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.。

2008考研英语真题答案详解完型填空1、答案：B解析：本题测试语义逻辑衔接。

“ selected” 意为“挑驯; “prepared”意为“准备”；“obliged”意为“迫使，责成”；“pleased”意为“高兴地，满足地”，前一句“人们不敢说”，本句中由“but ”一词可推出意思与上句相反，即“Cochran 准备说”，所以选B.2、答案：D解析：本题测试词义辨析。

“unique”意为“唯一的，独特的”；“particular”意为“特殊的，独特的”；“special”意为“特别的，特殊的”；“rare”意为“稀罕的，珍贵的”，rare bird 意为“稀有的人”，空格相关意思是“只有Cochra准备说”，而且“rare bird” 是固定搭配,所以选D3、答案：A解析：本题测试介词的语意搭配, independently of 意为“不依赖于，独立”，所以选A4、答案：C解析：本题测试词义辨析。

由“actually”推出本句是对现在和以前对疾病看法的对比，所以选C5、答案：C解析：本题测试副词的用法及语段的连贯性。

Even 做程度副词，表示递进关系，意为“即使他自己也…”.所以选C6、答案：A解析：本题测试词义搭配。

空格相关意思是“一想到他即将要做的，即使他自己也….” “At thought of ”意为“一看到…”；at sight of意为年“一看见”；at cost of 意为“以…的代价”；at risk of意为“冒着….的危险”，所以选A7、答案：B解析：本题测试动词辨析。

advice意为“建议”；suggest意为“建议，提出’”；protest“主张，断言”；object“反对”，此句指“在论文中，他建议…”，所以选B8、答案：D解析：本题测试词组搭配，in progress 意为“进行中”；in fact 意为“事实上”；in need意为“在危难中”；in question 意为“正在被讨论的”，前一句正在谈论“ group群体” ,本句衔接上一句表达“正在被讨论的这个群体”，所以选D9. 答案：B解析：本题考查动词辨析。

08高考英语答案解析广东卷Ⅱ语言知识及应用(共两节，满分35分)第一节完形填空(共10小题；每小题2分，满分20分)阅读下面短文，掌握其大意，然后从21—30各题所给的A、B、C和D项中，选出最佳选项，并在答题卡上将该项涂黑。

Tales of the supernatural are common in all parts of Britain. In particular, there was (and perhaps still is) a belief in fairies(仙女). Not all of these 21 are the friendly, people-loving characters that appear in Disney films, and in some folktales they are 22 and cause much human suffering. This is true in the tales about the Changeling. These tell the story of a mother whose baby grows 23 and pale and has changed so much that it is almost 24 to the parents. It was then 25 that the fairies had come and stolen the baby away and 26 the human baby with a fairy Changeling. There were many ways to prevent this from happening: hanging a knife over the baby‟s head while he slept or covering him with some of his father‟s clothes were just two of the recommended 27 . However, hope was not lost even if the baby had been 28 . In those cases there was often a way to get the 29 baby back. You could 30the Changeling on the fire--then it would rise up the chimney, and you would hear the sound of fairies‟ laughter and soon after you would find your own child safe and sound nearby.21. A. babies B. believers C. fairies D. supermen22. A. powerful B. cruel C. frightened D. extraordinary23. A. sick B. slim C. short D. small24. A. uncomfortable B. unbelievable C. unacceptable D. unrecognizable25. A. feared B. predicted C. heard D. reported26. A. covered B. changed C. replaced D. terrified27. A. cases B. tools C. steps D. methods28. A. missed B. stolen C. found D. lost29. A.1ittle B. pale C. sad D. real30. A. seize B. burn C. place D. hold第二节语法填空(共10小题，每小题1.5分，满分15分)阅读下面短文，按照句子结构的语法性和上下文连贯的要求，在空格处填入一个适当的词或使用括号中词语的正确形式填空，并将答案填写在答题卡标号为31～40的相应位置上。

2008年普通高等学校招生全国统一考试（全国卷2）理科数学(必修+选修Ⅱ)1．设集合{|32}M m m =∈-<<Z ，{|13}N n n M N =∈-=Z 则，≤≤（ ） A ．{}01，B ．{}101-，，C ．{}012，，D ．{}1012-，，，2．设a b ∈R ，且0b ≠，若复数3()a bi +是实数，则（ ） A ．223b a = B ．223a b = C ．229b a = D ．229a b =3．函数1()f x x x=-的图像关于（ ）A ．y 轴对称B ． 直线x y -=对称C ． 坐标原点对称D ． 直线x y =对称4．若13(1)ln 2ln ln x e a x b x c x -∈===，，，，，则（ ）A ．a <b <cB ．c <a <bC ． b <a <cD ． b <c <a5．设变量x y ，满足约束条件：222y x x y x ⎧⎪+⎨⎪-⎩，，．≥≤≥，则y x z 3-=的最小值（ ）A ．2-B ．4-C ．6-D ．8-6．从20名男同学，10名女同学中任选3名参加体能测试，则选到的3名同学中既有男同学又有女同学的概率为（ ） A ．929B ．1029C ．1929D ．20297．64(1)(1)x x -+的展开式中x 的系数是（ ）A ．4-B ．3-C ．3D ．48．若动直线x a =与函数()sin f x x =和()cos g x x =的图像分别交于M N ，两点，则MN 的最大值为（ ） A ．1B ．2C ．3D ．29．设1a >，则双曲线22221(1)x yaa -=+的离心率e 的取值范围是（ ）A ．(22)，B ．(25)，C ．(25)，D ．(25)，10．已知正四棱锥S A B C D -的侧棱长与底面边长都相等，E 是SB 的中点，则A E SD ，所成的角的余弦值为（ ） A ．13B ．23C ．33D ．2311．等腰三角形两腰所在直线的方程分别为20x y +-=与740x y --=，原点在等腰三角形的底边上，A ．3B ．2C ．13-D ．12-12．已知球的半径为2，相互垂直的两个平面分别截球面得两个圆．若两圆的公共弦长为2，则两圆的圆心距等于（ ） A ．1B ．2C ．3D ．2二、填空题：本大题共4小题，每小题5分，共20分．把答案填在题中横线上． 13．设向量(12)(23)==，，，a b ，若向量λ+a b 与向量(47)=--，c 共线，则=λ ． 14．设曲线ax y e =在点(01)，处的切线与直线210x y ++=垂直，则a = ．15．已知F 是抛物线24C y x =：的焦点，过F 且斜率为1的直线交C 于A B ，两点．设FA FB >，则FA 与FB 的比值等于 ．16．平面内的一个四边形为平行四边形的充要条件有多个，如两组对边分别平行，类似地，写出空间中的一个四棱柱为平行六面体的两个充要条件：充要条件① ； 充要条件② ． （写出你认为正确的两个充要条件）三、解答题：本大题共6小题，共70分．解答应写出文字说明，证明过程或演算步骤． 17．（本小题满分10分） 在A B C △中，5cos 13B =-，4cos 5C =．（Ⅰ）求sin A 的值；（Ⅱ）设A B C △的面积332A B C S =△，求B C 的长．18．（本小题满分12分）购买某种保险，每个投保人每年度向保险公司交纳保费a 元，若投保人在购买保险的一年度内出险，则可以获得10 000元的赔偿金．假定在一年度内有10 000人购买了这种保险，且各投保人是否出险相互独立．已知保险公司在一年度内至少支付赔偿金10 000元的概率为41010.999-．（Ⅰ）求一投保人在一年度内出险的概率p ；（Ⅱ）设保险公司开办该项险种业务除赔偿金外的成本为50 000元，为保证盈利的期望不小于0，求每位投保人应交纳的最低保费（单位：元）．如图，正四棱柱1111ABC D A B C D -中，124AA AB ==，点E 在1CC 上且EC E C 31=． （Ⅰ）证明：1A C ⊥平面B E D ； （Ⅱ）求二面角1A D E B --的大小．20．（本小题满分12分）设数列{}n a 的前n 项和为n S ．已知1a a =，13nn n a S +=+，*n ∈N ．（Ⅰ）设3nn n b S =-，求数列{}n b 的通项公式；（Ⅱ）若1n n a a +≥，*n ∈N ，求a 的取值范围．AB CD EA 1B 1C 1D 1设椭圆中心在坐标原点，(20)(01)A B ，，，是它的两个顶点，直线)0(>=k kx y 与AB 相交于点D ，与椭圆相交于E 、F 两点．（Ⅰ）若6ED DF =，求k 的值； （Ⅱ）求四边形AEBF 面积的最大值．22．（本小题满分12分） 设函数sin ()2cos x f x x=+．（Ⅰ）求()f x 的单调区间；（Ⅱ）如果对任何0x ≥，都有()f x ax ≤，求a 的取值范围．。

08一、填空（每空2分，共10分） 1、f （5-2t ）是如下运算的结果 （1）f （-2t ）右移5 （2）f （-2t ）左移5 （3）f （-2t ）右移25 （4）f （-2t ）左移252、()cos t td ?3、(1cos )()2t t pd --= 4、0()cos td d t w t t - =ò 5、()at t e dt d ¥--=ò二、画图（共16分）1、画出题图所示信号f （t ）的偶分量f e （t ）与奇分量f o （t ）。

（4分）t2、某线性时不变系统在零状态条件下的输入e （t ）与输出r （t ）的波形如图所示，当输入波形为x （t ）时，试画出输出波形y （t ）。

（8分）t t3、 已知()x t 和()h t 如图,求()()()y t x t h t =*的波形。

（4分）三、已知电路如下图所示，激励信号为() ()f t t ε=,在=0t 和=1t 时测得系统的输出为0.5(0)1,(1) y y e-==，利用时域分析分别求系统的零输入响应、零状态响应、全响应、以及自由响应和强迫响应。

（共20分）C=1F四、已知()()f t F j ω⇔，求下列信号的傅里叶变换。

（共18分，每小题3分）1、()F jt ；2、0()f t ω ；3、()df t dt； 4、(2)f t -；5、1[(2)(2)]2t t εδ++- ； 6、0()cos()f t t ω五、在图所示系统中，()H j ω为理想低通滤波器的传输函数， ()0,ϕω=若∞<<∞-=t t t s ,1000cos )(，,,1000cos )()(0∞<<∞-=t t t f t f 01()()f t Sa t π=。

（1）求响应()y t 。

（20分）（t ）（2）若分别对f （t ）、y （t ）和x （t ）采样，则它们的最低抽样率与奈奎斯特间隔分别是多少。

详解08年国考申论真题（附参考答案）一、在怒江开发水电资源问题上有重大争议。

请根据给定资料1-8，指出争议的焦点是什么，并对主张怒江水电开发和反对怒江水电开发的理由分别加以概述。

（20分）要求：指明“焦点”，概括全面，条理清晰，语言流畅，不超过500字。

分析：对于这道题目的解答，戴斌老师认为关键是看争议焦点的确定问题，本题的主要参考材料应该是集中在第六和第七个材料中所反映的两种态度倾向。

而考生在回答争议的焦点是什么时，可以有两种表达方式：（一）怒江开发水电资源对于当地甚至全国的人民群众而言，究竟是利大于弊，还是弊大于利。

（二）怒江适不适合通过开发水电资源这种方式来发展经济。

但在这里，广州新东方的戴斌老师需要提醒广大考生留意的是，不能认为争议的焦点是“在‘保护’和‘开发’之间我们应该选择哪一个”，因为从原材料中，争议的双方都没有反对“开发”，也没有反对“保护”。

双方只是对实现“当地经济发展”这个目的所采取的“手段”和“方案”有明显的争议而已。

参考答案：随着我国经济社会的不断发展，经济发展与生态保护之间的矛盾越来越激烈。

材料中所反映的是我国怒江水电资源的开发问题。

对此，我国各界人士之间存在重大的争议，而争议的焦点是：在怒江开发水电资源对于当地甚至全国的人民群众而言，究竟是利大于弊，还是弊大于利。

反对者认为，修建水坝首先会带来泥沙淤积、污水等严重的生态问题，同时还会导致大规模的水库移民。

从我国过去的历史经验来看，部分地方由于缺乏对水电项目可行性的反复论证，使得目前尚有近千万的水库移民生活在贫困当中，许多当地群众并没有从水电资源的开发中直接受益。

而支持者们认为，怒江的地理条件好，适合发展水电，而且怒江地区长期以来经济发展缓慢，当地群众波且希望脱离贫困，水电工程不仅可以带来就业机会，促进财政增收，有效帮助群众脱贫致富，而且当地水电资源的对外输出也具有重要的战略意义。

开发水电资源虽不是唯一的致富途径，却是目前一项可实施的重要脱贫方案。

2008年北京市高级中等学校招生考试数 学 试 卷下列各题均有四个选项，其中只有一个是符合题意的．用铅笔把“机读答题卡”上对应题目答案的相应字母处涂黑．1．6-的绝对值等于（ ）A ．6B ．16C ．16- D ．6- 2．截止到2008年5月19日，已有21 600名中外记者成为北京奥运会的注册记者，创历届奥运会之最．将21 600用科学记数法表示应为（ ）A ．50.21610⨯B ．321.610⨯C ．32.1610⨯D ．42.1610⨯3．若两圆的半径分别是1cm 和5cm ，圆心距为6cm ，则这两圆的位置关系是（ ）A ．内切B ．相交C ．外切D ．外离4．众志成城，抗震救灾．某小组7名同学积极捐出自己的零花钱支援灾区，他们捐款的数额分别是（单位：元）：50，20，50，30，50，25，135．这组数据的众数和中位数分别是（ ）A ．50，20B ．50，30C ．50，50D ．135，505．若一个多边形的内角和等于720，则这个多边形的边数是（ ）A ．5B ．6C ．7D ．86．如图，有5张形状、大小、质地均相同的卡片，正面分别印有北京奥运会的会徽、吉祥物（福娃）、火炬和奖牌等四种不同的图案，背面完全相同．现将这5张卡片洗匀后正面向下放在桌子上，从中随机抽取一张，抽出的卡片正面图案恰好是吉祥物（福娃）的概率是（ ）A ．15B ．25C ．12D ．357．若20x +=，则xy 的值为（ ）A ．8-B ．6-C ．5D ．68．已知O 为圆锥的顶点，M 为圆锥底面上一点，点P 在OM 上．一只蜗牛从P 点出发，绕圆锥侧面爬行，回到P 点时所爬过的最短路线的痕迹如右图所示．若沿OM 将圆锥侧面剪开并展开，所得侧面展开图是（ ）2008年北京市高级中等学校招生考试数 学 试 卷二、填空题（共4道小题，每小题4分，共16分）9．在函数121y x =-中，自变量x 的取值范围是 ． 10．分解因式：32a ab -= ． 11．如图，在ABC △中，D E ，分别是AB AC ，的中点，若2cm DE =，则BC = cm ． 12．一组按规律排列的式子：2b a -，53b a ，83b a-，114b a ，…（0ab ≠），其中第7个式子是 ，第n 个式子是 （n 为正整数）．三、解答题（共5道小题，共25分）13．（本小题满分5分）1012sin 45(2)3-⎛⎫+-π- ⎪⎝⎭． 解：CAE DB OP M O M ' M P A ． O M ' M P B ． O M 'M P C ．O M ' M P D ．14．（本小题满分5分）解不等式5122(43)x x --≤，并把它的解集在数轴上表示出来．解：15．（本小题满分5分）已知：如图，C 为BE 上一点，点A D ，分别在BE 两侧．AB ED ∥，AB CE =，BC ED =．求证：AC CD =． 证明：16．（本小题满分5分）如图，已知直线3y kx =-经过点M ，求此直线与x 轴，y 轴的交点坐标．解：17．（本小题满分5分）已知30x y -=，求222()2x y x y x xy y +--+的值． 解：四、解答题（共2道小题，共10分）18．（本小题满分5分）如图，在梯形ABCD 中，AD BC ∥，AB AC ⊥，45B ∠=，AD =BC =求DC 的长．解： A C E D B y xA D19．（本小题满分5分）已知：如图，在Rt ABC △中，90C ∠=，点O 在AB 上，以O 为圆心，OA 长为半径的圆与AC AB ，分别交于点D E ，，且CBD A ∠=∠．（1）判断直线BD 与O（2）若:8:5AD AO =，2BC =，求解：（1）（2）五、解答题（本题满分6分）20．为减少环境污染，自2008年6月1日起，全国的商品零售场所开始实行“塑料购物袋有偿使用制度”（以下简称“限塑令”）．某班同学于6月上旬的一天，在某超市门口采用问卷调查的方式，随机调查了“限塑令”实施前后，顾客在该超市用购物袋的情况，以下是根据100位顾客的100份有效答卷画出的统计图表的一部分：B 图1 “限塑令”实施前，平均一次购物使用不同数量塑料购物袋的人“限塑令”实施后，使用各种 购物袋的人数分布统计图 其它 _______％ 24%（1）补全图1，“限塑令”实施前，如果每天约有2 000人次到该超市购物．根据这100位顾客平均一次购物使用塑料购物袋的平均数，估计这个超市每天需要为顾客提供多少个塑料购物袋？（2）补全图2，并根据统计图和统计表说明，购物时怎样选用购物袋，塑料购物袋使用后怎样处理，能对环境保护带来积极的影响．解：（1）（2）六、解答题（共2道小题，共9分）21．（本小题满分5分）列方程或方程组解应用题：京津城际铁路将于2008年8月1日开通运营，预计高速列车在北京、天津间单程直达运行时间为半小时．某次试车时，试验列车由北京到天津的行驶时间比预计时间多用了6分钟，由天津返回北京的行驶时间与预计时间相同．如果这次试车时，由天津返回北京比去天津时平均每小时多行驶40千米，那么这次试车时由北京到天津的平均速度是每小时多少千米？解：22．（本小题满分4分）已知等边三角形纸片ABC的边长为8，D为AB边上的点，过点D作DG BC∥交AC于点G．DE BC⊥于点E，过点G作GF BC⊥于点F，把三角形纸片ABC 分别沿DG DE GF，，按图1所示方式折叠，点A B C，，分别落在点A'，B'，C'处．若点A'，B'，C'在矩形DEFG内或其边上，且互不重合，此时我们称A B C'''△（1）若把三角形纸片ABC放在等边三角形网格中（图中每个小三角形都是边长为1的等边三角形），点A B C D，，，恰好落在网格图中的格点上．如图2所示，请直接写出此时重叠三角形A B C'''的面积；（2）实验探究：设AD的长为m，若重叠三角形A B C'''存在．试用含m的代数式表示重叠三角形A B C'''的面积，并写出m的取值范围（直接写出结果，备用图供实验，探究使用）．图1图2A A解：（1）重叠三角形A B C '''的面积为 ；（2）用含m 的代数式表示重叠三角形A B C '''的面积为 ；m 的取值范围为 ．七、解答题（本题满分7分）23．已知：关于x 的一元二次方程2(32)220(0)mx m x m m -+++=>．（1）求证：方程有两个不相等的实数根；（2）设方程的两个实数根分别为1x ，2x （其中12x x <）．若y 是关于m 的函数，且212y x x =-，求这个函数的解析式；（3）在（2）的条件下，结合函数的图象回答：当自变量m 的取值范围满足什么条件时，2y m ≤．（1）证明：（2）解：（3八、解答题（本题满分7分）24．在平面直角坐标系xOy 中，抛物线2y x bx c =++与x 轴交于A B ，两点（点A在点B 的左侧），与y 轴交于点C ，点B 的坐标为(30)，，将直线y kx =沿y 轴向上平移3个单位长度后恰好经过B C ，两点．（1）求直线BC 及抛物线的解析式；x（2）设抛物线的顶点为D ，点P 在抛物线的对称轴上，且APD ACB ∠=∠，求点P 的坐标；（3）连结CD ，求OCA ∠与OCD ∠解：（1）（2）（3）九、解答题（本题满分8分）25．请阅读下列材料：问题：如图1，在菱形ABCD 和菱形BEFG 中，点A B E ，，在同一条直线上，P 是线段DF 的中点，连结PG PC ，．若60ABC BEF ∠=∠=，探究PG 与PC 的位置关系及PG PC的值． 小聪同学的思路是：延长GP 交DC 于点H ，构造全等三角形，经过推理使问题得到解决．请你参考小聪同学的思路，探究并解决下列问题：（1）写出上面问题中线段PG 与PC 的位置关系及PG PC的值； （2）将图1中的菱形BEFG 绕点B 顺时针旋转，使菱形BEFG 的对角线BF 恰好与菱形ABCD 的边AB 在同一条直线上，原问题中的其他条件不变（如图2）．你在（1）中得到的两个结论是否发生变化？写出你的猜想并加以证明． x D A B E F C P G 图1 D C G P A B F 图2（3）若图1中2(090)ABC BEFαα∠=∠=<<，将菱形BEFG绕点B顺时针旋转任意角度，原问题中的其他条件不变，请你直接写出PGPC的值（用含α的式子表示）．解：（1）线段PG与PC的位置关系是；PGPC=．（2）2008年北京市高级中等学校招生考试数学试卷答案及评分参考阅卷须知：1．一律用红钢笔或红圆珠笔批阅，按要求签名．2．第Ⅰ卷是选择题，机读阅卷．3．第Ⅱ卷包括填空题和解答题．为了阅卷方便，解答题中的推导步骤写得较为详细，考生只要写明主要过程即可．若考生的解法与本解法不同，正确者可参照评分参考给分．解答右端所注分数，表示考生正确做到这一步应得的累加分数．第Ⅰ卷（机读卷共32分）第Ⅱ卷（非机读卷共88分）13．（本小题满分5分）112sin45(2π)3-⎛⎫+-- ⎪⎝⎭2132=⨯+-········································································· 4分2=． ····················································································· 5分14．（本小题满分5分）解：去括号，得51286x x --≤． ························································ 1分 移项，得58612x x --+≤． ······························································· 2分 合并，得36x -≤． ·········································································· 3分 系数化为1，得2x -≥． ··································································· 4分···································································································· 5分15．（本小题满分5分）证明：AB ED ∥，B E ∴∠=∠． ·················································································· 2分 在ABC △和CED △中，AB CE B E BC ED =⎧⎪∠=∠⎨⎪=⎩，，， ABC CED ∴△≌△．········································································· 4分 AC CD ∴=． ·················································································· 5分 16．（本小题满分5分）解：由图象可知，点(21)M -，在直线3y kx =-上， ·································· 1分 231k ∴--=．解得2k =-． ·················································································· 2分 ∴直线的解析式为23y x =--． ······································································· 3分令0y =，可得32x =-． ∴直线与x 轴的交点坐标为302⎛⎫- ⎪⎝⎭，． ··················································· 4分 令0x =，可得3y =-．∴直线与y 轴的交点坐标为(03)-，． ···················································· 5分17．（本小题满分5分）解：222()2x y x y x xy y+--+ 22()()x y x y x y +=-- ·············································································· 2分2x y x y +=-． ····················································································· 3分 当30x y -=时，3x y =． ·································································· 4分 原式677322y y y y y y +===-． ··································································· 5分 四、解答题（共2道小题，共10分）18．（本小题满分5分）解法一：如图1，分别过点A D ，作AE BC ⊥于点E ，DF BC ⊥于点F ． ······························· 1分 ∴AE DF ∥．又AD BC ∥，∴四边形AEFD 是矩形．EF AD ∴==． ································ 2分 AB AC ⊥，45B ∠=，BC =AB AC ∴=．12AE EC BC ∴===DF AE ∴==CF EC EF =-=········································································· 4分在Rt DFC △中，90DFC ∠=，DC ∴=== ······································ 5分 解法二：如图2，过点D 作DF AB ∥，分别交AC BC ，于点E F ，． ·········· 1分AB AC ⊥，90AED BAC ∴∠=∠=． AD BC ∥， 18045DAE B BAC ∴∠=-∠-∠=． 在Rt ABC △中，90BAC ∠=，45B ∠=，BC =sin 454242AC BC ∴=== ························································ 2分 在Rt ADE △中，90AED ∠=，45DAE ∠=，AD =AB CD F E2 A B C D F E 图11DE AE ∴==．3CE AC AE ∴=-=． ······································································· 4分 在Rt DEC △中，90CED ∠=，DC ∴===． ················································· 5分 19． （本小题满分5分）解：（1）直线BD 与O 相切． ························································· 1分证明：如图1，连结OD ．OA OD =，A ADO ∴∠=∠．90C ∠=，CBD ∴∠+∠又CBD A ∠=∠，90ADO CDB ∴∠+∠=．90ODB ∴∠=． ∴直线BD 与O 相切． ···································································· 2分（2）解法一：如图1，连结DE ．AE 是O 的直径， 90ADE ∴∠=．:8:5AD AO =，4cos 5AD A AE ∴==． ·········································································· 3分 90C ∠=，CBD A ∠=∠，4cos 5BC CBD BD ∴∠==． ···································································· 4分 2BC =， 52BD ∴=． ·························································· 5分 解法二：如图2，过点O 作OH AD ⊥于点H ． 12A H D H A D ∴==． :8:5AD AO =， 4cos 5AH A AO ∴==．················· 3分 90C ∠=，CBD A ∠=∠， 4cos 5BC CBD BD ∴∠==． ························2BC =，BB52BD ∴=． ···················································································· 5分 五、解答题（本题满分6分）解：（1）补全图1见下图． ······························································ 1分913723100100⨯+⨯+==（个）． 这100位顾客平均一次购物使用塑料购物袋的平均数为3个． ·················· 3分200036000⨯=．估计这个超市每天需要为顾客提供6000个塑料购物袋． ·························· 4分（2）图2中，使用收费塑料购物袋的人数所占百分比为25%． ················· 5分 根据图表回答正确给1分，例如：由图2和统计表可知，购物时应尽量使用自备袋和押金式环保袋，少用塑料购物袋；塑料购物袋应尽量循环使用，以便减少塑料购物袋的使用量，为环保做贡献． ··················································· 6分六、解答题（共2道小题，共9分）21．解：设这次试车时，由北京到天津的平均速度是每小时x 千米，则由天津返回北京的平均速度是每小时(40)x +千米． ············································ 1分依题意，得3061(40)602x x +=+． ························································ 3分 解得200x =． ················································································· 4分 答：这次试车时，由北京到天津的平均速度是每小时200千米． ··············· 5分 22．解：（1）重叠三角形A B C '''． ···································· 1分（2）用含m 的代数式表示重叠三角形A B C '''2)m -； ··········· 2分m 的取值范围为843m <≤． ······························································ 4分 七、解答题（本题满分7分）23．（1）证明：2(32)220mx m x m -+++=是关于x 的一元二次方程，222[(32)]4(22)44(2)m m m m m m ∴∆=-+-+=++=+．当0m >时，2(2)0m +>，即0∆>．∴方程有两个不相等的实数根． ·························································· 2分 图1 塑料袋数／个 “限塑令”实施前，平均一次购物使用不同数量塑料购物袋的人（2）解：由求根公式，得(32)(2)2m m x m+±+=． 22m x m+∴=或1x =． ······································································· 3分 0m >，222(1)1m m m m++∴=>． 12x x <，11x ∴=，222m x m+=． ····································································· 4分 21222221m y x x m m+∴=-=-⨯=． 即2(0)y m m =>为所求． ·····（32(0)y m m =>与2(y m m => ·······································由图象可得，当1m ≥时，y ≤八、解答题（本题满分24．解：（1）y kx =沿y 轴向上平移3个单位长度后经过y 轴上的点C ，(03)C ∴，．设直线BC 的解析式为3y kx =+．(30)B ，在直线BC 上，330k ∴+=．解得1k =-．∴直线BC 的解析式为3y x =-+． ······················································· 1分抛物线2y x bx c =++过点B C ，，9303b c c ++=⎧∴⎨=⎩，．解得43b c =-⎧⎨=⎩，． ∴抛物线的解析式为243y x x =-+． ··················································· 2分 x 0)（2）由24y x x =-+可得(21)(1D A -，，3OB ∴=，3OC =，1OA =可得OBC △45OBC ∴∠=，CB =如图1，设抛物线对称轴与x 112AF AB ∴==过点A 作AE BC ⊥于点E ．90AEB ∴∠=． 可得BE AE ==CE =在AEC △与AFP △中，90AEC AFP ∠=∠=，ACE APF ∠=∠，AEC AFP ∴△∽△．AE CE AF PF∴=，1PF =． 解得2PF =．点P 在抛物线的对称轴上，∴点P 的坐标为(22)，或(22)-，． ························································· 5分（3）解法一：如图2，作点(10)A ，关于y 轴的对称点A '，则(10)A '-，． 连结A C A D ''，，可得A C AC '==OCA '∠=由勾股定理可得220CD =，2A D '又210A C '=， 222A D A C CD ''∴+=． A DC '∴△是等腰直角三角形，CA '∠45DCA '∴∠=． 45OCA OCD '∴∠+∠=．45OCA OCD ∴∠+∠=．x图1 x图2即OCA∠与OCD∠两角和的度数为45．·············································· 7分解法二：如图3同解法一可得CD=在Rt DBF△中，90DFB∠=DB∴==在CBD△和COA△1DBAO==3BCOC==DB BC CDAO OC CA∴==．CBD COA∴△∽△．BCD OCA∴∠=∠．45OCB∠=，45OCA OCD∴∠+∠=．即OCA∠与OCD∠两角和的度数为45．·············································· 7分九、解答题（本题满分8分）25．解：（1）线段PG与PC的位置关系是PG PC⊥；PGPC= ···················································································· 2分（2）猜想：（1）中的结论没有发生变化．证明：如图，延长GP交AD于点H，连结CH CG，．P是线段DF的中点，FP DP∴=．由题意可知AD FG∥．GFP HDP∴∠=∠．GPF HPD∠=∠，GFP HDP∴△≌△．GP HP∴=，GF HD=．四边形ABCD是菱形，CD CB∴=，60HDC ABC∠=∠=．由60ABC BEF∠=∠=，且菱形BEFG的对角线BF恰好与菱形ABCD的边AB在同一条直线上，可得60GBC∠=．xD CGPA BEFH。

最新整理
08年大学物理部分（50分）
一．简答题（4×5分）
1.解释火箭发射原理，并说明采用多级火箭发射的必要性。

2.简述“准静态过程”和“可逆过程”。

3.给出面束缚电荷密度和电极化强度P的关系。

4.给出矫顽力的物理意义。

二．给出能量均分定理的适用范围，并说明理想气体体积不变情况下摩尔热熔Cvm=3/2R(10分)
三．证明地球卫星单位时间内扫过的面积相等（10分）
四．相距为d，面积为s的平行板电容器，内充满两中等厚的电解质，求此电容器的电容。

其中两电解质的相对电导率分别为Er1,Er2.（10分）
.。

专题08 三角恒等变换问题【高考真题】1．(2022·新高考Ⅱ)若sin(α＋β)＋cos(α＋β)＝22cos(α＋π4)sin β，则( )A ．tan(α－β)＝1B ．tan(α＋β)＝1C ．tan(α－β)＝－1D ．tan(α＋β)＝－11．答案 C 解析 由已知得，sin αcos β＋cos αsin β＋cos αcos β＋sin αsin β＝2(cos α－sin α)sin β，即sin αcos β ＋cos αsin β＋cos αcos β＋sin αsin β＝0，即sin(α－β)＋cos(α－β)＝0．所以tan(α－β)＝－1．故选C ． 2．(2022·浙江)若3sin α－sin β＝10，α＋β＝π2，则sin α＝__________，cos2β＝__________．2．答案31010 45 解析 α＋β＝π2，∴sin β＝cos α，即3sin α－cos α＝10，即10(31010sin α－1010cos α) ＝10，令sin θ＝1010，cos θ＝31010，则10sin(α－θ)＝10，∴α－θ＝π2＋2k π，k ∈Z ，即α＝θ＋π2＋2k π，∴sin α＝sin(θ＋π2＋2k π)＝cos θ＝31010，则cos2β＝2cos 2β－1＝2sin 2α－1＝45．故答案为31010与45．【知识总结】1．同角三角函数的基本关系(1)平方关系：sin 2α＋cos 2α＝1⇒sin α＝±1－cos 2α. (2)商的关系：sin αcos α＝tan α⎝⎛⎭⎫α≠k π＋π2(k ∈Z ). 2．三角函数的诱导公式3．三角恒等变换 (1) 和角差角公式：cos(α＋β)＝cos αcos β－sin αsin β，cos(α－β)＝cos αcos β＋sin αsin β， sin(α＋β)＝sin αcos β＋cos αsin β，sin(α－β)＝sin αcos β－cos αsin β， tan(α＋β)＝tan α＋tan β1－tan αtan β，tan(α－β)＝tan α－tan β1＋tan αtan β.(2)二倍角公式： sin 2α＝2sin αcos α，cos 2α＝cos 2α－sin 2α＝2cos 2α－1＝1－2sin 2α，tan 2α＝2tan α1－tan 2α.(3)降幂公式：sin 2α＝1－cos 2α2，cos 2α＝1＋cos 2α2.(4)辅助角公式：a sin x ＋b cos x ＝a 2＋b 2sin(x ＋φ)，其中tan φ＝ba .【同类问题】 题型一 给角求值 1．tan 105°等于( )A ．2－3B ．－2－3C ．3－2D ．－31．答案 B 解析 tan 105°＝tan(60°＋45°)＝tan 60°＋tan 45°1－tan 60°·tan 45°＝3＋11－3＝(3＋1)2(1－3)(1＋3)＝4＋23－2＝－2－3．2．sin 10°1－3tan 10°等于( ) A ．1 B ．14 C ．12 D ．322．答案 B 解析sin 10°1－3tan 10°＝sin 10°cos 10°cos 10°－3sin 10°＝2sin 10°cos 10°4⎝⎛⎭⎫12cos 10°－32sin 10°＝sin 20°4sin (30°－10°)＝14．3．化简tan 27.5°＋1tan 27.5°－7sin 27.5°＋cos 27.5°等于( )A ．33 B ．233C ． 3D ．2 3．答案 B 解析 原式＝tan 27.5°＋1tan 27.5°－8sin 27.5°＋1＝sin 27.5°＋cos 27.5°sin 27.5°－8sin 27.5°cos 27.5°＋cos 27.5°＝11－2sin 215°＝ 1cos 30°＝233． 4．sin 40°(tan 10°－3)等于( )A ．2B ．－2C ．1D ．－14．答案 D 解析 sin 40°·(tan 10°－3)＝sin 40°·⎝⎛⎭⎫sin 10°cos 10°－3＝sin 40°·sin 10°－3cos 10°cos 10°＝sin 40°·2⎝⎛⎭⎫12sin 10°－32cos 10°cos 10°＝sin 40°·2(cos 60°·sin 10°－sin 60°·cos 10°)cos 10°＝sin 40°·2sin (10°－60°)cos 10°＝sin40°·－2sin 50°cos 10°＝－2sin 40°·cos 40°cos 10°＝－sin 80°cos 10°＝－1．5．cos 20°·cos 40°·cos 100°＝ ．5．答案 －18解析 cos 20°·cos 40°·cos 100°＝－cos 20°·cos 40°·cos 80°＝－sin 20°·cos 20°·cos 40°·cos 80°sin 20°＝－12sin 40°·cos 40°·cos 80°sin 20°＝－14sin 80°·cos 80°sin 20°＝－18sin 160°sin 20°＝－18sin 20°sin 20°＝－18．6．cos 40°cos 25°1－sin 40°的值为( ) A ．1 B ．3 C ． 2 D ．2 6．答案 C 解析 原式＝cos 220°－sin 220°cos 25°(cos 20°－sin 20°)＝cos 20°＋sin 20°cos 25°＝2cos 25°cos 25°＝2．7．tan 67.5°－1tan 67.5°的值为( )A ．1B ．2C ．2D ．47．答案 C 解析 tan 67.5°－1tan 67.5°＝sin 67.5°cos 67.5°－1sin 67.5°cos 67.5°＝sin 67.5°cos 67.5°－cos 67.5°sin 67.5°＝sin 267.5°－cos 267.5°sin 67.5°cos 67.5°＝－cos 135°12sin 135°＝2．8．求值：3－tan 12°(2cos 212°－1)sin 12°＝ ． 8．答案 8 解析 原式＝3－sin 12°cos 12°cos 24°sin 12°＝3cos 12°－sin 12°cos 24°sin 12°cos 12°＝2sin (60°－12°)14sin 48°＝2sin 48°14sin 48°＝8．9．已知m ＝2sin 18°，若m 2＋n ＝4，则1－2cos 2153°m n等于( )A ．－14B ．－12C ．14D ．129．答案 B 解析 因为m ＝2sin 18°，m 2＋n ＝4，所以n ＝4－m 2＝4－4sin 218°＝4cos 218°，因此 1－2cos 2153°m n ＝－cos 306°2sin 18°·2cos 18°＝－cos 54°2sin 36°＝－sin 36°2sin 36°＝－12． 10．(多选)下列各式中，值为12的是( )A ．cos 2π12－sin 2π12 B ．tan 22.5°1－tan 222.5°C ．2sin 195°cos 195°D ．1＋cosπ6210．答案 BC 解析 cos 2π12－sin 2π12＝cos ⎝⎛⎭⎫2×π12＝cos π6＝32，故A 错误；tan 22.5°1－tan 222.5°＝12·2tan 22.5°1－tan 222.5＝ 12tan 45°＝12，故B 正确；2sin 195°cos 195°＝2sin(180°＋15°)cos(180°＋15°)＝2sin 15°cos 15°＝sin 30°＝12，故C 正确；1＋cosπ62＝2＋34＝2＋32≠12，故D 错误． 题型二 给值求值11．(2021·全国乙)cos 2π12－cos 25π12等于( )A ．12B ．33C ．22D ．3211．答案 D 解析 因为cos 5π12＝sin ⎝⎛⎭⎫π2－5π12＝sin π12，所以cos 2π12－cos 25π12＝cos 2π12－sin 2π12＝cos ⎝⎛⎭⎫2×π12 ＝cos π6＝32．12．(2020·全国Ⅰ)已知α∈(0，π)，且3cos 2α－8cos α＝5，则sin α等于( )A ．53 B ．23 C ．13 D ．5912．答案 A 解析 由3cos 2α－8cos α＝5，得3(2cos 2α－1)－8cos α＝5，即3cos 2α－4cos α－4＝0，解得cos α＝－23或cos α＝2(舍去)．又因为α∈(0，π)，所以sin α>0，所以sin α＝1－cos 2α＝1－⎝⎛⎭⎫－232＝53． 13．(2019·全国Ⅱ)已知α∈⎝⎛⎭⎫0，π2，2sin 2α＝cos 2α＋1，则sin α等于( ) A ．15 B ．55 C ．33 D ．25513．答案 B 解析 由2sin 2α＝cos 2α＋1，得4sin αcos α＝1－2sin 2α＋1，即2sin αcos α＝1－sin 2α．因为α∈⎝⎛⎭⎫0，π2，所以cos α＝1－sin 2α，所以2sin α1－sin 2α＝1－sin 2α，解得sin α＝55． 14．(2021·全国甲)若α∈⎝⎛⎭⎫0，π2，tan 2α＝cos α2－sin α，则tan α等于( ) A ．1515 B ．55 C ．53 D ．15314．答案 A 解析 方法一 因为tan 2α＝sin 2αcos 2α＝2sin αcos α1－2sin 2α，且tan 2α＝cos α2－sin α，所以2sin αcos α1－2sin 2α＝ cos α2－sin α，解得sin α＝14．因为α∈⎝⎛⎭⎫0，π2，所以cos α＝154，tan α＝sin αcos α＝1515． 方法二 因为tan 2α＝2tan α1－tan 2α＝2sin αcos α1－sin 2αcos 2α＝2sin αcos αcos 2α－sin 2α＝2sin αcos α1－2sin 2α，且tan 2α＝cos α2－sin α，所以2sin αcos α1－2sin 2α＝cos α2－sin α，解得sin α＝14．因为α∈⎝⎛⎭⎫0，π2，所以cos α＝154，tan α＝sin αcos α＝1515． 15．若cos ⎝⎛⎭⎫π6－α＝13，则cos ⎝⎛⎭⎫2π3＋2α等于( )A ．29B ．－29C ．79D ．－7915．答案 C 解析 ∵cos ⎝⎛⎭⎫π6－α＝13．∴cos ⎝⎛⎭⎫π6－α＝sin ⎣⎡⎦⎤π2－⎝⎛⎭⎫π6－α＝sin ⎝⎛⎭⎫π3＋α＝13，∴cos ⎝⎛⎭⎫2π3＋2α＝1 －2sin 2⎝⎛⎭⎫π3＋α＝1－29＝79． 16．已知sin ⎝⎛⎭⎫α－π3＋3cos α＝13，则sin ⎝⎛⎭⎫2α＋π6等于( ) A ．23 B ．29 C ．－19 D ．－7916．答案 D 解析 ∵sin ⎝⎛⎭⎫α－π3＋3cos α＝13，∴sin αcos π3－cos αsin π3＋3cos α＝13，∴12sin α－32cos α ＋3cos α＝13，∴12sin α＋32cos α＝13，∴cos ⎝⎛⎭⎫α－π6＝13，∴sin ⎝⎛⎭⎫2α＋π6＝sin ⎣⎡⎦⎤2⎝⎛⎭⎫α－π6＋π2＝cos 2⎝⎛⎭⎫α－π6＝2cos 2⎝⎛⎭⎫α－π6－1＝2×⎝⎛⎭⎫132－1＝－79． 17．已知cos ⎝⎛⎭⎫π2－α＝2cos(π－α)，则tan ⎝⎛⎭⎫π4＋α等于( ) A ．－3 B ．13 C ．－13D ．317．答案 C 解析 由cos ⎝⎛⎭⎫π2－α＝2cos(π－α)得sin α＝－2cos α，即tan α＝－2，∴tan ⎝⎛⎭⎫π4＋α＝ tan π4＋tan α1－tan π4tan α＝1－21－1×(－2)＝－13． 18．已知α，β∈⎝⎛⎭⎫3π4，π，sin(α＋β)＝－35，sin ⎝⎛⎭⎫β－π4＝1213，则cos ⎝⎛⎭⎫α＋π4＝ ． 18．答案 －5665 解析 因为α，β∈⎝⎛⎭⎫3π4，π，所以3π2<α＋β<2π，π2<β－π4<3π4，因为sin(α＋β)＝－35，sin ⎝⎛⎭⎫β－π4 ＝1213，所以cos(α＋β)＝45，cos ⎝⎛⎭⎫β－π4＝－513，所以cos ⎝⎛⎭⎫α＋π4＝cos ⎣⎡⎦⎤α＋β－⎝⎛⎭⎫β－π4＝cos(α＋β)cos ⎝⎛⎭⎫β－π4＋sin(α＋β)sin ⎝⎛⎭⎫β－π4＝45×⎝⎛⎭⎫－513＋⎝⎛⎭⎫－35×1213＝－5665． 19．已知cos ⎝⎛⎭⎫θ＋π4＝1010，θ∈⎝⎛⎭⎫0，π2，则sin ⎝⎛⎭⎫2θ－π3＝ ． 19．答案 4－3310 解析 由题意可得cos 2⎝⎛⎭⎫θ＋π4＝1＋cos ⎝⎛⎭⎫2θ＋π22＝110，cos ⎝⎛⎭⎫2θ＋π2＝－sin 2θ＝－45，即 sin 2θ＝45．因为cos ⎝⎛⎭⎫θ＋π4＝1010>0，θ∈⎝⎛⎭⎫0，π2，所以0<θ<π4，2θ∈⎝⎛⎭⎫0，π2，根据同角三角函数基本关系式，可得cos 2θ＝35，由两角差的正弦公式，可得sin ⎝⎛⎭⎫2θ－π3＝sin 2θcos π3－cos 2θsin π3＝45×12－35×32＝4－3310．20．设α，β∈(0，π)，sin(α＋β)＝513，tan α2＝12，则cos β＝________．20．答案 －1665 解析 因为tan α2＝12，所以sin α＝2sin α2cos α2＝2sin α2cos α2sin 2α2＋cos 2α2＝2tanα21＋tan 2α2＝45，cos α＝cos 2α2－sin 2α2＝cos 2α2－sin 2α2cos 2α2＋sin 2α2＝1－tan 2α21＋tan2α2＝35∈⎝⎛⎭⎫12，22．又α∈(0，π)，所以a ∈⎝⎛⎭⎫π4，π3，又β∈(0，π)，所以α＋β∈⎝⎛⎭⎫π4，4π3．又sin(α＋β)＝513∈⎝⎛⎭⎫0，12，所以α＋β∈⎝⎛⎭⎫56π，π，所以cos(α＋β)＝－1213，所以cos β＝cos[(α＋β)－α]＝cos(α＋β)cos α＋sin(α＋β)sin α＝－1665．题型三 给值求角与多选题21．已知A ，B 均为钝角，且sin 2A 2＋cos ⎝⎛⎭⎫A ＋π3＝5－1510，sin B ＝1010，则A ＋B 等于( ) A ．3π4 B ．5π4 C ．7π4 D ．7π621．答案 C 解析 因为sin 2A 2＋cos ⎝⎛⎭⎫A ＋π3＝5－1510，所以1－cos A 2＋12cos A －32sin A ＝5－1510，即12－ 32sin A ＝5－1510，解得sin A ＝55，因为A 为钝角，所以cos A ＝－1－sin 2A ＝－1－⎝⎛⎭⎫552＝－255．由sin B ＝1010，且B 为钝角，得cos B ＝－1－sin 2B ＝－1－⎝⎛⎭⎫10102＝－31010．所以cos(A＋B )＝cos A cos B －sin A sin B ＝⎝⎛⎭⎫－255×⎝⎛⎭⎫－31010－55×1010＝22．又A ，B 都为钝角，即A ，B ∈⎝⎛⎭⎫π2，π，所以A ＋B ∈(π，2π)，所以A ＋B ＝7π4．22．已知α，β均为锐角，cos α＝277，sin β＝3314，则cos 2α＝ ，2α－β＝ ．22．答案 17 π3 解析 因为cos α＝277，所以cos 2α＝2cos 2α－1＝17．又因为α，β均为锐角，sin β＝3314，所以sin α＝217，cos β＝1314，因此sin 2α＝2sin αcos α＝437，所以sin(2α－β)＝sin 2αcos β－cos 2αsin β＝437×1314－17×3314＝32．因为α为锐角，所以0<2α<π．又cos 2α>0，所以0<2α<π2，又β为锐角，所以－π2<2α－β<π2，又sin(2α－β)＝32，所以2α－β＝π3．23．已知α，β∈(0，π)，且tan(α－β)＝12，tan β＝－17，则2α－β的值为 ．23．答案 －3π4 解析 ∵tan α＝tan [(α－β)＋β]＝tan (α－β)＋tan β1－tan (α－β)tan β＝12－171＋12×17＝13>0，且α∈(0，π)，∴0<α<π2．又∵tan 2α＝2tan α1－tan 2α＝2×131－⎝⎛⎭⎫132＝34>0，∴0<2α<π2．∵tan β＝－17<0，β∈(0，π)，∴π2<β<π，∴－π<2α－β<0．∵tan(2α－β)＝tan 2α－tan β1＋tan 2αtan β＝34＋171－34×17＝1，∴2α－β＝－3π4．24．已知锐角α，β满足sin α＝55，cos β＝31010，则α＋β等于( ) A ．3π4 B ．π4或3π4 C ．π4 D ．2k π＋π4(k ∈Z )24．答案 C 解析 由sin α＝55，cos β＝31010，且α，β为锐角，可知cos α＝255，sin β＝1010，故cos(α ＋β)＝cos αcos β－sin αsin β＝255×31010－55×1010＝22，又0<α＋β<π，故α＋β＝π4．25．已知方程x 2＋3ax ＋3a ＋1＝0(a >1)的两根分别为tan α，tan β，且α，β∈⎝⎛⎭⎫－π2，π2，则α＋β＝ ．25．答案 －3π4 解析 依题意有⎩⎪⎨⎪⎧tan α＋tan β＝－3a ，tan α·tan β＝3a ＋1，所以tan(α＋β)＝tan α＋tan β1－tan α·tan β＝－3a 1－3a ＋1＝1．又⎩⎪⎨⎪⎧tan α＋tan β<0，tan α·tan β>0，所以tan α<0且tan β<0，所以－π2<α<0且－π2<β<0，即－π<α＋β<0，结合tan(α＋β)＝1，得α＋β＝－3π4．26．设α，β∈[0，π]，且满足sin αcos β－cos αsin β＝1，则sin(2α－β)＋sin(α－2β)的取值范围为 ． 26．答案 [－1，1] 解析 由sin αcos β－cos αsin β＝1，得sin(α－β)＝1，又α，β∈[0，π]，∴－π≤α－β≤π，∴α－β＝π2，∴⎩⎪⎨⎪⎧0≤α≤π，0≤β＝α－π2≤π，即π2≤α≤π，∴sin(2α－β)＋sin(α－2β)＝sin ⎝⎛⎭⎫2α－α＋π2＋sin(α－2α＋π)＝cos α＋sin α＝2sin ⎝⎛⎭⎫α＋π4．∵π2≤α≤π，∴3π4≤α＋π4≤5π4，∴－1≤2sin ⎝⎛⎭⎫α＋π4≤1，即sin(2α－β)＋sin(α－2β)的取值范围为[－1，1]．27．已知x ，y ∈⎝⎛⎭⎫0，π2，sin(x ＋y )＝2sin(x －y )，则x －y 的最大值为( ) A ．π3 B ．π6 C ．π4 D ．π827．答案 B 解析 由sin(x ＋y )＝2sin(x －y )得sin x cos y ＋cos x sin y ＝2sin x cos y －2cos x sin y ，则tan x ＝3tan y ，所以tan(x －y )＝tan x －tan y 1＋tan x tan y ＝2tan y 1＋3tan 2y＝21tan y＋3tan y ≤33，当且仅当tan y ＝33时等号成立，由于f (x )＝tan x 在x ∈⎝⎛⎭⎫0，π2上单调递增，又x ，y ∈⎝⎛⎭⎫0，π2，则x －y 的最大值为π6． 28．(多选)下列四个选项中，化简正确的是( ) A ．cos(－15°)＝6－24B ．cos 15°cos 105°＋sin 15°sin 105°＝cos(15°－105°)＝0C ．cos(α－35°)cos(25°＋α)＋sin(α－35°)sin(25°＋α)＝cos[(α－35°)－(25°＋α)]＝cos(－60°)＝cos 60°＝12D ．sin 14°cos 16°＋sin 76°cos 74°＝1228．答案 BCD 解析 对于A ，方法一 原式＝cos(30°－45°)＝cos 30°·cos 45°＋sin 30°sin 45°＝32×22＋12×22＝6＋24． 方法二 原式＝cos 15°＝cos(45°－30°)＝cos 45°cos 30°＋sin 45°sin 30°＝22×32＋22×12＝6＋24，A 错误．对于B ，原式＝cos(15°－105°)＝cos(－90°)＝cos 90°＝0，B 正确．对于C ，原式＝cos[(α－35°)－(25°＋α)]＝cos(－60°)＝cos 60°＝12，C 正确．对于D ，原式＝cos 76°cos 16°＋sin 76°sin 16°＝cos(76°－16°)＝cos 60°＝12，D 正确．29．(多选)已知cos(α＋β)＝－55，cos 2α＝－513，其中α，β为锐角，以下判断正确的是( ) A ．sin 2α＝1213 B ．cos(α－β)＝19565 C ．cos αcos β＝8565 D ．tan αtan β＝11829．答案 AC 解析 因为cos(α＋β)＝－55，cos 2α＝－513，其中α，β为锐角，所以sin 2α＝1－cos 22α ＝1213，故A 正确；因为sin(α＋β)＝255，所以cos(α－β)＝cos [2α－(α＋β)]＝cos 2αcos(α＋β)＋sin 2αsin(α＋β)＝⎝⎛⎭⎫－513×⎝⎛⎭⎫－55＋1213×255＝29565，故B 错误；cos αcos β＝12[cos(α＋β)＋cos(α－β)]＝12⎝⎛⎭⎫－55＋29565＝8565，故C 正确；sin αsin β＝12[cos(α－β)－cos(α＋β)]＝12⎣⎡⎦⎤29565－⎝⎛⎭⎫－55＝21565，所以tan αtan β＝218，故D 错误．30．(多选)下列结论正确的是( )A ．sin(α－β)sin(β－γ)－cos(α－β)cos(γ－β)＝－cos(α－γ)B ．315sin x ＋35cos x ＝35sin ⎝⎛⎭⎫x ＋π6C ．f (x )＝sin x 2＋cos x2的最大值为2D ．tan 12°＋tan 33°＋tan 12°tan 33°＝130．答案 AD 解析 对于A ，左边＝－[cos(α－β)cos(β－γ)－sin(α－β)·sin(β－γ)]＝－cos[(α－β)＋(β－γ)]＝－cos(α－γ)，故A 正确；对于B ，315sin x ＋35cos x ＝65⎝⎛⎭⎫32sin x ＋12cos x ＝65sin ⎝⎛⎭⎫x ＋π6，故B 错误；对于C ，f (x )＝sin x 2＋cos x2＝2sin ⎝⎛⎭⎫x 2＋π4，所以f (x )的最大值为2，故C 错误；对于D ，tan 12°＋tan 33°＋tan 12°tan 33°＝tan(12°＋33°)·(1－tan 12°tan 33°)＋tan 12°tan 33°＝1，故D 正确．。

2008年1、机构的自由度就是构件的自由度。

( )2、复合铰链与移动副无关。

( )3、曲柄摇杆机构的行程速比系数K 不可能等于1。

( )4、铰链四杆机构中，若存在曲柄，其曲柄一定是最短杆。

( )5、曲柄滑块机构一定具有急回运动性质。

( )6、平底直动从动件凸轮机构，其压力角为90°。

( )7、凸轮机构中，基圆半径越小，则压力角越大。

( )8、凡是有滚子的地方都存在局部自由度。

( )9、同一模数和同一压力角，但不同齿数的两个，可以使用一把齿轮刀具进行齿轮加工。

( ) 10、圆锥齿轮的当量齿数为δ3VCOS Z Z =。

( )11、设计V 带传动时，适当增大带轮直径是减少带根数的措施之一。

（ ） 12、为了提高滚子链传动的平稳性，设计时通常将链条节数取为偶数，而将链轮齿数取为奇数。

（ ） 13、设计圆柱齿轮传动时，通常使小齿轮的齿宽略大于大齿轮的齿宽，主要目的是为了提高小齿轮的强度。

（ ）14螺纹联接中，有时在一个螺栓上拧上两个螺母，目的是为了增加受载螺纹的圈数，有利于提高螺栓的强度。

（ ）15、工作面磨损不是普通平键联接的主要失效形式。

（ ） 16、万向联轴器既能用于两轴线有较大角位移的场合，也能用于有较大径向位移的场合。

（ ） 17、滚柱式定向离合器只能单方向传递转矩，且从动端的转速可超过主动端的转速。

（ ）18、现有A 、B 两个圆柱形螺旋弹簧，A 弹簧的中径D 2大于B 弹簧的，其他条件相同，则在相同的外载F 作用下B 弹簧的变形大一些。

（ ）1、试计算图示（注意：若有复合铰链、局部自由度或虚约束，必须明确指出；必须先列出自由度的计算公式，再代入数值进行计算）。

2、图示为凸轮机构从动件的速度线图，试画出加速度线图，并指出何处发生刚性冲击？又何处发生柔性冲击？3、如图所示的曲柄滑块机构，请画出C 处的压力角α和传动角γ。

注：① 作图过程可不作文字说明，但应保留作图线； ② α、γ只需标出，不必度量。