 为来自总体 X 的简单随机样本，则当 n时， Y n1 n X i2 依概率收敛于 .n i 1二、选择题：本题共 6 小题，每小题 4 分，共 24 分，下列每小题给出的四个选项中，只有一项符合题目要求，把所选项前的字母填在题后的括号内 .(1) 设 f ( x) 为不恒等于零的奇函数，且f (0) 存在，则函数 g( x)f ( x) ()x(A) 在 x 0 处左极限不存在 . (B) 有跳跃间断点 x 0 .(C) 在 x 0 处右极限不存在 .(D) 有可去间断点 x0 .(2) 设可微函数 f ( x, y) 在点 (x 0 , y 0 ) 取得极小值，则下列结论正确的是( )(A) f (x 0 , y) 在 y y 0 处的导数等于零 . (B) f (x 0 , y) 在 y y 0 处的导数大于零 .(C)f ( x 0 , y) 在 y y 0 处的导数小于零 .(D)f (x 0 , y) 在 yy 0 处的导数不存在 .(3) 设 p na na n ， q na na n， n 1,2,，则下列命题正确的是()(A) 若a n 条件收敛，则p n 与q n 都收敛 .n 1n 1n 1(B) 若a n 绝对收敛，则p n 与q n 都收敛 .n 1n 1n 1a b (C) 若a n 条件收敛，则p n 与q n 敛散性都不定 .n 1n 1n 1(D) 若a n 绝对收敛，则p n 与q n 敛散性都不定 .n 1n 1n 1a b b(4) 设三阶矩阵 Ab ab ，若 A 的伴随矩阵的秩为1，则必有 ()b b a(A)a b 或 a 2b0 . (B) a b 或 a 2b 0 . (C) a b 且 a 2b0 .(D)a b 且 a 2b 0 .(5) 设1 ,2 , , s 均为 n 维向量，下列结论不正确的是( )(A) 若对于任意一组不全为零的数k 1, k 2 , , k s ，都有 k 11k2 2k s s 0 ，则1 ,2 , , s 线性无关 .(B) 若1, 2,,s 线性相关，则对于任意一组不全为零的数k 1 , k 2 , , k s ，都有k1 1k2 2k s s 0.(C) 1 ,2 ,,s 线性无关的充分必要条件是此向量组的秩为s.(D)1 ,2 ,, s 线性无关的必要条件是其中任意两个向量线性无关.(6) 将一枚硬币独立地掷两次，引进事件： A 1 ={ 掷第一次出现正面} ， A 2 ={ 掷第二次出现正面 } ， A 3 ={ 正、反面各出现一次 } ， A 4 ={ 正面出现两次 } ，则事件 ( )(A)A 1, A 2 , A 3 相互独立 . (B) A 2 , A 3 , A 4 相互独立 .(C)A 1 , A 2 , A 3 两两独立 .(D) A 2 , A 3 , A 4 两两独立 .三 、(本题满分 8 分)设 f ( x)1 1 1 , x [ 1 ,1) ，试补充定义 f (1)使得 f ( x) 在 [ 1,1] 上连xsin x(1 x) 22 续.四 、 (本题满分 8 分 )设 f (u, v) 具有二阶连续偏导数， 且满足2 f2 f1，又g( x, y) f [ xy,1(x 2 y 2 )] ,u 2v 222g2g求x 2y 2 .五 、 (本题满分 8 分 )计算二重积分Ie ( x 2 y 2 ) sin( x 2y 2 )dxdy.D其中积分区域 D{( x, y) x 2y 2}.六、 (本题满分 9 分 )求幂级数 1( 1) n x 2n ( x 1) 的和函数 f (x) 及其极值 .n 12n七、 (本题满分 9 分 )设 F ( x) f (x) g( x) , 其中函数 f (x), g (x) 在 ( ,) 内满足以下条件：f ( x) g( x) ，g ( x) f ( x) ，且 f (0)0 , f ( x)g (x)2e x .(1) 求 F ( x) 所满足的一阶微分方程；(2) 求出 F ( x) 的表达式 . 八、 (本题满分 8 分 )设函数f ( x) 在 [0， 3]上连续，在 (0， 3)内可导，且 f (0) f (1) f (2) 3, f (3)1 .试证：必存在(0,3) ，使 f ( ) 0.九、 (本题满分 13 分 )已知齐次线性方程组(a1 a1 x1 a1 x1a1 x1b)x1( a2a2 x2a2 x2a2 x2a3 x3a n x n0,b) x2a3 x3a n x n0,(a3b) x3a n x n0,a3 x3(a n b) x n0,n其中a i 0. 试讨论a1, a2,,a n和b满足何种关系时，i 1(1)方程组仅有零解；(2)方程组有非零解 . 在有非零解时，求此方程组的一个基础解系.十、 (本题满分13 分 )设二次型f (x1,x2,x3)XT222222(b0) ，AX ax1x2x3bx1x3中二次型的矩阵 A 的特征值之和为1，特征值之积为 -12.(1)求 a, b 的值；(2) 利用正交变换将二次型 f 化为标准形，并写出所用的正交变换和对应的正交矩阵.十一、 (本题满分13分)设随机变量 X 的概率密度为1, 若x [1,8],f ( x)3x23其他 ;0,F(X ) 是 X 的分布函数.求随机变量 Y F (X ) 的分布函数.十二、 (本题满分13 分 )设随机变量X 与 Y 独立，其中X 的概率分布为X ~120.3，0.7而 Y 的概率密度为 f ( y) ，求随机变量 U X Y 的概率密度 g(u) .2003 年全国硕士研究生入学统一考试数学三试题解析一、填空题(1) 【答案】2【分析】无穷小量乘以有界函数的极限仍是无穷小量.【详解】是参变量， x 是函数f(x) 的自变量f ( x) f (0)x cos1lim x 1 cos1f(0)lim lim x0 ，x 0x0x0x x 0x要使该式成立，必须lim x10 ，即 1 .x 0当 x(,0)(0,) 时，f( x)x1 cos1x 2 sin1x x要使 f ( x)0 在x0 处连续，由函数连续的定义应有lim f( x)lim x1 cos 1x 2 sin1f (x) 0x0x 0x x由该式得出 2 .所以f( x) 在x0处右连续的充要条件是 2 ．(2)【答案】 4a 6【详解】设曲线与x 轴相切的切点为( x0,0) ，则yx x00 .而 y 3x23a 2，有 3x023a2又在此点 y 坐标为0(切点在x轴上)，于是有x033a2 x0 b 0，故b x033a2 x0x0 ( x023a2 ) ，所以22(322)224446.b x0x0aa a a(3)【答案】 a2【详解】本题积分区域为全平面，但只有当0 x 1,0 y x 1 时，被积函数才不为零，则二重积分只需在积分区域与被积函数不为零的区域的公共部分商积分即可，因此实际上只需在满足此不等式的区域内积分即可．If ( x) g( y=2dxdy= a21x 1212 dx dy a[( x 1) x]dx ax)dxdy a0x0 D0x 10y x 1(4) 【答案】 -1【详解】这里T为 n 阶矩阵，而T2a 2 为数，直接通过 AB E 进行计算并注意利用乘法的结合律即可．由题设，有AB (ET)(E 1T)=ET1 T1 TTaaaET1 T1 (T )T =ET1 T2aTaaaE( 1 2a 1 )TE ，1a1, a于是有1 2a0 ，即 2a 2a 1 0 ，解得 a1. 已知 a0 ，故 a1 ．a2(5) 【答案】 0.9.【详解】利用方差和相关系数的性质D ( X a) DX ， Cov( X ,Ya) Cov( X ,Y ) ，又因为 Z 仅是 X 减去一个常数，故方差不会变， Z 与 Y 的协方差也不会变，因此相关系数也不会变．Cov(Y, Z ) Cov (Y, X 0.4)E[(Y (X 0.4)] E(Y ) E( X0.4)E(XY) 0.4E(Y) E(Y) E( X )0.4E(Y)E(XY)E(Y )E( X ) Cov ( X ,Y ) ，且 D ZD X . 又 Cov (Y, Z ) Cov ( X , Y) ，所以Cov(Y, Z )Cov(X ,Y) XY0.9.D YD ZD XD Y(6) 【答案】1．2【分析】本题考查大数定律：一组相互独立且具有有限期望与方差的随机变量X 1 , X 2 , , X n ，当方差一致有界时， 其算术平均值依概率收敛于其数学期望的算术平均值：1np1n).X iEX i (nn i 1n i 1【详解】本题中X 12, X 22 , , X n 2 满足大数定律的条件，且EX i 2 DX i(EX i ) 2 = 1(1)21 ，422因此根据大数定律有1 n 2依概率收敛于1 n2 1Y nX i EX i.n i 1n i 12二、选择题(1) 【答案】 (D)【详解】 方法 1：直接法：由f (x) 为奇函数知， f (0) 0 ；又由 g( x)f ( x) ，知g (x) 在xx 0 处没定义，显然 x 0 为 g( x) 的间断点，为了讨论函数g( x) 的连续性，求函数g(x) 在 x0 的极限．lim g ( x) lim f ( x) lim f (x) f (0) 导数的定义f (0)存在，x 0 x 0x x 0x故 x 0 为可去间断点．方法 2：间接法：取f ( x)x ，此时 g( x) =x1, x 0,可排除 (A) (B) (C)三项．x 0, x0,(2) 【答案】 ( A)【详解】 由函数 f ( x, y) 在点 ( x 0 , y 0 ) 处可微， 知函数 f ( x, y) 在点 ( x 0 , y 0 ) 处的两个偏导数都存在，又由二元函数极值的必要条件即得 f (x, y) 在点 (x 0 , y 0 ) 处的两个偏导数都等于零． 从而有df ( x 0 , y) fdyy y 0y( x, y ) ( x 0 , y 0 )选项 ( A) 正确．(3) 【答案】 ( B)【详解】由 p na n an， qna n an，知 0 pa ， 0q a n2nnn2若a n 绝对收敛，则 a n 收敛 . 再由比较判别法，p n 与q n 都收敛，后者n 1n 1n 1n 1与 q n 仅差一个系数，故q n 也收敛，选 (B) ．n 1n 1(4) 【答案】 (C)【分析】A 的伴随矩阵的秩为 1， 说明 A 的秩为 2，由此可确定a, b 应满足的条件．【详解】 方法 1：根据 A 与其伴随矩阵A 秩之间的关系n r Anr A *1 r A n 1 0 r An 1知秩 ( A )=2，它的秩小于它的列数或者行数，故有a b b 1 b b1 b b A b a b(a 2b) 1 a b(a 2b) 0 a b0 b b a1 b aa b( a 2b)( a b)2 0有 a 2b0 或 a b ．当 a b 时，b b bAb b b b b b2 1 1 b b b3 1 10 0 00 0 0显然秩 A1 2 ， 故必有 a b 且 a 2b0 ． 应选 (C)．n r An 方法 2：根据 A 与其伴随矩阵A 秩之间的关系， rA *1 r A n 1 ，0 r An 1知 r A *1 ， r A2 . 对 A 作初等行变换a b b 2 1 13 1 1Ab a bb b aa b b b a a b 0 b aa b当 a b 时，从矩阵中可以看到A 的秩为 1，与秩 A2 ，不合题意 (排除 (A) 、 (B))故 ab ，这时ab bAb a a b 02 b a 3b aa bba 2b bb11 01b a0a b12 00110113故 a 2b0 ，且 ab 时，秩 ( A )=2 ，故应选．(5) 【答案】 (B)【分析】本题涉及到线性相关、线性无关概念的理解，以及线性相关、线性无关的等价表现形式．应注意是寻找不正确的命题．【详解】 (A): 若对于任意一组不全为零的数k 1, k 2 , , k s ，都有 k 11k 22k s s 0 ，则1 ,2 ,,s 必线性无关 .因 为 若1, 2,, s 线 性 相 关 ， 则 存 在 一 组 不 全 为 零 的 数 k 1, k 2 , , k s ， 使 得k 11k 22ks s0 ，矛盾． 可见 (A) 成立．(B):若 1, 2, , s 线 性 相 关 ， 则 存 在 一 组 ( 而 不 是 对 任 意 一 组 不 全 为 零 的 ) 数k 1 , k 2 , ,k s ，都有 k 11k2 2k ss0. (B) 不成立．(C)1 ,2 ,, s 线性无关，则此向量组的秩为s ；反过来，若向量组1 ,2 ,, s 的秩为 s ，则1 ,2 ,, s 线性无关，因此 (C)成立．(D)1 ,2 ,, s 线性无关，则其任一部分组线性无关， 则其中任意两个向量线性无关，可见 (D) 也成立．综上所述，应选 (B)．【评注】 原命题与其逆否命题是等价的 ． 例如，原命题：若存在一组不全为零的数k 1 , k 2 , , k s ，使得 k 1 1k2 2k ss0成立，则 1,2 ,, s 线性相关．其逆否命题为：若对于任意一组不全为零的数k 1 , k 2 , , k s ，都有 k 11k 22ks s0 ，则 1 , 2 , , s 线性无关． 在平时的学习过程中，应经常注意这种原命题与其逆否命题的等价性．(6) 【答案】 C【分析】 (1) A, B 两事件相互独立的充要条件：P AB P A P B(2) A, B,C 三事件相互独立的充要条件：(i) A, B, C 两两相互独立；(ii) P ABCP AP BP C【详解】 方法 1：因为1 ，P A 21 A 31 1 P A 1， P ，P A 4，且2224P A 1A 21 ，P A 1 A 31 11 ，P A 1 A2 A 30 ，4，P A 2 A 3，P A 2 A 4444可见有P A 1A 2 P A 1 P A 2 ，P A 1A 3 P A 1 P A 3 ，P A 2A 3PA 2PA 3，PA1A2A3PA1PA2PA3，PA2A4PA2PA4．故 A1 , A2 , A3两两独立但不相互独立； A2 , A3 , A4不两两独立更不相互独立，应选(C) ．方法 2：由三事件相互独立的定义可知：相互独立必两两独立；反之，两两独立不一定相互独立．可见 (A) 不正确，因为如果正确，则(C)也正确，但正确答案不能有两个；同理，(B)也不正确 . 因此只要检查 (C) 和 (D)P A2 A3A4P0 PA2P A3111 P A4442故(D) 错，应选 (C)．三【详解】为使函数 f ( x) 在1,1]上连续，只需求出函数 f (x) 在 x1的左极限 lim f( ) ，[x1x2然后定义 f (1) 为此极限值即可．lim f ( x)lim[11x 1]x 1x1x sin(1x)1lim[11]1lim(1 x) sin xsin x(1(1x)sin xx1x)x 1令 u 1 x ，则当 x 1 时， u0，所以lim f ( x)1lim u sin(1u)u sin(1u)x 1u01lim u sin(1u)1lim u sin(1u)u (sin cos u cos sin u)u sin u u 0u01lim u sin(1u)1limcos(1u)等2u2洛22u u0u01lim 2 sin(1u)10=1洛22=u0定义 f (1)1，从而有 lim f ( x)1f (1)， f(x) 在 x1处连续．又 f ( x) 在[1,1) x12上连续，所以 f ( x) 在 [ 1,1] 上连续．2四【详解】由复合函数z f [( x, y), ( x, y)] 的求导法则，得g f( xy)f 1( x2y2 )f f 2y xx u x v x u vg f( xy)f 1 ( x2y2 )f f 2xy u y v x u y .v从而2 g y 2 f y 2 f x f x 2 f y 2 f xx2u2u v v u v v2y2 2 f2xy 2 f x2 2 f fu2u v v2v2 g x 2 f x 2 f y f y 2 f x 2 f yy2u2u v v u v v2x2 2 f2xy 2 f y2 2 f fu2u v v2v2 g 2 g2y22f( x2y2)2 f( x2y2)(2 f 2 f)=x2y2.所以x 2y2( x)2v2u2v2u五【详解】从被积函数与积分区域可以看出，应利用极坐标进行计算．作极坐标变换：设x r cos, y r sin，有I e ( x2y2) sin( x2y2 )dxdy e e ( x2 y2 ) sin( x2y2 ) dxdyD De2e r 2sin r2rdr e2e r2d2d sin0000记 A e t sin tdt ，则A e t sin tdt e t d cost e t cost000e1 e t d sin te1 e t sin t00因此A 1(1 e) ， I e(1 e )2(1 e ).22t r 2r 2 dr 2 e e t sin tdt.e t costdte t sin tdt = e 1 A.六【分析】 (1) 和函数一般经过适当的变换后，考虑对其逐项求积分后求和，再求导即可得和函数；或者先通过逐项求导后求和，再积分即可得和函数．本题可直接采用后者．(2)等比级数求和公式x n 1 x x2x n1( 1 x 1)n 01x【详解】先对和函数 f (x)1( 1)n x2n求导n 12nf ( x)( 1)n x2 n 1x( 1)n x2 n 2x( 1)n x2nn 1n 1n0x( x2 ) n x1xn 01x2 1 x2对上式两边从0 到x积分x(t )dt x t dt f ( x) f (0)1ln(1 x2 )f0 1t 202由 f (0) 1，得f ( x) 11ln(1 x2 )( x 1).2为了求极值，对 f ( x) 求一阶导数，12x xf ( x)1 x2 1 x22令 f (x)0 ，求得唯一驻点 x0．由于1x2，f(0)10f ( x)x2 )(12由极值的第二充分条件，得 f ( x) 在 x0 处取得极大值，且极大值为 f (0) 1．七【分析】题目要求 F ( x) 所满足的微分方程，而微分方程中含有其导函数，自然想到对 F ( x)求导，并将其余部分转化为用 F ( x) 表示，导出相应的微分方程，然后再求解相应的微分方程即可．【详解】 (1) 方法1：由F ( x) f (x)g (x) ，有F (x) f (x) g( x) f ( x) g (x) =g2( x) f 2 ( x)[ f ( x) g(x)]2 2 f ( x) g( x) = (2e x) 22F ( x)可见 F ( x) 所满足的一阶微分方程为F (x)2F ( x)4e2x .相应的初始条件为 F (0) f (0) g(0) 0 ．方法 2：由F (x) f ( x) g (x)，有F ( x) f ( x)g( x) f (x)g ( x) =[ f ( x)]2[g ( x)] 2[ f ( x)g ( x)] 2 2 f ( x)g ( x)又由f ()() 2x. 有f ( x)xf (x)g( x)g (x) f (x)g ( x)2e ，，，于是x g x eF ( x)4e2 x 2 f (x) g( x)4e2 x2F ( x)可见 F ( x) 所满足的一阶微分方程为F (x)2F ( x)4e2x .相应的初始条件为 F (0) f (0) g(0)0(2)题 (1) 得到F ( x)所满足的一阶微分方程，求 F (x) 的表达式只需解一阶微分方程．又一阶线性非齐次微分方程dyP( x) y Q( x) 的通解为dxy e P ( x ) dxQ( x)eP ( x) dxCdx2dx2x2dx 2 x4 x 2 x 2 x所以()e [ 4e dx C]= e [ 4e dx C ]=e Ce .F x e将 F(0)0 代入上式，得 01C, C 1 .所以 F ( x)e2 x e 2 x.八【分析】题目要证存在(0,3) ，使得其一阶导数为零，自然想到用罗尔定理. 而罗尔定理要求函数在某闭区间连续，且端点处函数值相等．题目中已知 f (3) 1 ，只需要再证明存在一点 c[0,3) ，使得 f (c) 1 f (3) ，然后在 [ c,3] 上应用罗尔定理即可．条件 f (0) f (1) f (2) 3 等价于f (0)f (1) f ( 2)1．问题转化为1介于 f (x) 的最3值之间，最终用介值定理可以达到目的．【详解】方法 1：因为f ( x)在[0，3]上连续，所以 f ( x) 在[0，2]上连续，则在[0，2]上必有最大值 M 和最小值m(连续函数的最大值最小值定理)，于是m f (0)M ， m f (1)M ， m f (2) M ．三式相加3m f (0) f (1) f (2) 3M .从而f ( 0 ) f( 1 )f( 2 )m31 M .由介值定理知，至少存在一点c[0,2] ，使f (c)f (0) f (1) f (2)1.3因为 f ( c) f (3) 1 ，且f (x)在[c,3]上连续，在(c,3)内可导，由罗尔定理知，必存在(c,3) (0,3) ，使 f ( )0.方法2：由于f (0) f (1) f (2) 3，如果 f (0), f (1), f (2) 中至少有一个等于1，例如f (2) 1 ，则在区间[ 2, 3]上对 f ( x) 使用罗尔定理知，存在(0, 2)(0, 3)使f ( ) 0. 如果 f (0), f (1), f (2) 中没有一个等于1，那么它们不可能全大于1，也不可能全小于1．即至少有一个大于1，至少有一个小于1，由连续函数的介值定理知，在区间 (0, 2) 内至少存在一点使f () 1．在区间 [ ,3] 对 f ( x) 用罗尔定理知，存在( ,3) (0,3) ，使 f ( )0. 证毕．九【分析】方程的个数与未知量的个数相同，问题转化为系数矩阵行列式是否为零，而系数行列式的计算具有明显的特征：所有行对应元素相加后相等．可先将所有行对应元素相加，然后提出公因式，再将第一行的 (-1) 倍加到其余各行，即可计算出行列式的值．【详解】方程组的系数行列式a1 b a2a3a na1a2 b a3a nA a1a2a3 b a na1a2a3a n bnb a i a2a3a ni 1nb a i a2b a3a ni 1nb a i a2a3b a ni1nb a i a2a3a n bi11a2a3a n1a2b a3a nn(b a i ) 1a2a3 b a ni11a2a3a n b1a2a3a nn 0b00n0 = b n 1 (b(b a i ) 0 0b a i ).i1i1000bn(1)当 A0 ，即b0且 b a i0 时，秩A n ，方程组仅有零解．i1(2)当 b0时，A0，原方程组的同解方程组为a1 x1a2 x2a n x n0.n0 可知，a i(i由a i1,2,, n) 不全为零．不妨设 a10 ，得原方程组的一个基础解系i1a2,1,0,,0)T，(a3,0,1,,0)T，, na n,0,0,,1)T.1(2a1(a1a1n时， A0.这时 b0 ，原方程组的系数矩阵可化为(3)当 b a ii 1na1a i a2a3a ni1na1a2a i a3a ni1A na1a2a3a i a ni 1na1a2a3a n a ii 1a1na i a2a3a ni 1n na i a i00将第 1行的(1)倍i1i 1n n加到其余各行a i0a i0i1i 1n na i00a ii1i1n从第 2行到第 n行a1i 1a i a2a3a n同乘以1倍1100n1010a ii110010000将第 i行的 ( a )倍1100i加到第 1行，.i 2,3,, n10001001由此得原方程组的同解方程组为x2x1， x3x1，, x n x1．原方程组的一个基础解系为(1,1, ,1)T .十【分析】特征值之和等于 A 的主对角线上元素之和，特征值之积等于 A 的行列式，由此可求出 a, b 的值；进一步求出 A 的特征值和特征向量，并将相同特征值的特征向量正交化(若有必要 )，然后将特征向量单位化并以此为列所构造的矩阵即为所求的正交矩阵．a0b【详解】 (1)二次型f的矩阵为A020. 设 A 的特征值为i (i 1,2,3) ，由题设得b02123a11a22a33 a 2 ( 2) 1，a0b123| A |0204a 2b212.b02解得 a 1,b2．(2)求矩阵 A 的特征值，令102E A020(2)2(3) 0，202得矩阵 A 的特征值122, 3 3.对于基础解系10 2 122, 解齐次线性方程组 (2EA) x 0 ，系数矩阵为 00 ，得 2 041 (2,0,1)T ，2(0,1,0)T .4 02对于 33 ，解齐次线性方程组 ( 3E A)x 0 ，系数矩阵为 0 5 0 ，得2 01基础解系3(1,0, 2)T .由于 1,2 ,3 已是正交向量组，为了得到规范正交向量组，只需将1, 2, 3 单位化，由此得1( 2 ,0, 1 )T ， 2 (0,1,0)T ， 3 ( 1 ,0,2 )T .5 55 5令矩阵2155Q1230 1 0 ，1 0255则 Q 为正交矩阵．在正交变换 XQY 下，有2 0 0 Q T AQ0 2 0 ，0 03且二次型的标准形为f2 y 12 2 y 223y 32 .【评注】本题求 a, b 也可先计算特征多项式，再利用根与系数的关系确定：二次型 f 的矩阵 A 对应特征多项式为abE A0 2 0(2)[ 2(a 2) (2ab 2 )].b2设 A 的特征值为1 , 2,3，则12,2 31232 (a 2) 1， 1 2 3a 2,2 3(2a b 2 ). 由题设得 2(2a b 2 )12.解得 a 1,b2 ．第一步求参数见 《数学复习指南》 P361 重要公式与结论 4，完全类似例题见 《文登数学全真模拟试卷》数学三 P47 第九题．十一【分析】先求出分布函数 F ( x) 的具体形式，从而可确定 YF(X) ，然后按定义求 Y的分布函数即可．注意应先确定 Y F (x) 的值域范围 (0F(X)1) ，再对 y 分段讨论．【详解】易见，当 x1时， F (x) 0; 当 x 8时， F ( x) 1．对于 x [1,8] ，有x1 3 x 1.F ( x)dt133 t 2设 G ( y) 是随机变量 YF (x) 的分布函数． 显然，当 y0 时， G ( y) =0；当 y 1时，G ( y) =1 ． 对于 y [ 0,1) ，有G ( y) P{ Yy} P{F(X) y}P{3 X 1y}P{ X ( y 1)3} F [( y 1)3 ] y.于是， YF ( x) 的分布函数为0,若 y 0,G ( y)y, 若 0y1,1,若 y 1.十二 【分析】本题属新题型，求两个随机变量和的分布，其中一个是连续型一个是离散型，要求用全概率公式进行计算，类似问题以前从未出现过，具有一定的难度和综合性．求二维随机变量函数的分布， 一般用分布函数法转化为求相应的概率． 注意 X 只有两个可能的取值，求概率时可用全概率公式进行计算．求概率密度 g(u) ，一般应先求分布函数G (u) P{ U u}P{ X Y u} ，在计算概率的时候，应充分利用X 只有可能取值 X 1和 X2．全概率公式：如果事件A 1, , A n 构成一个完备事件组，即它们是两两互不相容，其和为(总体的样本空间 ) ；并且0,1,2, , .则对任一事件B 有nP B P( A i )P(B | A i )．i 1【详解】设 F ( y) 是 Y 的分布函数，由全概率公式，得U X Y 的分布函数G (u) P{ X Y u}P{X 1}P{X Y 0.3P{ X Y u X 0.3P{Y u 1 X u X 1}P{ X2}P{ X Y u X 2} 1}0.7P{X Y u X2}1}0.7P{Y u 2 X2} ．由于 X 和 Y 相互独立，所以P{Y u 1} P{ Y u1X 1}， P{Y u 2}P{ Y u 2 X2}所以G (u)0.3P{ Y u1}0.7 P{ Y u 2}0.3F (u1)0.7 F (u2).由此，因为连续型随机变量密度函数是分布函数在对应区间上的微分得到，得U 的概率密度g (u)G (u)0.3F(u1) 0.7F (u2) 0.3 f (u 1)0.7 f (u2).。

2003年英语真题+答案解析河南省2003年普通高等学校选拔优秀专科毕业生进入本科阶段学习考试公共英语Part Ⅰ Vocabulary and Structure (1×30 points)Directions:There are 30 incomplete sentences in this part. For each sentence there are 4 choices marked A,B,C and D. Choose the one that best completes the sentence. Then mark the corresponding letter on the Answer Sheet with a single line through the center.1._______that the trade between the two countries reached its highest point.A. It was the 1990sB. That it was in the 1990sC. It was in the 1990sD. During the 1990s2. Mary said that Hemingway was her_______writer and that she had read nearly all of his novels.A. FamousB. popularC. CommonD. favorite3. She_______English since she was a child.A. LearningB. had learnedC. is learningD. has been learning4. Not until ten o’clock _______it was too late to return.A. they realizedB. they did realizeC. did they realizeD. realized they5. Once a decision is made，it must be_______ firmly.A. carried onB. carried outC. carried awayD. carried off6. _______born in Chicago，the writer is most famous for his stories about New York City.A. AlthoughB. SinceC. WhenD. As7. The pen I am writing my letter with is different from______.A. that oneB. oneC. the oneD. the ones8. Without his wise mother，he______such a successful scientist.A. would not becomeB. should not have becomeC. may not have becomeD. could not have become9. ______，we shall go out for a picnic on Sunday.A. Weather permitsB. Weather permittingC. With weather permitsD. With weather permitting10. The color______ from yellow through green to black.A. RangesB. constitutesC. ComposesD. consists11. Experiments ______that accurate measurements be made.A. ShowB. proveC. DemandD. head12. I tried to catch the ball but it was ______my reach.A. BeyondB. besidesC. in addition toD. as well as13. Those scientists were conducting an experiment and expected a good______ .A. EffectB. resultC. ConsequenceD. affect14. Under heavy gunfire，those cameramen risked their lives to give______battle field reports.A. word-for -wordB. face- to- faceC.down -to- earthD. on- the- spot15. I appreciate ______to your birthday party.A. to be invitedB. to have invitedC. having invitedD. being invited16. The rain was heavy and ______the house was damaged.A. ConsequentlyB. constantlyC. ConsistentlyD. continuously17. When it ______school work，the professor will treat his students equally.A. comes to evaluateB. comes to evaluatingC. will come to evaluateD. will come to evaluating18. _____, you will never convince him.A. However long you argueB. However you argue longC. How you argue longD. How long you argue19. ______new products have been successfully trial produced.A. A great dealB. A large amount ofC. A plenty ofD. A large number of20. He has made a discovery，______of great importance to the progress of science and technology.A. I think which isB. which I think isC. that I think isD. of which I think it is21. Smoking is so harmful to personal health that it killspeople ______each year than automobile accidents.A. six more timesB. six times moreC. over six timesD. six times22. What they have done for us can’t be measured in ______of money.A. WayB. meansC. TermsD. place23. Go and get some water，______?A. don’t youB. shall youC. can’t youD. won’t you24. You must pack plenty of food for the journey，______，you’ll need warm clothes，so pack them too.A. on the wholeB. otherwiseC. HoweverD. likewise25. Meat ______easily in hot weather.A. turns badlyB. becomes badlyC. goes badD. changes worse26. I couldn’t find ______，and so I took this one.A. a large coat enoughB. a large enough coatC. an enough large coatD. a coat enough large27. What_____ would happen if he knew you felt that way?A. will you thinkB. do you thinkC. you thinkD. you would think28. It is _____impossible to find a good educational computer program in this city.A. BarelyB. merelyC. HardlyD. nearly29. _____him do this job by himself?A. Why not letB. Why not to letC. Why don’t letD. Why you not to let30. Almost _____of the population of this country is literate.A. Ninth tenthsB. nine tenthC. Nine tenthsD. ninth tenPart Ⅱ Cloze (1×20 points)Directions：In this section，there are 20 blanks in the following. For each blank there are four choices marked A，B，C and D. You should choose the right answer that best fits into the passage.Scientists used to explore 31 the surface of the ocean. Now they 32 below the surface，too. They want to know about theocean water and the 33 and animal life 34 in the ocean.In 1934 the scientist William Beebe dived 3，000 feet below the surface in a hollow steel ball. In 1935 Auguste Picard dived 10，330 feet. In 1960 his son Jean dived to a 35 of 35，800 feet.All these early dives were deep. But the divers could not stay down for very long. They had to 36 the surface after a few seconds. Scientists needed to stay down longer to study life below the surface. 37 ，they succeeded. Cousteau，a Frenchman，was able to 38 down to a depth of 36 feet for one month and to a depth of 90 feet for a week.Now scientists are developing even 39 equipment. With this new equipment，men can stay 40 the surface for days or 41 weeks. In 1962 Consteau 42 a research station 35 feet below the surface. Then in 1964 he set up another station on the ocean floor of the Red Sea.This was the first undersea station to operate 43 help from the surface.Many countries are now studying undersea 44 . The Soviet Union has an undersea laboratory in the Crimean Sea. The United States has a laboratory 50 feet 45 on the ocean floor 46 the Virgin Islands. In 1970 five men lived there for two weeks. Then a 47 of five women scientists stayed in the laboratory. 48 came other teams of men. All were there to explore the ocean depths and 49 plans for the use of its resources. Scientists hope to find enough 50 ，vegetable，and animal wealth there to provide food for the whole world.31. A. in B. to C. On D. under32. A. explore B. are exploring C. explored D. will explore33. A. plant B. situation C.surroundings D. circumstance34. A. deeply B. normally C. commonly D. deep35. A. depth B. range C. length D. rate36. A. come to B. come over C. come across D. come back up to37. A. However B. Gradually C. moreover D. Though38. A. stay B. remain C. keep D. take39. A. good B. well C. better D. more40. A. below B. on C. in D. to41. A. even B. more C. several D. some42. A. put up B. came up C. made up D. set up43. A. with B. under C. for D. without44. A. living B. situation C. structure D. environment45. A. below B. down C. under D. deep46. A. away B. on C. off D. to47. A. group B. gang C. crowd D. team48. A. after B. next C. later D. then49. A. make B. to make C. making D. made50. A. mineral B. mine C. minefield D. mine layerPart Ⅲ Reading Comprehension(3×20 points)Directions: There are four passages in this part. Each passage is followed by some questions orunfinished statements. For each of them there are four choices marked A, B, C and D, you should decide the best choice.Passage 1With a tremendous roar from its rocket engine，the satellite is sent up into the sky. Minutes later，at an altitude of 300 miles，this tiny electronic moon begins to orbit about the earth. Its radio begins to transmit a staggering amount of information about the satellite’s orbital path，the amount of radiation it detects，and the presence of meteorites. Information of all kinds races back to the earth. No human being could possibly copy down all thesefacts，much less remember and organize them. But an electronic computer can.The marvel of the machine age，the electronic computer has been in use only since 1946. It can do simple computations—add，subtract，multiply，and divide—with lightning speed and perfect accuracy. It can multiply two 10digit numbers in 1／1，000 second，a problem that would take an average person five minutes to do with pencil and paper. Some computers can work 500，000 times faster than any person can.Once it is given a program，that is，a carefully worked out set of instructions devised by a technician trained in computer language，a computer can gather a wide range of information for many purposes. For the scientist it can get information from outer space or from the depths of the ocean. In business and industry the computer prepares factory inventories，keeps track of sales trends and production needs，mails dividend checks，and makes out company payrolls. It can keep bank accounts up to date and make out electric bills. If you are planning a trip by plane，the computer will find out what route to take and what space is available.51. Why does the author regard the electronic computer as the marvel of the machine age?A. Because electronic computers are rare.B. Because people know little about electronic computers.C. Because electronic computers can do much more kinds of work that human beings can’t.D. Because electronic computers have been widely suspected.52. Electronic computers were given the name in the beginning just for the simple reason that_______ .A. they could do computationsB. they could work much faster than human beingsC. they looked like an abacusD. they could remember data quickly53. According to the passage，which of the following is NOT true?A. Computers began to be used in 1946.B. Computers can add，subtract，multiply and divide.C. Computers were widely used during World War Ⅱ.D. No human being can work as fast as a computer.54. A computer can calculate_______.A. with lightning speedB. accuratelyC. with a speed 500，000 times faster than a personD. all above55. In the first sentence of last paragraph，“program” would probably mean_______.A. a performanceB. a showC. a worked out set of instructionsD. a TV playPassage 2On the old time farm in America there were chickens and turkeys. There were also cows，pigs，and other livestock. But there were very few machines. Most of the work was done by the entire farm family with the h elp of a “hired” man. Sometimes extra labourers were needed in busy seasons. Horses provided 79 percent of the power used，human labor 15 percent，and machines only 6 percent.Today all that has changed. On many modern farms machines now supply 96 percent of the power，human labor 3percent，and horses 1 percent. Modern farms are enterprising businesses which keep only the livestock that can pay its way. The children go to school by bus every morning，the parents work on the farm or in the house，and hired help is seldom needed. Their work has been replaced by a whole army of farm machines.Farmers in the machine age also use the new fertilizers，new sprays，new feeds，new hybrid seeds，and other helps developed by farm sciences. As a result the farmers are able to produce more food with less labour. This means fewer but larger farms and fewer but moreprosperous farmers.56. In old days，most of the work on a farm was done by_______.A. all the farm familyB. livestockC. farm machinesD. both A and B57. From the first paragraph，we learn that in old days the most important farming power was____.A. LivestockB. farmersC. MachinesD. extra laborers58. On today’s farms，the chief reason why livestock is still raised would probably be____.A. that farmers conventions are difficult to be given upB. that farmers want to gain more profitC. that farmers have to do soD. that farmers work has been replaced by machines59. On modern farms，farmers need mostly all thefollowings EXCEPT_______.A. farm scienceB. seedsC. FertilizersD. hard work60. In the last sentence of Paragraph 3，“fewer but larger farms and fewer but more prosperous farmers” means_______.A. hired help is seldom neededB. productivity on the farms has been raised greatlyC. productivity on the farms has fallen sharplyD. more food is never neededPassage 3City traffic jam—one of the least wanted effects of the motor vehicle—is something with which we’re all familiar and for which most of us have an answer. But which solution is best?Some people suggest for better roads，others for cars to be banned(禁止) from city centers and yet others say better public transport would attract drivers from their lonely and boring journeys.But the important question is what natural power creates a big city center. We are，after all，in an age of electronic communication; our big shopping areas have moved out of city centers，and our living areas moved out of them long ago.Yet some force causes offices and service industries related to them to gather in London or New York or Tokyo. This suggests that far from the problems of a crowded environment forcing companies and people to move out，there is a critical (重大的) size beyond which more companies are attracted to move in. Nobody seems to know why，yet the answer is important to theway traffic jam is dealt with.61. Which of the following is NOT mentioned in the passage as the cause of the traffic problem?A. The poor public transport.B. The over concentration of shopping centers.C. The great number of cars in the city centers.D. The bad road conditions.62. According to the passage，offices and their associated service industries move to big cities because of_______.A. the convenience of communicationB. the gathering of companiesC. some unknown forceD. the convenience of shopping63. The word “This”(Line 2，Para.4) refers to_______.A. some forceB. traffic jamC. the force that causes offices to move in or outD. the fact that companies gather in big cities64. This passage is most likely taken from_______.A. a novelB. a TV playC. an instructionD. a news report65. The topic of this passage would probably be_______.A. Best Answer to Traffic ProblemB. The Banning of Cars in the City CenterC. The Formation of City CenterD. Searching for Ways to Solve Traffic ProblemPassage 4Mrs. Cox teaches English in a large high school located in theinner area of a big city on the West Coast. Ever since she was a young girl，Mrs. Cox had wanted to become a teacher. She has taught eight years now and hasn’t changed her mind.After she graduated from high school，Mrs. Cox went on to college. Four years later，she received her bachelor’s degree (B.A.) in English and her teaching certificate. Then she was qualified to teach in the secondary schools of her state. In the summers，Mrs. Cox takes more classes. Someday she hopes to get a master’s degree (M.A.).With an M.A.，she will receive a higher salary.The school day at Mrs. Cox’s high school，like that in many high schools in the United States，is divided into six periods of one hour each. Mrs. Cox must teach five of these six periods. During her free period，which for her is from 2 to 3 p.m.，Mrs. Cox must meet with parents，order supplies，make out examinations，check assignments，and take care of many other things. In short，her free period isn’t really free at all. Mrs. Cox works steadily from the time she arrives at school in the morning until the time she leaves for home late in the afternoon.66. Mrs. Cox wants to be a teacher because_______.A. she likes teachingB. she is a young girlC. she has many problems to deal withD. she doesn’t mind what she is doing67. From paragraph two，we can infer_______.A. Mrs. Cox has received a teaching certificateB. Mrs. Cox likes teaching very muchC. Mrs. Cox takes more classesD. Mrs. Cox is a qualified teacher68. She will receive a higher salary if_______.A. she gets a master’s degreeB. she takes more classesC. she has studies normal teachingD. she gets a bachelor’s degree69. According to the passage, all the followings are true EXCEPT_______.A. she graduated from high schoolB. she graduated from collegeC. she has got her bachelor’s degreeD. she teaches five periods for a school day70. The best title for the passage would probably be_______.A. A Typical School DayB. Teacher Mrs. CoxC. Mrs. Cox Likes T eachingD. Mrs. Cox Has Got Her Teaching CertificatePart Ⅳ Translation (2.5×8 points)Section ADirections：There are 4 sentences in this section. You are required to translate them from Chinese into English.71.这口大钟大约有三个人那么高。

2003年全国硕士研究生入学统一考试数学一试题一、填空题：本题共6小题,每小题4分,共24分,请将答案写在答题纸指定位置上.(1)21ln(1)0lim(cos )x x x +→=(2) 曲面22y x z +=与平面042=-+z y x 平行的切平面的方程是.(3) 设)(cos 02ππ≤≤-=∑∞=x nx ax n n,则2a = .(4) 从2R 的基⎪⎪⎭⎫ ⎝⎛-=⎪⎪⎭⎫ ⎝⎛=11,0121αα到基⎪⎪⎭⎫⎝⎛=⎪⎪⎭⎫ ⎝⎛=21,1121ββ的过渡矩阵为.(5) 设二维随机变量(,)X Y 的概率密度为，y x x y x f 其他,10,0,6),(≤≤≤⎩⎨⎧=则=≤+}1{Y X P.(6) 已知一批零件的长度X (单位：cm cm)服从正态分布)1,(μN ,从中随机地抽取16个 零件,得到长度的平均值为40 (cm ),则μ的置信度为0.95的置信区间是.(注：标准正态分布函数值.)95.0)645.1(,975.0)96.1(=Φ=Φ二、选择题：本题共6小题,每小题4分,共24分,下列每小题给出的四个选项中,只有一项符合题目要求,把所选项前的字母填在题后的括号内.(1) 设函数()f x 在),(+∞-∞内连续,其导函数的图形如图所示, 则()f x 有( )(A)一个极小值点和两个极大值点. (B)两个极小值点和一个极大值点. (C)两个极小值点和两个极大值点. (D)三个极小值点和一个极大值点.(2) 设}{},{},{n n n c b a 均为非负数列,且0lim =∞→n n a ,1lim =∞→n n b ,∞=∞→n n c lim ,则必有( )(A) n n b a <对任意n 成立. (B) n n c b <对任意n 成立. (C) 极限n n n c a ∞→lim 不存在. (D) 极限n n n c b ∞→lim 不存在.(3) 已知函数(,)f x y 在点(0,0)的某个邻域内连续,且1)(),(lim2220,0=+-→→y x xyy x f y x ,则( ) (A) 点(0,0)不是(,)f x y 的极值点. (B) 点(0,0)是(,)f x y 的极大值点. (C) 点(0,0)是(,)f x y 的极小值点.(D) 根据所给条件无法判断点(0,0)是否为(,)f x y 的极值点.(4) 设向量组I ：r ααα,,,21 可由向量组II ：s βββ,,,21 线性表示,则( )(A) 当s r <时,向量组II 必线性相关. (B) 当s r >时,向量组II 必线性相关. (C) 当s r <时,向量组I 必线性相关. (D) 当s r >时,向量组I 必线性相关.(5) 设有齐次线性方程组0Ax =和0Bx =, 其中,A B 均为n m ⨯矩阵,现有4个命题：① 若0Ax =的解均是0Bx =的解,则秩(A )≥秩(B )； ② 若秩(A )≥秩(B ),则0Ax =的解均是0Bx =的解； ③ 若0Ax =与0Bx =同解,则秩(A )=秩(B )； ④ 若秩(A )=秩(B ), 则0Ax =与0Bx =同解. 以上命题中正确的是( )(A) ① ②. (B) ① ③.(C) ② ④. (D) ③ ④.(6) 设随机变量21),1)((~X Y n n t X =>,则( ) (A) )(~2n Y χ. (B) )1(~2-n Y χ.(C) )1,(~n F Y . (D) ),1(~n F Y .三 、(本题满分10分)过坐标原点作曲线ln y x =的切线,该切线与曲线ln y x =及x 轴围成平面图形D . (1) 求D 的面积A ;(2) 求D 绕直线x e =旋转一周所得旋转体的体积V .四 、(本题满分12分)将函数x x x f 2121arctan )(+-=展开成x 的幂级数,并求级数∑∞=+-012)1(n nn 的和.已知平面区域}0,0),{(ππ≤≤≤≤=y x y x D ,L 为D 的正向边界. 试证： (1) dx ye dy xe dx ye dy xex Ly x L ysin sin sin sin -=-⎰⎰--;(2).22sin sin π≥--⎰dx ye dy xe x Ly六 、(本题满分10分)某建筑工程打地基时,需用汽锤将桩打进土层. 汽锤每次击打,都将克服土层对桩的阻力而作功. 设土层对桩的阻力的大小与桩被打进地下的深度成正比(比例系数为,0k k >).汽锤第一次击打将桩打进地下a m . 根据设计方案,要求汽锤每次击打桩时所作的功与前一次击打时所作的功之比为常数(01)r r <<. 问(1) 汽锤击打桩3次后,可将桩打进地下多深？(2) 若击打次数不限,汽锤至多能将桩打进地下多深？ (注：m 表示长度单位米.)七 、(本题满分12分)设函数()y y x =)在),(+∞-∞内具有二阶导数,且)(,0y x x y =≠'是()y y x =的反函数.(1) 试将()x x y =所满足的微分方程0))(sin (322=++dy dx x y dyx d 变换为()y y x =满足的微分方程；(2) 求变换后的微分方程满足初始条件23)0(,0)0(='=y y 的解.八 、(本题满分12分)设函数()f x 连续且恒大于零,⎰⎰⎰⎰⎰+++=Ω)(22)(222)()()(t D t d y xf dvz y x f t F σ,⎰⎰⎰-+=tt D dxx f d y x f t G 12)(22)()()(σ,其中}),,{()(2222t z y x z y x t ≤++=Ω,}.),{()(222t y x y x t D ≤+=(1) 讨论()F t 在区间),0(+∞内的单调性. (2) 证明当0t >时,).(2)(t G t F π>设矩阵⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=322232223A ,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=100101010P ,P A P B *1-=,求2B E +的特征值与特征向量,其中*A 为A 的伴随矩阵,E 为3阶单位矩阵.十 、(本题满分8分)已知平面上三条不同直线的方程分别为1:230l ax by c ++=,2:230l bx cy a ++=,3:230l cx ay b ++=.试证: 这三条直线交于一点的充分必要条件为.0=++c b a十一 、(本题满分10分)已知甲、乙两箱中装有同种产品,其中甲箱中装有3件合格品和3件次品,乙箱中仅装有3件合格品. 从甲箱中任取3件产品放入乙箱后,求：(1) 乙箱中次品件数X 的数学期望； (2) 从乙箱中任取一件产品是次品的概率.十二 、(本题满分8分)设总体X 的概率密度为⎩⎨⎧≤>=--,,,0,2)()(2θθθx x e x f x其中0>θ是未知参数. 从总体X 中抽取简单随机样本n X X X ,,,21 ,记).,,,min(ˆ21nX X X =θ (1) 求总体X 的分布函数()F x ; (2) 求统计量θˆ的分布函数)(ˆx F θ；(3) 如果用θˆ作为θ的估计量,讨论它是否具有无偏性.2003年全国硕士研究生入学统一考试数学一试题解析一、填空题 (1)【详解】方法1：求()lim ()v x u x 型极限,一般先化为指数形式()()ln ()lim ()lim v x v x u x u x e =然后求lim ()ln ()v x u x ,再回到指数上去．)1ln(12)(cos lim x x x +→=220ln cos ln cos limln(1)ln(1)lim x xxx x x e e→++→=,而2200ln cos ln(1cos 1)limlim ln(1)ln(1)x x x x x x →→+-=++20cos 1lim x x x →-=(等价无穷小替换ln(1)x x +) 220112lim 2x x x →-==-(等价无穷小替换211cos 2x x -) 故 原式=.121ee=-方法2：令21ln(1)(cos )x y x +=,有2ln cos ln ln(1)xy x =+,以下同方法1．(2)【答案】542=-+z y x【详解】由题意,只要满足所求切平面的法向量与已知平面的法向量平行即可．平面042=-+z y x 的法向量：1{2,4,1}n =-；曲面22y x z +=在点),,(000z y x 的法向量：20000{(,),(,),1}x y n z x y z x y =-00{2,2,1}x y =- 由于12//n n ,因此有00221241x y -==- 可解得,2,100==y x ,相应地有.520200=+=y x z所求切平面过点(1,2,5),法向量为：2{2,4,1}n =-,故所求的切平面方程为0)5()2(4)1(2=---+-z y x ,即 542=-+z y x(3)【答案】1【详解】将)()(2ππ≤≤-=x x x f 展开为余弦级数2()cos ()n n f x x a nx x ππ∞===-≤≤∑,其中⎰=ππcos )(2nxdx x f a n ．所以 x d x xdx x a 2sin 12cos 2222⎰⎰=⋅=ππππ21[sin2sin22]x xx xdx πππ=-⋅⎰1cos2xd x ππ=⎰001[cos2cos2]x x xdx πππ=-⎰1=(4)【答案】⎪⎪⎭⎫ ⎝⎛--2132【详解】n 维向量空间中,从基n ααα,,,21 到基n βββ,,,21 的过渡矩阵P 满足[n βββ,,,21 ]=[n ααα,,,21 ]P ,因此过渡矩阵P 为：P =[121],,,-n ααα [],,,21n βββ ．根据定义,从2R 的基⎪⎪⎭⎫ ⎝⎛-=⎪⎪⎭⎫ ⎝⎛=11,0121αα到基⎪⎪⎭⎫⎝⎛=⎪⎪⎭⎫ ⎝⎛=21,1121ββ的过渡矩阵为P =[121],-αα[⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡-=-21111011],121ββ=.213221111011⎥⎦⎤⎢⎣⎡--=⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡-(5)【答案】14． 【分析】本题为已知二维随机变量(,)X Y 的概率密度(,)f x y ,求满足一定条件的概率}),({0z Y X g P ≤．连续型二维随机变量(,)X Y 概率的求解方法(,)(,),y xF x y f u v dudv -∞-∞=⎰⎰此题可转化为二重积分}),({0z Y X g P ≤0(,)(,)g x y z f x y dxdy ≤=⎰⎰进行计算．【详解】图中阴影区域为积分区域. 由题设,有=≤+}1{Y X P 1(,)x y f x y dxdy +≤⎰⎰11206xxdx xdy -=⎰⎰1220(612)x x dx =-⎰14=(6)【答案】)49.40,51.39(． 【分析】可以用两种方法求解：(1) 已知方差12=σ,对正态总体的数学期望μ进行估计. 因为(,1)X N μ,设有n 个样本,样本均值11ni i X X n ==∑,则1(,)XN n μ,将其标准化,~(0,1)X N 得：)1,0(~1N nX μ- 由正态分布分为点的定义αμα-=<-1}1{2u nX P 可确定临界值2αu ,进而确定相应的置信区间22(x u x u αα-+．(2)本题是在单个正态总体方差已知条件下,求期望值μ的置信区间问题．由教材上已经求出的置信区间22(x u x u αα-+,其中2{}1,(0,1)P U u UN αα<=-,可以直接得出答案．【详解】方法1：由题设,95.01=-α,可见.05.0=α 查标准正态分布表知分位点.96.12=αu 本题16n =, 40=x .根据 1.96}0.95P <=,有 1.96}0.95P <=,即{39.5140.49}0.95P μ<<=,故μ的置信度为0．95的置信区间是)49.40,51.39(．方法2：由题设,95.01=-α,22222{}{}2()10.95,()0.975P U u P u U u u u ααααα<=-<<=Φ-=Φ=查得.96.12=αu 将1σ=,16n =, 40=x代入22(x u x u αα-+得置信区间)49.40,51.39(二、选择题(1)【答案】()Cy【分析】函数的极值点可能是驻点(一阶导数为零) 或导数不存在的点,极值点是极大值点还是极小值 点可进一步由取极值的第一或第二充分条件判定． 【详解】根据导函数的图形可知,一阶导数为零的 点有3个(导函数与x 轴交点的个数)；0x =是导数 不存在的点．对3个一阶导数为零的点左右两侧导数符号均 不一致,故必为极值点,其中第一个交点左右两侧导数符号由正变为负,是极大值点；第二个交点和第三个交点左右两侧导数符号由负变为正,是极小值点,则三个驻点中有两个极小值点,一个极大值点；对导数不存在的点：0x =．左侧一阶导数为正,右侧一阶导数为负,可见0x =为极大值点．故()f x 共有两个极小值点和两个极大值点,应选(C)．(2)【答案】()D 【详解】方法1：推理法由题设lim 1n n b →∞=,假设lim n n n b c →∞存在并记为A ,则lim limn nn n n nb c c A b →∞→∞==,这与lim n n c →∞=∞矛盾,故假设不成立,lim n n n b c →∞不存在． 所以选项()D 正确．方法2：排除法取1n a n =,1n n b n-=,满足0lim =∞→n n a ,1lim =∞→n n b , 而11111,0,a b a b ==>,()A 不正确；取1n n b n-=,2n c n =-,满足1lim =∞→n n b ,∞=∞→n n c lim ,而1101b c =>-=,()B 不正确；取1n a n=,2n c n =-,满足0lim =∞→n n a ,∞=∞→n n c lim ,而lim 1n n n a c →∞=,()C 不正确．(3)【答案】()A 【详解】由2220,0(,)lim1()x y f x y xyx y →→-=+222(,)(1)()f x y xy x y α⇒-=++,其中00lim 0x y α→→=． 由(,)f x y 在点(0,0)连续知,(0,0)0f =．取y x =,x 充分小,0x ≠,有222(,)(1)(2)0f x y x x α=++>； 取y x =-,x 充分小,0x ≠,有222(,)(1)(2)0f x y x x α=-++<故点(0,0)不是(,)f x y 的极值点,应选()A ． (极值的定义)(4)【分析】 本题为一般教材上均有的比较两组向量个数的定理：若向量组I ：r ααα,,,21 可由向量组II ：s βββ,,,21 线性表示,则当s r >时,向量组I 必线性相关． 或其逆否命题：若向量组I ：r ααα,,,21 可由向量组II ：s βββ,,,21 线性表示,且向量组I 线性无关,则必有s r ≤． 可见正确选项为(D)． 本题也可通过举反例用排除法找到答案．【详解】 用排除法：⎪⎪⎭⎫⎝⎛=⎪⎪⎭⎫ ⎝⎛=⎪⎪⎭⎫ ⎝⎛=10,01,00211ββα,则21100ββα⋅+⋅=,但21,ββ线性无关,排除(A)；⎪⎪⎭⎫ ⎝⎛=⎪⎪⎭⎫ ⎝⎛=⎪⎪⎭⎫ ⎝⎛=01,01,00121βαα,则21,αα可由1β线性表示,但1β线性无关,排除(B)；⎪⎪⎭⎫⎝⎛=⎪⎪⎭⎫ ⎝⎛=⎪⎪⎭⎫ ⎝⎛=10,01,01211ββα,1α可由21,ββ线性表示,但1α线性无关,排除(C)．(5)【答案】(B)【分析】本题可找反例用排除法进行分析,但①、②两个命题的反例比较复杂一些,关键是抓住③、④,迅速排除不正确的选项．【详解】若0AX =与0BX =同解,则它们的解空间中的基础解系所含向量个数相同,即n -秩(A )=n -秩(B ), 得秩(A )=秩(B ),命题③成立,可排除(A), (C)；但反过来,若秩(A )=秩(B ),则不能推出0AX =与0BX =同解,通过举一反例证明,若⎥⎦⎤⎢⎣⎡=0001A ,⎥⎦⎤⎢⎣⎡=1000B ,则秩(A )=秩(B )=1,但0AX =与0BX =不同解,可见命题④不成立,排除(D). 故正确选项为(B)．(6)【答案】(C)．【分析】求解这类问题关键在于了解产生2χ变量、t 变量、F 变量的典型模式．(1)2χ分布：设12,,,n X X X 相互独立且均服从标准正态分布,则随机变量21ni i Z X ==∑服从自由度为n 的2χ分布．记做2().Zn χ(2)t 分布：设1(0,1)X N ,22~()X n χ,且12,X X 相互独立,则随机变量Z =服从自由度为n 的t 分布．记做()Zt n(3)F 分布：设2212(),(),Xn Y n χχ且,X Y 相互独立,则随机变量12X n Z Y n =服从F 分布,其第一、二自由度分别为12,.n n 记做12(,).ZF n n【详解】其实,由F 分布的性质以及t 分布和F 分布的关系得,(1) 如果统计量 ()T t n ,则有2(1,)T F n ；(2) 如果统计量12(,)FF n n ,则有211(,)F n n F．由以上两条性质可以直接得出本题的答案为(C)．先由t分布的定义知()X t n =,其中)(~),1,0(~2n V N U χ,于是 21XY ==122U n V U n V =,分母中只含有一个标准正态分布的平方,所以)1(~22χU . 由F 分布的定义知~(,1).Y F n故应选(C)．三【分析】圆锥体体积公式：213V r h π=⋅；旋转体的体积：(1) 连续曲线()y f x =,直线x a =、x b =所围成的图形绕直线0x x =旋转一周而成的立体的体积[]210()ba V f x x dx π=-⎰(2) 连续曲线()x g x =,直线y c =、y d =所围成的图形绕直线0y y =旋转一周而成的立体的体积[]220()dc V g y y dy π=-⎰【详解】为了求D 的面积,首先要求出切点的坐标,设切点的横坐标为0x ,则曲线ln y x =在点)ln ,(00x x 处的切线方程是：).(1ln 000x x x x y -+= 切线的斜率为01x y x '=,由于该切线过原点,将(0,0)点代入切线方程,得01ln 0=-x ,从而.0e x = 所以该切线的方程为.1x ey =(1) 利用平面图形D 的面积公式()()S y y dy βαϕψ=-⎰,得⎰-=-=1.121)(e dy ey e A y (2) 旋转体体积可用一大立体(圆锥)体积减去一小立体体积进行计算,为了帮助理解,可画一草图．切线x ey 1=与x 轴及直线x e =所围成的三角形绕直线x e =旋转所得的圆锥体积为： 122101().3V e ey dy e ππ=-=⎰曲线ln y x =与x 轴及直线x e =所围成的图形绕直线x e =旋转所得的旋转体体积为：dy e e V y 212)(⎰-=π1220(2)y y e e e e dy π=-⋅+⎰12201(2)2yy e y e e e π=-⋅+211(2)22e e π=-+-因此所求旋转体的体积为).3125(6)(312102221+-=--=-=⎰e e dy e e e V V V y πππ四【分析】幂级数展开有直接法与间接法,一般考查间接法展开,即通过适当的恒等变形、求导或积分等,转化为可利用已知幂级数展开的情形．另外,由于函数展开成的幂级数,经两边求导或积分(其中一边是逐项求导或逐项积分)后,其新的展开式收敛区间不变,但在收敛区间端点处,求导(积分)后的展开式成立与否,要另行单独处理,设已有00()()n n n f x a x x ∞==-∑收敛区间为00(,)x R x R -+． 如果在0x x R =+处级数收敛,并且()f x (左)连续,则展开式成立的范围可扩大到0x x R =+处,在0x x R =-处亦有类似的结论,不过此时()f x (左)连续应改称(右)连续．【详解】本题可先求导,()f x '()2222(12)2(12)1212121212111212x x x x x x x x x '-+---⎛⎫ ⎪++⎝⎭==--⎛⎫⎛⎫++ ⎪ ⎪++⎝⎭⎝⎭基本求导公式 22422(14)14x x --==++21214x=-+ 对于函数2114x+,可以利用我们所熟悉的函数x -11的幂级数展开： 2011(11)1nnn x x x x x x ∞==+++++=-<<-∑所以 2222001(4)(1)414114n n n nn n x x x x ∞∞===-=--<-<+∑∑ (把x 换成24x -) 有 22111()22(1)4,(,).1422n n n n f x x x x ∞='=-=--∈-+∑对上式两边求积分,得200()(0)()2(1)4xxn n n n f x f f t dt t dt ∞=⎛⎫'-==-- ⎪⎝⎭∑⎰⎰221000(1)4112(1)42,(,)2122n n x nnnn n n t dt x x n ∞∞+==-=--=-∈-+∑∑⎰,又因为04f π=（）,所以()(0)()xf x f f t dt '=+⎰=).21,21(,124)1(24120-∈+--+∞=∑x x n n n nn π即 21012(1)411arctan 2,(,).1242122n n n n x x x x n π∞+=--=-∈-++∑ (*)在21=x 处,右边级数成为0(1)1212n n n ∞=-⋅+∑,收敛(利用莱布尼茨定理),左边函数()f x 连续,所以成立范围可扩大到21=x 处．而在12x =-处,右边级数虽然收敛,但左边函数()f x 不连续,所以成立范围只能是11(,]22x ∈-．为了求∑∞=+-012)1(n nn ,令21=x 代入(*)得∑∑∞=+∞=+--=⋅+--=012012)1(4]21124)1([24)21(n nn n n n n f ππ,再由0)21(=f ,得.4)21(412)1(0ππ=-=+-∑∞=f n n n五【详解】(1) 方法1：用格林公式证明. 由曲线为正向封闭曲线,自然想到用格林公式L D Q P Pdx Qdy dxdy x y ⎛⎫∂∂+=- ⎪∂∂⎝⎭⎰⎰⎰． 所以 ⎰⎰⎰--+=-D x y x L ydxdy e e dx ye dy xe)(sin sin sin sin所以⎰⎰⎰+=---Dx y x Ly dxdy e e dx ye dy xe )(sin sin sin sin 因为积分区域D 关于y x =对称,所以sin sin sin sin ()()x y yxyx DDeedxdyee dxdy --+=+⎰⎰⎰⎰与互换故dx ye dy xe dx ye dy xe x Ly x Ly sin sin sin sin -=-⎰⎰-- 方法2：化为定积分证明左边sin sin y x LLxe dy ye dx -=-⎰⎰=dx edy exy⎰⎰--0sin 0sin ππππ=⎰-+ππ0sin sin )(dx e e x x右边sin sin y x LLxe dy ye dx -=-⎰⎰=⎰⎰--ππππ00sin sin dx e dy e x y =⎰-+ππ0sin sin )(dx e e x x所以dx ye dy xe dx ye dy xe x Ly x Ly sin sin sin sin -=-⎰⎰--． (2) 方法1：用格林公式证明⎰⎰⎰--+=-Dx y x Ly dxdy e e dx ye dy xe )(sin sin sin sin =dxdy e dxdy eDDx y⎰⎰⎰⎰-+sin sin =dxdy e dxdy e DDx x ⎰⎰⎰⎰-+sin sin 利用轮换对称性=sin sin ()2x x DDe e dxdy dxdy -+≥⎰⎰⎰⎰22π=(因为0,0a b a b +≥>>)方法2：由(1)知,sin sin sin sin 0()2y x x x Lxe dy ye dx e e dx dx ππππ---=+≥⎰⎰⎰22π=六【详解】(1) 建立坐标系,地面作为坐标原点,向下为x 轴正向,设第n 次击打后,桩被打进地下n x ,第n 次击打时,汽锤所作的功为),3,2,1( =n W n ．由题设,当桩被打进地下的深度为x 时,土层对桩的阻力的大小为kx ,汽锤所作的功等于克服阻力所做的功．121102x k W kxdx x ==⎰,2122221()2x x k W kxdx x x ==-⎰,3222332()2x x k W kxdx x x ==-⎰,1x a =从而 212332k W W W x ++=又 12rW W =,2321W rW r W ==, 从而222231231(1)(1)22k k x W W W r r W r r a =++=++=++于是 3x =(2) 第n 次击打后,桩被打进地下n x ,第n 次击打时,汽锤所作的功为),3,2,1( =n W n ． 则汽锤前n 次所功的和等于克服桩被打进地下n x m 所做的功．11210(1)nx n n kxdx W W W r r W -=+++=+++⎰而 2102a kW kxdx a ==⎰ 牛-莱公式所以212(1)22n n k k x r r a -=+++从而 1n n x r-=++= 等比数列求和公式由于01r <<,所以1lim n n x +→∞．七【详解】 (1) 将题中的dy dx 与22d xdy变换成以x 为自变量y 为因变量的导数dx dy 与22d y dx 来表示(即通常所说的反函数变量变换),有dy dx =y dxdy '=11,)(22dy dx dy d dy x d ==dy dx y dx d ⋅')1(=32)(1y y y y y '''-='⋅'''-． 代入原方程,得 .sin x y y =-'' ( * )(2) 方程( * )所对应的齐次方程为0=-''y y ,特征方程为210r -=,根1,21r =±,因此通解为.21xxe C e C Y -+= 由于i λω+不是特征方程得根,所以设方程( * )的特解为x B x A y sin cos *+=则 *sin cos y A x B x '=-+,*cos sin y A x B x ''=--代入方程( * ),得：cos sin cos sin 2cos 2sin sin A x B x A x B x A x B x x ----=--= 解得21,0-==B A ,故x y sin 21*-=. 从而x y y sin =-''的通解为 .sin 2121*x e C e C y Y y x x -+=+=-由23)0(,0)0(='=y y ,得1,121-==C C ．故变换后的微分方程满足初始条件23)0(,0)0(='=y y 的解为.sin 21x e e y x x --=-且()y x 的导函数1()cos 02x x y x e e x -'=+->,满足题设0y '≠条件．八【详解】(1) 首先对()F t 进行化简,三重积分转化为在球面坐标系中的计算；二重积分转化为在极坐标系中的计算．222222220()()()sin 2sin ()t tt f x y z dv d d f r r dr d f r r dr πππθϕϕπϕϕΩ++==⎰⎰⎰⎰⎰⎰⎰⎰()2222002()cos 4()t tf r r dr f r r dr ππϕπ=⋅-=⎰⎰ (球面坐标)222220()()()2()t tD t f x y d d f r rdr f r rdr πσθπ+==⎰⎰⎰⎰⎰ (极坐标)所以222220000222()sin 4()()()2()ttttd d f r r drf r r drF t d f r rdrf r rdrπππθϕϕπθπ==⎰⎰⎰⎰⎰⎰⎰22022()()ttf r r drf r rdr=⎰⎰为了讨论()F t 在区间),0(+∞内的单调性,对()F t 求导：222222022()()()()()2[()]t ttt f t f r rdr f r r dr f t tF t f r rdr ⋅-⋅'=⎰⎰⎰22022()()()2[()]tttf t f r r t r drf r rdr ⋅-=⎰⎰由于()0,0,0f t r t r >>->,所以2()()0f r r t r ->. 再利用定积分的性质：若在区间[,]a b 上()0f x >,则()0baf x dx >⎰. 所以()0F t '>,所以()F t 在区间),0(+∞内严格单调增加．(2) 将待证的不等式作适当的恒等变形后,构造辅助函数,再用单调性进行证明即可． 因为 2220()2()2()tt ttf x dx f x dx f r dr -==⎰⎰⎰,所以2222()0022200()2()()()()2()()ttD t ttttf x y d f r rdr f r rdrG t f x dxf r drf r drσππ-+===⎰⎰⎰⎰⎰⎰⎰要证明0t >时)(2)(t G t F π>,只需证明0t >时,0)(2)(>-t G t F π,即22200222()2()2()()()()t tttf r r drf r rdrF tG t f r rdrf r drπ-=-⎰⎰⎰⎰()()()()()222222202()()()()()tt tttf r r dr f r dr f r rdr f r rdr f r dr⎡⎤⋅-⎢⎥⎣⎦=⋅⎰⎰⎰⎰⎰令 ()()()22222()()()()tt tg t f r r dr f r dr f r rdr =⋅-⎰⎰⎰222222220222()()()()()2()()()()()0t t ttg t f t t f r dr f t f r r dr f t t f r rdrf t f r t r dr t '=+-=->>⎰⎰⎰⎰故()g t 在),0(+∞内单调增加,又因为(0)0g =,所以当0t >时,有()0)0g t g>=（, 从而0t >时,).(2)(t G t F π>九【分析】 法1：可先求出*1,A P -,进而确定P A P B *1-=及2B E +,再按通常方法确定其特征值和特征向量；法2：先求出A 的特征值与特征向量,再相应地确定*A 的特征值与特征向量,最终根据2B E +与*2A E +相似求出其特征值与特征向量． 【详解】方法1：经计算可得⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡------=522252225*A ,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=-1000011101P ,所以 P A P B *1-==⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡----322452007,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡----=+5224720092E B ． 令 2900(2)274(9)(3)0225E B E λλλλλλ--+=-=--=-,故2B E +的特征值为.3,9321===λλλ当921==λλ时,解0)9(=-x A E ,得线性无关的特征向量为,0111⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=η ,1022⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=η所以属于特征值921==λλ的所有特征向量为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-+⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=+102011212211k k k k ηη,其中21,k k 是不全为零的任意常数．当33=λ时,解0)3(=-x A E ,得线性无关的特征向量为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=1103η,所以属于特征值33=λ的所有特征向量为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=110333k k η,其中03≠k 为任意常数． 方法2：设A 的特征值为λ,对应的特征向量为η,即ληη=A ．由于07≠=A ,所以.0≠λ所以 ***()()A A A E A A A E A A A E ηηηη=⇒=⇒=***()AA A A A A ληηληηηηλ⇒=⇒=⇒=,于是 11*11()()()AB P P A P P P ηηηλ----==,.)2()2(11ηλη--+=+P AP E B因此,2+λA为2B E +的特征值,对应的特征向量为.1η-P由于)7()1(3222322232--=---------=-λλλλλλA E ,故A 的特征值为1231,7λλλ===当121==λλ时,对应的线性无关特征向量可取为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=0111η, .1012⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=η当73=λ时,对应的一个特征向量为.1113⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=η 由⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=-1000011101P,得⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=-01111ηP ,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡--=-11121ηP ,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=-11031ηP ．因此,2B E +的三个特征值分别为9,9,3．对应于特征值9的全部特征向量为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡--+⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=+--11101121212111k k P k P k ηη,其中21,k k 是不全为零的任意常数；对应于特征值3的全部特征向量为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=-1103313k P k η,其中3k 是不为零的任意常数．十【分析】三条直线相交于一点,相当于对应线性方程组有唯一解,进而转化为系数矩阵与增广矩阵的秩均为2．【详解】方法1：“必要性”. 设三条直线321,,l l l 交于一点,则线性方程组⎪⎩⎪⎨⎧-=+-=+-=+,32,32,32b ay cx a cy bx c by ax (*) 有唯一解,故系数矩阵⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=a c c b b a A 222与增广矩阵⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡---=b a c a c b c b a A 323232的秩均为2,于是.0=A232()3()23232323a b c a b c b c a c a b A bca b c a c a bc ab -++++-++=-=---123111()236()23a b c b ca abc b ca c abc a b-=++-=-++-1006()6()c b a ba b c b c b a b a b c a c b cc a c b c--=-++--=-++----6()[()()()()]a b c c b b c a b a c =-++-----2226()()a b c bc c b bc a ac ab bc =-++--+-++- 2226()()a b c a b c ac ab bc =++++--- 2223()[()()()]a b c a b b c c a =++-+-+-,由于三条直线互不相同,所以0)()()(222≠-+-+-a c c b b a ,故.0=++c b a“充分性”. 由0=++c b a ,则从必要性的证明可知,0=A ,故秩.3)(<A由于])([2)(22222b b a a b ac cb b a ++-=-==0]43)21[(222≠++-b b a ,故秩()2A =．于是,秩(A )=秩)(A =2．因此方程组(*)有唯一解,即三直线321,,l l l 交于一点．方法2：“必要性”设三直线交于一点),(00y x ,则⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡100y x 为0BX =的非零解,其中2323.23a b c B b c a c a b ⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦ 所以||0B =．而232323232323a b c a b cB bc a bca A c a bca b-==--=-- 2223()[()()()]a b c a b b c c a =-++-+-+-,(解法同方法1)但根据题设 0)()()(222≠-+-+-a c c b b a ,故.0=++c b a“充分性”：考虑线性方程组⎪⎩⎪⎨⎧-=+-=+-=+,32,32,32b ay cx a cy bx c by ax (*)将方程组(*)的三个方程相加,并由.0=++c b a 可知,方程组(*)等价于方程组⎩⎨⎧-=+-=+.32,32a cy bx c by ax (* *) 因为])([2)(22222b b a a b ac cb ba ++-=-==222[()]0ab a b -+++≠,故方程组(* *)有唯一解,所以方程组(*)有唯一解,即三直线321,,l l l 交于一点．十一【详解】乙箱中可能的次品件数为0,1,2,3,分别求出其概率,再按定义求数学期望即可；而求从乙箱中任取一件产品是次品的概率,涉及到两次试验,是典型的用全概率公式的情形,第一次试验的各种可能结果(取到的次品数)就是要找的完备事件组．(1) 方法1：X 的可能取值为0,1,2,3, 取出k 件次品()0,1,2,3k =的取法有333k kC C -种；样本空间即从两个箱子中取出3件产品的总的取法数为36C ．所以有,X 的概率分布为36333}{C C C k X P kk -==, k 0,1,2,3.= 即 X 0 1 2 3 P201 209 209 201 因此,由离散型数学期望的定义{}1()nk k k E X x P X x ==⋅=∑易得 19913()0123.202020202E X =⨯+⨯+⨯+⨯= 方法2：本题对数学期望的计算也可用分解法：设0, ,1,i i X i ⎧=⎨⎩从甲箱中取出的第件产品是合格品从甲箱中取出的第件产品是次品. 则i X 的概率分布为i X 0 1P21 21.3,2,1=i 因为321X X X X ++=,所以由数学期望的线性可加性,有200321 ()()()()1233.2E X E X E X E X =++= (2) 设A 表示事件“从乙箱中任取一件产品是次品”,由于}0{=X ,}1{=X ,}2{=X ,}3{=X 构成完备事件组,因此根据全概率公式,有∑====30}{}{)(k k X A P k X P A P =33001{}{}66k k k P X k k P X k ===⋅=⋅=∑∑ ()1131.6624E X ==⋅=十二【分析】本题表面上是一数理统计问题,实际上考查了求分布函数、随机变量的函数求分布和概率密度以及数学期望的计算等多个知识点．将数理统计的概念与随机变量求分布与数字特征结合起来是一种典型的命题形式．求分布函数()F X 是基本题型：求统计量θˆ的分布函数)(ˆx F θ,可作为多维相互独立且同分布的随机变量函数求分布函数,直接用定义即可；是否具有无偏性,只需检验θθ=ˆE 是否成立．【详解】(1) 由连续型随机变量分布函数的定义,有.,,0,1)()()(2θθθ≤>⎩⎨⎧-==⎰∞---x x e dt t f x F xx (2) 由题给).,,,min(ˆ21nX X X =θ,有 }),,,{min(}ˆ{)(21ˆx X X X P x P x F n≤=≤= θθ 121{min(,,,)}n P X X X x =->121{,,,}n P X x X x X x =->>> 1[1()]n F x =--2(),1,.0,n x x e x θθθ-->⎧-=⎨≤⎩(3) 由连续型随机变量概率密度是分布函数在相应区间上的微分得θˆ概率密度为.,,0,2)()()(2ˆˆθθθθθ≤>⎩⎨⎧==--x x ne dxx dF x f x n 因为 2()ˆˆ()()2n x E xf x dx nxe dx θθθθ+∞+∞---∞==⎰⎰12nθθ=+≠, 所以θˆ作为θ的估计量不具有无偏性．。

梅花香自苦寒来，岁月共理想，人生气高飞！2003年考研数学（二）真题一、填空题(本题共6小题，每小题4分，满分24分。

把答案填在题中横线上）(1） 若0→x 时，1)1(412--ax 与x x sin 是等价无穷小，则a= 。

（2） 设函数y=f （x)由方程4ln 2y x xy =+所确定，则曲线y=f （x)在点（1，1)处的切线方程是 . （3） x y 2=的麦克劳林公式中nx 项的系数是__________.（4） 设曲线的极坐标方程为)0(>=a e a θρ ，则该曲线上相应于θ从0变到π2的一段弧与极轴所围成的图形的面积为__________。

（5） 设α为3维列向量，Tα是α的转置. 若⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡----=111111111T αα,则ααT = .（6） 设三阶方阵A ，B 满足E B A B A =--2，其中E 为三阶单位矩阵，若⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=102020101A ，则B =________。

二、选择题（本题共6小题,每小题4分，满分24分。

每小题给出的四个选项中，只有一项符合题目要求，把所选项前的字母填在题后的括号内)（1）设}{},{},{n n n c b a 均为非负数列，且0lim =∞→n n a ，1lim =∞→n n b ，∞=∞→n n c lim ,则必有（A) n n b a <对任意n 成立。

（B ） n n c b <对任意n 成立.（C ） 极限n n n c a ∞→lim 不存在。

（D ） 极限n n n c b ∞→lim 不存在. ［ ］（2）设dx x xa n n nn n +=⎰+-123101, 则极限n n na ∞→lim 等于 （A) 1)1(23++e 。

(B) 1)1(231-+-e 。

(C) 1)1(231++-e 。

（D) 1)1(23-+e . [ ］(3）已知x x y ln =是微分方程)(y x x y y ϕ+='的解，则)(yxϕ的表达式为 （A ） .22xy - （B ） .22x y梅花香自苦寒来，岁月共理想，人生气高飞！(C) .22yx - (D ） .22y x [ ]（4）设函数f （x)在),(+∞-∞内连续，其导函数的图形如图所示，则f （x ）有 (A) 38312 95A8 閨39651 9AE3 髣30806 7856 硖25001 61A9 憩p^;L(B)(C) 一个极小值点和两个极大值点. (D) 两个极小值点和一个极大值点。

2003年9月CET-4真题大学英语四级考试COLLEGE ENGLISH TEST—Band Four—Part I Listening Comprehension (20 minutes)Section ADirections: In this section, you will hear 10 short conversation. At the end of each conversation. a question wilt be asked about what was said. Both the conversation and the question will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A), B), C) and D). and decide which is the best answer Then mark the corresponding letter on the Answer Sheet with a single line through the centre.Example: You will hear:You will read:A) At thee office.B) In the waiting room.C) At the airport.D) In a restaurant.From tile conversation we know that the two were talking about some work they had to finish in the evening. This conversation is most likely to have taken place at the office. Therefore, A) 'At the office' is the best answer You should choose [A] on the Answer Sheet and mark it with a single line through the centre.Sample Answer [A] [B] [C] ID]1. A) Give Bob a phone call. C) Go look for Bob.B) Go and pick Bob up. D) Wait for Bob.2. A) She is working in the city. C) Jobs are easier to find in the city.B) Life in the suburbs is lonely. D) It's less expensive l/ring in the city.3. A) In a printing shop. C) At a bookstore.B) At a publishing house. D) In a library.4. A) The woman be more careful next time. C) The woman find a spare key.B) They try to think of a solution. D) They come downstairs.5. A) Sending an e-mail. C) Talking on the phone.B) Working in an office. D) Doing spelling practice.6. A) Buy something for the picnic. C) Go shopping with the man.C) Go for a ride around town. D) Have a picnic.7. A) The woman misplaced her class permit for biology.B)The woman arrived for registration too early.C) The woman missed registration for the biology course.D) The woman got a wrong class permit.8. A) The woman likes the weather in New York very much.B) The woman will stay in New York a long time.C) The man is planning to visit New York.D) It's quite cold in New York now.9. A) The old lady sitting next to the couple likes toys very much.B) An old lady took the couple’s suitcase for her own.C) The couple's suitcase was stolen in the restaurant.D) The man forgot to put the toys in their suitcase.10. A) She's flying to Hong Kong.B) She's going to buy an air ticket.C) She's going to say good-bye to Bill.D) She's leaving for Hoog Kong with Bill.Section BDirections: In this section, you will hear 3 short passages. At the end of each passage. you will hear some questions. Both the passage and the questions will be spoken only once. After you hear a question, you must choose the best answer from the four choices marked A),B),C)and D). Then mark the corresponding letter on the Answer Sheet with a single line through the centre.Passage OneQuestions 11 to 13 are based on the passage you have just heard.11. A)They him only retired workers.B) They each do jobs they are good at.C) They close the hotel during low seasons.D) They employ as few workers as possible.12. A) Staff training. C) Cleaning and washing up.B) Book-keeping. D) Gardening and flower arranging. 13. A) They have their hotel beautifully decorated.B) They provide delicious food.C) They make their guests feel at home.D) They give parties regularly for their visitors.Passage TwoQuestions 14 to 17 are based on the passage you have just heard.14. A) To withdraw his deposit. C) To rob the bank.B) To cash a cheek. D) To get his prize.15. A) A radio announcer C) A car mechanic.B) A bank employee. D) A movie actor.16. A) They let him do what he wanted to. C) They pressed the alarm.B) They helped him find large bills. D) They called the police.17. A) He was afraid that be would be caught on the spot.B) Large bills were not within his reach.C) The maximum sum allowed was 55,000.D) He was limited by time and the size of his pockets.Passage ThreeQuestions 18 to 20 are based on the passage you have just heard.18. A) A rescuer on the Golden Gate Bridge. C) A telephone operator.B) A professional diver. D) A guard on the Golden Gate Bridge.19. A) Someone ham fallen off the bridge.B) Someone on the bridge is being attacked.C) Someone is threatening to destroy the bridge.D) Someone on the bridge is attempting to kill himself.20. A) Call the mother to come fight away.B)Try to communicate with them first.C) Help them to get out of their misty.D) Remind them that they have children to take care of.Part Ⅱ Reading Comprehension (35 minutes)Directions: There are 4 passages in this part. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A), B), C)and D). You should decide on the best choice and mark the corresponding letter on the Answer Sheet with a single ling through the centre.Passage OneQuestions 21 to 25 are based on the following passage.A rectal study, published in last week’s Journal of the American Medical Associati on, offers a picture of how risky it is to get a lift from a teenage driver, Indeed, a 16-year-old driver with three or more passengers is three times as likely to have a fatal accident as a teenager driving alone, By contrast, the risk of death for drivers between 30 and 59 decreases with each additional passenger.The autboes also found that the death rates for teenage drivers increased dramatically after 10 p.m., and especially after midnight, With passengers in the car, the driver was even more likely to die in a late-night accident.Robert Foss, a scientist at the University of North Carolina Highway Safety Research Center, says the higher death rates for teenage drivers have less to do with “really stupid behavior” than with just a lack of drivin g experience. “The basic issue.” Be says, “is that adults who are responsible for issuing licenses fail to recognize how complex and skilled a task driving is.”Both he and the author of the study believe that the way to mitigate (使……缓解)the problem is to have states institute so-called graduated licensing systems, in which getting a license is a multistage process. A graduated license requires that a leenager first prove himself capable of driving in the presence of an adult, followed by a period of driving with night of passcager restrictions, before graduating to full driving privileges.Graduated licensing systems have reduced leenage driver crashes, according to recent studies, About half ofthe states now have some sort of graduated Hcensing system in place, but only 10 of those states have restrictions on passengers, California is the strictest, with a novice(新手)driver prohibited from carrying any passenger under 20(without the presence of an adult over 25)for the first six months.21. Which of the following situations is most dangerous according to the passage?A) Adults giving a lift to teenagers on the highway after 10 p.m.B) A teenager driving after midnight with passengers in the car.C) Adults driving with three or more teenage passengers late at night.D) A teenager getting a lift from a stranger on the highway at midnight.22. According to Robert Foss. The high death rate of teenage drivers is mainly due to ________A) their frequent driving at night C) their lack of driving experienceB) their improper way of driving D) their driving with passengers23. According to Paragraph 3. which of the following statements is TRUE?A) Teenagers should spend more time learning to drive.B) Driving is a skill too complicated for teenagers to learn.C) Restrictions should be imposed on teenagers applying to take driving lessons.D) The licensing authonties are partly responsible for teenagers' driving accidents.24. A suggested measure to be taken to reduce teenagers' driving accidents is that ________ .A) driving in the presence of an adult should be made a ruleB) they should be prohibited from taking on passengersC) they should not be allowed to drive after 10 p.m.D) the licensing system should be improved25. The present situation in about half of the states is that the graduated licensing system ________.A) is under discussion C) has been put into effectB) is about to be set up D) has been perfectedPassage TwoPassage TwoQuestions 26 to 30 are based on the following passage.If you know exactly what you want, the best route to a job is to get specialized training. A recent survey shows that companies the graduates in such fields as business and health care who can go to work immediately with very little on-the-job training.That's especially true of booing fields that are challenging for workers. At Cornell's School of Hotel Administration, for example, bachelor's degree graduates get an average of four or five job offers with salaries ranging from the high teens to the low 20s and plenty of chances for rapid advancement. Large companies, especially, like a background of formal education coupled with work experience.But in the long run, too much specialization doesn't pay off. Business, which has been flooded with MBAs, no longer considers the degree an automatic stamp of approval. The MBA may open doors and command a higher salary injtially, but the impact of a degree washes out after five years.As further evidence of the erosion (销蚀) of corporate(公司的) faith in specialized degrees, Michigan State’sScheetz cites a pattern in corporate hiring practices, Although companies tend to take on specialists as new hires, they often seek out gencralists for middle and upper-level management. “They want someone who isn’t constrained(限制)by nuts and bolts to look at the big picture,”says Scheetz.This sounds suspiciously like a formal statement that you approve of the liberal-arts graduate. Time and again labor-market analysts mention a need for talents that liberal-arts majors are assumed to have: writing and communication skills, organizational skills, open-mindedness and adapeability, and the ability to analyze and solve problems, David Birch claims he does not hire anybody with an MBA or an engineering degree, “I hire only liberal-arts people because they have a less-than-canned way of doing things,” says Birch. Liberal-arts means an academically thorough and strict program that includes literature, history, mathematics, economics, science, human behavior—plus a computer course or two. With that under your belt, you can feel free to specialize, “A liberal-arts degree coupled with an MBA or some other technical training is a very good combination in the marketplace,” says Scheetz.26. What kinds of people are in high demand on the job market?A) Students with a bachelor's degree in humanities.B) People with an MBA degree front top universities.C) People with formal schooling plus work experience.D) People with special training in engineering27. By saying “…but the impact of a degree washes out after five years” (Line 3, Para, 3), the author means ________.A) most MBA programs fail to provide students with a solid foundationB) an MBA degree does not help promotion to managerial positionsC) MBA programs will not be as popular in five years' time as they are nowD) in five people will forget about the degree the MBA graduates have got28. According to Scheetz's statement (Lines 4-5. Para. 4), companies prefer ________.A) people who have a strategic mindB) people who are talented in fine artsC) people who are ambitious and aggressiveD) people who have received training in mechanics29. David Birch claims that he only hires liberal-arts people because ________.A) they are more capable of handling changing situationsB) they can stick to established ways of solving problemsC) they are thoroughly trained in a variety of specialized fieldsD) they have attended special programs in management30. Which of the following statements does the author support?A) Specialists are more expensive to hire than generalists.B) Formal schooling is less important than job training.C) On-the-job training is, in the long run, less costly.D) Generalists will outdo specialists in management.Passage ThreeQuestions 31 to 35 are based on the following passage.About six years ago I was eating lunch in a restaurant in New York City when a woman and a young boy sat down at the next table, I couldn’t help overhearing parts of their conversation. At one point the womanasked: 'So, how have you been?' And the boy—who could not have been more than seven or eight years old —replied. 'Frankly, I've been feeling a little depressed lately.''This incident stuck in my mind because it confirmed my growing belief that children are changing. As far as I can remember, my friends and I didn’t find out we were “depressed” until we were in high school.The evidence of a change in children has increased steadily in recent years. Children don’t seem childlike anymore. Children speak more like adults, dress more like adults and behave more like adults than they used to.Whether this is good or bad is difficult to say, but it certainly is different. Childhood as it once was no longer exists, Why?Human development is based not only on innate (天生的) biological states, but also on patterns of access to social knowledge. Movement from one social rote to another usually involves learning the secrets of the new status. Children have always been taught adult secrets, but slowly and in stages: traditionally, we tell sixth graders things we keep hidden from fifth graders.In the last 30 years. however, a secret-revelation (揭示) machine has been installed in 98 percent of American homes. It is called television, Television passes information, and indiscriminately (不加区分地), to all viewers alike, be they children or adults. Unable to resist the temptation, many children turn their attention from printed texts to the less challenging, more vivid moving pictures.Communication through print, as a matter of fact, allows for a great deal of control over the social information to which children have access. Reading and writing involve a complex code of symbols that must be memorized and practices. Children must read simple books before they can read complex materials.31. According to the author, feeling depressed is ________.A) a sure sign of a psychological problem in a childB) something hardly to be expected in a young childC) an inevitable has of children's mental developmentD) a mental scale present in all humans, including children32. Traditionally, a child is supposed to learn about the adult world ________.A) through contact with society C) naturally and by biological instinctB) gradually and under guidance D)through exposure to social information33. The phenomenon that today’s children seem adultiike is attributed by the author to ________.A) the widespread influence of televisionB) the poor arrangement of teaching contentC) the fast pace of human intellectual developmentD) the constantly rising standard of living34. Why is the author in favor of communication through print for children?A) It enables children to gain more social information.B) It develops children's interest in reading and writing.C) It helps children to memorize and practice more.D) It can control what children are to learn.35. What does the author think of the change in today’s children?A) He feels amused by chair premature behavior.B) He thinks it is a phenomenon worthy of note.C) He considers it a positive development.D) He seems to be upset about it.Passage FourQuestions 36 to 40 are based on the following passage.'Opinion' is a word that is used carelessly today. It is used to refer to matters of taste, belief, and judgment. This casual use would probably cause little confusion if people didn’t attach too much importance to opinion. Unfortunately, most to attach great importance to it. 'I have as much right to my opinion as you to yours, '' and ''Everyone’s entitled to his opinion, '' are common expressions. In fact, anyone who would challenge another's opinion is likely to be branded intolerant.Is that label accurate? Is it intolerant to challenge another's opinion? It depends on what definition of opinion you have in mind. For example, you may ask a friend ''What do you think of the new Ford cars?' And he may reply, 'In my opinion, they're ugly.' In this case, it would not only be intolerant to challenge his statement, but foolish. For it's obvious that by opinion he means his personal preference, a matter of taste. And as the old saying goes, ''It's pointless to argue about matters of taste.'But consider this very different use of the term, A newspaper reports that the Supreme Court has delivered its opinion in a controversial case. Obviously the justices did not shale their personal preferences, their mere likes and dislikes, They stated their considered judgment, painstakingly arrived at after thorough inquiry and deliberation.Most of what is referred to as opinion falls somewhere between these two extremes. It is not an expression of taste. Nor is it careful judgment. Yet it may contain elements of both. It is a view or belief more or less casually arrived at, with or without examining the evidence.Is everyone entitled to his opinion? Of course, this is not only permitted, but guaranteed. We are free to act on our opinions only so long as, in doing so, we do not harm others.36. Which of the following statements is TRUE, according to the author?A) Everyone has a right to hold his own opinion.B) Free expression of opinions often leads to confusion.C) Most people tend to be careless in forming their opinions.D) Casual use of the word 'opinion' often brings about quarrels.37. According to the author, who of the following would be labored as intolerant?A) Someone who turns a deaf ear to others' opinions.B) Someone who can't put up with others' tastes.C) Someone who values only their own opinions.D) Someone whose opinion harm. other people.38. The new Ford cars are cited as an example to show that ________.A) it is foolish to criticize a famous brandB) one should not always agree to others' opinionsC) personal tastes are not something to be challengedD) it is unwise to express one's likes and dislikes in public39. Considered judgment is different from personal preference in that ________.A) it is stated by judges in the courtB) it reflects public like and dislikesC) it is a result of a lot of controversyD) it is based on careful thought40. As indicated in the passage, being free to act on one's opinion ________.A) means that one can ignore other people's criticismB) means that one can impose his pre6ereaccs on othersC) doesn't mean that one has the right to do things at willD) doesn't mean that one has the right to charge others without evidencePart Ⅲ Vocabulary and Structure (20 minutes)Directions: There are 30 incomplete sentences it: this part. For each sentence there are four choices marked A), B), C) and D). Choose cite ONE answer that best completes the sentence. Then mark the Corresponding letter on the Answer Sheet with a single line through the centre.41. The beam that is ________by a laser differs in several ways from the light that comes out of a flashlight.A) emitted C ) motivatedB) transported D) translated42. We booked rooms at the hotel ________we should find no vacancies on our arrival.A) whenever C) sinceB) if D) lest43. Modern forms of transportation and communication have done much to ________the isolation of life in Alaska.A) break through C) break intoB) break down D) break out44. We know through painful experience that freedom is never by the oppressor; it must be ________by the oppressed.A) demanded C) requiredB) commanded D) requested45. Color and sex are not relevant ________whether a person is suitable for the job.A) on C) toB) for D) with46. ________the enormous flow of food from the entire globe, these countries have for many years not felt any population pressure.A)Thanks to C) In line withB) By means of D) With regard to47. Kesearch universities have to keep up with the latest computer and scientific hardware ________price.A) On account of C) in addition toB) regardless of D) not to mention48. Three university departments have been ________ 0,000 to develop good practice in teaching and learning.A) promoted C) securedB) included D) awarded49. The rapid development of communications technology is transforming the ________in which people communicate across time and space.A) mood C) mannerB) mission D) vision50. Mr.Jones holds strong views against video games and ________the clsing of all recreation facilities for such games.A) assists C) advocatesB) acknowledges D) admits51. Workers in the fine arts ________thoughts and feelings through their creative works.A) transmit C) conveyB) elaborate D) contribute52. Small as it is, the ant is as much a creature as ________all other animals on earth.A) are C) isB) do D) have53. The policeman declared that the blow on the victim's head ________from behind.A) should have been made C) would have been madeB) must have been made D) ought to have been made54. Finding a job can be ________and disappointing, and therefore it is important that you are prepared.A) exploiting C) profitingB) frustrating D) misleading55. It British government often says that furnishing children with ________ to the information superhighway is a top priority.A) procedure C) exploreB) protection D) acceis56. Louis Herman, at the University of Hawall, has ________a serics of new experiments in which some animals have learned to understand sentences.A) installed C) devisedB) equipped D) formatted57. Researchers at the University of Illanois determined that the ________of a father can help improve a child’s grades.A) involvement C) accociationB) intetaction D) communcation58.We can accept your order ________payment is made in advance.A)in the bellef that C) on the excuse thatB) in order that D) on condition that59.Many in the crodit industry expect that credit cards will eventually ________paper money for almost every purchase.A) exchange C)ceplaceB) reduce D)trade60.Any donation you can give will help us ________the suffering and isolation of the homeless this New Year.A) lift C) comfortB) patch D) ease61. In India more than oce hundred languages are spoken, ________ which only fourteen are tecognized as official.A) of C) withB) in D) within62. Techniques for ________sleep would involve learning to control both mind and body so that sleep can occur.A) cultivating C) pushingB) promocing D) streagthening63. It is important to ________between the rules of grammar and the conventions of written language.A) determine C)exploreB) identify D)distinguish64. It is too early to say whether IBM’s competito rs will be able to ________their products to the new hardware at an affordable cost.A)adapt C) yieldB)stick D)adopt65. This research has attracted wide coverage in the ________and has featured on BBC television’s Tomorrow’s World.A) data C)messageB)source D)media66.I had just posted the letter when I remembered that hadn’t ________the cheque.A) imposed C)enclosedB) involved D)contained67.She had a tense expression on her face, ________she were expecting trouble.A) even though C)even asB) as though D) now that68.They were ________admission to the military exhibition because they were foreigners.A) denied C)deprivedB) declined D) rejected69.It gave me a strange feeling of excitement to see my name in ________.A) prospect C) processB) print D) press70. Residents were cutting their lawns, washing their cars and otherwise ________a pleasant, sunny day.A) idling away C) chasing awayB) taking away D) driving awayPart Ⅳ Short Answer Questions (15 minutes)Directions: In this part there is a short passage with 8 questions or incomplete statements. R the passage carefully. Then answer the questions or complete the statements in fewest possible words. Your answer may be a word, a phrase, or a short sente. Fewest possible words. Your answer may be a word, a phrase, or a short sente. Write your answers in the spaces provided on the right of the page.Sports is one of the world’s largest industries, and most athletes are professionals who are paid for their efforts. Because an athlete succeeds by achievement only—not by economic b ground or family connections—sports can be a fast route to wealth, and many athletes play n for money than for love.This has not always been true. In the ancient Olympics the winner got only a wreath of leaves (橄榄叶花环). Even though the winners became national heroes, the games remained teur for centuries. Athletes won fame, but no money. As time passed, however, the contests bec increasingly less amateur and cities began to hire athletes to represent them. By the fourth can A.D., the Olympics were ruined, and they were soon ended.In 1896, the Olympic games were revived (使再度兴起)with the same goal of pure ama competition. The rules bar athletes who have ever received a prize or an athletic scholars or who have spent four weeks in a training camp. At least one competitor in the 1896 games me these qualifications. He was Spiridon Loues, awater carrier who won the marathon race, After race, a rich Athenian offered him anything he wanted. A true amateur, Loues accepted only a cart and a horse. Then he gave up running forever. But Loues was an exception and now, as the Chairman of the German Olympic Committee said, “Nobody pays any attention to these rules.” Many countries pay their athletes to train year-round, and Olympic athletes are eager to sell their names to companies that make everything from ski equipment to fast food.Even the games themselves have become a huge business. Countries fight to hold the Olympics not only for honor, but for money. The 1972 games in Munich cost the Germans 545 million dollars, but by selling medal symbols, TV rights, food, drink ,hotel rooms, and souvenirs (纪念品), they managed to make a profit. Appropriately, the symbol of victory in the Olympic games is no longer a simple olive wreath—it is a gold medal.S1. To many people, sports today is nothing S1.________but S1 .S2. What do most athletes of today go after? S2.________S2 .S3. What reward could an ancient Greek athlete S3.________expect? S3 .S4. By the fourth century A.D., Olympic contests S4.________became increasingly more S4 .thus ruining the Olympics.S5.When the Olympic games were revived in S5.________1896, athletes who had received specialtraining in camps would be S5 .S6. What did Spiridon Loues do after he accepted S6.________the Athenian’s gift? S6 .S7. According to the author, some athletes are S7.________Even willing to advertise for businessesWhich sell things like S7 .S8. The 1972 Munich games managed to make S8.(1)________a big profit mainly by S8(1) services (2)________and selling S8(2) .Part Ⅴ Writing (30 minutes)Directions: For this part, you are allowed 30 minutes to write a composition on the topic The Day My Classmate Fell Ill (or Got Injured). You should write at least 120 words according to the outline given below in Chinese:1.简单叙述一下这位同学生病（或受伤）的情况2.同学、老师和我是如何帮助他/她的3.人与人之间的这种相互关爱给我的感受是……The Day My Classmate Fell Ill (or Got Injured)。