08真题

2008年全国硕士研究生入学统一考试数学四试题解析一、选择题：1～8小题，每小题4分，共32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0a b <<，则()10lim nnnn ab--→+（ ）()A a .()B 1a -. ()C b .()D 1b -.（2）设函数()f x 在区间[1,1]-上连续，则0x =是函数0()()x f t dt g x x=⎰的（ ）()A 跳跃间断点. ()B 可去间断点.()C 无穷.()D 振荡.（3）设()f x 是连续奇函数，()g x 是连续偶函数，区域{(,)01,D x y x y =≤≤≤≤则正确的（ ）()A ()()0Df yg x dxdy =⎰⎰.()B ()()0D f x g y d x d y =⎰⎰.()C [()()]0Df xg y dxdy +=⎰⎰.()D [()()]0Df yg x dxdy +=⎰⎰.（4）曲线方程为()y f x =函数在区间[0,]a 上有连续导数，则定积分'0()axf x dx ⎰（ ）()A 曲边梯形ABCD 面积.()B 梯形ABCD 面积.()C 曲边三角形ACD 面积.()D 三角形ACD 面积.（5）设A 为n 阶非零矩阵，E 为n 阶单位矩阵. 若30A =，则（ ）()A E A -不可逆，E A +不可逆.()B E A -不可逆，E A +可逆.()C E A -可逆，E A +可逆.()D E A -可逆，E A +不可逆.（6）设1221A ⎛⎫=⎪⎝⎭，则在实数域上与A 合同的矩阵为（ ） ()A 2112-⎛⎫⎪-⎝⎭ ()B 2112-⎛⎫ ⎪-⎝⎭ ()C 2112⎛⎫ ⎪⎝⎭()D 1221-⎛⎫⎪-⎝⎭. （7）随机变量,X Y 独立同分布且X 的分布函数为()F x ，则{}max ,Z X Y =的分布函数为（ ）()A ()2F x .()B ()()F x F y .()C ()211F x --⎡⎤⎣⎦.()D ()()11F x F y --⎡⎤⎡⎤⎣⎦⎣⎦.（8）随机变量()0,1X N ，()1,4Y N 且相关系数1XY ρ=，则（ ）()A {}211P Y X =--=. ()B {}211P Y X =-=. ()C {}211P Y X =-+=.()D {}211P Y X =+=.二、填空题：9-14小题，每小题4分，共24分，请将答案写在答题纸指定位置上.（9）设函数21,()2,x x cf x x c x ⎧+≤⎪=⎨>⎪⎩在(,)-∞+∞内连续，则c = .（10）已知函数()f x 连续且0()lim2x f x x→=，则曲线()y f x =上对应0x =处切线方程为 . （11）2113ln y dx x xdy =⎰⎰ .（12）微分方程2()0x y x e dx xdy -+-=通解是y = .（13）设3阶矩阵A 的特征值互不相同，若行列式0A =，则A 的秩为 .（14）设随机变量X 服从参数为1的泊松分布，则{}2P X EX == .三、解答题：15－23小题，共94分.请将解答写在答题纸指定的位置上.解答应写出文字说明、证明过程或演算步骤.(15)（本题满分10分）求极限201sin limln x x x x→. (16) （本题满分10分） 设()()1f x t t x dt =-⎰，01x <<，求()f x 的极值、单调区间和凹凸区间.(17)（本题满分10分）求函数222u x y z =++在在约束条件22z x y =+和4x y z ++=下的最大和最小值.(18)（本题满分10分）设(),z z x y =是由方程()22x y z x y z ϕ+-=++所确定的函数，其中ϕ具有2阶导数且1ϕ'≠-时，求(1)dz （2）记()1,z z u x y x y x y ⎛⎫∂∂=- ⎪-∂∂⎝⎭，求u x ∂∂.(19)（本题满分10分）()f x 是周期为2的连续函数，（1）证明对任意实数都有()()22t tf x dx f x dx +=⎰⎰（2）证明()()()202x t t g x f t f s ds dt +⎡⎤=-⎢⎥⎣⎦⎰⎰是周期为2的周期函数． （20）（本题满分11分）设矩阵2221212n na a a A a a ⨯⎛⎫⎪ ⎪= ⎪ ⎪⎝⎭ ，现矩阵A 满足方程AX B =，其中()1,,T n X x x = ，()1,0,,0B = ，（1）求证()1nA n a =+（2）a 为何值，方程组有唯一解（3）a 为何值，方程组有无穷多解 (21)（本题满分11分）设A 为3阶矩阵，12,αα为A 的分别属于特征值1,1-特征向量，向量3α满足323A ααα=+，证明（1）123,,ααα线性无关； （2）令()123,,P ααα=，求1P AP -.（22）（本题满分9分）设随机变量X 与Y 相互独立，X 概率分布为{}()11,0,13P X i i ===-，Y 概率密度为()1010Y y f y ≤≤⎧=⎨⎩其它，记Z X Y =+（1）求102P Z X ⎧⎫≤=⎨⎬⎩⎭（2）求Z 的概率密度（23）（本题满分9分）设某企业生产线上产品合格率为0.96，不合格产品中只有34产品可进行再加工且再加工的合格率为0.8，其余均为废品，每件合格品获利80元，每件废品亏损20元，为保证该企业每天平均利润不低于2万元，问企业每天至少生产多少产品？.。

08年专升本公共英语真题及解析(第一部分)Part Ⅰ Vocabulary and Structure (40 points)Directions： There are 40 incomplete sentences in this part. For each sentence there are four choices marked A， B， C and D. Choose the ONE answer that best completes each sentence， and then write the choice in the brackets.1. John and I _____ friends for eight years.We first got to know each other at a Christmas party. But we _____ each other a couple of times before that.A. had been; have seenB. have been; have seenC. had been; had seenD. have been; had seen【翻译】我和约翰已是八年的好友，我俩第一次相识在一个圣诞晚会上，在此以前我们曾见过几面。

［考点］谓语动词的时态【解析】 D 从时间短语for eight years 推知，第一句的谓语动词须用现在完成时。

最后一句谓语动词的动作发生在第二句谓语动词动作之前，所以要选用过去完成时。

2. When _____ the education systems of China and Britain， the professor gave his own comment.A. asking to be comparedB. asked him to compareC. asking him to compareD. asked to compare【翻译】当要求对比中英教育体制时，教授提出了自己的看法。

08年英语真题-CAL-FENGHAI-(2020YEAR-YICAI)_JINGBIANGrammar and VocabularyI.1. We are not on very good _____ with the people next door.A. freindshipB. relationsC. willD. terms2. Usually newspapers _______ for people with intellectual interests.A. suitB. furnishC. regardD. cater3. The overcrowded living conditions ______ a heavy strain on the family.A. setB. putC. madeD. pressed4. The supply of apples exceeds the _______ this year.A. requestB. claimC. requirementD. demand5. I must take this watch to be repaired: it ____ over 20 minutes a day.A. increasesB. progressesC. acceleratesD. gains6. If this animal had escaped from its cage it could______ have killed or hurt several people.A. equallyB. bothC. wellD. severely7. I’m sorry we gave you such short ______of our visit.A. cautionB. noticeC. informationD. preparation8. That old vase will _____ an attractive lamp-holder.A. composeB. formC. makeD. assemble9. The World Bank has criticized the country for not giving enough financial ____ to developing countries.A. allowanceB. aidC. loanD. provision10. Nothing would stop me from _____ my ambition.A. reachingB. completingC. achievingD. obtaining11. He showed his _____ for the TV program by switching it off.A. distasteB. discontentC. annoyanceD. boredom12. They are _____ the woods for the missing child.A. seekingB. lookingC. investigatingD. combing13. To prevent flooding in winter the water flowing from the dam is constantly ___by a computer.A. managedB. gradedC. monitoredD. conducted14.______ I know the money is safe I shall not worry about it.A. Even thoughB. UnlessC. As long asD. However15. He couldn’t lie convincingly enough to take a child _______.A. awayB. downC. inD. up16. The parents were worried about Dorothy because no one was aware _____she had gone.A. where thatB. of whereC. of the place whereD. the place17. It was not until she returned home_______ she realized she had almost wasted 10 of her valuable hours.A. andB. whenC. thenD. that18. There has not been a great response to the sale, _______A. does itB. has itC. does thereD. has there19. Anthropology is a science ______anthropologists use a rigorous set of methods andtechniques to document observations that can be checked by others.A. in thatB. that inC. thatD. in20. The activities of the international marketing researchers are frequently much broaderthan ______.A. the domestic marketer hasB. those of the domestic marketerC. the domestic marketer doesD. that which has the domestic marketer21. I’m surprised at there _______ an index.A. not to beB. to be notC. not beingD. bring not22. _______ this soup. I_______ pepper in it.A. am tasting…am tastingB. am tasting…tasteC. taste…am tastingD. taste…have tasted23._____, explorers could never have found the cave.A. But for the fissures had been spottedB. If not the fissures had been spottedC. Had the fissures not been spottedD. Had not the fissures been spotted24. John often sits in a small bar, drinking and smoking considerably more_________.A. than that he is healthyB. than good for his healthC. than his health couldD. than is good for his health25.This ______ girl is Mary’s cousin.A. pretty little SwedishB. Swedish little prettyC. Swedish pretty littleD. Little pretty Swedish2.1. This is a most peculiar letter. What do you ______ of it?A. gatherB. makeC. getD. feel2. Now that we’ve identified the problem, we must decide on an appropriate course of______.A. actionB. progressC. solutionD. development3. Since the couple couldn’t _____ their differences, they decided to get a divorce.A. reconcileB. identifyC. adjustD. coincide4. We attended a ______ of the new manufacturing process.A. demonstrationB. displayC. showingD. manifestation5. How many people do you think this car would _______A. occupyB. holdC. fitD. load6. It never_____ my mind that he might refuse the request.A. passedB. filledC. crossedD. occurred7. People become less ______to new ideas as they grow older.A. receptiveB. availableC. attentiveD. attractive8. Is he really _____ to judge a brass band contest?A. competentB. skillfulC. capableD. efficient9. The new airport will be _____ from all directions.A. availableB. accessibleC. obtainableD. achievable10.The team’s recent wins have now_____ them for the semi-finals.A. fittedB. promotedC. qualifiedD. selected11. For parents, one of the problems ____by rising prices is the continual demand for more pocket money.A. givenB. posedC. providedD. forced12. The police managed to ______ down the owner of the car.A. traceB. trackC. searchD. pursue13. The party’s reduced vote was _____ of lack of support for its policies.A. indicativeB. confirmingC. revealingD. evident14. The football match was televised _____ from the Workers’ Stadium.A. aliveB. lifeC. liveD. lively15. Having considered the problem for a while she thought better_____ her first solution.A. toB. thanC. fromD. of16. If that idea was wrong, the project is bound to fail,_____ good all the other ideas might be.A. whateverB. thoughC. whatsoeverD. however17. The less the surface of the ground yields to the weight of the body of a runner, ____ to the body.A. the greater the stressB. the stress is greaterC. greater the stress isD. greater is the stress18. That’s your sister, ______A. isn’t itB. isn’t thatC. isn’t sheD. aren’t you19. It’s high time we ______a rest.A. haveB. hadC. are havingD. should have20. If you ______, you’d better go outside in the fresh air.A. faintB. have faintedC. are going to faintD. will faint21. I don’t know _______.A. why do thisB. why to do thisC. why doing thisD. why we ought to do this22. The man over there is _____ our principal.A. no other butB. no other thanC. no one thanD. none other than23. No one can walk the wire without a bit of fear unless_____ very young.A. having been trainedB. trainedC. to be trainedD. being trained24. –-- When can we come to visit you–-- Any time you feel________.A. for itB. to itC. like itD. so25. His honesty is ______: nobody can doubt it.A. in questionB. out of the questionC. beside the questionD. without question3.1. We covered a wide _____ of topics in the interview.A. extentB. collectionC. numberD. range2. What you say is true, but you could have _____it more tactfully.A. talkedB. phrasedC. observedD. remarked3. If you are under 18, you are not ________to join this club.A. legitimateB. legibleC. eligibleD. permissive4. When I arrived in this country I had to start learning the language from ______.A. scratchB. introductionC. ignoranceD. blank5. I spoke to him, but he was too ______ to hear what I said.A. preoccupiedB. concentratedC. absent-mindedD. thoughtful6. To ______ greater accuracy, all invoices will be double-checked before leaving for the office.A. assureB. insureC. insureD. ascertain7. His letter was so confused that I could hardly make any_____ of it at all.A. interpretationB. messageC. senseD. meaning8. According to the weather forecast, which is usually _______, it will snow this afternoon.A. accurateB. preciseC. exactD. perfect9. I cannot bear the noise of my brother’s radio, it ______ me from my work.A. disturbsB. perturbsC. interruptsD. distracts10. I congratulate you on your ______ in jewellery.A. selectionB. choiceC. flavorD. taste11. Even though the football match was not very exciting, the _____ managed to make it sound interesting.A. commentatorB. newscasterC. announcerD. narrator12. Ask the publisher to send you their latest _____ of English textbooks.A. catalogueB. brochureC. pamphletD. booklet13. I haven’t the ______idea what you mean.A. lightestB. dimmestC. faintestD. smallest14. ______ some countries have ruined their agriculture, squandering money on uneconomic factories, the Ivory Coast has stuck to what it is good at.A. AfterB. DuringC. WhenD. While15. Apparently one person _____ten now attends a university in this country.A. ofB. overC. inD. from16. All of the plants now raised on farms have been developed from plants_____ wild.A. once they grewB. they grew onceC. that once grewD. once grew17. This is the best book ______this year.A. appearingB. having appearedC. to appearD. appeared18. What annoys me is that tomorrow _____the third time I _____ take my car in to berepaired.A. is …have toB. will be … have had toC. is …will have toD. will be… have to19. Our neighbors have _____ours.A. as a big house asB. as big a house asC. a big house as same asD. a house the same big as20. She is _______ biting her nails.A. oftenB. usuallyC. continuallyD. hardly21. It is ten years since I _______ you last.A. seeB. sawC. didn’t seeD. haven’t seen22._______ is such a spitfire.A. His that third brotherB. His third that brotherC. That third brother of hisD. That his third brother23. I owe a special debt of ______ to my wife and child for their willingness to put up with myfrequent bouts of ill-temper or sheer absent-mindedness while I was writing this book.A. thankB. thankingC. thanksD. thankings25. An application to join this scheme places you under no obligation________.A. indeedB. eventuallyC. apartD. whatsoever4.1. At the casualty department my brother had his injury_________.A. curedB. healedC. relievedD. treated2. He told his father a long and _______story to explain his lateness.A. inconceivableB. unconvincingC. unimaginableD. incredulous3. Milk has a _______ to go sour in hot weather.A. tendencyB. habitC. problemD. characteristic4. Too many hotels have been built and this has _____down prices, making holidays cheaper.A. forcedB. cutC. slowedD. reduced5. The lecture ______from prehistory to modern times and gave the audience much to think about.A. coveredB. includedC. rangedD. dealt6. At first I was of the _____that you were decidedly right.A. attitudeB. opinionC. thoughtD. idea7. Protests died down when they realized that the new tax ______to only 50p a week.A. addedB. reachedC. approachedD. amounted8. The accused was given a short sentence as he had committed only a ______offence.A. subordinateB. minimalC. secondaryD. minor9. She _____wanted a house overlooking the sea.A. particularlyB. stronglyC. essentiallyD. extremely11. At the university of Oxford and Cambridge the ______of teachers to students is very high.A. proportionB. numberC. ratioD. percentage12. I hope you must not take _____ at my frankness.A. annoyanceB. offenceC. resentmentD. irritation13. With his lack of experience and smaller physique, we don’t think he _____ a chance of winning the fight.A. stoodB. gainedC. possessedD. took14. He lost his job ______no fault of his own.A. throughB. byC. withD. over15. He didn’t know anyone at the wedding_____ than the bride and groom.A. exceptB. otherC. apartD. rather17. Supposing I _______to agree to your request, how do you think the other students would feel?A. wouldB. amC. wereD. could18._______ her inexperience her failure to secure the contract was not surprising.A. In view ofB. By virtue ofC. With regard toD. In recognition of19. The University of Georgia, _____ in 1785, was the first state-supported university in theU.S.A. charteredB. was charteredC. it was charteredD. to be chartered20. This rule_____ to everyone who ________ for this post.A. will apply… will applyB. applies… will applyC. will apply… appliesD. is applying… is applying21. Are you suggesting that Joe_______ the murder when you don’t believe his alibi.A. commitsB. will commitC. commitD. committed22. You look frozen. I _____ you a cup of coffee.A. will makeB. am going to makeC. am makingD. am to make23. Who _____ in but the President himself?A. is comingB. should comeC. cameD. has come24. She will be 21 _____.A. come MayB. when May is comingC. if May will comeD. that May comes25. He did it ______ it took me.A. one-third the timeB. the one-third timeC. one-third a timeD. a one-third time5.1. Ted couldn’t remember the exact date of the storm, but he knew it was _____ Sundaybecause everybody was at_______ church.A. ,/ theB. a , /C. , / aD. the, /2. When I arrived at the meeting, the first speaker____ and theaudience ______.A . had finished speaking, were clapping B. had finished speaking, had clappedC. finished speaking, clappedD. finished speaking, were clapping3. “The door was opened.”“It ______ open. I had locked it myself and the key was in my pocket.”A. can’t beB. mustn’t beC. can’t have beenD. mustn’t have been4. We could go to a concert______ you’d prefer to visit a museum.A. ifB. becauseC. unlessD. since5. If you ______ in such a hurry you _____ sugar into the sauce instead of salt.A. were not, would notB. were, would putC. had been, would have putD. had not been, would not have put6. The doctor is feeling the little girl’s pulse. He says it_____ normal.A. feelsB. is feelingC. has feltD. is felt7. Home is home, ______ ever so homely.A. it isB. it wereC. be itD. it be8. Mary is ______ than Alice.A. more experienced a teacherB. a more experienced teacherC. more an experienced teacherD. more experienced teacher9. They fulfilled the task in ______ it took us.A. three-fourths timeB. three-fourths timesC. three-fourths the timeD. the three-fourths time10.______ their help, we would not have succeeded.A. Hadn’t been forB. Had it not been forC. It had been forD. Had not it been for11. This question admits ______ several answers.A. forB. withC. ofD. to12._______all probability nobody would have complained if Mary had not told the negotiators about it.A. ToB. InC. ForD. At13. The compositions contained so few errors that the teacher got the students ____ one another’s papers.A. correctB. to correctC. correctingD. to be correcting14. A hibernating animal needs hardly any food all through the winter, ______A. need itB. needn’t itC. does itD. doesn’t it15. I don’t like ______bills but when I get them I like ______ them promptly.A. to get, payB. getting, to payC. to get, to payD. getting, paying16. He used so much jargon that I hadn’t a ______ what he was talking about.A. queryB. hintC. thoughtD. clue17. Isn’t it time that you ______ some serious work before the examination?A. got down toB. took up withC. got off withD. put down to18. Please put your empty cigarette packets and paper bags in the _____ bins provided.A. junkB. litterC. scrapD. deposit19. The service was held to ______ the sacrifice of those who died in the war.A. commemorateB. memorizeC. rememberD. remind20. His _____ of the basic structure is good but his vocabulary is limited.A. holdB. gripC. graspD. seizure21. The horses have returned to their ______ after the morning exercise.A. barnsB. stablesC. kennelsD. sheds22. I couldn’t sleep because the tap in the bathroom was _______.A. drainingB. droppingC. spillingD. dripping23. “It’s hot, isn’t it?” he said, _____ his brow with a handkerchief.A. rinsingB. wipingC. sweepingD. scrubbing24. He is so ______ in his work that it would be a pity to disturb him.A. absorbedB. attentiveC. consumedD. intent25. I ______ with him to abandon the ship before it was too late.A. appealedB. claimedC. beggedD. pleaded26. I was about to say something, but ______ the temptation.A. challengedB. obstructedC. resistedD. struggled27. We will accept your check, although it is not our normal _______.A. practiceB. intentionC. stateD. occasion28. Following the elections, a completely new situation is likely to________.A. arouseB. ariseC. raiseD. rise29. Production has been delayed because of a shortage of _______ materials.A. baseB. primeC. rawD. rough30. Susan found that her new job didn’t provide her with sufficient ______ for her ability.A. capacityB. openingC. rangeD. scope6.1.______ their policy can be changed the future of that country will be indeed bleak.A. Even ifB. UnlessC. Now thatD. As long as2.She said she would work it out herself _______ ask me for help.A. and not toB. but notC. and prefer notD. rather than3.“I bought this shirt for 35 yuan yesterday.”“It’s on sale only for 29. You should have waited.”“Oh really But how ______ I know”A. wouldB. canC. didD. do4.They were pushed into battle _______ .A. unpreparedB. unpreparedlyC. not preparing itD. without preparing it5.She asked that she ______ allowed to see her son in police custody.A. would beB. could beC. beD. was6.Mr. Anderson presided ______ the board meeting on behalf of the Chairman.A. atB. overC. onD. in7.The rising crime rate is ______ major concern of __________ society.A. the, theB. a, /C. a, theD. /, the8.I never regretted ________ the offer, for it was not where my interest lay.A. not to acceptB. not having acceptedC. having not acceptedD. not accepting9.I _______ writing the paper as scheduled, but my mother’s illness interfered.A. am to have finishedB. was to have finishedC. was to finishD. ought to finish10.Some dieters find that after their diet is over, they eat twice ______ they did before their diet.A. more thanB. as many asC. much thanD. as much as11.She may be _______ experience, but she learns quickly.A. lackingB. lacking inC. in need forD. in lack of12.David Singer, my friend‘s father, _______ raised and educated in New York, lived and lectured in Africamost of his life.A. whoB. ifC. whileD. though13.My Scottish friend says there is ______ monster in Loch Ness.A. no such thing asB. no such thing as aC. no such a thing asD. no such a thing as a14.The university authorities are seriously considering abandoning the traditional ________ class.A. fifty minutesB. fifty-minutesC. fifty-minuteD. fifty minute’s15._________ the snake in superstitious awe.A. Mankind has held longB. Long has held mankindC. Has mankind long heldD. Mankind has long held16.On the desert, travelers often see _______ rivers and lakes.A. imaginingB. imaginativeC. imaginableD. imaginary17.Inside the apartment was an unpleasant smell of ______ air.A. staleB. smokedC. mistyD. wet18.The album might well have ______ had it been less expensive.A. worked outB. fallen throughC. caught onD. fitted in19.In order to be successful as an engineer, she had to become ______ at maths.A. proficientB. outstandingC. prominentD. experienced.20.This move deprived the prisoner of his _______ of escape.A. waysB. possibilitiesC. plansD. means21.The house that we used to live in is in a very _______ state.A. neglectfulB. negligibleC. neglectedD. negligent22.The ticket taker at the football game tore the ticket ________.A. in halfB. by halfC. in halvesD. at half23.I wish, if possible, to avoid any ______ of my family.A. hintB. mentionC. clueD. comment24.I’m afraid this painting is not Qi Baishi. It’s only a copy and so it’s ________.A. worthlessB. invaluableC. unworthyD. priceless25.When her parents died, Brenda _______ of the house and all its contents.A. discardedB. dispelledC. disposedD. discharged26.The plans for the building were _______ a few months ago.A. drawn onB. drawn backC. drawn outD. drawn up27.We were filled with _______ about flying in such bad weather.A. troublesB. obscurityC. ignoranceD. misgivings28.We are all astonished to learn that the apparently ______ professor was really a spy.A. respectfulB. respectiveC. respectableD. respected29.It is important that the schedule be not too ______ to allow for relaxation and hobbies.A. loadedB. crowdedC. filledD. squeezed30.The millionaire in the story had a(n) _______ habit of sleeping with his sack of money laid beside him inplace of a wife.A. economicB. miserlyC. disgustedD. playful7.1. A ship with a heavy load of timber is reported to have sunk_____ the coast of California.A. offB. onC. atD. in2.Arriving at the bus stop, ______ waiting there.A. a lot of people wereB. he found a lot of peopleC. a lot of peopleD. people were found3.____ your timely advice, I would never have known how to go about the work.A. UnlessB. But forC. Except forD. Not for4.We can assign the task to _____ is capable and trustworthy.A. whomeverB. whoC. whomD. whoever5._____ regular training in nursing, she could hardly cope with the work at first.A. Not receivedB. Since receivingC. Having receivedD. Not having received6.So badly ____in the car accident that he had to stay in hospital for a few months.A. did he injuredB. injured himC. was he injuredD. he was injured7.The country’s chief exports are coal, cars and cotton goods, cards ____ the most important of these.A. have beenB. areC. beingD. are being8.It was recommended that passengers ______ smoke during the flight.A. notB. need notC. could notD. would not9.“She must be in the dormitory now”. “No, she ____ be there. I saw her in the classroom a minute ago.”A. mustn’tB. can’tC. couldn’tD. wouldn’t10._____ human problems that repeat themselves in _____ life repeat themselves in _______ literature.A. /, /, theB. /, the, /C. The, / , /D. The, the, the11.Only take such clothes ____ really necessary.A. as wereB. as they areC. as they wereD. as are12.______ you were busy, I wouldn’t have bothered you with my questions.A. If I realizedB. Had I realizedC. I realized thatD. As I realized13.She has taken great pains to conceal her emotions, and thereby made them _____ conspicuous.A. all the moreB. all the muchC. all moreD. all much14.He ____ the 8:20 bus because he didn’t leave home till 8:25.A. couldn’t have caughtB. ought to have caughtC. shouldn’t have caughtD. must not have caught15.______ is often the case with a new idea, much preliminary activity and optimistic discussion producedno concrete proposals.A. ThatB. ItC. ThisD. As16.Please dispose _____ those old newspapers while you’re cleaning up the room.A. outB. ofC. awayD. in17.One can ______ even from one’s unpleasant experiences.A. obtainB. improveC. benefitD. continue18.This automobile plant has a monthly _______ of 500 cars.A. proficiencyB. capabilityC. strengthD. capacity19.At present there is a ______ of iron and steel and more must be produced.A. limitB. lossC. povertyD. scarcity20.He was ______ admittance to the concert hall for not being properly dressed.A. rejectedB. deniedC. withheldD. deprived21.Because of the strong sun the new sitting-room curtain have _____ from dark blue to grey.A. faintedB. paledC. bleachedD. faded22.My new sweater ______ when I washed it.A. shrankB. shortenedC. contractedD. condensed23.He was so ______ on his work that he didn’t hear her come in.A. intentB. absorbedC. engrossedD. involved24.George has a big coffee _____ on the front of his jacket.A. spotB. markC. stainD. patch25.The problem has _____simply because you didn’t follow the instructions in the handbook.A. assembledB. arisenC. risenD. resulted26.Try not to say anything harmful to her. She is a very _______person.A. sensibleB. sensitiveC. toughD. reasonable27.The ______ driver thinks accidents only happen to other people.A. averageB. commonC. usualD. normal28.The boxer ______ his opponent as hard as he could.A. punchedB. slappedC. knockedD. whipped29.The Christmas presents were all _____ in shiny papers.A. done overB. done withC. done outD. done up30.In the next few years major changes will be ______ in China’s industry.A. brought forwardB. brought aboutC. brought onD. brought up8.1. Most people can’t get ____ the day without at least one cup of coffee.A. onB. throughC. overD. by2. He noticed the helicopter hovering over the field. Then to his astonishment, he saw arope ladder _____out and three men climbing down it.A. throwingB. being thrownC. having thrownD. having been thrown3. He resented _____ to wait. He expected the minister _____ him at once.A. to be asked, to seeB. being asked, to seeC. to be asked, seeingD. being asked, seeing4. The idea of traveling through _____space to other planets interests many people today.A. aB. theC. /D. one5. The meeting’s been cancelled. Ann _____ all that work.A. need to doB. need haveC. needn’t have doneD. needed not to do6. It was not until midnight _____ the snowcapped peak.A. that they sightedB. that they didn’t sightC. did they sightD. had they sighted7. You’d better look at the difficulty ______.A. the other wayB. by the other wayC. another wayD. by another way8. ____ I was very mistaken, there was something wrong with Lousie.A. UnlessB. AsC. ThoughD. Since9.He prefers _______.A.to write his letters rather than dictating them.B.to write his letters rather than dictate them.C.writing his letters rather than dictate them.D.writing his letters rather than have dictated them.10.You and I could hardly understand _______A. could IB. couldn’t youC. couldn’t weD. could we11.He is not under arrest, _____ any restriction on him.A. or the police have placedB. or have the police placedC. nor the police have placedD. nor have the police placed12. We could ____ him with a detached house when he came, but he had specifically asked for a small flat.A. provideB. have providedC. not provideD. not have provided13.This missile is designed so that once _____ nothing can be done to retrieve it.A. firedB. being firedC. they firedD. having fired14.____ the two, Bob is ______ student.A. Of, more diligentB. In, more diligentC. Of, the more diligentD. In, the more diligent15.____, he would not have recovered so quickly.A. Hadn’t he been taken good care ofB. Had he not been taken good care ofC. Had not he been taken good care ofD. Had he been not taken good care of16.The local council has decided to take the _____ of the hotel to court.A. landlordB. tenantC. clientD. proprietor17.Swarms of wasps are always invading my garden. They are a thorough ______.A. nuisanceB. disturbanceC. troubleD. annoyance18.The cold drink _____him after his long hot journey.A. reducedB. refreshedC. releasedD. recovered19.For years she suffered from the ____ that her husband might come back to her.A. visionB. ideaC. imaginationD. illusion20.He went to Australia hoping to find a teaching_____ without too much difficulty.A. workB. careerC. postD. employment。

08年10月份全国自考，中国近现代史纲要真题一、单项选择题（本大题共30小题，每小题1分，共30分）在每小题列出的四个备选项中只有一个是符合题目要求的，请将其代码填写在题后的括号内。

错选、多选或未选均无分。

1.鸦片战争前中国封建社会的主要矛盾是（）A.地主阶级和农民阶级的矛盾B.帝国主义和中华民族的矛盾C.资产阶级和工人阶级的矛盾D.封建主义和资本主义的矛盾答案：A2.中国封建社会产生过诸多“盛世”，出现在清代的是（）A.文景之治B.贞观之治C.开元之治D.康乾盛世答案：D3.将中国领土台湾割让给日本的不平等条约是（）A.《南京条约》B.《北京条约》C.《马关条约》D.《瑗珲条约》答案：C4.西方列强对中国的侵略，首先和主要的是（）A.政治控制B.军事侵略C.经济掠夺D.文化渗透答案：B5.1839年组织编写成《四洲志》，向中国人介绍西方情况的是（）A.林则徐B.魏源C.马建忠D.郑观应答案：A6.19世纪末，在帝国主义列强瓜分中国的狂潮中提出“门户开放”政策的国家是（）A.俄国B.日本D.德国答案：C7.太平天国农民起义爆发的时间是（）A.1851年B.1853年C.1856年D.1864年答案：A8.太平天国由盛而衰的转折点是（）A.永安建制B.北伐失利C.天京事变D.洪秀全病逝答案：C9.最早对兴办洋务的指导思想作出完整表述的人是（）A.冯桂芬B.马建忠C.王韬D.郑观应答案：A10.洋务运动时期最早创办的翻译学堂是（）A.同文馆B.广方言馆C.译书局D.译书馆答案：A11.1898年发表《劝学篇》一文，对抗维新变法的洋务派官僚是（）A.李鸿章B.左宗棠C.张之洞D.刘坤一答案：C12.戊戌维新时期，维新派在上海创办的影响较大的报刊是（）A.《时务报》B.《国闻报》C.《湘报》D.《万国公报》答案：A13.中国第一个资产阶级革命政党是（）B.中国同盟会C.中华革命党D.中国国民党答案：B14.武昌起义前夕，在保路运动中规模最大、斗争最激烈的省份是（）A.湖南B.湖北C.广东D.四川答案：D15.中国历史上第一部具有资产阶级共和国宪法性质的法典是（）A.《中华民国宪法》B.《钦定宪法大纲》C.《中华民国约法》D.《中华民国临时约法》答案：D16.为反对袁世凯刺杀宋教仁和“善后大借款”，孙中山在1913年领导革命党人发动了（）A.二次革命B.护国战争C.护法战争D.北伐战争答案：A17.1930年成立的中国国民党临时行动委员会(又称第三党)，其主要领导人是（）A.梁漱溟B.黄炎培C.张君劢D.邓演达答案：D18.1930年1月，毛泽东进一步从理论上阐述农村包围城市、武装夺取政权理论的文章是（）A.《中国的红色政权为什么能够存在?》B.《星星之火，可以燎原》C.《井冈山的斗争》D.《中国革命战争的战略问题》答案：B19.1928年12月，毛泽东主持制定的中国共产党历史上第一个土地法是（）A.《井冈山土地法》B.《兴国土地法》C.《关于清算、减租及土地问题的指示》D.《中国土地法大纲》答案：A20.国民党四大家族官僚资本的性质是（）A.私人垄断资本主义B.封建的买办的国家垄断资本主义C.私人资本主义D.国家资本主义答案：B21.1936年10月，中国工农红军第一、二、四方面军胜利会师于（）A.陕北保安地区B.陕北洛川地区C.陕北瓦窑堡地区D.甘肃会宁、静宁地区答案：D22.遵义会议后，中共中央政治局成立了新的三人团负责红军的军事行动，其成员是（）A.毛泽东、朱德、周恩来B.毛泽东、朱德、王稼祥C.毛泽东、周恩来、王稼祥D.毛泽东、张闻天、周恩来答案：C23.中华民族进入全民族抗战是在（）A.九一八事变后B.一二?八事变后C.华北事变后D.卢沟桥事变后答案：D24.1935年12月，中国共产党确定抗日民族统一战线政策的会议是（）A.遵义会议B.瓦窑堡会议C.洛川会议D.晋绥干部会议答案：B25.在抗日战争的战略防御阶段，国民党军队在正面战场上取得胜利的战役是（）A.台儿庄战役B.桂南战役C.枣宜战役D.中条山战役答案：A26.毛泽东在《论持久战》中指出，中国抗日战争取得胜利最关键的阶段是（）A.战略防御阶段B.战略相持阶段C.战略反攻阶段D.战略决战阶段答案：B27.1945年4月，出席联合国制宪会议中国代表团中的解放区代表是（）A.周恩来B.刘少奇C.董必武D.王若飞答案：C28.抗日战争胜利后，国共双方通过重庆谈判签订《政府与中共代表会谈纪要》的时间是（）A.1945年8月B.1945年9月C.1945年10月D.1945年11月答案：C解析：（P125）1945年10月10日，国共双方签署《政府与中共代表会谈纪要》（即双十协定），确认和平建国的基本方针。

2008年考研小作文真题解析及参考范文一、考试真题Part A:Directions: You have just come back from Canada and found a music CD in your luggage that you forgot to return to Bob, your landlord there. Write him a letter to1）make an apology, and2）suggest a solutionYou should write about 100 words on ANSWER SHEET 2.Do not sign your own name at the end of the letter. Use Li Ming instead.Do not write the address.二、命题解析今年小作文相对简单，预计全国平均分5－6分之间,略高于07年的4.93分。

自2005年开考小作文以来，今年第四次考察了书信这一题型，再次印证了考研小作文的重点还是书信作文,而备忘录、摘要、报告、告示只需简单准备即可。

05年考察辞职信＋道歉信,06年考察请求信,07年考察建议信。

今年则再次考察了道歉信,充分表明真题是考研的根本,写作也不例外。

只要充分重视真题，,必将受益匪浅。

我们的写作教材中附有教育部公布的历年真题高分作文,历年经典句型均可借鉴。

需要注意的是,根据08年教育部最新大纲，考研小作文无需书写日期,使用缩进式,段间不空行，每段首行缩进4－5个字母。

称呼需要顶头写,由于题目中出现了人名，写成Dear + 人名即可。

正文中务必客气,礼多人不怪。

表示感谢的句型不可或缺,感谢房东对你的热情照顾。

同时表示道歉和提出解决方法两点提纲务必写到。

落款写在稿纸中间偏后的位置，Yours sincerely,或Sincerely yours，均可,注意大小写和逗号。

2008年法律硕士联考试题参考答案及解析刑法学一、单项选择题1．C 【解析】直接考察刑法第十七条第 2 款：已满十四周不满十六周岁的人，犯故意杀人、故意伤害致人重伤或者死亡、强奸、抢劫、贩卖毒品、放火、爆炸、投毒罪的，应当负刑事责任。

该知识点必考知识点，几乎每年涉及。

如 2004 年单选题 1、下列行为中已满 14 周岁不满 16 周岁的人应当负刑事责任的是（B）。

A、走私毒品 B、贩卖毒品 C、决水 D、拐卖妇女、儿童。

2．B 【解析】修正的犯罪构成。

该知识点重点，2006 年单选题 3 曾经涉及到，而且比该题难度要大。

如：2006 年单选题 3、甲教唆乙在某学校食堂的面粉中投放“毒鼠强”一包，造成数十人中毒死亡的结果。

法院认定甲构成投放危险物质罪。

甲的行为具备（D）:A、标准的犯罪构成 B、复杂的犯罪构成 C、基本的犯罪构成 D、修正的犯罪构成。

3．D 【解析】不作为行为。

该知识点为重点，2005 年单选题 3 曾经涉及到，难度比该题大很多，还涉及纯正不纯正的判断。

如：2005 年单选题 3、甲因为重男轻女，将妻子刚生下才 3 天的女婴包裹好放在医院门口，躲在一边观察。

见有群众围观、议论，便放心离开。

第二天一早，甲又到医院门口察看，见女婴还在，但女婴却因晚间气温过低被冻死。

法官据此判决甲构成遗弃罪。

甲的行为属于（C）。

A、纯正的作为犯 B、不纯正的作为犯 C、纯正的不作为犯 D、不纯正的不作为犯4．B【解析】直接考察刑法第十八条第 1 款：精神病人在不能辨认或者不能控制自己行为的时候造成危害结果，经法定程序鉴定确认的，不负刑事责任，但是应当责令他的家属或者监护人严加看管和医疗；在必要的时候，由政府强制医疗。

5．C 【解析】直接考察刑法第二十一条第 3 款：第一款中关于避免本人危险的规定，不适用于职务上、业务上负有特定责任的人。

----小结，单单从以上 5 道选择题来看，选择题或以法条直接出题，或以以往的题为基础出题，但总的来看，难度有所降低。

安全知识真题08安全知识答题【⾼校】单选1. 下列哪项是扑救精密仪器⽕灾的最佳选择（）A. ⽔B. 泡沫灭⽕器C. ⼲粉灭⽕器D. ⼆氧化碳灭⽕器2. 李某因和家⼈闹⽭盾，⼀时想不开，骑⾃⾏车在⼀辆⼤货车临近时故意猛拐，发⽣交通事故，造成李某受伤，此事故⼤货车驾驶员（）责任。

A. 不承担B. 承担C. 减轻D. 适当承担3. 机动车号牌和⾏驶证A. 经有关部门同意、可以暂时转借B. 不准转借、涂改、伪造C. 根据需要可以临时借⽤D. 随时可以借⽤4. ⼀般⽐较有效的运动种类或锻炼⽅式有三种基本形式，以下哪⼀个是不属于这三种基本形式A. ⼒量型运动B. 伸展运动C. ⽆氧运动D. 有氧运动5. （）对增强呼吸系统摄取氧、⼼⾎管系统载荷及输送氧的能⼒，以及组织的有氧代谢利⽤氧的能⼒有显著的训练作⽤A. ⽆氧运动B. 有氧运动C. 耐⼒运动D. 恒常运动6. 运动处⽅的核⼼是A. 运动强度B. 运动频率C. 运动量D. 运动时间7. 集体活动不慎擦伤时，⼈体表现为（）A. 表⽪受损B. 出⾎C. 流积液D. 以上都对8. 我们平时所说的计算机病毒，实际是A. 病毒B. ⽂章C. 程序D. 微⽣物9. ⼤学⽣⼩吴在⽹上以⼀个知名作家的名义写博客,但事先没有征得该作家同意。

⼩吴应当承担A. 违约责任B. 侵权责任C. 刑事责任D. ⾏政责任10. 以下哪些属于健康的⽹站内容可以浏览？A. 养⽣B. 暴⼒C. ⾊情D. 迷信11. 以下不属于台风中常见的急救事故的是A. 外伤B. ⾻折C. 触电D. 溺⽔12. 外出旅游避免遭遇滑坡不正确的说法是A. 夏季不去⼭上的风景区旅游B. 不在⼤⾬天⾛进易滑坡地段C. 远离陡峭、破碎、疏松的斜坡D. 必须通过滑坡易发区时，选择⼲燥的季节与⽓象条件13. 当我们外出实践乘坐的车辆落⼊⽔中，如果⾬⽔过⼤把整个车门都淹没了，我们应该如何⾃救？A. ⼿机呼救B. 在车内等待救援C. 想办法砸破车窗D. ⽤⼒打开车门14. 国家对检举、揭发毒品犯罪的⼈员A. ⼀般对待B. 给予奖励C. 没有规定D. 没有奖励15. 《国际禁毒公约》规定的毒品是A. 药品B. ⿇醉药品和精神药品C. ⿇醉药D. ⿇醉药品16. 《刑法》规定⾮法种植罂粟（）株以上构成犯罪A. 500B. 600C. 700D. 100017. 下列哪样是⼈⼯合成的毒品A. 鸦⽚B. 咖啡C. ⼤⿇D. 冰毒18. 下⾯表述正确的是A. 禁毒是全社会的共同责任B. 禁毒主要是⼈民政府的责任C. 禁毒主要是公安机关的责任D. 禁毒主要是每个公民的责任19. “法轮功”主要反宣媒体在境内采访的主要欺骗⼿法不包括A. 利⽤投资者⾝份利⽤⾦钱收买⼴⼤民众和部分政府官员B. 冒充境外媒体打电话采访普通民众、专家学者甚⾄政府官员C. 通过境内特定关系⼈联系采访D. 以境内弱势群体代⾔⼈的⾝份，骗取境内部分弱势群体⼈员的信任，并煽动这些⼈通过其媒体攻击政府和我有关政策20. 邪教组织往往打着（）和⽓功的幌⼦骗⼈A. 国际组织B. 民间组织C. 健康团体D. 合法宗教21. 当代邪教的主要特征是A. 民间秘密结社B. 神话教主，⼤搞教主崇拜C. 民间秘密集会D. 严禁成员脱离和背叛组织22. “法轮功”进⾏违法犯罪活动宣传的⼀个突出特点是A. 利⽤神权B. 利⽤⾦钱C. 利⽤暴⼒威胁D. 利⽤⾼科技⼿段23. 在接到⾃称公安或法院电话要求交纳罚款后应该A. 110咨询查仔细B. 积极付款保名声C. 拒之不理放⼀边D. 犹豫不决24. 俯卧压背法⼤约每（）秒⼀次A. 3B. 4C. 5D. 625. 下列关于艾滋病传播途径的表述，错误的⼀项是（）A. 性接触传播B. 空⽓传播C. ⾎液传播D. 母婴传播26. 以下哪种接触不会感染艾滋病？A. 同性性⾏为B. 共⽤被艾滋病病毒污染的注射器C. 使⽤被艾滋病病毒污染的⾎液制品D. 共⽤餐饮具，共同进餐27. 检验机构在实施检验检测活动中发现安全隐患的，应当（）告知被检验单位A. 及时B. 电话C. 书⾯D. 传真28. 遇到⾼楼发⽣⽕灾，下列处理措施正确的是（）A. 乘坐普通电梯逃⽣B. 乘坐扶梯逃⽣C. 躲在电梯⾥D. 躲到⽕灾专⽤电梯逃⽣29. 根据《中华⼈民共和国国家安全法》的规定，任何个⼈和组织违反国家安全法和有关法律，（）或者从事危害国家安全活动的，依法追究法律责任。

08年6月份大学生英语四级真题试卷及详细答案三套全word版2008年6月份大学生英语四级真题试卷及详细答案（三套全）试卷一Part I Writing (30 minutes)Directions: For this part, you are allowed 30 minutes to write a short essay on how to handle the relationship between work and leisure. You should write at least 120 words but no more than 180 words.It seems nowadays people are leading an increasingly busy and hectic lifestyle with work taking up a significant portion of their time. Many individuals struggle to find a balance between work and leisure, which, in turn, affects their mental well-being, productivity, and overall quality of life. Therefore, it is crucial to address this issue and find effective ways to manage the relationship between work and leisure.First and foremost, time management plays a vital role in balancing work and leisure. Prioritizing tasks and setting clear boundaries can help individuals allocate time for both work and leisure activities. Creating a schedule or using time-management tools can aid in improving efficiency and reducing work-related stress.Secondly, it is important to disconnect from work during leisure time. Engaging in activities such as hobbies, sports, or spending time with loved ones can provide a much-needed break from work-related stress. It isessential to establish a clear distinction between work and leisure to avoid the negative consequences of being constantly connected to work.Moreover, employers should promote a healthy work-life balance by encouraging employees to take breaks, vacations, and provide flexible working arrangements. Employees who feel supported in achieving work-life balance are more likely to be productive, motivated, and satisfied with their jobs.In conclusion, managing the relationship between work and leisure is crucial for a balanced and fulfilling life. By adopting effective time management techniques, disconnecting from work during leisure time, and promoting a healthy work-life balance, individuals can enhance their well-being, productivity, and overall satisfaction.试卷二Part I Writing (30 minutes)Directions: For this part, you are allowed 30 minutes to write a short essay on the impact of online shopping. You should write at least 120 words but no more than 180 words.The advent of online shopping has revolutionized the way people shop, with profound implications for both consumers and businesses. The impact of online shopping can be observed in several aspects of modern life.Firstly, online shopping offers unparalleled convenience. Consumers can browse and purchase products from the comfort of their homes, eliminating the need to physically visit stores. This saves time and energy, making shopping more efficient and accessible.Secondly, online shopping provides a wider range of options. Consumers are no longer limited to local stores and can access a global marketplace. This enables them to compare prices, read reviews, and make informed decisions. Additionally, online shopping allows for personalized recommendations based on previous purchases, enhancing the overall shopping experience.However, online shopping also presents challenges. The rise of online retail has led to the closure of traditional brick-and-mortar stores, resulting in job losses and economic changes. Moreover, privacy and security concerns are major issues associated with online shopping, as personal information and financial data are vulnerable to cybercrime.In conclusion, online shopping has had a significant impact on consumer behavior and the retail industry. While it offers convenience and a wide range of options, there are concerns regarding job losses and cybersecurity. Therefore, it is important for individuals and businesses to adapt and embrace the opportunities and challenges presented by online shopping.试卷三Part I Writing (30 minutes)Directions: For this part, you are allowed 30 minutes to write a short essay on the importance of physical exercise. You should write at least 120 words but no more than 180 words.Physical exercise plays a crucial role in maintaining overall health and well-being. In today's sedentary lifestyle, where technology dominates ourdaily activities, the significance of physical exercise cannot be emphasized enough.Firstly, regular exercise helps prevent obesity and related health issues. Engaging in physical activities promotes calorie burning, helps build muscle mass, and improves metabolism. It also reduces the risk of chronic diseases such as heart disease, diabetes, and certain types of cancer.Secondly, exercise has a positive impact on mental health. Physical activity triggers the release of endorphins, also known as "feel-good" hormones, which improve mood and reduce symptoms of stress, anxiety, and depression. Regular exercise also enhances cognitive function and memory.Furthermore, physical exercise promotes social interaction. Participating in group sports or fitness classes allows individuals to meet new people, expand their social networks, and strengthen relationships with friends and family. It fosters a sense of community and support, which contributes to emotional well-being.In conclusion, physical exercise is essential for maintaining a healthy lifestyle. It helps prevent obesity, improves mental health, and promotes social interaction. Incorporating regular exercise into daily routines is crucial for individuals of all ages to enjoy a good quality of life.。

2008年河南省普通高等学校 选拔优秀专科生进入本科阶段学习考试高等数学 答案及解析一. 单项选择题（每题2分，共计60分）1.答案：C 【解析】：C x x x ⇒<≤-⇒⎩⎨⎧≥+>-120201.2.答案：C【解析】：0033sin cos 21lim===⎪⎭⎫ ⎝⎛π--π→x x x D x xx ⇒=⨯=⎪⎭⎫ ⎝⎛π-π→312323cos sin 2lim 3.3.答案：B【解析】： ,1111313lim 11-=-=+--→xxx B x xx x xx ⇒===+-++→→13ln 33ln 3lim 1313lim 11000110. 4.答案：B【解析】：显然只有22sin lim 0=→xxx ,其他三个都不存在,应选B.5.答案：D【解析】： 22~)1ln(x x +,D x x x ⇒=-2~2sin 2cos 122. 6.答案：A【解析】：⇒=-==+--→-→1)1(,1)(lim ,1)(lim 111f x f x f x x )(x f 在1-=x 处连续;⇒===+-→→1)0(,0)(lim ,1)(lim 001f x f x f x x )(x f 在0=x 处不连续;应选A.7.答案：D 【解析】： D k f e xy x⇒-=⇒='⇒++='212)0(112法. 8.答案：C【解析】：3)(lim 3)(3lim 0)0()(lim )0(000-=α+-=α+-=--='→→→xx x x x x f x f f x x x ,应选C. 9.答案：B【解析】：='='⇒==])ln(ln [)(ln )(ln )()ln(ln x x x y e x x f x x x x )ln(ln )(ln )(ln 1x x x x x +-,应选B. 10.答案：D【解析】：⇒⨯=⇒-=t t t dx y d t t dx dy sin cos 31cos 1cos sin 2222 =π=422x dxyd 234,应选D. 11.答案：C【解析】：验证罗尔中值定理的条件,只有21x y -=满足,应选C. 12.答案：B【解析】：⇒=⇒==''006x x y )2,0(-,应选B. 13.答案：B 【解析】：,0|1|1lim =-∞→x x B x x ⇒∞=-→|1|1lim 1.14.答案：D【解析】：⇒-=''⇒+='=21)(ln 1)ln ()(xx f x x x x f C x dx dx x f x +-=-=''⎰⎰)(2,应选D. 15.答案：A 【解析】：C x x dx x x x x dx x x dx +--=⎥⎦⎤⎢⎣⎡---=--=+-⎰⎰⎰13ln 21113121)1)(3(342,应选A. 16.答案：B【解析】：此题有问题,定积分是一个常数,有111214≤+≤x ,根据定积分的估值性质,有121≤≤I ,但这个常数也在其它三个区间,都应该正确,但真题中答案是B.17.答案：D 【解析】：显然应选D. 18.答案：D 【解析】：=-⎰-33|1|dx x =-+-⎰⎰-3113|1||1|dx x dx x ⎰⎰-+--3113)1()1(dx x dx x ,应选D.19.答案：A【解析】：对⎰+-=xdt t t t f x f 022cos 1sin )(22ln )(两边求有:xxx f x f x f cos 1sin )(2)()(2+-=', 即有 ⎰⎰++=+-=⇒+-='xx d dx x x x f x x x f cos 1)cos 1(cos 1sin )(cos 1sin )( C x ++=)cos 1ln(,还初始条件2ln )0(=f ,代入得0=C ,应选A.20.答案：C【解析】：令⎰-=11)(dx x f a ,则a x x f 211)(-+=, 故有⎰⎰--⇒=⇒-=-+==111112)211()(a a dx a x dx x f a =)(x f 21+x ,应选C.21.答案：C【解析】：⎰⎰⎰======22200222)()(21)()(21)()(21e e t x e x d x xf t d t tf x d x f x I ,应选C.22.答案：D【解析】：n s n s⊥⇒-==}7,3,4{},1,9,5{ ,而点(-2,-4,0)不在平面内,为平行,应选D. 23.答案：A 【解析】： 22222200222200)11)((lim11limy x y x y x y x y x y x y x +++++=-+++→→→→2)11(lim 2200=+++=→→y x y x ,应选A.24.答案：A【解析】：令z y x z y x F -+=22),,(,⇒-='='='1)5,2,1(,4)5,2,1(,2)5,2,1(z y x F F F⇒=---+-0)5()2(4)1(2z y x 542=-+z y x ,也可以把点（1，2，5）代入方程验证,应选A.25.答案：B【解析】： ⇒-=∂∂233xy x y z =∂∂∂xy z 22233y x -,应选B. 26.答案：C【解析】：根据二重积分的可加性, 6),(=⎰⎰dxdy y x f D,应选C.27.答案：C 【解析】：有⇒=∂∂=∂∂2x x Qy P 此积分与路径无关,取直线段x y x x ,0⎩⎨⎧==从π2变到0,则 02020232)(333)sin 31()3(πππ-===-++⎰⎰⎰x x x x x L e xe xde dx xe dy y y x dx xe y x ]1)21([32-π-=πe ,应选C. 28.答案：B【解析】：0=-'⇒='⇒=y y Ce y Ce y xx,应选B. 29.答案：A【解析】：-1是单特征方程的根,x 是一次多项式,应设xe b ax x y -+=*)(,应选A.30.答案：B 【解析】：级数∑∞=-1100032n n n 的一般项n n 100032-的极限为05001≠,是发散的,应选B. 二、填空题（每题2分，共30分）31.答案：充要条件【解析】：显然为充要条件(充分且必要). 32.答案：单调增加，凹函数【解析】：⇒>-='0cos 1x y 在)2,0(π内单调增加,x y sin =''在π0,2⎛⎫⎪⎝⎭内大于零,应为凹的. 33.答案：zx 3-【解析】：⇒='='⇒-++=x F z F a z y x F x z 6,223222zxF F x z z x 3-=''-=∂∂. 34.答案：C x x ++-)1ln(22【解析】：⎰⎰⎰++-=⎪⎭⎫ ⎝⎛+-=+==+=C t t dt t t tdt xdx tx )1ln(221112121C x x ++-=)1ln(22.35.答案：0【解析】：函数x x cos 1+在区间⎥⎦⎤⎢⎣⎡ππ-3,3是奇函数，所以⎰ππ⋅-=+330cos 1dx x x .36. 答案：26 【解析】：}2,1,1{102011}1,0,2{},0,1,1{---=--=⨯⇒-=-=kj i AC AB AC AB ，所以ABC ∆的面积为26=. 37.答案：两条平行直线 【解析】：是椭圆柱面与平面2-=x 的交线,为两条平行直线. 38.答案：)1,1(),0,0(【解析】： )1,1(),0,0(03303322⇒⎪⎪⎩⎪⎪⎨⎧=-=∂∂=-=∂∂x y yz y x xz.39.答案：0【解析】：⇒=∂∂⇒=00)0,(x z x f 0)0,1(=∂∂xz.40.答案：22【解析】： 22sin cos cos 1cos 14040040440====πππππ⎰⎰⎰⎰⎰x ydy ydx y dy ydy y dx y x. 41.答案：⎰⎰3120)sin ,cos (rdr r r f d θθθπ【解析】：⎰⎰⎰⎰θθθ=π3120)sin ,cos (),(rdr r r f d dxdy y x f D.42.答案：096=+'+''y y y 【解析】： 由x xxe C eC y 3231--+=为通解知,有二重特征根-3,从而9,6==q p ,微分方程为096=+'+''y y y .43.答案：1||<q ，1||≥q 【解析】： 级数∑∞=0n naq是等比级数, 当1||<q 时,级数收敛,当1||≥q 时,级数发散.44.答案：()()11,23131011<<-⎥⎦⎤⎢⎣⎡⋅--∑∞=++x x nn n n 【解析】：21161113121113121)(2x x x x x x x f -⨯-+⨯-=⎥⎦⎤⎢⎣⎡-++-=--=1100011(1)1(1),(11)362332n n n nn n n n n n x x x x +∞∞∞+===⎡⎤-=---=--<<⎢⎥⋅⎣⎦∑∑∑. 45.答案：发散 【解析】：021lim 2lim lim 2)2(2≠=⎪⎭⎫⎝⎛-=⎪⎭⎫⎝⎛-=--⨯-∞→∞→∞→e n n n u nn nn n n ,级数发散.三、计算题（每小题5分，共40分）46．求2522232lim +∞→⎪⎪⎭⎫⎝⎛-+x x x x .【解析】：252)23(32252222522252231312121lim3121lim 32lim 2222⎪⎭⎫ ⎝⎛-⨯⎪⎭⎫ ⎝⎛-⎪⎭⎫ ⎝⎛+⨯⎪⎭⎫ ⎝⎛+=⎪⎪⎪⎪⎭⎫ ⎝⎛-+=⎪⎪⎭⎫⎝⎛-+-⨯-∞→+∞→+∞→x x x x x x x x x x x x x x x2523252)23(32252223131lim 2121lim 22e eex x x x x x x x ==⎪⎭⎫ ⎝⎛-⨯⎪⎭⎫ ⎝⎛-⎪⎭⎫ ⎝⎛+⨯⎪⎭⎫ ⎝⎛+=--⨯-∞→∞→.47. 求⎰+→23241limx x dtt t x .【解析】：212lim214lim1lim3403423003242=+=⨯+===+→→→⎰xxx xx dtt t xx x x x .48.已知)21sin(ln x y -=,求dxdy. 【解析】：[][])21sin()21cos(221)21sin()21cos()21sin()21sin(1x x x x x x x dx dy ---='---='--=)21cot(2x --=. 49. 计算不定积分⎰xdx x arctan .【解析】：⎰⎰⎰+⨯-=⎪⎪⎭⎫ ⎝⎛=dx x x x x x xd xdx x 2222112arctan 22arctan arctan ⎰⎪⎭⎫ ⎝⎛+--=dx x x x 2211121arctan 2 C x x x x ++-=arctan 2121arctan 22. 50.求函数)cos(y x e z x+=的全微分. 【解析】：利用微分的不变性,x x x de y x y x d e y x e d dz )cos()cos()]cos([+++=+=dx e y x y x d y x e x x )cos()()sin(++++-= dx e y x dy dx y x e x x )cos(])[sin(++++-= dy y x e dx y x y x e x x )sin()]sin()[cos(+-+-+=.51．计算⎰⎰σDd y x2，其中D 是由1,,2===xy x y y 所围成的闭区域. 【解析】：积分区域D 如图所示:把区域看作 Y 型,则有⎭⎬⎫⎩⎨⎧≤≤≤≤=y x y y y x D 1,21|),(,故 ⎰⎰⎰⎰=y y D dx y x dy dxdy yx12212yyy yx dy y xdx dy y 122121212211⨯==⎰⎰⎰481731211121213214=⎪⎪⎭⎫ ⎝⎛+=⎥⎦⎤⎢⎣⎡-=⎰y y dy y . 52．求微分方程xex y y sin cos -=+'满足初始条件1)0(-=y 的特解.【解析】：这是一阶线性非齐次微分方程,它对应的齐次微分方程0cos =+'x y y 的通解为x Ce y sin -=,设x e x C y sin )(-=是原方程解,代入方程有x x e e x C sin sin )(--=',即有1)(='x C ,所以C x x C +=)(,故原方程的通解为x xxe Cey sin sin --+=,把初始条件1)0(-=y 代入得:1-=C ,故所求的特解为xex y sin )1(--=.53．求级数∑∞=+013n nn x n 的收敛半径及收敛区间(考虑区间端点).【解析】：这是标准的不缺项的幂级数,收敛半径ρ=1R ,而321lim 33123lim lim 11=++=+⨯+==ρ∞→+∞→+∞→n n n n a a n n n n nn n ,故收敛半径31=R .当31=x 时,级数化为∑∞=+011n n ,这是调和级数,发散的;当31-=x 时,级数化为∑∞=+-01)1(n nn ,这是交错级数,满足莱布尼兹定理的条件,收敛的;所以级数的收敛域为⎪⎭⎫⎢⎣⎡-31,31.四、应用题（每题7分，共计14分）54. 过曲线2x y =上一点)1,1(M 作切线L ，D 是由曲线2x y =，切线L 及x 轴所围成的平面图形，求（1）平面图形D 的面积;y x =→yx 11=→ 1（2）该平面图形D 绕x 轴旋转一周所成的旋转体的体积.【解析】：平面图形D 如图所示：因x y 2=',所以切线L 的斜率2)1(='=y k , 切线L 的方程为)1(21-=-x y ,即12-=x y 取x 为积分变量，且]1,0[∈x .（1）平面图形D 的面积为12)(3)12(1212103121102=--=--=⎰⎰x x x dx x dx x S （2）平面图形D 绕x 轴旋转一周所生成旋转体的体积为302345)12(1212315121214π=⎪⎪⎭⎫ ⎝⎛+-π-π=-π-π=⎰⎰x x x xdx x dx x V x .55.一块铁皮宽为24厘米,把它的两边折上去,做成一正截面为等腰梯形的槽(如下图),要使梯形的面积A 最大,求腰长x 和它对底边的倾斜角α. 【解析】：梯形截面的下底长为x 224-,上底长为 α+-cos 2224x x ,高为αsin x ,所以截面面积为 α⋅-+α+-=sin )224cos 2224(21x x x x A , )20,120(π<α<<<x即αα+α-α=cos sin sin 2sin 2422x x x A ,令⎪⎪⎩⎪⎪⎨⎧=α-α+α-α=α∂∂=αα+α-α=∂∂0)sin (cos cos 2cos 240cos sin 2sin 4sin 242222x x x A x x xA得唯一驻点⎪⎩⎪⎨⎧π=α=38x .根据题意可知,截面的面积最大值一定存在,且在20,120:π<α<<<x D 内取得,又函数在D 内只有一个可能的最值点,因此可以断定3,8π=α=x 时,截面的面积最大. 五、证明题（6分）56. 证明方程⎰π--=2cos 1ln dx x e xx 在区间),(3e e 内仅有一个实根. 【证明】：构造函数 ⎰π-+-=02cos 1ln )(dx x e xx x f ,即有22ln sin 2ln )(0+-=+-=⎰πex x xdx e x x x f ,显然函数)(x f 在区间],[3e e 连续,且有06223)(,022)(223<-<+-=>=e e e f e f ,由连续函数的零点定理知方程0)(=x f 即⎰π--=2cos 1ln dx x e xx 在区间),(3e e 有至少有一实数根. 另一方面, e x x f 11)(-='在区间),(3e e 内恒小于零,有方程0)(=xf ,即⎰π--=02cos 1ln dx x e x x 在区间),(3e e 有至多有一实数根.xy x =→2x 224-x α综上所述, 方程⎰π--=02cos 1ln dx x e xx 在区间),(3e e 内仅有一个实根.。