高三单选错题集
江苏省启东中学高中英语复习错题集之错题6牛津译林版解析
错题6I. 单选题：1.---How would you like your coffee? ---________.A. It’s well doneB. Very nice, thank youC. One cup, that’s enoughD. The stronger , the better.2. It was dark; we decided to _____ for the night at a farmhouse?A. put awayB. put downC. put upD. put on3. ST Petersbury was in ruins: _____ fires burned everywhere.A. thatB. whichC. whereD./4. The beginning of agriculture was a big step in human progress with which nothing could _____ until our information age.A. matchB. combineC. satisfyD. compare5.In our childhood, we were often _____ by Grandma to pay attention to our table manners.A. demandedB. remindedC. allowedD. hoped6. The flu is believed _____by viruses that like to reproduce in the cells insidethe human nose and throat.A. to have been causedB. to have causedC. to be causedD. to caused7. ____much we admire Shakespeare’s comedies, we can’t agree that they are superior to his tragedies.A. AsB. HoweverC. WhileD. Although8. Much_____ we admire Shakespeare’s comedies, we can’t agree that they are superior to his tragedies.A. AsB. HoweverC. WhileD. Although9. What good is it _____ a boat when you don’t have enough spare time to use it ?A. having boughtB. to have boughtC. buyingD. to buy10. I’ve visited a lot of different places and stayed in lots of different hotels, but none ___ yours.A. matchesB. goes withC. suitsD. compares11.To most people acting is attractive, business isn't. It works ________ way around for John.A. anotherB. the otherC. otherD. any other12. After great efforts President Obama was elected to a second _____ of office.A. turnB. term C round. D. stage13. The priest made the ______ of the cross when he entered the church.A. markB. signC. signalD. gesture14. Health experts believe that even a little exercise is far better than ______ at all.A. anythingB. littleC. everythingD. none15. ----The criminal was finally sentenced to death.--- Just as a biblical idiom says, “_________________.”A. See the handwriting on the wallB. An eye for an eyeC. You reap what you sowD. Kill the fatted calf16. These years, more students have gone abroad to study, but some of them seem unable to ______ , so they have to quit.A. stick outB. hang outC. participate inD. fit in17. It snowed heavily last night and we had to use thick sticks to _____ the roof of the hut.A. hold upB. hold onC. hold backD. hold out18. Frank used to be _______ strong. But now he’s down to his last tooth.A. more thanB. far from C too much. D. less than19. On Christmas Eve, there were so many customers that the shop assistants couldn’t ______ them well.A. correspond toB. appeal toC. commit toD. attend to20. Philosophical problems arise when people ask questions that, though very _______ , have certain characteristics in common.A. relevantB. diverseC. abstractD. consistent21. _______your proposal, I’m pleased to inform you that most committee members consider it acceptable.A. ConcerningB. SeeingC. SupposingD. Considering22. ---Was his father very strict with him when he was at school?--- Yes. He had never praised him ______ he became one of the top students in his grade.A. afterB. unlessC. untilD. when23. She’s ______ is known as a nosy person---she is always dying to know what’sgoing on in others’ lives.A. whoB. whatC. whichD. that24. —You ought to have made an apology to Tom yesterday evening．—Yes, I know I ____________．A．should B．have to C．ought to have D．must have25. The serious accident and the suffering _______has caused have a great influenceon the whole company.A. theyB. itC. whichD. what26. Though_________ my opinion, my mother didn’t say anything to show that she stoodby me.A. forB. inC. onD. of27. Look! If we had begun to do the work yesterday morning, we ____ ourselves justlike them．A.would have enjoyed B．were to enjoy C．would be enjoyingD．should enjoy28. I __________in a foreign trade company for five years. Still, I don’t regretgiving up the well-paid job.A. have workedB. workedC. had workedD. wasworking29. What is concerning us greatly is ________ the workers held up in that areayesterday will be set free.A. thatB. whenC. whatD. which30. While addressing a conference Thursday, President Xi Jinping said that China-USties are not a win-loser game but ______ in which both can be winners.A. oneB. thatC. the oneD. it31. The nationwide smog should serve as a reminder to all, indicating a high timethat we ______ on what we’ve done to the environment.A. have reflectedB. reflectedC. will reflectD. arereflecting32. This will be a year of action, and that action should begin by extendingunemployment insurance for American who were _______ in the economic slowdown.A. laid offB. laid outC. laid onD. laid down33. One of the characteristics that make me different from many people is myadaptability ---I’m _______ and comfortable in new or unusual situations. A. acceptable B. respectable C. flexible D.reliable34. ---Tom, were all the students on the school bus injured?---- No, _____ only the three who got hurt.A. there wasB. there wereC. it wasD. that was35. You should be grateful to your employees, because you wouldn’t be ______ youare now without them.A. whyB. whereC. howD. which36. ---Haven’t you handed in your project?---- Yes, My classmates and I _____ on it for the whole weekend.A. have workedB. are workingC. have been workingD.worked37. ---One cannot achieve anything by sitting around and talking about it.--- I can’t agree more. ________. That’s why Johnson failed to get into college.A. A roaring lion kills no game.B. An old pan is the one that makesgood food.C. A book is a garden carried in the pocketD. A bad workman always blames histools.38. ---The scarf is nice, but the price is a little bit high.--- _______, but if you want good quality, you have to pay more.A. No wonderB. No doubtC. No problemD. No offence39. Mom often phones me, asking ______ I am getting along with my studies.A. howB. whenC. whetherD. why40. Mom often phones me, asking ______ I am getting along well with my studies.A. howB. whenC. whetherD. why41.---Have you told your parents about your decision?---Not yet. I can hardly imagine _____ they will react.A. whatB. thatC. howD. when42. A Chinese girl student was kidnapped while traveling abroad, ______ shocked us Chinese.A. a fact thatB. thatC. one thatD. the one that43.It is hard for elderly people to see ______ convenience a smart hone can bring to us.A. whichB. whoseC. whatD. how44.Many restaurant menus include the origins of a dish, _______ it is prepared, what the main ingredients are, and which farms the ingredients come from.A. whenB. howC. whatD. which45._____ matters much ______ our headmaster supports our plan.A. As, thatB. It, whetherC. That, ifD. What, whether46. _____ matters much is ______ our headmaster supports our plan.A. As, thatB. It, whetherC. That, ifD. What, whether47.Jim, your sister has done most of the cleaning. Could you finish ______ when you are free?A. the othersB. the otherC. anotherD. the rest48.---How many of you made it to the top of the mountain in the end?---_______. It was really tough.A. No oneB. NeitherC. NoneD. Nobody49. ---What can I do for you?---I’d like to buy a present for my son, ______ at a proper price but of great use.A. oneB. itC. whichD. that50.Some day, we are sure to understand the things that matter are ______ that can’t always be bought with money.A. theseB. thoseC. onesD. what51.Nowadays, the approaches to language teaching are more advanced than ______ in the 1960s.A. theseB. themC. onesD. those52.Although it doesn’t look like _______, the entire cathedral is made of wood.A. itB. thatC. thisD. such53. As Mrs Roosevelt put ______, I’d rather light a candle than complain about the darkness.A. itB. thatC. thisD. them54.---Have you bought the newly-produced equipment on display?---Not yet, for I still prefer _____ at my home.A. the oneB. itC. thisD. that55.When you are faced with failure, ______ you need is to take courage and try again.A. thatB. allC. whichD. it56. ---Is Tony a man with good manners?---I don’t think so. As a matter of fact, he is _____ but polite.A. somethingB. anythingC. everythingD. nothing57. Please write the word here _____ meaning escapes you.A. whereB. thoseC. whoseD. which58.---When did he come back last night?---It was at 8 _______ I was watching a documentary on TV.A. sinceB. thatC. whenD. which59.There are many examples in our life _______ a word of appreciation changes a person completely.A. whichB. thatC. whenD. where60.It is wise to find a place to travel ______ has a lot to present but hasn’t yet been hit by high price of admission as well as mass popularity.A. whereB. thatC. in whichD. what61.The school library is a resource _______ you can take advantage to make progress.A. in whichB. on whichC. from whichD. of which62.More than ten family members gathered at the table _____ were traditional local oods such as preserved ham sausage.A. whatB. whichC. thatD. where63.Between classes is a ten-minute break, ______ students can relax themselves.A. whenB. whereC. whoseD. which64.Steven Jobs , ______ rise to fame inspires millions of people, will be remembered generation after generation.A. whatB. whichC. whoseD. who65.You should realize the fact that when you graduate from university, you are still not prepared for the possible situations_______ you may face in the working world.A. whereB. thatC. whatD. when66.You should realize the fact that when you graduate from university, you are still not prepared for the possible situations____ you don’t know how to solve the problems that appear in the job.A. whereB. thatC. whatD. when67.Now there is just one point ______I wish you to make quite clear.A. whereB. whichC. whatD. when68. They have reached the point _____ they have to separate with each other.A. whereB. whichC. whatD. when69.He said it was this classroom _____ he found his lost watch and _____ he would take good care of it from then on.A. where, /B. when, whatC. that, whatD. where, that70.______, I attended the meeting instead of him.A. He was illB. His being illC. Him being illD. He being ill71. I wronged the poor honest man very much, _____ I made an apology afterwards.A. for whomB. for whichC. with whomD. with which72. He was admitted to our school two years ago, a top school in our hometown, ______ he has been crazy about reading electronic novels, killing time.A. after thatB. since thatC. after whenD. since when73. Today is my grandfather’s 100th birthday, an occasion _____ we are going to celebrate with all the family and a few friends in for the evening.A. whoB. whichC. whereD. when74. Today is my grandfather’s 100th birthday, an occasion _____ we are going to stay together with all the family and a few friends in for the evening.A. whoB. whichC. whereD. when75.Actually you can make learning English a process, _______ you can not only learn much knowledge but also interesting cultures.A. whichB. whereC. whenD. what76.---Frank, I have learned your plan. Could I make some suggestions? ---_________.A. Just for funB. With pleasureC. Go right aheadD. Take it easy.77.---Can I come and have a look at your new house? ---Yes, ________!A. by all meansB. I quite agreeC. I like itD. with pleasure78.________ with too much work, he spent little time playing with his little child, even during the holiday.A. Kept occupiedB. Kept occupyingC. Keeping being occupiedD. Keeping occupied79.I know it will be difficult to pick him out in the crowd, but if you _______ happen to see him, give him this packet.A. wouldB. mightC. shouldD. could80.---How do y find your new classmate?---Most of them are kind, but ______ is so good to me as Bruce.A. noneB. no oneC. every oneD. some oneII. 动词的适当形式填空：1. All the school needs _______ (add) to its beauty is a tennis court2. All the schools need _______ (add) to from time to time.3. The machine _______( work) for 4 hours continuously! We must stop it or it will break down.4. I would like to _____(visit) a friend of mine last night but I had an unexpected visitor.5. He works in a firm now, but he _______ (work) on a farm for ten years.6. There are waiting rooms in the new station, ______(seat) over 1000 passengers.7.I don’t want there ______( be) any students falling behind.8. Don’t worry. When you arrive, I ___________(wait) for you at the exit of the airport.9. The design they have spent so much time on ______( prove) to be a success in the near future.10.I would rather you _______(not tell) him the news that day.错题6答案：1-5 DCDDB 6-10 ABACA 11-15BBBDC 16-20 DAADB 21-25 ACBCB 26-30 ACBBA31-35 BACCB 36-40 DADAC 41-45 CACBB 46-50DDCAB 51-55 DAADB 56-60BCCDB61-65DDACB 66-70 ABADD 71-75 BDBDB 76-80 CAACA动词填空：1. to add2. adding3. has been working4. have visited5. worked6. seating7. to be8. will/shall be waiting9. will prove 10. hadn’t told。
2020年江苏高考英语单选错题集1
2020年江苏高考英语单选错题集1-CAL-FENGHAI-(2020YEAR-YICAI)_JINGBIAN【2020年江苏高考单选错题集1】1 There is ______ thing as failure. Failure is just life trying to move us inanother direction.A. not suchB. such noC. no suchD. such not2. His failure in the college entrance exam _______ him the opportunityto go to university.A. spentB. tookC. paidD. cost3. ----- What do you think of my homework?----- Good work, ________a few slight mistakes.A. in addition toB. exceptC. as well asD. apart from4. Dick enjoys painting but he knows the fact _____ he doesn’t have_____ it takes to be a painter.A. which; whatB. that; whatC. what; thatD. that; that5. We believe her design is _______ because it is completely differentfrom anyone else’s.A. originalB. initialC. vividD. previous6. The MH370 from Malaysia crashed in the southern Indian Ocean,______ global concern about flight safety.A. to causeB. causingC. having causedD. caused7. ________ to the current education system of China, the Ministry ofEducation should make changes to make it efficient for selectingtalents.A. Most of us are so accustomedB. so are most of us accustomedC. Accustomed as most of us areD. As most of us are accustomed8. He accidentally _______ that he had been laid off and had to make aliving away from home.A. let outB. let aloneC. let downD. let off9. If it hadn’t rained so hard last night, it _______ so cold today.A. wouldn’t beB. hadn’t beenC. wouldn’t have beenD. weren’t10. On Sundays there were a lot of children playing in the park, _______parents seated together joking.A. whoseB. theirC. whichD. where11. Loneliness is a feeling where people experience a powerful ______ofemptiness and solitude(孤独).A. trendB. dashC. crashD. rush12. Tony _____ the invitation, otherwise he would have attended yourbirthday party.A. couldn’t have received C. needn’t have receivedB. mustn’t have received D. shouldn’t have received13. ---- Is this the first time you ____ Shanghai?----- No. But the first time I ____ here, the city wasn’t so beautiful.A. visit; came C. have visited; have comeB. have visited; came D. visit; have come14. _______ a scenic spot worth _______, Hangzhou, a friendly city,attracts many visitors from all over the world.A. Considering; visiting C. Considered; visitingB. Considering; being visited D. Considered; visited15. ---- I’m sorry. Jack, please don’t ________---- I had a little accident with the car, but it wasn’t my fault.A. be on cloud nine C. promise me the moonB. be down in the dumps D. fly off the handle16. _____ as the most excellent student in her university, as mostclassmates had expected, made her mother very happy..A Mary was chosen C Mary being chosenB Mary chosen D Mary’s being chosen17. I was disappointed to see the watch I had had ____ stopped again.A itB it repairedC repairedD to be repaired18. It is reported that China will not buy the Euro debt until somethorough research ________.A. has been done C. will be doneB. will have been done D. had been done19. ---I’ve studied your program, Peter. Could I make some sugg estions?--- . I am all ears.A. By no means C. Go right aheadB. Take it easy D. With pleasure20. by flowers and applauses does not necessarily mean one is livinga happy life.A. Accompanied C. To be accompaniedB. Having accompanied D. Being accompanied21. Carbon dioxide is said the earth twice as quickly as previouslyfeared.A. to be heated C. to have heatedB. to be heating D. to have been heated22. It’s fairly common in Africa for a group musicians surrounded byothers who also join in the performances.A. there are C. there to beB. there being D. there be23. to sunlight for a long time, you are bound to get burnt in summer.A. ExposingB. ExposedC. Being exposedD. To be exposed24. After searching the place inside out, she finally found the book underthe bookcase, torn and dog-eared.A. many of which pages C. many of whose pagesB. many of its pages D. whose many pages25. ----- I’m afraid I can only make a small contribution this time.-----_______. We really appreciate your assistance.A. The best things come in small packagesB. The more, the betterC. It’s better to give than to receiveD. Every little helps26. The generous donation from China to the sufferers in the killingIndian Ocean Quake-tsunami has __________ the Chinese people's unselfishness and internationalism.A. let outB. brought outC. given outD. taken out27. China has been pushing the reform of public hospitals ____all itscitizens.A in charge of C in honor ofB for the purpose of D for the benefit of28. Not until ____in the river ____how serious the pollution was.A. did all the fish die, didn’t the villagers realizeB. all the fish died , the villagers realizedC. all the fish died , did the villagers realizeD. did all the fish die, the villagers did realize29. --- How long have you been studying in No. 2 Middle School?---Less than half a year. And it will be two years and a half,according to the school rules, ________ I graduate from this school.A. whenB. afterC. beforeD. since30. _______ more energies to my study，I would be sitting in acomfortable office now.A．If I devoted C．Would I devoteB．Had I devoted D．Should I devote31. Of the two brothers, Bill, younger one, and he is a quiet boy,that most adults like very much.A. the; the oneB. the; oneC. a; the oneD. a; the one32. What troubled the teacher was that on one present made an answerwhen asked who had br oken the glasses, so he didn’t knowwho .A. was blamed C. would be blamedB. was to be blamed D. was to blame33. The wild flowers looked like a soft orange blanket the desert.A. coveredB. coveringC. to coverD. cover34. ---It’s many years since I saw you last; I you at all.---I wouldn’t have, either, if someone you by the name.A. haven’t recognize; didn’t callB. didn’t recognize; didn’t callC. didn’t recognize; hadn’t calledD. recognized; had called35. any TV reports on places there is a war, and you’ll see soldierswearing blue berets.A. Having watched C. To watchB. Watched D. Watch36. Nobody but doctors and those by Dr. Hu to enter the patient’sroom.A. are invited; are allowed C. invited; is allowedB. being invited; allowed D. invited; are allowed37. Chinese arts have won the of a lot of people outside China.A. enjoymentB. entertainmentC. appreciationD. reputation38. ----He ought to have been warned of the danger.---- , but he wouldn’t listen to me.A. Yes, he ought to. C. So it was with himB. So he was. D. So he did.39. With a large amount of work , the chief manager couldn’t s paretime for a holiday.A. remained to be done C. remaining to be doneB. remained being done D. remaining to do40. ----Can I pay the bill by check?----Sorry, sir. But it is the management rules of our hotel thatpayment be made in cash.A. shouldB. shallC. canD. will41. So quickly are science and technology advancing is a possibilitytoday may be a reality tomorrow.A. that whatB. whichC. whatD. that which42. My uncle hasn’t been able to quit smoking, but at le ast he has .A. cut outB. cut offC. cut downD. cut up43. ----It’s a long time I saw you last.----And what is a pity now that it will be a long time we seeeach other again.A. before; since C. when; beforeB. since; when D. since; before44. Hardly could he this amount of work in such a shot time.A. get throughB. get downC. get acrossD. get into45. ---- Never say never, and you’ll make it.----That’s it. .A. I can’t agree with it. C. You’ve got me there.B. You’ve got a point there. D. Action speaks louder than words.46. ----Tom’s still angry with me.----You are ______. How dare you call him a liar! He’s the last person ______.A. to be blamed; lying C. to blame; lyingB. to be blamed; to lie D. to blame; to lie47. No sooner ______ than it began to rain heavily.A. did the game start C. had the game startedB. the game started D. the game had started48. Limited natural resources should be made full use of ______ the______ need of energy.A. meeting; increased C. meeting; increasingB. to meet; increased D. to meet; increasing49. Research has been limited to increasing production profits, ______making sure that GM food is safe.A. insteadB. other thanC. rather thanD. otherwise50. Was it at midnight ______ you fell asleep while reading, with thecandles still burning?A. whenB. whichC. whereD. that51. It was announced that only when the fire was under control _______to return to their homes.A. the residents would be permittedB. had the residents been permittedC. would the residents be permittedD. the residents had been permitted52. I went by plane; otherwise I ________ much longer time.A. could take C. will have takenB. would take D. would have taken53. ______ today, he would get there by Friday.A. Would he leave C. Were he to leaveB. Was he leaving D. If he leaves54. ----What made the host and hostess so disappointed----________to attend the evening party.A. Tom failed C. Tom’s failingB. As Tom failed D. Because Tom failed55. They failed to pass the exam last time. I regretted ____ them.A. to be not able to help C. being not able to helpB. not being able to help D. not to be able to help56. All the scientific evidence _____ that the increasing use of chemicalsin farming _______ damaging our health.A. show; areB. shows; areC. shows; isD. show; is57. In the eastern part of New Jersey ____, a major American shippingcenter.A. the city of Elizabeth liesB. lies the city of ElizabethC. does the city of Elizabeth lieD. the city of Elizabeth lie58. It is out of ______ question for him to do that for ____ fun. He isalways working very hard, you know.A. the；不填B. a；不填C. the; theD.不填;不填59. No one _______ the national lab without written permission from theprime minister, according to the new lab management rule.A. is going to enterB. will enterC. shall enterD. might enter60. ________ two o’clock in the morning _________ and sent hometogether with the taxi-driver.A. Not until; was the journalist freedB. Until; the journalist was freedC. It was not until; was the journalist freedD. It was until; the journalist was freed61. ----Why didn’t the old man attend his grandson’s wedding party?----Nobody ________ him about _______ a party that evening.A. told;; there to be C. told; there wasB. had told; there to be D. had told; there being62. Much to our surprise, word spread in the village _______ many moreyoung people would be needed to join the army.A. whenB. whichC. thatD. what63. The manager，______ it clear to us that he didn’t agree with us，leftthe meeting room.A. who has madeB. having madeC. madeD. making64. Thanks to the work of UNICEF. Otherwise many children__________ the chance of living a good life.A. will not have C. do not haveB. have not had D. would not have65. Apart from the urgent problems caused by wars and conflicts，theUN helps countries with other problems such as ______ education, starvation, disasters, AIDs and other diseases.A. lack forB. lack inC. lack ofD. lack66. It was at twelve o’clock _______ we finally arrived at the village______we spent our happy childhood.A. that; thatB. when; thatC. when; whatD. that; where67. ----How often do you go out for supper?----_____, once a week.A. Have no idea C. As usualB. It depends D. Generally speaking68. The astronaut did many experiments in the spaceship, _____muchhelp for knowing space.A .which we think it isB .which we think are ofC .of which we think isD.I think which is of69. One of our rules is that everyone _______ wear school uniform whileattending the school flag-rising ceremony.A. mightB. shallC. couldD. will70. My mind wasn't on what he was saying so I'm afraid I ___ half of it.A. was missingB. had missedC. will missD. missed71.______ from the operation, the patient was advised to stay in hospitalfor another two weeks.A. Having not fully recoveredB. Being not fully recoveredC. Not having fully recoveredD. Not fully recovering72. _______ the potential benefit, some scientists argue that humanembryo cloning may not be a bad idea.A. To considerB. ConsideringC. ConsideredD. Consider73. He became excited when it ______ his experiences in Africa.A. came aboutB. referred toC. came toD. talked about74. Lucy is a college student who is hard-working, so she passed theCollege English Test Band 4 at her first________.A. attemptB. effortC. struggleD. factor75. It is obvious that talking about something behind others is whateveryone will not________.A. come up with C. catch up withB. keep up with D. put up with76. ______ the window, my finger was cut unexpectedly.A. While I was cleaning C. CleaningB. To clean D. While cleaning77. ----Is this the only one of the poems which _____ rhymes----______ . I think all poems should have rhymes.A. have; Don’t agree with youB. has; I couldn’t agree moreC. have; That’s rightD. has; You can’t be serious78. I was told that ______ 14:15 flight would take us to Beijing in timeto reach ________ Tsinghua University.A. a; theB. the; aC. the; /D. /; the79. If you had spoken to him last time you saw him, you ______ what todo now.A. would have known C. should have knownB. would know D. may know80. ----Do you know ______ they got to know each other?----It was last year _____ they both taught Chinese in ScotlandA. when was it that; whenB. when it was that; thatC. when it was that; whenD. when was it that; that81. After the long journey, the three of them went back home, ______.A. hungry and tiredly C. hungrily and tiredlyB. hungrily and tired D. hungry and tired82. On the floor _______ piles of books, magazines and newspaper, all ofwhich are her favorites.A. lieB. does lieC. layD. lying83. No matter how_____, you can find something animate, a kind of plant,an animal or human being.A. may a desert be dry C. dry a desert may beB. a desert dry may be D. a desert may be dry84. The Premier says that bilateral relations will grow smoothly andsteadily _____ both countries follow the principle contained in thejoint documents.A. as far asB. thoughC. as long asD. unless85. I am ________ about what I say because careless remarks are likelyto hurt others’ feelings．A. enthusiasticB. concernedC. cautiousD. doubtful86. There isn’t a lot of food in our home. How long do you think it will_______A. hold onB. hold backC. hold outD. hold together87. ---- Tommy is planning to buy a car.---- I know. By the time he returns from abroad, he _____ enoughfor a used one.A. will have savedB. savesC. had savedD. will save88. This computer will certainly ________ all your expectations if youbuy it, sir.A. live up toB. look up toC. keep up withD. come up with89. ---- Come on, please give me some ideas about the project.---- With so much work ________ my mind, I’ll almost ________.A. filling; break up C. filled; break offB. filled; break out D. filling; break down90. In the last century, more and more women arose ____ their legalrights.A. in defence ofB. in honor ofC. in memory ofD. in place of91. ---- Steven, where did you come across the famous novelist fromEngland---- Believe it or not, it was in the supermarket ____ we wentshopping last Sunday.A. whichB. thatC. thereD. where92. ---- I think Tom’s team will lose tomorrow’s game.---- Oh, really _________A. Let’s make a decision C. I beg your pardon?B. What makes you think so? D. That’s my opinion.93. It's _________ to see crosstalk actors make ________ of each other.A. such fun, fun C. so fun, funB. such a fun, a fun D. so funny, a fun94. He rubbed his eyes and yawned as if ________ after a long sleep.A. waking upB. to wake upC. woke upD. wake up95. Don’t worry about the child. Next to him _______ a lady, _______ hecan turn when he is in trouble.A. sits; whom C. is sitting; with whomB. sits; to whom D. was sitting; to whom96. By the time scientists _______ the fundamental structure of darkmatter, I'm sure that man _____ amazing advances in science.A. figure out; has madeB. will figure out; will makeC. figure out; will have madeD. will figure out; will be making97. It is ______ for her to notice that playing with the doll can keep herdaughter _____ for hours.A. amazing; amusingB. amazing; amusedC. amused; amazingD. amused; amazed98. While this kind of paper is ultra-thin, it _______ easily.A. tearsB. doesn't tearC. is tornD. isn't torn99. ______ of danger in the street at night, she had to go home, with afriend __________ her.A. Warned; accompaniedB. Having warned; accompanyingC. Warning; accompanyingD. Having been warned; accompanying100. ___different life today is from _____ was fifty years ago!A. What a, whatB. How, whatC. What, whatD. What a, how 101. All the citizens here strongly insist those caught ______ “harmful”advertisements in the streets _______ punished strictly.A. putting up; will be C. being put up; shallB. to put up; should be D. putting up; be102. An important question still ________ is what are the factors that explain student success or failure in the distance learning programs.A. remained to be answered C. remaining to answerB. remaining to be answered D. remaining answering103. When it comes to The Voice of China, the audience prefers _______ singing to recorded singing, and the former makes the scene more_______.A. lively; liveB. live; liveC. live; livelyD. lively; alive104. ----What impressed you most during your stay in the UK?---- The way of their museums ______________.A. to be rebuiltB. are operatedC. displayedD. being run105. ________ the help from his relatives, he does a part-time job to support his study at college.A. Regardless of C. But forB. Instead of D. Apart from106. I did love my mum very much but it got to a point ______ even she did not want me to see her as she was.A. whereB. whenC. thatD. which107. Difficult as rumors on micro blog, or Weibo are _______, the authorities will set up supervision so that people will not be easilymisled.A. preventing C. to preventB. to be prevented D. being prevented108. Barack Obama’s decision to attend ________ ceremony tomorrow can be seen as ________ gesture of his intention to improve therelationship.A. the; theB. the; aC. a; aD. a; the109. People rarely succeed ____ they have fun in what they are doing.A. ifB. unlessC. sinceD. when110. It may well be the ability to use languages that distinguishes humans, setting them ________ other animals.A. along withB. rather thanC. due toD. apart from111. ----Alice, how come you failed the English examination once again?----I didn’t work hard and I wish I ________ more attention in class.A. paidB. had paidC. have paidD. was paying112. Many developers use Google Maps to show app users their locations and ________ close they are to their friends and restaurants.A. whatB. whenC. howD. where113. ----As we know, keeping positive is beneficial to the process of our work and study.----You can say that again. Struggle not to let negativeideas_______.A. take overB. take offC. take onD. take up114. The Chinese women’s volleyball team won the World Cup victory, which was beyond our wildest ________.A. inspirationsB. expectationsC. invitationsD. cooperations 115. ----I ordered Pizza for dinner. It should be here any minute now.----Pizza againWe ________ Pizza every night for a week now!A. hadB. were havingC. have been havingD. will be having116. Chinese culture _____ a particularly high value to the idea that families should live together.A. chargesB. pointsC. presentsD. attaches117. It will take time and patience to get these changes ________.A. to accept C. acceptedB. having been accepted D. accepting118. Research suggests that children ________ parents split up are more likely to drop out of high school.A. whoseB. whoC. thatD. which119. _________ in the adult ceremony, the senior students feel they are shouldering heavier responsibilities now.A. SwearB. SwornC. Having swornD. To have sworn120. Many consumers prefer to make their own choices rather than ________ into buying what they don’t really want.A. persuading C. to persuadeB. be persuaded D. being persuaded121. When taking an examination, you’d better relax yourself to prevent your mind from going ________.A. aggressiveB. blankC. accurateD. cautious122. ----Would you like another drink?----________. Thanks a lot.A. You don’t say C. I have a say in itB. You said it D. I wouldn’t say no【参考答案】15CDDBA 610BCAAB 1115DABCD 1620DCACD 2125BCBBD 2630BDCCB 3135BDBCD 3640CCBCB 4145 ACDAB 4650DCDCD 5155CDCCB 5660CBACA 6165DCBDC 6670DDBBD 7175CBCAD 7680ABCBC 8185DABCC 8690CAADA 9195DBAAB 96100CBBDB 101105DBCDD 106110ACBBD 111115BCABC 116120DCABB。
高考单选易错题
2009高三英语模拟试题单项填空错题集1. ______ of the truth of the reports, he told his colleagues about it.A. ConvincingB. ConvincedC. To convinceD. Having convinced2. Thank you for the great difficulty you have had ______ me with my designing work.A. helpingB. to helpC. with helpingD. to have helped3. ______ to the sunlight for long will do harm to your skin.A. ExposedB. Being exposedC. Having been exposedD. Exposing4. ______ every day, our web provides readers with latest news.A. To updateB. UpdateC. UpdatingD. Updated5. ______ by the rising price of gas, many car owners use their cars less frequently.A. DrivenB. Being drivenC. To driveD. Having driven6. A hurricane swept through my village. Just as we were beginning to lose hope, it suddenly stopped. It is really “______”.A. All‟s well that ends wellB. Lightening never strikes twice in the same placeC. It never rains but it poursD. A friend in need is a friend indeed7. The boss ______ department Ms Li worked ten years ago looks down upon women.A. in whichB. in thatC. in whoseD. whose8. The great moment came in the early 1930s ______ famous writers translated both novels and poetry into Chinese.A. whileB. asC. whenD. that9. Please tell me how the accident ______. I am still in the dark.A. came byB. came uponC. came toD. came about10. Your account about the event doesn‟t ______ what the police have found out.A. consistent withB. connect withC. correspond toD. relate to11. ______ by the moving scene, the young man determined to ______ his ways and be good.A. Being touched; repairB. Touched; mendC. Having been touched; findD. To be touched; fix12. The bird flu ______ through Asia has jumped from birds to humans at least 20 times so far, ______ 16 persons.A. sweeps; killedB. swept; killingC. sweeping; to killD. sweeping; killing13. —It‟s so late. Our son ______ be back!—Don‟t worry. I dare say he ______ have some extra work to do.A. can; mustB. will; mightC. should; mustD. must; may14. —Are you going to take the job?—Certainly, though the salary is not so good. ______, you know.A. A bird in hand is worth two in the bushB. A golden key can open any doorC. Actions speak louder than wordsD. Better late than never15. In the past few years, the fast food restaurant has improved the cooking skills and ______ different customers‟ popular demands.A. applied toB. catered toC. contributed toD. turned to16. We wanted to get home before dark, but it didn‟t quite ______ as planned.A. make outB. turn outC. go onD. come up17. Seeing the happy ______ of children playing in the park, I‟m full of joy and confidence in the future of our country.A. sightB. sceneC. viewD. sign18. Understanding the cultural habits of another country, especially ______ containing many different subcultures like the USA, is a difficult thing.A. whichB. thatC. oneD. those19. Someone ______ up your seat to the lady with a baby, please.A. will giveB. would giveC. givesD. give20. —Are you coming tonight?—I‟d love to, but I‟m afraid I ______ then.A. will be teachingB. will teachC. will have taughtD. am teaching21. —You finally made it, didn‟t you?—Yes, ______ your help, I wouldn‟t have succeeded.A. in spite ofB. but forC. due toD. thanks to22. —Mary, ______ Mr. White wants to see you at the gate.—That is out of ______ question. I‟ve never known any Mr. White.A. / ;/B. a; theC. the; /D. the; a23. Her health ______ under the pressure of work and she had to stay in hospital for a month.A. broke upB. broke awayC. broke outD. broke down24. Once ______, everyone taking the examination will be given test papers.A. seatedB. seatingC. being seatedD. having seated25. —I don‟t feel like going out. Why don‟t we just stay home and watch TV instead?—______ You promised to take me out for dinner and to the theatre on my birthday.A. Great!B. Why me?C. Come on!D. Not at all.26. —Why on earth didn‟t you answer the phone?—I‟m terribly sorry, but the doorbell ______, too.A. is ringingB. rangC. was ringingD. was about to ring27. If you keep practicing your son in football, he ______ to be a famous player.A. wantsB. hopesC. wishesD. promises28. The speech which he made ______ the football match bored a lot of fans to death.A. being concernedB. be concernedC. concernedD. concerning29. Although he knew little about the large amount of work done in the field, he succeeded ______ other more well-informed experimenters failed.A. asB. unlessC. whatD. where30. When we are in new places, we must ______ our manners and try to follow the customs of the place.A. look outB. keep eyes outC. mindD. put up with31. ______ for the terrible coal mine accident, as the public thought, the mayor of the city felt nervous and was at a loss what to do.A. Having blamedB. He was to blameC. Being to be blamedD. Being to blame32. ______, I really believe that I‟d prefer not to make any change now.A. Considered all the possibilitiesB. Taking all the possibilities into considerationC. Taken all the possibilities into considerationD. Giving all the possibilities33. This series of books is said to be a special one, which ______ many events not found in other history books.A. writesB. coversC. dealsD. refers34. —I didn‟t take notes at yesterday‟s meeting because I had left my pen at home.—You ______ mine. I ______ it.A. must have borrowed; wasn‟t usingB. may have borrowed; didn‟t useC. could have borrowed; wasn‟t usingD. should have borrowed; hadn‟t used35. ______, they had no chance of winning the war.A. As they fought bravelyB. Bravely as they fought36. —Why didn‟t you go to help her when she needed your help badly?—I would have, but I ______ as busy as a bee then.A. would beB. had beenC. wasD. were37. I found him sitting in his chair, completely ______ a magazine.A. absorbingB. being absorbedC. absorbed inD. absorbing in38. I think a cold drink can ______ you after your long hot journey.A. recoverB. rewardC. relieveD. refresh39. I would have helped you, but I ______ really occupied the whole week.A. wasB. amC. had beenD. were40. When the spaceship traveled above, ______ new-looking earth appeared before us, ______ earth that we had never seen before.A. a; theB. the; anC. / ;theD. a; an41. She asked the young man to be brief and ______ as she had little time to spare.A. at bestB. in placeC. to the pointD. on the spot42. What worried the boy most was ______ to visit his father in the hospital.A. his not being allowedB. his not allowingC. his not been allowedD. his being not allowed43. —You seem to be deeply struck by her beauty.—Not exactly. It was her skill and courage ______ her beauty that really struck me most.A. other thanB. rather thanC. as well asD. more than44. He was told that it would be at least three more months ______ he could recover and return to work.A. beforeB. whenC. sinceD. that45. —Why did John asked me about the problem?—______, he tried to find a better way to settle it.A. Not to be satisfiedB. Don‟t satisfyC. Not being satisfiedD. Not satisfied46. While tidying the room, Jim found the ______ toy bought for him as a birthday present.A. fine plastic smallB. plastic fine smallC. small fine plasticD. fine small plastic47. December saw a more than average rainfall; ______, the possibility of a drought is still strong.A. thereforeB. neverthelessC. whereasD. although48. I prefer a flat in the suburb to ______ in downtown, because I want to live near my Mom‟s.A. oneB. thatC. itD. this49. The driver got out of the car ______ it caught fire.A. immediatelyB. thatC. unlessD. until50. —______that he managed to pass TOEFL?—Oh, he had studied English in the New Oriental School for several years.A. Where was itB. What was itC. How was itD. When was it51. Have you learned enough spoken English to ______ a conversation with the foreigners?A. carry onB. go onC. take onD. keep on52. The US president Bush said his country will sign a peace treaty with the DPRK（朝鲜）______ the latter gets rid of all its nuclear facilities.A. whileB. even ifC. so thatD. provided53. Be more careful and I‟m sure you‟ll do ______ better next time.A. ratherB. fairlyC. veryD. quite54. The doctor always turned up ______ he was most needed. No wonder he was called “doctor sent by …God‟”.A. the place whereB. in the placeC. in whichD. where55. As many as 150 miners died in the accident. If only the mine-owners ______ enough attention to the safety measures!A. paidB. should payC. would payD. had paid56. I don‟t remember how many years ago ______ I last showed you round the farm.A. it was thatB. was it thatC. it was whenD. was it when57. —Will another fifty be enough?—Just twenty will ______.A. workB. doC. suitD. fit58. ______ she will be back home for her glasses.A. It is long before thatB. It won‟t be long beforeC. It will be long beforeD. It is before long that59. I‟ll ______ my decision and never change it.A. stick toB. insist onC. understandD. give up60. It‟s strange that they ______ without saying good-bye to anybody.A. must have leftB. should have leftC. can have leftD. may have left61. —______ helps others will be helped.—So I‟m thankful to and try to help ______ has helped us.A. Whoever; whomeverB. Who; whoeverC. Whoever; whoeverD. Who; whomever62. It‟s time to stop work. Let‟s ______ the tools and ______ for the night in the woods.A. put into; put onB. put down; put offC. put aside; put outD. put away; put up63. Only when ______ masters of their own country ______ really serve them.A. the people have become; science canB. the people have become; can scienceC. have the people become; science canD. do the people become; can science64. While building a tunnel through the mountain, ______.A. an underground lake was discoveredB. there was an underground lake was discoveredC. a lake was discovered undergroundD. the workers discovered an underground lake65. —Well, lost again!—It is not very important. We ______ forget about it. OK?A. can‟tB. may as soonC. might as wellD. ought to have had to66. He was lucky to win a prize of 500, 000 dollars, ______ known all over the country.A. making himselfB. making himC. to make himD. which make himself67. ______ it ______ for your help, I couldn‟t have made my progress.A. Had; not beenB. Should; not beC. Did; not beD. Not‟ be68. —Why do the boys ______ Liu Jun as “Panda”?—Because he is short and fat with thick glasses.A. refer toB. turn toC. call upD. call for。
长度与时间的测量错题集
一、单选题1．下列物体的长度最接近8厘米的是（）A．物理课本的长度B．书桌的高度C．普通粉笔的长度D．黑板的宽度2.“握手礼”是一种中华传统礼仪，在“新冠”疫情期间，为了更好地满足防疫需要，某班学生倡导了“夸赞礼”，并将其画在了海报上，在照片中，两个学生的脸之间的距离D（）。
A．4.5m B．3 m C．1.5m D．0.5m3.自中美摩擦后，美国对EUV光刻机进行了严格的控制，EUV光束以极高的精度冲击晶圆（这在材料领域堪称奇迹），就像是一支从地球射出的箭，直接命中了月球上的苹果。
EUV 光刻机是一种通过一系列运算，把晶体管拉到5。
的晶片上，5 nm差不多就是指甲长出来的5秒钟。
下列各项中最短得是（）A．52.5m B．5.25×103nm C．5.25×103μm D．5.25×10﹣1m 4．用分度值为1mm的刻度尺多次测量文具袋的长度，结果为18.64cm、18.63cm、18.640cm、18.66cm，则文具袋的长度为（）A．18.643cm B．18.65cm C．18.64cm D．18.645cm5.一名初二学生和一架火箭模型在科技馆里合影，请你估算一下这架火箭的高度是（）。
A．24 米B．12 米C．6 米D．3 米6．2.小明用一把刻度尺测量同一物体的长度，四次测得的结果分别为：15.26cm、15.28cm、15.27cm、14.79cm，那么物体的长度为（）A．15.28cm B．15.26cm C．15.27cm D．15.15cm7．某个物体的长度约为3000mm，这个物体可能是（）A．一支铅笔的长B．旗杆的高度C．一层楼的高度D．一个中学生的高8．用一把刻度尺测量同一物体的长度，先后四次测得的结果分别为：13.26cm、13.28cm、13.27cm、12.79cm，那么物体的长度为（）A．13.28cm B．13.27cm C．13.26cm D．13.15cm9．在用刻度尺测量物体长度时，下列要求错误的是（）A．测量时刻度尺不能歪斜B．读数时视线要与尺面垂直C．记录测量结果时必须在数字后面注明单位D．测量时必须从刻度尺的零刻度线量起10.下列关于刻度尺测量物体长度的说法错误的是（）A．测量时，刻度尺要放正，有刻度的一边要紧贴被测物体B．读数时，视线应与尺面垂直C．记录测量结果时，必须在数字后面写上单位D．测量时，必须从刻度尺的零刻度线处量起11．小明利用最小分度值为 1mm 的刻度尺测量一个物体的长度，四次测量的数据分别为2.35cm、2.36cm、2.36cm、2.57cm，则测量结果应记为（）A．2.41cm B．2.357cm C．2.35cm D．2.36cm12．关于误差和错误，下列说法不正确的是（）A．受所用仪器和测量方法的限制，实验总会产生误差B．多次测量求平均值、选用精密的测量工具、改进测量方法，都可以减小误差，但不能完全消除误差C．测量错误是由于不遵守仪器的使用规则、读数时粗心大意造成的，是不该发生的，也是不能避免的D．虽然科学技术不断发展，但人们还是不能完全消除误差13．如图所示的两把刻度尺具有相同的（）A．长度B．误差C．分度值D．测量范围二、填空题14．如图所示，是某班同学利用“累积法”测定金属线直径的办法，根据图示情况，细金属线的直径是______cm；若在绕线时匝与匝之间有间隙，则测量结果将偏______。
高考数学常错、易错题集
高考数学常错题集2019-7-9我国的高考经历了艰难的历程，在这些历程中，出现了许许多多成功、优秀的试题，这在国家公布的“评价报告”、“分析报告、“试题分析”等文中已祥有阐述阐述，同时各地的期刊也不时发表许多专家对优秀试题的领悟与见解，这些都对中学教学及考试起了不可忽视的作用另一方面，对于命题者而言，纵观高考试题，可以发现，每换一帮人命题，总有一些“重蹈历史覆辙”的不尽人意的试题，这说明仅仅知晓什么样的试题优秀而去照着这个方向模拟、研究是不够的，还必须知道“有哪些经验教训”；同时由于教师职业正在由单纯的教书向教书育人及身兼研究者进行转化，因此对于中学教师及应试的考生而言，考的内容重在把握命题的“度”，不考的内容也需要一清二楚，而这些又得通过一定的教训及得出的一些经验来启示因此，笔者对历年高考试题进行了分析，搜集而成高考数学败题集高考数学试题随着国家政策的调整几度沉浮，而试题的成败又取决于考后的评价，就评价而言，高考试题走过了越来越受社会关注、越来越受社会评价影响的轨迹：原来的高考试题，社会关注评价比较少，因而试题评价形式以批评与自我批评为主，这一情况延续到1983年，虽然因为文化大革命而中断了些年；之后的1984――1993年，试题评价有了社会人员的参议，但仍然以国家公布的为主；1994年后，由于社会评价的参议，许多评价指标进行了量化（如：难度、标准分、区分度、信度等），又随着社会参与评价幅度的增大， 1999年，国家将评价报告改成“分析报告”，2002年定下“自主招生”的政策；2003年，高考试题进入以省市为主的自主招生阶段，并逐步向“高校自主招生”转移，相应的评价中心也在逐步向参加高考的高中转移，其中的师生逐步成为评价的主角，而这些评价无疑也会影响今后命题方向，同时更直接的影响着平时教学的检测方向及力度 这样，我们就更有必要对高考试题中的败题加以留意总结了一、1983年前的高考数学败题【说明】这一阶段高考数学试题评价是以批评与自我批评为主，因此，我们也就国家公布的没有提及优秀的试题来说明（1951一、13．）系数是实数的一元三次方程，最少有几个根是实数，最多有几个根是实数？答：最少是一个，最多是三个 【评析】该题根据实系数复数方程虚数根成对出现得到的结论，但这一结论在当时并没有在大范围的教材中出现（1952二、1 ）解方程x 4+5x 3-7x 2-8x-12=0解：左式=(x 4+5x 3-6x 2）-（x 2+8x+12）=(x+6)[x 2(x-1)-(x+2)]=(x+6)(x 3-x 2-x-2) =(x+6)[(x 3-2x 2)+(x 2-x-2)] =(x+6)(x-2)(x 2+x+1)=0可得原方程的四根为：.231,231,2,64321i x i x x x --=+-==-= 【评析】该题分解因式的技巧性过强，多数学生不能完成，竞赛性质太浓1963―5．根据对数表求10123.28-的值解：3670.110128.23lg 10128.23lg 101⨯-=-=-570.8,9330.0lg 9330.1390670.011390670.138________===-+=-=x x .10570.8570.81028.23139139101---⨯=⨯=∴ 【评析】对数值中的139符号，当时是否应该、有必要引入中学还在讨论当中，高考就出现了这样符号 结论：研究及有争议的内容不能在试题中出现1965附加题（1）已知,,a b c 为实数，证明,,a b c 均为正数的充要条件是 000a b c ab bc ca abc ++>⎧⎪++>⎨⎪>⎩（2）已知方程320x px qx r +++=的三根,,αβγ都是实数，证明,,αβγ是一个三角形的三边的充要条件是30,0,048.p q r p pq r <><⎧⎨>-⎩证明：（1）条件的必要性是显然的，因为已知,0,0,0>>>c b a所以立即可得0>++c b a ，0>++ca bc ab ，.0>abc下面证明条件的充分性：设c b a ,,是三次方程023=+++r qx px x 的三个根，则由根与系数的关系及已知条件有,0,0,0>=->++=>++=-abc r ca bc ab q c b a p此即.0,0,0<><r q p 由此即可知三次方程023=+++r qx px x 的系数正负相间，所以此方程无负根，即方程根均非负;又由0>abc 可知，方程无零根，故.0,0,0>>>c b a（2）由（1）的证明可知，γβα,,均为正数的充要条件是.0,0,0<><r q p 于是问题转化为证明γβα,,为三角形三条边的充要条件为r pq p 843-> 条件的必要性：若γβα,,为三角形的三边，则由三角形的性质必有.,,βαγαγβγβα>+>+>+于是.0,0,0>-+>-+>-+βαγαγβγβα由此可得))()((βαγαγβγβα-+-+-+84)842(]8)(4)(2[)2)(2)(2()2)(2)(2(33323>+-=-+--=αβγ+αβ+γα+βγ+γ+β+α+-=γ+β+α+-=γ--β--α--=r pq p r pq p p p p p p p p p p p即r pq p 843-> 条件的充分性：若r pq p 843->，则,0843>+-r pq p .0))()((,0])()[(,0)()()(,0))(()()(,08])(2)()][([,08)222)((,08))((4)(22222223222223>+--+++->--++->---+++->-+--+++->--++--++>----++++>-+++++++-γβαγβαγβαγβαγβαγβαγβγβααγβγβγβαγβαααβγαγβαγβγβααβγγβαγαβγαβγβααβγγαβγαβγβαγβα此式中至少有一因式大于0，今设,0>++-γβα则必有.0))((>+--+γβαγβα如果,0,0<+-<-+γβαγβα两式相加得02<a ，即0<α，此与0>α相矛盾 故有,0>++-γβα,0,0>+->-+γβαγβα此即⎪⎩⎪⎨⎧>+>+>+,,,βγαγβααγβ此即γβα,,可作为一个三角形的三条边综上所证可知，方程023=+++r qx px x 的三根γβα,,为一个三角形的三条边的充要条件是⎩⎨⎧-><><.840,0,03r pq p r q p 【评析】这个试题以附加题形式出现，难度较大，但也不能大到无一人（甚至参加国际数学竞赛的学生）能作上程度 结论：试题不能无线拔高（1977北京文4）不查表求sin1050的值 解：.462)4530sin(75sin 105sin +=︒+︒=︒=︒ 【评析】当时，并没有要求记特殊角三角函数值，所以题虽然不难，但会的人不多（1977年福建理科2（2）题）证明：22cos sin 290().2cos sin 22tg θθθθθ-︒-=+ .)290(tg )90cos(1)90cos(1sin 1sin 1)sin 1(cos 2)sin 1(cos 2:2右边左边证=θ-︒=θ-︒+θ-︒-=θ+θ-=θ+θθ-θ= （1977年河北试题第3题）．证明：sin 2111.1cos2sin 222tg αααα+=+++ 证：左边=)sin (cos cos 2)cos (sin cos sin 2cos 2cos sin cos sin 22222α+ααα+α=αα+αα+α+α⋅α αα+α=cos 2cos sin 2121+α=tg =右边 （1977年上海理科第1（4）题）求证：sin()cos()244cos2sin()cos().44ππθθππθθθ+++=--.2cos 22cos 211)4cos()4sin(2sin )4cos()4sin()4sin()4cos()4cos()4sin(:右边左边证=θ=θ=θ-πθ-ππ=θ-πθ-πθ-πθ+π+θ-πθ+π= 【评析】这些该题本身不难，但三角证明题几地都出现证法太多，标准不易统一，给阅卷带来非常大的难度 结论：三角证明一般不作为证明题出现（1977年福建理科第3题）在半径为R 的圆内接正六边形内，依次连结各边的中点，得一正六边形，又在这一正六边形内，再依次连结各边的中点，又得一正六边形，这样无限地继续下去，求：（1）前n 个正六边形的周长之和S n;（2）所有这些正六边形的周长之和S解：如图，半径为R 的圆内接正六边形的周长为6R ，设C 为AB 的中点，连结OC ，OB ，则OC ⊥AB ∴OC=CD=.2360sin R R =︒⋅ 第二个正六边形的周长.236⋅=R 同理可得,)23(62⋅=R 第四第三个正六边形的周长个正六边形的周长,)23(63⋅=R ………… 于是可以得到一个表示正六边形周长的数列：6R ，.236⋅R ,)23(62⋅R ,)23(63⋅R …,)23(61-⋅n R … BE D O①前n 个正六边形周长的和12)23(6)23(62366-⋅++⋅+⋅+=n n R R R R S ])23()23(231[612-++++=n R .])23(1)[32(12231)23(16R R n n -+=--⋅= ②所有这些正六边形周长的和.)32(1232122316R R RS +=-=-=【评析】从题本身上看，该题是一个好题，但是其答案在全国引起争议——归纳出的结论到底是否要证明是等比数列？即使不证明也要体现有等比数列的过程 从该题对以后影响是，出现了用式子表达等比、等差数列热潮（1977年福建文科第4题）．求抛物线29y x =和圆2236x y +=在第一象限的交点处的切线方程解：解方程组⎩⎨⎧=+=)2(36)1(9222 y x x y （1）代入（2）得,03692=-+x x x=3,x=-12（不合题意）将x=3代入（1），得33=y （仅取正值）， ∴在第一象限的交点为（33,3）从抛物线x y 92=得.29=p∴过点（33,3）的抛物线的切线方程是.09323),3(2933=+-+=y x x y 即 过点（33,3）的圆的切线方程是,36333=+y x 即.0123=-+y x【评析】该题的问题是表述不清：有人认为只求抛物线的切线方程，也有人认为只求圆的切线方程，答案倒认为是求圆和抛物线的方程（1977年黑龙江第2题第（1）问）．计算下列各题：解：当.2,22a m a ma m a m -=+-≥时当.2,22m a a ma m a m -=+-<时【评析】该题引发了分段表示法的争论，结论，如果是分段出现的，结果一般用分段函数形式给出（1977年江苏第1（5）题）把直角坐标方程22(3)9x y -+=化为极坐标方程解：原方程可展开为θ=ρθ=ρ=ρ∴=θρ⋅-ρ=+-cos 6cos 60,0cos 6,06222即或y x x【评析】该题从一般情况下考虑（直角坐标系的原点为极点，x 轴为极轴且长度单位不变），但没有交代清楚一般情况下，以致于该题出现的情况是：一般的学生答的好，程度很高的如参加竞赛的学生反倒没有答好！属于交代不明出现的失误（1977年上海理科第6题）已知两定点A （-4，0）、B （4，0），一动点P （x,y ）与两定点A 、B 的连线PA 、PB 的斜率的乘积为4-P 的轨迹方程，并把它化为标准方程，指出是什么曲线解：直线PA 、PB 的斜率分别是故此曲线为椭圆其标准方程为由题意,14161644144.4,4222221=+=+-=-⋅+-=+=y x y x x y x y x y k x y k 【评析】该题解答有误，应该加上条件(x≠±4，相应曲线为以（±）为焦点、以8为长轴的椭圆，去掉长轴的两个端点)结论：说明轨迹、图形的问题要保证惟一及等价（1979年文科理科第四题）叙述并证明勾股定理 证：略【评析】这个题当时答案是用坐标法的距离公式证明的，但是距离公式是由勾股定理推导出的，因而形成“因为A……所以A”的循环论证错误，而得出一般用拼图法得到；拼图法能否算作证明还在争论中，但当年多数省市按错对待 结论：数形结合的方法得到的结论不能以证明题的形式出现（1980年理科第八题）已知0＜α＜π，证明：2sin 2ctgαα≤并讨论α为何值时等号成立 解：即证：.sin cos 12sin 2ααα+≤两端乘以sinα，问题化为证明2sinαsin2α≤1+cosα 而 2sinαsin2α=4sinαcos 2α=4(1-cos 2α)cosα=4(1-cosα)(1+cosα)cosα所以问题又化为证明不等式 (1+cosα)[4(1-cosα)cosα-1]≤0（1+cosα)⎥⎥⎦⎤⎢⎢⎣⎡⎪⎭⎫ ⎝⎛--221cos 4α≤0∴不等式得证∵0＜α＜π,∴等号成立当且仅当cosα-21=0 即α=600【评析】这些该题本身不难，但三角证明题出现证法太多，标准不易统一，给阅卷带来非常大的难度 另一方面，这一答案给出的分析法证明格式也不对，一般分析法证明题格式“要证A ，只要证B”形式，B 是A 的充分不必要条件即可，而不是由A 导出B（1982年文科第七题）已知定点A ，B 且AB=2a ，如果动点P 到点A 的距离和到点B 的距离之比为2∶1，求点P 的轨迹方程，并说明它表示什么曲线解：选取AB 所在直线为横轴，从A 到B 为正方向，以AB 中点O 为原点，过O 作AB 的垂线为纵轴，则A 为（-a ，0），B 为（a ，0），设P为（x,y) .033103],)[(4)(.2)()(,1222222222222=++-∴+-=++∴=+-++∴=a y ax x y a x y a x ya x y a x PB PA 因为x 2,y 2两项的系数相等，且缺xy 项，所以轨迹的图形是圆（1983年文科第九题）如图，已知两条直线L 1:2x-3y+2=0,L 2:3x-2y+3=0 有一动圆（圆心和半径都在变动）与L 1，L 2都相交，并且L 1，L 2被截在圆内的两条线段的长度分别是定值26，24求圆心M解：设圆心M 的坐标为(x,y)，圆的半径为r ，点M 到L 1，L 2的距离分别为d 1,d 2根据弦、弦心距、半径三者之间的关系，有.5.)224(,)226(2212222222221=-=+=+d d r d r d 得根据点到直线的距离公式，得.16565)1(.651225)13323(13232(,13|323|,13|232|22222221=-+=-++=+--+-+-=+-=y x y x x y x y x y x d y x d 即化简得得方程代入上式轨迹是双曲线【评析】答案说法有误：说圆应为以…为圆心，以…为为半径的圆,说双曲线说明以…为焦点…为实轴长的双曲线二、1984――1993年高考数学败题【说明】这段时间，考试的目的是考察中学数学的基础知识、基本技能，命题的人员以中学教师为主，为减少败题的出现机率，采取了科研测试方法（科研测试题从1988年暂停,1992年恢复），因此，这一阶段的败题多是不复合教学大纲的试题（1984年理二2）函数20.5log (44)x x ++在什么区间上是增函数？ 答：x ＜-2【评析】该题用到了复合函数单调性，但这一内容在当时教学大纲中明确不要求（1984年理五）设c,d,x 为实数，c≠0，x 为未知数讨论方程()log 1d cx xx +=- Y L 1MO X在什么情况下有解有解时求出它的解解：原方程有解的充要条件是：⎪⎪⎪⎩⎪⎪⎪⎨⎧=+≠+>+>-(4))((3),0(2) ,0(1),01x x d cx x d cx x d cx x 由条件（4）知1)(=+xdcx x ，所以2=+d cx 再由c≠0，可得.12c dx -=又由1)(=+x d cx x 及x ＞0，知0>+xdcx ，即条件（2）包含在条件（1）及（4）中再由条件（3）及1)(=+xd cx x ，知.1≠x 因此，原条件可简化为以下的等价条件组：⎪⎪⎩⎪⎪⎨⎧-=≠>(6) .1x (5)1,x (1),02c d x 由条件（1）（6）知.01>-cd这个不等式仅在以下两种情形下成立：①c ＞0,1-d ＞0,即c ＞0,d ＜1; ②c ＜0,1-d ＜0,即c ＜0,d ＞1再由条件（1）（5）及（6）可知d c -≠1从而，当c ＞0,d ＜1且d c -≠1时，或者当c ＜0,d ＞1且d c -≠1时，原方程有解，它的解是x =【评析】该题即从两个层次考查了等价转化，中间又涉及了分类讨论，难度比较大，是一个考查能力的试题，与当时考查“双基”要求不符；结论：考查数学思想从深度及广度同时考查时，不能在某一思想上究得太深（1984年理六2）求经过定点M （1，2），以y 轴为准线，离心率为21的椭圆的左顶点的轨迹方程解：因为椭圆经过点M （1，2），且以y 轴为准线，所以椭圆在y 轴右侧，长轴平行于x 轴设椭圆左顶点为A （x,y ），因为椭圆的离心率为21，所以左顶点A 到左焦点F 的距离为A 到y 轴的距离的21，从而左焦点F 的坐标为,23(y x设d 为点M 到y 轴的距离，则d=1根据21||=d MF 及两点间距离公式，可得1)2(4)32(9,)21()2()123(22222=-+-=-+-y x y x 即【评析】该题在当时一改习惯于教材上直接法求轨迹方程的步骤，被认为是对教学大纲的偏执理解，没有考查基础知识与基本技能，所以当作一种研究性的材料还可以，并最终诞生了相关点法的应用 至于到了考查能力时，它则又成为一道好题，那是十年之后的事情了！（1984年理七）在△ABC 中，∠A ，∠B ，∠C 所对的边分别为a ,b,c ，且c=10，cos 4cos 3A bB a ==，P 为△ABC 的内切圆上的动点求点P 到顶点A ，B ，C 的距离的平方和的最大值与最小值解：由abB A =cos cos ，运用正弦定理，有.2sin 2sin cos sin cos sin ,sin sin cos cos B A B B A A ABB A =∴=∴=因为A≠B ，所以2A=π-2B ，即A+B=2由此可知△ABC 是直角三角形由c=10，.8,60,0,34222==>>=+=b a b a c b a a b 可得以及 如图，设△ABC 的内切圆圆心为O ＇，切点分别为D ，E ，F ，则 AD+DB+EC=.12)6810(21=++但上式中AD+DB=c=10， 所以内切圆半径r=EC=2如图建立坐标系， 则内切圆方程为: (x-2)2+(y-2)2=4设圆上动点P 的坐标为(x,y),则.48876443764])2()2[(3100121633)6()8(||||||2222222222222x x x y x y x y x y x y x y x PC PB PA S -=+-⨯=+--+-=+--+=++-+++-=++=因为P 点在内切圆上，所以40≤≤x ，S 最大值=88-0=88，S 最小值=88-16=72解二：同解一，设内切圆的参数方程为),20(sin 22cos 22π<α≤⎩⎨⎧α+=α+=y x 从而222||||||PC PB PA S ++= α-=α++α++-α+α++α++-α=cos 880)sin 22()cos 22()4sin 2()cos 22()sin 22()6cos 2(222222因为πα20<≤，所以S 最大值=80+8=88， S 最小值=80-8=72【评析】该题是对知识的大综合，对于学生而言难度较大，而且就1984E O ＇ P （x,y) XO C （0，0） A （8，0）年的高考试题，解答题基本上是题题设防、题题堡垒，从整体上脱离了中学教学的实际（1984年文五）把22411sin 2sin cos 4αβα---化成三角函数的积的形式(要求结果最简）)-)sin(sin( )2sin 2sin 2()2cos 2(2cos)cos )(cos cos (cos cos cos )cos (sin cos cos cos cos sin cos cos 2sin 41)sin 1(:2222224222422βαβ+α=α-βα+β-⨯α-βα+β=α-βα+β=α-β=α+αα-β=α-αα-β=α-α-β-=原式解【评析】当时三角式最简没有明确什么什么样算最简，这一名次的提出具有超前性，对于文科生更感不易，但它引领了一个各种化简结果最简的研究方向 结论：研究方向不能替代仅仅那么一点时间高考试题！（1985年全国文科第四题）证明三角恒等式424232sin sin 25cos cos3cos 2(1cos )4x x x x x x ++-=+证：x x x x x x x cos )cos 3cos 4(cos 5cos sin 3sin 224224--++=左边x x x x x 24224cos 3cos cos sin 3sin 2+++=右边=+=++=+++=x x x x x x x x x 222222222cos 22cos 3cos sin 2cos 3)cos )(sin cos sin 2(【评析】三角证明题不宜作为大题考查，这是几年前的经验，该题重蹈了历史覆辙 1988年的文科数学试题第三题是“证明α-α=αcos 3cos 43cos 3”，1989年全国理科19文、科20题“证明：x2cos x cos xsin 22x tg 2x 3tg+=-”继续重蹈历史覆辙！ （1986年理文科一（6）题）设甲是乙的充分条件，乙是丙的充要条件，丙是丁的必要条件，那么丁是甲的 （ ）（A ）充分条件 （B ）必要条件（C ）充要条件 （D ）既不充分也不必要的条件 答案D【评析】该题仅仅说了甲是乙的充分条件，没有说是否必要，因此该题的叙述不严格 这一不足，在以后命题中加以了改进，并渗透到平时教学中（1988年全国理科、文科一14）假设在200件产品中有3件次品，现在从中任意抽取5件，其中至少有2件次品的抽法有 （ ）（A ）233197C C 种 （B ）233231973197C C C C +种（C ）55200197C C -种 （D ）5142003197C C C -种 答案B【评析】该题不难，但是用符号而不用数值表示过多的限制了考试的思维，当年引起专家争议随后的再实验，用事实说明了“这种用符号表示的题要么太难，要么太易，还是以数值表示比较好！”（1989年全国理22、文23）已知,1a ,0a ≠>试求使方程222log ()log ()a a x ak x a -=-有解的k 的取值范围解：由对数函数的性质可知，原方程的解x 应满足⎪⎩⎪⎨⎧>->--=-)3(.0a x )2(,0ak x )1(,a x )ak x (22222 当（1），（2）同时成立时，（3）显然成立，因此只需解⎩⎨⎧>--=-)2(,0ak x )1(,a x )ak x (222 由（1）得)4()k 1(a kx 22+=当k=0时，由a>0知（4）无解，因而原方程无解 当k≠0时，（4）的解是)5(.k2)k 1(1x 2+=把（5）代入（2），得.k k2k 12>+ 解得：.1k 01k <<-<<∞-或综合得，当k 在集合)1,0()1,(⋃--∞内取值时，原方程有解【评析】该题从题本身而言是一个好题，但是该题在当年许多学校已经练习过，作为高考试题，照搬原题是不适当的（1989年上海14）两排座位，第一排有3个座位，第二排有5个座位，若8名学生入座（每人一个座位），则不同的坐法种数为（ ）A,C 58C 38 B,153288P C C C,5388P C D,38P答案：D【评析】该题是对1988年全国214题的延续再实验，事实说明 “排列组合问题结果这种用符号表示的题要么太难，要么太易，还是以数值表示比较好！而且这种命题从方式上也限制了学生的思维”（1990年全国理科第9题、文科11题）设全集I={(x,y)|x,y ∈R },集合M={(x,y)|312y x -=-, x 、y ∈R },N={(x,y)|y≠x+1, x 、y ∈R }，那么M N ⋃＝（ ）A, ∅ B,{(2,3)} C,(2,3) D,{(x,y)|y=x+1} 【答案】B【评析】该题基本上照搬了1986年上海理科第20题：若全集U={(x,y)|x 、y ∈R },A={(x,y)|123=--x y , x 、y ∈R },B={(x,y)|y=x+1, x 、y ∈R },则U A∩B是（ ）A,U AB,B C,∅ D,{(2,3)}，高考试题照搬应该不是件好事（1991年全国理23题） 已知ABCD 是边长为4的正方形，E 、F 分别是AB 、AD 的中点，GC 垂直于ABCD 所在的平面，且GC ＝2．求点B 到平面EFG 的距离．解：如图，连结EG 、FG 、EF 、BD 、AC 、EF 、BD 分别交AC 于H 、O ． 因为ABCD 是正方形，E 、F 分别为AB 和AD 的中点，故EF ∥BD ，H 为AO 的中点．BD 不在平面EFG 上．否则，平面EFG 和平面ABCD 重合，从而点G 在平面的ABCD 上，与题设矛盾．由直线和平面平行的判定定理知BD ∥平面EFG ，所以BD 和平面EFG 的距离就是点B 到平面EFG 的距离．∵ BD ⊥AC ， ∴ EF ⊥HC ． ∵ GC ⊥平面ABCD ， ∴ EF ⊥GC ，∴ EF ⊥平面HCG ．∴ 平面EFG ⊥平面HCG ，HG 是这两个垂直平面的交线． 作OK ⊥HG 交HG 于点K ，由两平面垂直的性质定理知OK ⊥平面EFG ，所以线段OK 的长就是点B 到平面EFG 的距离．∵ 正方形ABCD 的边长为4，GC=2， ∴ AC=42，HO=2，HC=32． ∴ 在Rt △HCG 中，HG=()2222322=+．由于Rt △HKO 和Rt △HCG 有一个锐角是公共的，故Rt △HKO ∽△HCG ．∴ OK=111122222=⨯=⋅HG GC HO ． 即点B 到平面EFG 的距离为11112． 【评析】该题作辅助线太多，难度过大，是历年立体几何题少见的难度；但它的出现，将中学教学的“距离”引向以点面距为核心的研究上，就当年而言，此题与考查双基的思想不符（1991年全国理科25题）已知n 为自然数，实数a>1，解关于x 的不等式log a x －log 2a x ＋12log 3a x ＋…＋n (n －2)1n -log n a x>1(2)3n--log a (x 2－a)解：利用对数换底公式，原不等式左端化为 log a x －4·2log log a x a a ＋12·3log log a x a a ＋…＋n(－2)n －1·na a ax log log =[1－2＋4＋…＋(－2)n－1]log a x =3)2(1n--log a x 故原不等式可化为3)2(1n--log a x>3)2(1n--log a (x 2－a)． ①当n 为奇数时，3)2(1n-->0，不等式①等价于 log a x>log a (x 2－a)． ②因为a>1，②式等价于⎪⎩⎪⎨⎧->>->a x x a x x 2200⎪⎩⎪⎨⎧<-->>⇔002a x x a x x ⎪⎩⎪⎨⎧++<<+->⇔24112411ax a a x 因为2411a +-<0， 2411a ++>24a=a ，所以，不等式②的解集为{x|a <x<2411a++}． 当n 为偶数时，3)2(1n--<0，不等式①等价于log a x>log a (x 2－a)． ③因为a>1，③式等价于⎪⎩⎪⎨⎧-<>->a x x a x x 2200⎪⎩⎪⎨⎧>-->>⇔002a x x a x x ⎪⎩⎪⎨⎧+-<>⇔2411a x a x 或⎪⎩⎪⎨⎧++>>2411a x ax 因为，，a aa a =>++<+-24241102411 所以，不等式③的解集为{x|x>2411a++}． 综合得：当n 为奇数时，原不等式的解集是{x|2411ax a ++<<}； 当n 为偶数时，原不等式的解集是{x|2411ax ++>} 【评析】该题照搬了当年湖北黄冈、河北辛集中学及北京海淀区的模拟试题，包括数值都没有变化（1991年三南高考数学第24题）设函数f(x)=x2+x+1的定义域是[n,n+1]2（n是自然数），那么在f(x)的值域中共有_____________个整数【答案】2n+2【评析】这是当年希望杯数学竞赛的一道数学试题，在高考中出现而且仍然以填空题出现，有照抄之嫌（1992年三南第14题）设数列{a n}是正数组成的等比数列，公比q=2,a1a2……a30=230,那么a3a6a9…a30=（）A,210B,220C,216D,215【答】B【评析】该题运算量比较大，也是希望杯竞赛中一个非常类似的题，在还没有将运算能力当作一种能力考查时，出此题显然违背了考查“双基”的初衷三、1994――－2002年高考数学败题【说明】该阶段，高考内容上以《考试说明》为准绳，目的逐步变化成“为大学选拔新生服务的选拔性能力考试”，命题的人员也逐步变化为以高校为主，出台了许多量化指标，该阶段的败题，主要体现为预估难度（考试说明的规定难度）与实际难度（实际分数）不符，这一原因现在多数专家认为是高校教师不了解中学教学的实际所致（1994年全国理文23题）如图，已知A1B1C1－ABC是正三棱柱，D是AC中点．(1)证明AB1∥平面DBC1；(2)假设AB1⊥BC1，求以BC1为棱，DBC1与CBC 1为面的二面角α的度数．【解答】(1)证明：∵A 1B 1C 1－ABC 是正三棱柱，∴四边形B 1BCC 1是矩形．连结B 1C交BC 1于E ，则B 1E=EC ．连结DE ．在△AB 1C中，∵AD=DC ，∴DE ∥AB 1．又AB 1⊄平面DBC 1，DE ⊂平面DBC 1，∴AB 1∥平面DBC 1．(2)解：作DF ⊥BC ，垂足为F ，则DF ⊥面B 1BCC 1，连结EF ，则EF 是ED 在平面B 1BCC 1上的射影．∵AB 1⊥BC 1，由(1)知AB 1∥DE ，∴DE ⊥BC 1，则BC 1⊥EF ，∴∠DEF 是二面角α的平面角．设AC=1，则DC=21．∵△ABC 是正三角形，∴在Rt △DCF 中，DF=DC·sinC=43，CF=DC·cosC=41．取BC 中点G ．∵EB=EC ，∴EG ⊥BC ．在Rt △BEF 中，EF 2=BF·GF ，又BF=BC －FC=43，GF=41，∴EF 2=43·41，即EF=43．∴tg ∠DEF=14343==EF DF ．∴∠DEF=45°．故二面角α为45°．【评析】该题作辅助线太多，难度过大；与当年的大环境有关：一、当年出台《考试说明》，明确数学高考考查的第一能力是计算能力；二、当年形成了立体几何的研究热潮但一次性将能力拔高到这种程度，是考生难于适应的 结果出现与《考试说明》要求不符的实际情况（1994年上海18）计划在某画廊展出10幅不同的画，其中1幅水彩画、4幅油画、5幅国画，排列一行陈列，要求同一品种的画必须连在一起，并且水彩画不放在两端，那么不同的陈列方式有（ ）种A,4545P P ∙ B,33P ∙ 4545P P ∙ C,13C ∙4545P P ∙ D,22P ∙4545P P ∙【答】D【评析】这种排列组合用符号表示的试题在全国1988年已经有了不宜出的结论，它再次重蹈了历史覆辙（1996年全国理22、文23）如图，在正三棱柱ABC －A 1B 1C 1中，E ∈BB 1，截面A 1EC ⊥侧面AC 1． (Ⅰ)求证：BE=EB 1;(Ⅱ)若AA 1=A 1B 1;求平面A 1EC 与平面A 1B 1C 1所成二面角(锐角)的度数．注意：在下面横线上填写适当内容，使之成为(Ⅰ)的完整证明，并解答(Ⅱ)．(右下图)(Ⅰ)证明：在截面A 1EC 内，过E 作EG ⊥A 1C ，G 是垂足．① ∵∴EG ⊥侧面AC 1;取AC 的中点F ，连结BF ，FG ，由AB=BC 得BF ⊥AC ，② ∵∴BF ⊥侧面AC 1;得BF ∥EG ，BF 、EG 确定一个平面，交侧面AC 1于FG ．③ ∵∴BE ∥FG ，四边形BEGF 是平行四边形，BE=FG ，④ ∵∴FG ∥AA 1，△AA 1C ∽△FGC ，⑤ ∵ ∴111122FG AA BB ==，即111,2BE BB BE EB ==故【解答】①∵面A 1EC ⊥侧面AC 1， ②∵面ABC ⊥侧面AC 1，③∵BE ∥侧面AC 1 ④∵BE ∥AA 1， ⑤∵AF=FC ， (Ⅱ)解：分别延长CE 、C 1B 1交于点D ，连结A 1D ．∵1EB ∥11112121,CC BB EB CC ==， ∴,21111111B A C B DC DB ===∵∠B 1A 1C 1=∠B 1 C 1A 1=60°，∠DA 1B 1=∠A 1DB 1=21（180°－∠D B 1A 1）=30°，∴∠DA 1C 1=∠DA 1B 1+∠B 1A 1C 1=90°，即1DA ⊥11C A ∵CC 1⊥面A 1C 1B 1，即A 1C 1是A 1C 在平面A 1C 1D 上的射影，根据三垂线定理得DA 1⊥A 1C ，所以∠CA 1C 1是所求二面角的平面角．∵CC 1=AA 1=A 1B 1=A 1C 1，∠A 1C 1C=90°，∴∠CA 1C 1=45°，即所求二面角为45°【评析】以这种填空题形式出现，过多地限制了学生思维，出现了实际结果与预估难度非常大的反差立体几何试题这样出不当；通过该题，也使近年立体几何的研究开始了降温同时也使不少专家反省：高考试题与研究热点及竞赛试题还是当有区别的同时，也确定了从1997年开始高考试题的进行量化评价（1997年全国理15）四面体的顶点和各棱中点共10个点，在其中取4个不共面的点，不同的取法共有( ) (A) 150种 (B) 147种(C) 144种 (D) 141种【解答】D【评析】该题无论从直接还是间接思路，都要进行三级分类讨论，体现为试题很难 难度为0 18，按照当年《考试说明》，难度低于0 2的，应该算作废题 结论：考查单一的知识与思想，层数不能超过三级（1997年全国理24）设二次函数f(x)=ax 2+bx+c(a>0),方程f(x)－x=0的两个根x 1,x 2满足0<x 1<x 2<1a ． I ．当x ∈(0, x 1)时，证明x<f (x)<x 1； II ．设函数f(x)的图像关于直线x=x 0对称，证明x 0<12x 【解析】证明:(Ⅰ)令F(x)=f(x)－x ．因为x 1，x 2是方程f(x)－x=0的根，所以F(x)=a(x －x 1)(x －x 2)．当x ∈(0，x 1)时，由于x 1<x 2，得(x －x 1)(x －x 2)>0，又a>0，得F(x)=a(x －x 1)(x －x 2)>0，即x<f(x)． )](1)[())(()]([)(2121111x x a x x x x x x a x x x F x x x f x -+-=--+-=+-=- 因为a x x x 1021<<<<所以x 1－x>0，1+a(x －x 2)=1+ax －ax 2>1－ax 2>0．得 x 1－f(x)>0．由此得f(x)<x 1．(Ⅱ)依题意知a b x 20-= 因为x 1，x 2是方程f(x)－x=0的根，即x 1，x 2是方程ax 2+(b －1)x+c=0的根．∴ab x x 121--=+， a ax ax a x x a a b x 2121)(221210-+=-+=-= 因为ax 2<1，所以22110x a ax x =<【评析】该题就某一知识进行了加深，竞赛味道过于浓厚 实际难度为0 09,也属于废题（1997年全国理25）设圆满足：①截y 轴所得弦长为2；②被x 轴分成两段圆弧，其弧长的比为3:1，在满足条件①、②的所有圆中，求圆心到直线l:x-2y=0的距离最小的圆的方程．【解析】解法一:设圆的圆心为P(a ，b)，半径为r ，则点P 到x 轴，y 轴的距离分别为│b│， │a│．由题设知圆P 截x 轴所得劣弧对的圆心角为90°，知圆P 截X 轴所得的弦长为r 2，故r 2=2b 2，又圆P 截y 轴所得的弦长为2，所以有r 2=a 2+1．从而得2b 2－a 2=1．又点P(a ，b)到直线x －2y=0的距离为52ba d -=，所以5d 2=│a －2b│2 =a 2+4b 2－4ab ≥a 2+4b 2－2(a 2+b 2) =2b 2－a 2=1，当且仅当a=b 时上式等号成立，此时5d 2=1，从而d 取得最小值． 由此有⎩⎨⎧=-=12,22a b b a 解此方程组得⎩⎨⎧==;1,1b a 或⎩⎨⎧-=-=.1,1b a 由于r 2=2b 2知2=r ． 于是，所求圆的方程是(x －1) 2+(y －1) 2=2，或(x+1) 2+(y+1) 2=2． 解法二:同解法一，得52ba d -=∴db a 52±=-得2225544d bd b a +±=①将a 2=2b 2－1代入①式，整理得 01554222=++±d db b ②把它看作b 的二次方程，由于方程有实根，故判别式非负，即△=8(5d 2－1)≥0，得 5d 2≥1．∴5d 2有最小值1，从而d 有最小值55． 将其代入②式得2b 2±4b+2=0．解得b=±1．将b=±1代入r 2=2b 2，得r 2=2．由r 2=a 2+1得a=±1．综上a=±1，b=±1，r 2=2．由b a 2-=1知a ，b 同号．于是，所求圆的方程是(x －1) 2+(y －1) 2=2，或(x+1) 2+(y+1) 2=2． 【评析】该题就某一知识进行了加深，竞赛味道过于浓厚 实际难度为0 20,属于废题 通过1997年高考数学试题，专家们得出这样结论：竞赛试题要对某一知识应用中强调技巧，高考试题不能过多地偏重于技巧（1999年全国文理16）在一块并排10垄的田地中，选择2垄分别种植A 、B 两种作物，每种作物种植一垄，为有利于作物生长，要求A 、B 两种作物的间隔不小于6垄，则不同的选垄方法共有___________种（用数字作答）【解答】12【评析】该题的愿意是选垄并种播，但是题目没有明确叙述清楚，而只是笼统的说有多少种选法（1999年全国文理23，广东20）右图为一台冷轧机的示意图 冷轧机由若干对轧辊组成，带钢从一端输入，经过各对轧辊逐步减薄后输出Ⅰ 输入带钢的厚度为α，输出带钢的厚度为β，若每对轧辊的减薄率不超过0r 问冷轧机至少需要安装多少对轧辊？ Ⅱ 已知一台冷轧机共有4对减薄率为20%的轧辊，所有轧辊周长均为1600.mm 若第k 对轧辊有缺陷，每滚动一周在带钢上压出一个疵点，在冷轧机输出的带钢上，疵点的间距为.k L 为了便于检修，请计算1L 、2L 、3L 并填入下表（轧钢过程中，带钢宽度不变，且不考虑损耗）【解答】Ⅰ 解：厚度为α的带钢经过减薄率均为0r 的n 对轧辊后厚度为().10n r a -为使输出带钢的厚度不超过β，冷轧机的轧辊数（以对为单位）应满足()β≤-n r a 01即().10a r n β≤- 由于(),0,010>>-a r n β对比上式两端取对数，得().lg 1lg 0a r n β≤-由于(),01lg 0<-r 所以().1lg lg lg 0r a n --≥β因此，至少需要安装不小于()01lg lg lg r a --β的整数对轧辊Ⅱ 解法一：第k 对轧辊出口处疵点间距离为轧辊周长，在此处出口的两疵点间带钢体积为()⋅-⋅k r a 11600宽度(),%20=r 其中而在冷轧机出口处两疵点间带钢的体积为()⋅-⋅41r a L k 宽度 因宽度相等，且无损耗，由体积相等得()=-⋅k r a 11600()41r a L k -⋅ (),%20=r 即.8.016004-⋅=k k L 由此得(),20003mm L =(),25002mm L =()mm L 31251=填表如下轧锟序号k 1 2 3 4。
山东省高密市第三中学高三政治一轮复习 错题精题集萃
经济生活错题精题集萃一、单项选择题：1.通货膨胀发生的主要原因是（）A．纸币升值，物价上涨 B. 纸币贬值，物价下降C. 纸币发行量超过流通中的实际需要量D. 纸币供应量与流通需要量不符2．下列对人民币升值影响的认识，错误的是（）A.降低进口企业的采购成本B.抑制中国企业的出口C.增强中国企业的国际竞争力D.有利于人们到境外旅游消费3．2014年3月21日，中国人民银行发行中国佛教圣地(峨眉山)金银纪念币一套。
该套纪念币共5枚，其中金币3枚，银币2枚，均为中华人民共和国法定货币。
该纪念币在本质上是（）A.商品B.纸币C.一般等价物D.铸币4、“家校通”使学校、家长之间的沟通交流更为方便、快捷。
目前我市部分家长按包月方式（5元/月）订制了“家校通”短信。
材料中的“家校通”短信（）A.是商品，因为它有使用价值B.不是商品，因为它没有用于交换C.不是商品，因为它不是劳动产品D.是商品，因为它是用于交换的劳动产品5.一个想要改变自己办公室环境的白领，用闲置多时的《音乐之声》碟片换来了一盆漂亮的君子兰；一个喜欢工艺品的收藏爱好者，用瑞士军刀换来了一个精致的木筷盒漆器……这样的故事每天都在易物网上发生。
这种以物易物的交换方式（）①是一种商品流通②可以使商品的价值最大化③可以使商品的使用价值最大化④遵循了等价交换的原则A.①②B.②④C.③④D.①④6.一定时期内，商品流通中所需要的货币量受到多种因素影响。
下列选项中,使我国货币需求量减少的因素有（）①人民币流通速度提高②信用卡的广泛使用③人民币境外流通规模缩小④商品的社会劳动生产率降低A.②④B.①②C.①③D.③④7.币的汇率变动会带来商品进出口数量的变动。
2013年1月4日人民币对美元汇率中间价为6.2897元，2014年6月26日为6.1538元。
不考虑其他因素，这一变动给我国带来的影响与下列四幅图中所示状况对应正确的是（A）8.价值规律要求，商品价值量由生产商品的社会必要劳动时间决定，商品交换以价值量为基础，实行等价交换。
错题集
单选1、客观唯心主义的基本观点是（）。
A、世界的本原只有一个B、世界的本原是客观实在决定的物质世界C、整个世界是绝对观念创造的D、整个世界是主观精神创造的2、马克思主义回答人的本质问题的立足点是（）。
A、人的社会关系B、人的自然属性C、人类的共同利益D、人的自身需要3、(世界的物质性及其发展规律易)古有一父，为解决家中鼠患，买了一只猫。
猫抓老鼠的同时，却也偷吃鸡，其子甚怨。
父道：“宁无鸡也不能无猫，因无鸡不会挨冻受饿，而无猫，则会挨冻受饿。
”遂其子不再怨。
这个故事启示我们在处理和解决问题时要注意（）A、整体与部分的辩证关系B、两点论和重点论的统一C、量变与质变的辩正关系D、矛盾的同一性和斗争性9、(世界的物质性及其发展规律易)辩证法所回答的问题是（）A、世界是否可以认识的问题B、世界的本原是什么的问题C、世界是否具有统一性的问题D、世界的状况怎么样的问题15、(人类社会及其发展规律中)社会意识对社会存在的反作用的性质取决于（）A、观念上层建筑和政治上层建筑的关系B、社会的性质和人类解放的程度C、剥削阶级与被剥削阶级斗争的状况D、它为之服务的经济基础的性质和它所武装的阶级社会势力的性质31、(历史唯物主义易)马克思主义认为，社会存在是社会生活的物质方面，主要包括生产方式、地理环境和人口因素。
但是，人类社会运动的主体是（）A、劳动者B、上层建筑C、生产方式D、阶级和阶级斗争16、(人类社会及其发展规律中)科学技术是生产力，是因为（）。
A、科学技术渗透到生产力诸要素中转为现实的生产力B、科学技术是构成生产力的最重要的独立因素C、科学技术能把生产力诸要素结合起来构成现实的生产力D、科学技术是直接现实的生产力33、(共产主义是人类最崇高的社会理想中)社会进步必然促进并直接表现为（）。
A、物的极大丰富B、生产力的高度发达C、人的发展D、社会形态的变更多选22、辩证唯物主义所理解的世界的物质统一性，是包括人类社会历史的物质性在内的统一性，这是马克思主义哲学对以往哲学的深刻革命。
高三数学易错数列多选题 易错题同步练习试卷
高三数学易错数列多选题 易错题同步练习试卷一、数列多选题1．已知数列{}n a 的前n 项和为n S ,则下列说法正确的是（ ）A ．若21,n S n =-则{}n a 是等差数列B ．若21,nn S =-则{}n a 是等比数列C ．若{}n a 是等差数列，则995099S a =D ．若{}n a 是等比数列，且10,0,a q >>则221212n n n S S S -+⋅>【答案】BC 【分析】由n S 求n a ，根据通项公式可判断AB 是否正确，由等差数列的性质可判断C ，取1n =时，结合等比数列求和公式作差比较13S S ⋅与22S 大小即可判断D. 【详解】对于A 选项，若21n S n =-，当2n ≥时，21n a n =-，10a =不满足21n a n =-，故A错误；对于B 选项，若21nn S =-，则1112,21,1n n n n S S n a S n --⎧-=≥=⎨==⎩，由于11a =满足12n n a -=，所以{}n a 是等比数列，故B 正确；对于C 选项，若{}n a 是等差数列，则()199995099992a a S a +==，故C 正确. 对于D 选项，当1n =时，()()222222132111110S S S a q qa q a q ⋅-=++-+=-<，故当1n =时不等式不等式，故221212n n n S S S -+⋅>不成立，所以D 错误.故选：BC 【点睛】本题考查数列的前n 项和为n S 与n a 之间的关系，等差数列的性质，等比数列的前n 项和为n S 的公式等，考查运算求解能力.本题D 选项解题的关键将问题特殊化，讨论1n =时，13S S ⋅与22S 大小情况.此外还需注意一下公式：11,2,1n n n S S n a S n --≥⎧=⎨=⎩；若{}n a 是等差数列，则()2121n n S n a -=-.2．已知数列{}n a ，{}n b 满足1n n n a a +-=，21n n n b a nb ⋅+=，且11a =，n S 是数列{}n b 的前n 项和，则下列结论正确的有（ ）A ．m +∃∈N ，55m m a a a +=+B ．n +∀∈N ，33314n a n +≥ C ．m +∃∈N ，16m b = D ．n +∀∈N ，113n S ≤<【答案】BD 【分析】用累加法得到222n n n a -+=，代入21n n n b a nb ⋅+=，得11212n b n n ⎛⎫=- ⎪++⎝⎭，代入5m a +5m a a =+求出m 可判断A ；代入33n a n+求最值可判断B ； 令1121612m b m m ⎛⎫=-= ⎪++⎝⎭解出m 可判断C ；裂项相消后可求出n S 的范围可判断D. 【详解】因为1n n n a a +-=，所以211a a -= 322a a -=11(2)n n n a a n -=-≥-以上各式累加得1121(1)2n a a n n n =+++-=--，所以(1)12n n n a -=+，当1n =时，11a =成立， 所以2(1)2122n n n n a n --+=+=，由21n n n b a nb ⋅+=，得112112(1)1222(1)(2)12n n b a n n n n n n n n ⎛⎫====- ⎪+++++⎝-+⎭+，对于A ，()()5254922122m a m m m m ++++++==，25(1)5(51)2411222m a a m m m m -⨯--+=+++=+ ， 当55m m a a a +=+时，222492222m m m m -+++=，得15m +=∉N ，A 错误； 对于B，(1)1(13333343411)22222n n n n a n n n n n ++==+=+-≥--+， 当且仅当268n =取等号，因为n +∀∈N ，所以8n =时，8333184a +=， 所以B 正确；对于C，令1121612mbm m⎛⎫=-=⎪++⎝⎭得，215308m m++=，解得m+=N，所以C错误；对于D，n+∀∈N，1231111112233412nS b b bn n⎛⎫=+++=-+-++-⎪++⎝⎭112211222n n⎛⎫=-=-<⎪++⎝⎭，可以看出n S是关于n递增的，所以1n=时有最小值13，所以113nS≤<，D正确.故选：BD.【点睛】本题考查了由递推数列求通项公式、裂项相消求数列和，关键点是用累加法求出n a，然后代入求出n b，考查了学生的推理能力、计算能力.3．已知数列{}n a的前n项和为2n33S n n=-，则下列说法正确的是（）A．342na n=-B．16S为nS的最小值C ．1216272a a a+++=D．1230450a a a+++=【答案】AC【分析】利用和与项的关系，分1n=和2n≥分别求得数列的通项公式，检验合并即可判定A;根据数列的项的正负情况可以否定B;根据前16项都是正值可计算判定C;注意到121617193300()a a a S a a a+++=+----16302S S=-可计算后否定D.【详解】1133132a S==-=,()()()2213333113422n n na S S n n n n n n-=-=---+-=-≥,对于1n=也成立，所以342na n=-，故A正确；当17n<时，0na>,当n=17时na0=,当17n>时，n a0<,nS∴只有最大值，没有最小值，故B错误；因为当17n<时，0na>,∴21216163316161716272a a a S+++==⨯-=⨯=，故C正确；121617193300()a a a S a a a+++=+----2163022272(333030S S =-=⨯-⨯-）54490454=-=， 故D 错误. 故选：AC. 【点睛】本题考查数列的和与项的关系，数列的和的最值性质，绝对值数列的求和问题，属小综合题.和与项的关系()()1112n nn S n a S S n -⎧=⎪=⎨-≥⎪⎩,若数列{}n a 的前 k 项为正值，往后都是小于等于零，则当n k ≥时有122n k n a a a S S ++⋯+=-，若数列{}n a 的前 k 项为负值，往后都是大于或等于零，则当n k ≥时有122n k n a a a S S ++⋯+=-+.若数列的前面一些项是非负，后面的项为负值，则前n 项和只有最大值，没有最小值，若数列的前面一些项是非正，后面的项为正值，则前n 项和只有最小值，没有最大值.4．将()23nn ≥个数排成n 行n 列的一个数阵，如图：11a 12a 13a ……1n a21a 22a 23a ……2n a 31a 32a 33a ……3n a……1n a 2n a 3n a ……nn a该数阵第一列的n 个数从上到下构成以m 为公差的等差数列，每一行的n 个数从左到右构成以m 为公比的等比数列（其中0m >）.已知113a =，61131a a =+，记这2n 个数的和为S .下列结论正确的有（ ）A ．2m =B ．767132a =⨯C ．()1212j ij a i -=+⨯D ．()()221nS n n =+-【答案】ACD 【分析】由题中条件113a =，61131a a =+，得23531m m +=+解得m 的值可判断A ；根据第一列的n 个数从上到下构成以m 为公差的等差数列，每一行的n 个数从左到右构成以m 为公比的等比数列可判断BC ；由等差数列、等比数列的前n 项和公式可判断D. 【详解】由113a =，61131a a =+，得23531m m +=+，所以2m =或13m =-（舍去），A 正确；()6635132a m m =+=⨯，B 错误；()()112132212j j ij a i i --=-+⨯=+⨯⎡⎤⎣⎦，C 正确；()()()111212122212n n n n nn S a a a a a a a a a =++++++++++++1121(12)(12)(12)121212n n n nn a a a ---=+++--- ()()()11211332(1)21212n nn n a a a n ++-⎛⎫=+++-=⨯- ⎪⎝⎭()()221n n n =+-，D 正确.故选：ACD. 【点睛】方法点睛：本题考查了分析问题、解决问题的能力，解答的关键是利用等比数列、等差数列的通项公式、求和公式求解，考查了学生的推理能力、计算能力.5．将2n 个数排成n 行n 列的一个数阵，如图：该数阵第一列的n 个数从上到下构成以m 为公差的等差数列，每一行的n 个数从左到右构成以m 为公比的等比数列(其中0m >).已知112a =，13611a a =+，记这2n 个数的和为S .下列结论正确的有（ ）A ．3m =B ．18181103354kk i a =⨯+=∑C ．(31)3ij ja i =-⨯ D ．()1(31)314n S n n =+- 【答案】ABD 【分析】根据第一列成等差，第一行成等比可求出1361,a a ，列式即可求出m ，从而求出通项ij a ，进而可得ii a ，根据错位相减法可求得181kki a=∑，再按照分组求和法，每一行求和可得S ，由此可以判断各选项的真假． 【详解】∵a 11＝2，a 13＝a 61+1，∴2m 2＝2+5m +1，解得m ＝3或m 12=-（舍去），A 正确； ∴()()11113213313j j j ij i a a i m i ---⎡⎤=⋅=+-⨯⋅=-⋅⎣⎦，C 错误；∴()1313i a i -=-⋅，0171811223318182353533S a a a a =+++⋯+=⨯+⨯+⋯+⨯① 12181832353533S =⨯+⨯+⋯+⨯②,①-②化简计算可得：1818103354S ⨯+=,B 正确；S ＝(a 11+a 12+a 13+……+a 1n )+(a 21+a 22+a 23+……+a 2n )+……+(a n 1＋a n2＋a n 3＋……＋a nn )()()()11211131313131313nnnn a a a ---=+++---()()231131.22nn n +-=- ()1=(31)314n n n +-，D 正确； 故选：ABD. 【点睛】方法点睛：数列求和的常用方法：（1）对于等差等比数列，利用公式法直接求和；（2）对于{}n n a b 型数列，其中{}n a 是等差数列，{}n b 是等比数列，利用错位相减法求和；（3）对于{}n n a b +型数列，利用分组求和法；（4）对于11n n a a +⎧⎫⎨⎬⎩⎭型数列，其中{}n a 是公差为()0d d ≠的等差数列，利用裂项相消法求和.6．已知数列{}n a ，下列结论正确的有（ ） A ．若12a ＝，11n n a a n +++＝，则20211a ＝.B ．若11132n n a a a ++＝，＝，则71457a =C ．若12nn S =3+，则数列{}n a 是等比数列 D ．若11212n n n a a a a ++＝，＝()*n N ∈，则15215a ＝ 【答案】AB 【分析】直接利用叠加法可判断选项A ，从而判断，利用构造新数列可求出B,D 中数列的通项公式，可判断，选项C 求出数列的前3项从而可判断. 【详解】选项A. 由11n n a a n +=++，即11n n a a n +-=+则()()()()19191818120207121a a a a a a a a a a =-+-+-++-+20191822211=+++++=故A 正确.选项B. 由132n n a a +=+，得()1311n n a a +=++，所以数列{}1n a +是以112a +=为首项，3为公比的等比数列.则1123n n a -+=⨯，即1231n n a -=⨯-，所以672311457a =⨯-=，故B 正确.选项C. 由12nn S =3+，可得当1n =时，11722a =+=3 当2n =时，得2211193622a S S ⎛⎫⎛⎫=-=+-+= ⎪ ⎪⎝⎭⎝⎭， 当3n =时，得332112791822a S S ⎛⎫⎛⎫=-=+-+= ⎪ ⎪⎝⎭⎝⎭，显然2213a a a ≠，所以数列{}n a 不是等比数列，故C 错误.选项D. 由122nn n a a a +=+，可得11112n n a a +-= 所以数列1n a ⎧⎫⎨⎬⎩⎭是以1为首项，12为公差的等差数列. 所以()1111122n n n a +=+-=，则1511826a ==，即1518a =，故D 错误. 故选：AB 【点睛】关键点睛：本题考查利用递推关系求数列的通项公式，解答的关键是掌握求数列通项公式的常见方法，由叠加法可得()()()()19191818120207121a a a a a a a a a a =-+-+-++-+，利用构造新数列()1311n n a a +=++，11112n n a a +-=解决问题，属于中档题.7．在n n n A B C （1,2,3,n =）中，内角,,n n n A B C 的对边分别为,,n n n a b c ，n n n A B C 的面积为n S ，若5n a =，14b =，13c =，且222124n n n a c b ++=，222124n n n a b c ++=，则（ ） A ．n n n A B C 一定是直角三角形 B ．{}n S 为递增数列 C ．{}n S 有最大值 D ．{}n S 有最小值【答案】ABD 【分析】先结合已知条件得到()222211125=252n n n n b c b c +++-+-，进而得到22225=n n n b c a +=，得A 正确，再利用面积公式得到递推关系1221875=644n n S S ++，通过作差法判定数列单调性和最值即可. 【详解】 由222124n n n a c b ++=，222124n n n a b c ++=得，222222112244n n n n n n a c a b bc+++++=+()2221122n n n a b c =++()2225122n n b c =++，故()222211125=252n n n n b c b c +++-+-， 又221125=0b c +-，22250n n b c ∴+-=，22225=n n n b c a ∴+=，故n n n A B C 一定是直角三角形，A 正确；n n n A B C 的面积为12n n n S b c =，而()4222222222221124224416n n n n n n n n n n n n a b c a b c a c a b bc+++++++=⨯=， 故()42222222222111241875161875==1616641n n n n n n n n n n n a b c a b bS S c c S +++++++==+，故22212218751875==6446434n n n n n S S SS S +-+--，又22125=244n n n n n b c b c S +=≤（当且仅当=n n b c 22121875=06344n n n S SS +∴--≥，又由14b =，13c =知n n b c ≠不是恒成立，即212n n S S +>，故1n n S S +>，故{}n S 为递增数列，{}n S 有最小值16=S ，无最大值，故BD 正确，C 错误. 故选：ABD. 【点睛】本题解题关键是利用递推关系得到()222211125=252n n n n b c b c +++-+-，进而得到22225=n n n b c a +=，再逐步突破.数列单调性常用作差法判定，也可以借助于函数单调性判断.8．下面是关于公差0d >的等差数列{}n a 的几个命题，其中正确的有（ ） A ．数列{}n a 递增B ．n S 为{}n a 的前n 项和,则数列n S n ⎧⎫⎨⎬⎩⎭是递增的等差数列 C ．若n a n =，n S 为{}n a 的前n 项和，且n S n c ⎧⎫⎨⎬+⎩⎭为等差数列，则0cD ．若70a =，n S 为{}n a 的前n 项和，则方程0n S =有唯一的根13n = 【答案】ABD 【分析】选项A. 由题意10n n a a d +-=>可判断；选项B.先求出112n S n a d n -=+⨯，根据1012n n S S dn n +-=>+可判断；选项C. 若n a n =,则()12n n n S +=，则0c 或1c =时n S n c ⎧⎫⎨⎬+⎩⎭为等差数列可判断；选项D.由1602n n S dn -⎛⎫=--= ⎪⎝⎭可判断. 【详解】选项A. 由题意10n n a a d +-=>，则1n n a a +>，所以数列{}n a 递增，故A 正确. 选项B. ()112n n n S na d -=+⨯,则112n S n a d n -=+⨯ 所以1012n n S S d n n +-=>+，则11n n S S n n +>+，所以数列n S n ⎧⎫⎨⎬⎩⎭是递增的等差数列. 故B 正确. 选项C. 若n a n =,则()12n n n S +=，则()()12n n n S n c n c =+++当0c时，12+n S n c n =+为等差数列. 当1c =时，2n S n c n=+为等差数列.所以选项C 不正确.选项D. 70a =,即7160a a d =+=，则16a d =- 又()()1111660222n n n n n n S na d dn d dn ---⎛⎫=+⨯=-+⨯=--= ⎪⎝⎭由0,0d n >>，所以1602n --=，得13n =，故选项D 正确. 故选：ABD 【点睛】关键点睛：本题考查等差数列的判定和单调性的单调，解答本题的关键是利用等差数列的定义和前n 项和公式进行判断，求出162n n S dn -⎛⎫=-+ ⎪⎝⎭，从而判断，属于中档题.二、平面向量多选题9．已知向量(4,3)a k =，(4,3)b k =，则（ ） A ．若a b ⊥，则0k = B ．若//a b ，则1k =C ．若a b >，则1k <D ．若a b a b +=-，则a b ⊥【答案】AD 【分析】先根据a b ⊥建立方程44330k k ⨯+⨯=解得0k =，判断选项A 正确；再根据//a b ，建立方程(4,3)(4,3)k k λ=解得1k =±，判断选项B 错误；接着根据a b >建立不等式4(3)(4)3k k +>+解得11k -<<，判断选项C 错误；最后根据a b a b +=-，化简整理得到a b ⊥，判断选项D 正确.【详解】解：因为(4,3)a k =，(4,3)b k =，a b ⊥，则44330k k ⨯+⨯=，解得0k =，故选项A 正确；因为(4,3)a k =，(4,3)b k =，//a b ，则λa b ，即(4,3)(4,3)k k λ=，解得1k =±，故选项B 错误；因为(4,3)a k =，(4,3)b k =，a b >，则>，解得11k -<<，故选项C 错误；因为(4,3)a k =，(4,3)b k =，a b a b +=-，则0a b ⋅=，0a ≠，0b ≠，所以a b ⊥，故选项D 正确. 故答案为：AD. 【点睛】本题考查利用向量垂直求参数、利用向量共线求参数、根据向量的模的大小关系求参数的范围、利用向量的运算判断向量垂直，是中档题.10．ABC 是边长为2的等边三角形，已知向量a 、b 满足AB a =、AC a b =+，则下列结论正确的是（ ） A ．2b = B ．a b ⊥C ．2a b ⋅=D ．(2)a b BC +⊥【答案】AD 【分析】本题首先可以根据向量的减法得出BC b =，然后根据ABC 是边长为2的等边三角形得出A 正确以及B 错误，再然后根据向量a 、b 之间的夹角为120计算出2a b ⋅=-，C 错误，最后通过计算得出(2)0a b BC +⋅=，D 正确. 【详解】因为AB a =，AC a b =+，所以BC AC AB a b a b =-=+-=， 因为ABC 是边长为2的等边三角形，所以2b BC ==，A 正确， 因为AB a =，BC b =， 所以向量a 、b 之间的夹角为120，B 错误， 所以1cos1202222a b a b ⎛⎫⋅=⋅⋅=⨯⨯-=- ⎪⎝⎭，C 错误， 因为()22(2)(2)22220a b BC a b b a b b +⋅=+⋅=⋅+=⨯-+=，所以(2)a b BC +⊥，D 正确，故选：AD.【点睛】 本题考查向量的减法运算以及向量的数量积，若向量a 、b 之间的夹角为θ，则cos a b a b θ⋅=⋅⋅，若0a b ⋅=，则a b ⊥，考查推理能力与计算能力，是中档题.。
错题集-过立交桥 右前左后
C.停车带
D.收费岛地面
答案：A
85.如图所示限制速度标记的含义是什么？
A.平均行驶速度标准
B.最低行驶速度不得低于标记所示规定
C.最高行驶速度不得超过标记所示规定
D.设计时速标准
答案：C
86.如图所示标线的含义是什么？
A.禁止路边长时停放车辆
B.禁止路边临时停放车辆
C.禁止路边长时或临时停放车辆
A.注意危险
B.禁止小型汽车通行
C.注意追尾
D.事故易发路段
答案：D
37.如图标志的含义是什么？
A.禁止双向驶入通行
B.会车先行
C.双向交通
D.会车让行
答案：D
38.如图标志的含义是什么？
A.准许直行
B.禁止直行
C.快速直行
D.禁止驶入
答案：B
39.如图标志的含义是什么？
A.限制轴重
B.限制高度
C.限制质量
D.禁止机动车驶入
答案：A
43.如图标志的含义是什么？
A.禁止车辆临时停放
B.停车让行
C.禁止车辆临时或长时停放
D.禁止机动车驶入
答案：B
44.如图标志的含义是什么？
A.停车让行
B.会车让行
C.禁止让行
D.减速让行
答案：D
45.如图标志的含义是什么？
A.禁止大型客车驶入
B.禁止驶入
C.禁止小型客车驶入
D.漫水桥
答案：C
30.如图标志的含义是什么？
A.过水路面
B.注意溅水
C.易滑
D.驼峰桥
答案：A
31.如图标志的含义是什么？
A.急弯路
B.连续弯路
人教版高三数学下学期平面向量多选题单元 易错题质量专项训练
人教版高三数学下学期平面向量多选题单元 易错题质量专项训练一、平面向量多选题1．已知集合()(){}=,M x y y f x =,若对于()11,x y M ∀∈,()22,x y M ∃∈,使得12120x x y y +=成立,则称集合M 是“互垂点集”.给出下列四个集合:(){}21,1M x y y x ==+;(){2,M x y y ==;(){}3,xM x y y e ==;(){}4,sin 1M x y y x ==+.其中是“互垂点集”集合的为( )A ．1MB ．2MC ．3MD ．4M【答案】BD 【分析】根据题意知，对于集合M 表示的函数图象上的任意点()11,P x y ，在图象上存在另一个点P '，使得OP OP '⊥，结合函数图象即可判断．【详解】由题意知，对于集合M 表示的函数图象上的任意点()11,P x y ，在图象上存在另一个点P '，使得OP OP '⊥．在21y x =+的图象上，当P 点坐标为(0,1)时，不存在对应的点P '， 所以1M 不是“互垂点集”集合；对y =所以在2M 中的任意点()11,P x y ，在2M 中存在另一个P '，使得OP OP '⊥， 所以2M 是“互垂点集”集合；在xy e =的图象上，当P 点坐标为(0,1)时，不存在对应的点P '， 所以3M 不是“互垂点集”集合；对sin 1y x =+的图象，将两坐标轴绕原点进行任意旋转，均与函数图象有交点， 所以所以4M 是“互垂点集”集合， 故选：BD ． 【点睛】本题主要考查命题的真假的判断，以及对新定义的理解与应用，意在考查学生的数学建模能力和数学抽象能力，属于较难题．2．下列命题中真命题的是（ ）A ．向量a 与向量b 共线，则存在实数λ使a =λb （λ∈R ）B ．a ，b 为单位向量，其夹角为θ，若|a b -|＞1，则3π＜θ≤πC ．A 、B 、C 、D 是空间不共面的四点，若AB •AC =0，AC •AD =0，AB •AD =0则△BCD 一定是锐角三角形D ．向量AB ，AC ，BC 满足AB AC BC =+，则AC 与BC 同向 【答案】BC 【分析】对于A ：利用共线定理判断 对于B ：利用平面向量的数量积判断 对于C ：利用数量积的应用判断 对于D ：利用向量的四则运算进行判断 【详解】对于A ：由向量共线定理可知，当0b =时，不成立.所以A 错误. 对于B ：若|a b -|＞1，则平方得2221a a b b -⋅+＞，即12a b ⋅＜，又1||2a b a b cos cos θθ⋅=⋅=＜，所以3π＜θ≤π，即B 正确.对于C ：()()220BC BD AC AB AD AB AC AD AC AB AB AD AB AB ⋅=-⋅-=⋅-⋅-⋅+=＞，0||BC BD cosB BC BD ⋅=⋅＞，即B 为锐角，同理A ，C 也为锐角，故△BCD 是锐角三角形，所以C 正确.对于D ：若AB AC BC =+，则AB AC BC CB -==，所以0CB =，所以则AC 与BC 共线，但不一定方向相同，所以D 错误. 故选：BC. 【点睛】（1）多项选择题是2020年高考新题型，需要要对选项一一验证；（2）要判断一个命题错误，只需举一个反例就可以；要证明一个命题正确，需要进行证明.3．已知ABC 是边长为2的等边三角形，D ，E 分别是,AC AB 上的点，且AE EB =，2AD DC =，BD 与CE 交于点O ，则（ ）A ．0OC EO +=B ．0AB CE ⋅=C ．3OA OB OC OD +++=D ．ED 在BC 方向上的投影为76【答案】BD 【分析】可证明EO CE =，结合平面向量线性运算法则可判断A ；由AB CE ⊥结合平面向量数量积的定义可判断B ；建立直角坐标系，由平面向量线性运算及模的坐标表示可判断C ；由投影的计算公式可判断D. 【详解】因为ABC 是边长为2的等边三角形，AE EB =，所以E 为AB 的中点，且CE AB ⊥，以E 为原点如图建立直角坐标系，则()0,0E ，()1,0A -，()10B ,，(3C ， 由2AD DC =可得222333AD AC ⎛== ⎝⎭，则1233D ⎛- ⎝⎭， 取BD 的中点G ，连接GE ，易得//GE AD 且12GE AD DC ==， 所以CDO ≌EGO △，EO CO =，则30,2O ⎛ ⎝⎭， 对于A ，0OC EO EC +=≠，故A 错误； 对于B ，由AB CE ⊥可得0AB CE ⋅=，故B 正确；对于C ，31,2OA ⎛=-- ⎝⎭，31,2OB ⎛⎫=- ⎪ ⎪⎝⎭，30,2OC ⎛⎫= ⎪ ⎪⎝⎭，13,36OD ⎛=- ⎝⎭，所以13,3OA OB OC OD ⎛+++=- ⎝⎭，所以23OA OB OC OD +++=，故C 错误； 对于D ，(3BC =-，123,33ED ⎛⎫=- ⎪ ⎪⎝⎭，所以ED 在BC 方向上的投影为127326BC ED BC+⋅==，故D 正确.故选：BD. 【点睛】关键点点睛：建立合理的平面直角坐标系是解题关键.4．如图所示，设Ox ，Oy 是平面内相交成2πθθ⎛⎫≠⎪⎝⎭角的两条数轴，1e ，2e 分别是与x ，y 轴正方向同向的单位向量，则称平面坐标系xOy 为θ反射坐标系中，若12OM xe ye =+，则把有序数对(),x y 叫做向量OM 的反射坐标，记为(),OM x y =.在23πθ=的反射坐标系中，()1,2a =，()2,1b =-.则下列结论中，正确的是（ ）A ．()1,3a b -=-B ．5a =C ．a b ⊥D ．a 在b 上的投影为3714-【答案】AD 【分析】123a b e e -=-+，则()1,3a b -=-，故A 正确；3a =，故B 错误；32a b ⋅=-，故C 错误；由于a 在b 上的投影为3372147a b b-⋅==-，故D 正确.【详解】()()121212223a b e e e e e e -=+--=-+，则()1,3a b -=-，故A 正确；()2122254cos33a e e π=+=+=B 错误；()()22121211223222322a b e e e e e e e e ⋅=+⋅-=+⋅-=-，故C 错误； 由于()22227b e e =-=a 在b 上的投影为3372147a b b-⋅==-，故D 正确。
中考英语单选错题集
中考英语单选错题集1. What do you think ____ solve the problem?A. you can doB. can you doC. you can do toD. can you do to2. In the past he often made his sister ____, but now he is often made ____ by his sister.A. to cry; to cryB. cry; cryC. to cry; cryD. cry; to cry3. The teacher told us that the sun ____ in the east.A. risesB. roseC. raisesD. raised4. He lives in a village ____ there are a lot of trees.A. thereB. whereC. thatD. which5. He ____ Alice for ten years.A. married toB. has married toC. has marriedD. has been married to6. We need fifteen more people ____ our team to do the job.A. butB. exceptC. as wellD. besides7. They won't allow us ____ at this beach.A. swimmingB. to swimC. swamD. swim8. Is this factory ____ you visited last week?A. thatB. whereC. the oneD. in which9. The reason ____ he was absent from the meeting was ____ his car broke down on the way.A. that; becauseB. why; thatC. that; thatD. for; that10. Is the river ____ through that town very large?A. which flowsB. flowsC. that flowingD. whose flows11. The teacher told me that the students I wanted to see were seen ____ football on the playground just now.A. playingB. to be playingC. playD. to play12. The red rose is the only one ____ I real like.A. whichB. whoC. thatD. whom13. All the apples ____ fell down were eaten by the pigs.A. thoseB. whichC. whatD. that14. Don`t forget the day ____ you were received into the Y outh League.A. whenB. thatC. at whichD. where15. I prefer ____ at home to ____ outside.A. staying, playingB. to stay, playC. staying, playD. to stay, playing16. The box is ____ what I saw in the shop.A. same asB. the same likeC. the same thatD. the same as17. The pen ____ she writes letters is broken.A. whichB. thatC. with whichD. by which18. Would you like to ____ us in our discussion.A. take part inB. joinC. taking part inD. joining19. I'm sure the red team will ____ the game.A. winB. beatC. defeatD. succeed20. Ahead of me I saw a woman ____ I thought was my aunt.A. whoB. whomC. of whomD. whose21. ____ your help, everything in the room is in good order now.A. SinceB. BecauseC. thanks forD. Thanks to22. He is known to the world and has a lot of friends ____.A. in and out of abroadB. at home and abroadC. at home and at abroadD. in home and out of abroad23. --Are you going there with them? --If you go, ____.A. I also goB. so do IC. so I willD. so will I24. --The flower is beautiful. --____.A. So is itB. So it isC. It is soD. So it is25. The number of people invited ____ fifty, but a number of them ____ absent for different reasons.A. were; wasB. was; wasC. was; wereD. were; were26. We haven`t had any success ____.A. before longB. so longC. by farD. so far27. Travellers ____ our country enjoy the beautiful sights in Beijing, Hangzhou and many other places of interest.A. forB. toC. tillD. by28. If a man ____ succeed, he must work as hard as he can.A. willB. shouldC. is going toD. is to29. --I am sorry I didn`t do a good job.--Never mind. ____ you have tried your best.A. Above allB. In allC. At allD. After all30. The best way to make sure that you can keep fit is to ____ healthy eating habits.A. findB. createC. developD. prepare31. We have spent ____ money on English books.A. a great deal ofB. a good manyC. a plenty ofD. a number of32. ____ met, it won`t be easily forgotten.A. If onlyB. When ifC. OnceD. Once you were33. The differences ____ these two pictures ____ colour are easy to see.A. in, ofB. from, ofC. between, inD. of, in34. Y ou should put ____ “s”at the end of this word.A. aB. /C. anD. the35. --What`s ____ population of China?--China has ____ population of 1.2 billion.A. a; theB. the; aC. /; /D. the; the36. It`s ____ here. We can`t work long hours here.A. very much coldB. much coldC. much too coldD. too much cold37. ____ terrible weather we`ve been having these days!A. How aB. What aC. HowD. What38. --Have you decided when ____?--Y es, tomorrow morning.A. will you leaveB. to be leavingC. are you leavingD. to leave39. The song ____ My heart will go on is liked by the young people.A. callB. callingC. calledD. to call40. Train services are now back to ____ after three days of typhoon.A. usualB. commonC. ordinaryD. normal41. He is the best ____ English in our class.A. atB. inC. forD. to42. The policeman caught hold of the thief and hit him ____ the head.A. in theB. on hisC. on theD. in his43. Did John hit Bob ____ eye?A. in theB. on theC. in hisD. on his44. There is ____ interesting ____ today`s newspaper.A. anything …inB. nothing …inC. something …onD. nothing …on45. Has your teacher given you any advice ____ your study?A. inB. toC. onD. with46. It`s bad manners to laugh ____ others when they are ____ trouble.A. at, inB. over, atC. with, onD. to, with47. Betty doesn`t have enough money to buy that coat. It`s very ____.The price is too ____.A. high, highB. expensive, expensiveC. expensive, highD. high, expensive48. This kind of glasses manufactured by experienced craftsmen ____ comfortably.A. wearingB. wearC. wearsD. is worn49. The diamond is ____.A. very valuableB. of great valueC. great valueD. A or B50. Behind the dancer there was a woman ____ a large diamond ring.A. carryingB. dressingC. wearingD. having51. The young teacher who has a ____ face can make his classes ____ and interesting.A. lovely, livelyB. lovely, lovelyC. likely, friendlyD. uglily, lively52 They were still ____ their friends after their child`s long illness.A. in debt toB. in the debt toC. in debt withD. in the debt with53. ____, my brother passed the exam.A. To my great joyB. To my great surprisedC. With my joyD. With my surprise54. I am all tears, ____, I am listening to you with all attention.A. in another wordsB. in the other wordsC. with other wordsD. in other words55. He started early ____ he could get there before nine.A. in order thatB. becauseC. so as toD. in order to56. As you know, whether the person will be elected president is matter of ____ interest.A. generalB. commonC. ordinaryD. mostly57. I ____ by his story that he made up.A. was taken onB. was taken outC. was taken inD. am taken in58. He didn`t go into detail on the subject, he spoke ____.A. in generalB. in particularC. in commonD. in short59. We designed the machine ____ the purpose ____ production.A. for, of increasingB. with, of increasingC. for, to increaseD. A or B60. Hospital doctors don`t go out very often as their work ____ all their time.A. takes awayB. takes inC. takes overD. takes up61. We offered him our congratulation ____ his passing the entrance exam.A. onB. forC. withD. at62. My mother ____ classical music while I am ____ rock music.A. is fond of, inB. likes, likeC. is interested in; intoD. interests; enjoy63. We each ____ strong points and each of us on the other hand ____ weak points.A. have, haveB. has, haveC. has, hasD. have, has64. He is one of the students who, I am sure, always do ____ best.A. hisB. one`sC. myD. their65. The police ____ determined to bring back the missing boy when his family ____almost given hope.A. is, hasB. are, haveC. are, hasD. is, have66. More than one girl ____ late for class this morning.A. areB. isC. wasD. were67. Many a student ____ in the exam.A. have failedB. had been failedC. has failedD. will be failed68. What he says and what he does ____.A. is not agreeB. are not agreeC. does not agreeD. do not agree69 Not only politics but also English is important. In other words, ____ is important.A. English, as well as politicsB. English as well as politicsC. both politics and EnglishD. politics, as well as English70. It was at the very beginning ____ Mr.Smith made a decision ____ we should send for a doctor.A. what, thatB. that, whichC. which, thatD. that, that71. On the way back home from the ball, she suddenly found her necklace ____.A. missedB. losingC. goneD. be stolen72. He didn't go to the party not ____ the time but ____ he was ill.A. because of, becauseB. because, becauseC. because, because ofD. because of, because of73. The teacher gave me a piece of paper ____.A. to write onB. to be written onC. to write inD. to be written74. I can`t believe he could jump ____ high.A. very muchB. suchC. thatD. this75. --The boys are not doing a good job at all, are they? --____.A. I guess not soB. I don`t guess soC. I don`t guessD. I guess not76. The magazine is ____ reading, so he advised me ____ it.A. well worth; to buyB. very worth; buyingC. worthing, buyingD. worthy, to buy77. She is on a special ____ to lose ____ weight.A. food; herB. food; / D. diet; her D. diet; /78. Jenny ____ a rich man. She has ____ him for 5 years.A. married with; married withB. married; marriedC. married to; been marriedD. married; been married to79. I am ____ hungry. Give me ____ of milk.A. a bit; a littleB. not a little; a bitC. little; a litD. not a little; a little80. A good friend is someone ____ makes you ____.A. which; happyB. who; happilyC. who; happyD. whose; happily81. He was about ____ when suddenly the telephone rang.A. to leaveB. to startingC. leavingD. setting off82. This task is ____ difficult for us. We need ____ people.A. much too; another threeB. too much; other threeC. much too; more threeD. too much; three more83. He seems to ____ to Jane. He knows her well.A. have been introducedB. be introducedC. have introducedD. introduced84. This is a film ____ Spielberg used real actors instead of stunt men.A. whichB. whoseC. in whichD. of which85. He ____ much of his success and happiness ____ his wife and children.A. thanks; toB. owes; toC. owns; toD. thinks; highly of86. He will never forget the days ____ he spent with you in Japan.A. whenB. thatC. on whichD. in which87. Which sentence is incorrect?A. I feel interested in classical musicB. I take interest in classical musicC. I am not into classical musicD. I don`t fond of classical music88. No one likes ____ in ____ public.A. to be laughed at; theB. laughing at; theC. being laughed at; /D. to be laughing at; /89. We are considering ____ a sports meet next month.A to holdB holdingC to be heldD as holding90. Which sentence is incorrect?A. He devoted himself to the work of children`s health care.B. He is devoted to his work.C. He devoted all his life to work hard in people`s interests.D. He is determined to make more money for his family.91. He doesn`t like classical music and ____ I.A. so doB. nor doC. or doD. nor am92. Friends should ____ happiness and sorrow ____ each other.A. share, withB. solve, withC. share, fromD. share, to93. --I missed the first part of the film .It was really a pity.--Y ou ____ home half an hour earlier.A. should have leftB. must have leftC. should leaveD. must leave94. The storm died away at last with the golden waves ____ the shore in peace.A. beatenB. beatC. to beatD. beating95. The whites are ____ holiday ,but I don`t know where they have gone ____ their holidays.A. in, forB. on, forC. for, inD. at, on96. The river ____ are covered with trees is very long.A. which banksB. of which banksC. whose the banksD. the banks of which97. She likes to use words ____ clear to her.A. of which the meaningB. of which meaningC. whose of meaningD. meaning of which98. The price of this washing machine has been increased ____ 15%.A. upB. toC. byD. from99. ____ someone`s health, you raise your glass.A. Drink toB. To drink toC. If you drinkD. If drink to100. Please ____ me about the interview ____ I forget.A. remind; in caseB. remember; in caseC. remember, in case ofD. remind of; in case of参考答案KEYS：1－5 C D A B D 6 -10 D B C B A 11-15 A C D A A16-20 D C B A A 21-25 D B D B C 26-30 D B D D C 31-35 A C C C B 36-40 C D D C D 41-45 B C A B C 46-50 A C C D C 51-55 A A A D A56-60 A C A D D 61-65 A C D D B 66-70 C C D B D 71-75 C A A C D 76-80 A D D B C 81-85 A A A C B 86-90 B D C B C 91-95 B A A D B 96-100 D A C B A (From:嘉兴英语网)。
高中英语语法单选题及答案
高中英语语法单选题及答案【0001】 The headmaster hurried to the concert hall only _________ the speaker_______.【译文】校长匆匆来到音乐大厅，结果发现演讲者早已走了。
A. to find; leftB. to find; goneC. finding; leftD. finding; gone【答案及简析】 B。
不定式表结果时,常指出人意料的结果。
第二个考察点是find+宾语+形容词补语，表状态。
【0002】―I failed again. I wish I _________ harder.?―But you _________.【译文】――我又失败了。
我真该努力学习。
――但是你没有哇。
A. had worked; hadn’tB. worked; don’tC. had worked; didn’tD. worked; did n’t【答案及简析】 C。
第一空表达与过去事实相反的愿望,所以用过去完成时态表虚拟语气。
第二空说明过去的事实,用一般过去时态。
【0003】―Why not go out for a walk before breakfast? ―Oh，yes._________ is my favorite time of day.【译文】――早饭前你为什么不出去散步呢? ――嗯。
是的。
那是我一天最美好的时光。
A. In the early morningB. Early morningC. The early of morningD. The early morning that【答案及简析】 B。
空处缺少一主语,而非状语。
【0004】 It was not until liberation that _________ to his hometown.【译文】直到解放他才回到家乡。
A. did he returnB. was he returnedC. he did returnD. he returned【答案及简析】 D。
言语理解与表达错题集
言语理解与表达1我在农村________了我的童年。
填入划横线部分最恰当的一项是（）。
A. 度过B. 渡过C. 经历D. 回顾“度过”主要是带时间性的经过，“渡过”主要指的是由此岸到彼岸，是空间的经过，首先是涉水的空间转移答案为A2.从社会主义公有制已经显示的优越性和这种优越性还未充分发挥，可以看出，目前许多国有企业存在的某些弊端，______公有制自身的问题，______其表现的具体形式问题，是经济体制问题。
填入横线处词语最恰当的一项是（）。
A. 既是也是B. 确定不是C. 不是而是D. 不是也不是根据对文意的理解可以发现“公有制自身问题”和“其表现的具体形式问题”是并列关系，所以正确答案应该是D项文明的进展并不完全像是一股奔腾直前、日趋佳境的巨流。
如果我们用一种相当大的比例尺把它绘制成图，也许会具有上述外观。
但这种广泛的看法往往会_____细节，而我们对这一过程的全部理解却必须______于这种细节。
假如我们从绵延几万年的全部人类历史来看，新时代的出现往往是相当突然的。
依次填入划横线部分最恰当的一项是：A. 淡化超越B. 忽视定位C. 模糊着眼D. 无视立足逻辑填空做题两步骤：辨析词义，结合语境。
第一空前面说形成了一种画面，画面只能模糊或者清晰，第二空知道，我们要以细节为出发点和落脚点，因此排除A,B第一空又说广泛的看法往往——细节，说明我们把细节宽泛化了，但是细节是真实存在的，不能无视，因此本题答案选择C.( 单选题)但丁说过：“道德常常能够填补人们智慧的缺陷，而智慧却不能同样填补道德的缺陷。
对这句话理解无误的是（）。
A. 在某种意义上，道德比智慧对人更重要B. 一个人可以缺乏智慧，但是不能缺乏道德C. 智慧的缺陷可以填补，而道德的缺陷不可填补D. 道德的缺陷，常可带来智慧上无可弥补的缺陷从但丁的话可知，既然道德能够弥补智慧的缺陷，而智慧不能填补道德的缺陷，那么道德对人来说比智慧更重要，只有A项符合。
音乐欣赏错题集
专业课《音乐欣赏》错题集单选题----------------------------------------------------------------------------------------------------1.谁是“交响音乐之父”（）。
正确答案：B.海顿2.《索尔维格之歌》的前半部分属于哪种调式，且色彩暗淡（）。
正确答案：C.小调式3.下列哪一部作品是商调式的谱例（）。
正确答案：C.《绣荷包》多选题----------------------------------------------------------------------------------------------------2.连音节奏型的基本特征是对正常节拍组织样式的突破，请问其主要特点有哪些（）。
正确答案：A.异常性 B.突然性3.如果将高潮部分分解，它应该包括什么（）。
正确答案：A.上升 B.到达 C.爆发 D.下降4.下列关于乐句的表述中，正确的有哪些（）。
正确答案：B.末尾是长时值音 C.在无长时值音的情况下，通常靠“换气”的节奏感“断句”来加以区分 D.两个以上的乐句即构成一个乐段6.下列关于《阿莱城姑娘》变奏3的论述正确的有哪些（）。
正确答案：A.主题又回到弦乐声部 C.主题改造为大调式 D.主题由大提琴奏出判断题----------------------------------------------------------------------------------------------------2.装饰变奏会改变旋律框架。
正确答案：错5.《天鹅湖·场景》音乐开始于由弦乐器奏出的弱起转强的颤弓音响，气氛紧张。
正确答案：错7.“虽然胜利了，仍然不能失掉警惕，那些躲在阴暗角落里的反动的东西说不定还要再来的！”这句话出自“贝五”第三乐章。
正确答案：错。
执法证错题集
执法证错题集⾏政强制法1.单选题1.对“限制公民⼈⾝⾃由”与“冻结存款、汇款”，只能法律设定，不能由⾏政法规和地⽅性法规设定，这⼀要求在法学理论上属于（绝对法律保留）2.依照法律规定冻结存款、汇款的，作出决定的⾏政机关应当在（3）⽇内向当事⼈交付冻结决定书。
3.⾃冻结存款、汇款之⽇起（30）⽇内，⾏政机关应当作出处理决定或者作出解除冻结决定；情况复杂的，经⾏政机关负责⼈批准，可以延长，但是延长期限不得超过（30）⽇。
法律另有规定的除外。
4.经⼈民法院院长批准的⽴即执⾏申请，⼈民法院应当⾃作出执⾏裁定之⽇起（5）内执⾏。
5.法律规定以外的⾏政机关或者组织要求划拨当事⼈存款、汇款的，⾦融机构（应当拒绝）6.关于⾦钱给付义务的执⾏，说法错误的是（⾦融机构接到⾏政机关依法作出划拨存款、汇款的决定后，应当在⼀定期限内划拨）7.公民、法⼈或者其他组织对⾏政机关实施⾏政强制，有权依法申请⾏政复议或者提起⾏政诉讼，体现了下列哪个原则（权利救济原则）8.⾏政机关解除查封、扣押(应当⽴即退还财物)；9.⾦融机构接到⾏政机关依法作出的冻结通知书后，（应当⽴即予以冻结）10.在作出裁定前，⼈民法院发现有哪些情形的，可以听取被执⾏⼈和⾏政机关的意见？A：明显缺乏事实根据的11.由两名以上⾏政执法⼈员实施并表明⾝份”体现了下列哪项制度的要求（公开制度）12.代履⾏完毕，⾏政机关到场监督的⼯作⼈员、代履⾏⼈和（当事⼈或见证⼈）应当在执⾏⽂书上签名或者盖章。
13.下列哪项属于⾏政强制执⾏的⽅式（加处罚款）14.在（催告）期间，对有证据证明有转移或者隐匿财物迹象的，⾏政机关可以作出⽴即强制执⾏决定。
15.在执⾏中或者执⾏完毕后，据以执⾏的⾏政决定被撤销、变更，或者执⾏错误的，应当恢复原状或者（退还财物）16.. 关于强制执⾏，下列说法错误的是（在催告期间，有转移或者隐匿财物迹象的，⾏政机关可以作出⽴即强制执⾏决定）17.下列哪项不属于⾏政强制措施的种类（划拨存款、汇款）18.⾏政机关对查封、扣押的物品检测、检验、检疫或者技术鉴定的费⽤ (由⾏政机关承担)19.⾏政机关逾期未作出处理决定或者解除冻结决定的，⾦融机构（应当⾃冻结期满之⽇起解除冻结)20.代履⾏（三⽇）前，催告当事⼈履⾏，当事⼈履⾏的，停⽌代履⾏。
高压电工证考试错题集一
理论试题共1326题单选题：677题判断题：649题错题：237题高压错题（一）高老师整理1、绝缘电阻可以用接地电阻测量仪来测量。
错：（不可以，接地电阻测量仪是用来测量接地电阻的）2、用数字万用表测量直流电压时，极性接反会损坏数字万用表。
错：（指针式万用表，指针接反时会损坏）3、三相电度表应按正相序接线，经电流互感器接线者极性错误也不影响测量结果。
错：（会造成测量误差，有时连表都不会转）4、钳表是用电流互感器的原理制造的，所以只能用来测量交流电流。
错：（万用表有的功能它也都有）5、钳表铁芯内的剩磁只影响大电流测量，而对小电流测量无影响。
错：（都影响）6、万用表测量电压时是通过改变并联附加电阻的阻值来改变测量不同电压的量程。
错：（串联）7、摇表多采用手摇交流发电机作为电源。
错：（直流发动机）8、使用绝缘棒，可以不用戴绝缘手套、穿绝缘靴。
错：（必须）9、为确保安全，户外变电装置的围墙高度一般应不低于3米。
错：（2.5米）10、在电气施工中,必须遵守国家有关安全的规章制度安装电气线路时应根据实际情况以方便使用者的原则来安装。
错：（严格按国家规定）11、安全色标中“黑色"表示强制执行。
错：（没有强制执行的颜色）12、电工刀可以用于带电作业。
错：（不可以）13、临时遮栏设置在可能发生人体接近带电体的巡视通道和检修设备的周围。
错：（巡视通道不能安装）错：（有关系。
在易燃易爆场所作业的移动电气设备就要选择防爆性能的）15、工作票是准许在电气设备上工作的书面命令，是执行保证安全技术措施的书面依据，一般有三种格式。
错：（二种）16、电容器正常运行时，可在1.3倍额定电压下长期运行。
错：（不可以）17、真空断路器是利用空气作绝缘介质和灭弧介质的断路器。
错：（真空）18、当电容器内部设有放电电阻时，电容器组可不设放电装置。
错：（仍应设合格的）19、高压熔断器在110kV及以上供电网中被广泛应用。
错：（电压低于35KV）20、正常情况下，高压电容器组的投入或退出运行与系统功率因素无关。
高三物理错题集
1【知识点标签】相互作用与牛顿运动规律 【陷阱标签】推导计算 【题干】 如图，一个质量为m=10 kg 的物体A 放在倾角的斜面体上，给A 以F1=100N 沿斜面向上的力，A 恰好沿斜面匀速上升，若给A 以F2=20N 沿斜面向下的力，A 刚好沿斜面匀速下滑。
现将此斜面变为水平面，欲使A 水平匀速运动，则要对A 沿水平方向施多大F ？【错解/易错点】易忽略了的值可以具体计算出来。
【正解】解：当A 恰好能匀速上升时，有：100100sin 100cos θμθ=⋅+⋅⋅ ①当A 刚好匀速下滑时，有：20100sin 100cos θμθ+⋅=⋅⋅ ②联合①②，得：sin 0.4cos 0.6θμθ=⎧⎨⋅=⎩，所以3tan 2μθ=。
而2sin sin 221tan cos 211sin θθθθθ===-，所以32121μ=。
若使A 水平匀速运动，则3002121F fG μ===【点评】本题主要考察了匀速运动时受力平衡的分析以及计算能力。
2【知识点标签】相互作用与牛顿运动规律 【陷阱标签】审题不细 【题干】如图，利用一块粗糙木板，可以将一个木箱推上一辆载重汽车，如果沿木板方向施推力，至少需要推力为F1，假设木板与水平方向夹角为,木箱质量为m ，货箱与木板间动摩擦因数为。
现用一水平力推它，至少需F2。
求F1:F2.【错解/易错点】误认为以F 2的力在水平面上推动木箱。
【正解】解：沿木板方向推动木箱时：1cos sin F mg mg μθθ=+ ① 用水平力推动木箱时：22cos (cos sin )sin F mg F mg θμθθθ=++ ② 所以：2cos sin cos sin mg mg F μθθθμθ+=-所以12:cos sin F F θμθ=-【点评】本题主要考察了牛顿运动定律的应用以及审题能力。
3【知识点标签】相互作用与牛顿运动规律 【陷阱标签】复杂推理 【题干】如图，重为G1的三角形滑块置于水平面上，滑块与地面间的动摩擦因数为。
高三数学下学期多选题单元 易错题同步练习试题
一、函数的概念与基本初等函数多选题1．已知函数()()124,01,21,1,x x f x af x x ⎧--≤≤⎪=⎨⎪->⎩其中a R ∈，下列关于函数()f x 的判断正确的为（ ） A ．当2a =时，342f ⎛⎫=⎪⎝⎭B ．当1a <时，函数()f x 的值域[]22-,C ．当2a =且[]()*1,x n n n ∈-∈N时，()1212242n n f x x --⎛⎫=-- ⎪⎝⎭D ．当0a >时，不等式()122x f x a -≤在[)0,+∞上恒成立 【答案】AC 【分析】对于A 选项，直接代入计算即可；对于B 选项，由题得当(]*,1,x m m m N ∈+∈时，()()m f x a f x m =-，进而得当(]*,1,x m m m N ∈+∈时，()()2,2f x ∈-，故()f x 的值域(]2,2-；对于C 选项，结合B 选项得当2a =且[]()*1,x n n n ∈-∈N时，()()121n f x f x n -=-+进而得解析式；对于D 选项，取特殊值即可得答案.【详解】解：对于A 选项，当2a =时，3111222442222f f ⎛⎫⎛⎫⎛⎫==--= ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭，故A 选项正确； 对于B 选项，由于当01x ≤≤，函数的值域为[]0,2，所以当(]*,1,x m m m N ∈+∈时，()()m f x a f x m =-，由于(]0,1x m -∈，所以()[]0,2f x m -∈，因为1a <，所以()1,1m a ∈-，所以当(]*,1,x m m m N ∈+∈时，()()2,2f x ∈-，综上，当1a <时，函数()f x 的值域(]2,2-，故B 选项错误；对于C 选项，由B 选项得当(]*,1,x m m m N ∈+∈时，()()mf x a f x m =-，故当2a =且[]()*1,x n n n ∈-∈N时，()()1112122412n n f x f x n x n --⎛⎫=-+=--+- ⎪⎝⎭1112122422422n n n x n x --⎛⎫⎛-⎫=--+=-- ⎪ ⎪⎝⎭⎝⎭，故C 选项正确；对于D 选项，取812a =，34x =，则331241442f ⎛⎫=--= ⎪⎝⎭，122x a-=()311142482488111222222222---⎛⎫⎛⎫==⨯=⨯= ⎪ ⎪⎝⎭⎝⎭，不满足式()122x f x a -≤，故D选项错误. 故选：AC. 【点睛】本题考查函数的综合应用，考查分析能力与运算求解能力，是难题.本题解题的关键在于根据题意得当(]*,1,x m m m N ∈+∈时，()()mf x a f x m =-，且当01x ≤≤，函数的值域为[]0,2，进而利用函数平移与伸缩变换即可求解.2．已知函数()()2214sin 2xxex f x e -=+，则下列说法正确的是（ ）A ．函数()y f x =是偶函数，且在(),-∞+∞上不单调B ．函数()y f x '=是奇函数，且在(),-∞+∞上不单调递增C ．函数()y f x =在π,02⎛⎫- ⎪⎝⎭上单调递增D ．对任意m ∈R ，都有()()f m f m =，且()0f m ≥【答案】AD 【分析】由函数的奇偶性以及函数的单调性即可判断A 、B 、C 、D. 【详解】 解：对A ，()()222114sin =2cos 2xx xx e x e f x x e e-+=+-，定义域为R ，关于原点对称，()2211=2cos()2cos()()x x x xe ef x x x f x e e --++---=-=，()y f x ∴=是偶函数，其图像关于y 轴对称，()f x ∴在(),-∞+∞上不单调，故A 正确；对B ，1()2sin xxf x e x e '=-+， 11()2sin()=(2sin )()x xx xf x e x e x f x e e --''-=-+---+=-， ()f x '∴是奇函数，令1()2sin xxg x e x e =-+， 则1()+2cos 2+2cos 0xxg x e x x e '=+≥≥， ()f x '∴在(),-∞+∞上单调递增，故B 错误；对C ，1()2sin x x f x e x e'=-+，且()'f x 在(),-∞+∞上单调递增， 又(0)0f '=，π,02x ⎛⎫∴∈- ⎪⎝⎭时，()0f x '<，()y f x ∴=在π,02⎛⎫- ⎪⎝⎭上单调递减，故C 错误；对D ，()y f x =是偶函数，且在(0,)+∞上单调递增，()()f m f m ∴=，且()(0)0f m f ≥=，故D 正确.故选：AD. 【点睛】用导数求函数的单调区间或判断函数的单调性问题时应注意如下几方面： (1)在利用导数讨论函数的单调区间时，首先要确定函数的定义域； (2)不能随意将函数的2个独立的单调递增（或递减）区间写成并集形式；(3)利用导数解决含参函数的单调性问题时，一般将其转化为不等式恒成立问题，解题过程中要注意分类讨论和数形结合思想的应用.3．已知函数()()()52log 1,122,1x x f x x x ⎧-<⎪=⎨--+≥⎪⎩，则方程12f x a x ⎛⎫+-= ⎪⎝⎭的实根个数可能为（ ） A ．8 B ．7C ．6D ．5【答案】ABC 【分析】以()1f x =的特殊情形为突破口，解出1x =或3或45或4-，将12x x+-看作整体，利用换元的思想进一步讨论即可. 【详解】 由基本不等式可得120x x +-≥或124x x+-≤-，作出函数()()()52log 1,122,1x x f x x x ⎧-<⎪=⎨--+≥⎪⎩的图像，如下：①当2a >时，1224x x +-≤-或1021x x<+-<， 故方程12f x a x ⎛⎫+-= ⎪⎝⎭的实数根个数为4； ②当2a =时，1224x x +-=-或1021x x <+-<或122x x+-=， 故方程12f x a x ⎛⎫+-= ⎪⎝⎭的实数根个数为6； ③当12a <<时，12424x x -<+-<-或1021x x <+-<或1122x x<+-< 或1223x x<+-<， 故方程12f x a x ⎛⎫+-= ⎪⎝⎭的实数根个数为8； ④当1a =时，124x x +-=-或1021x x <+-<或121x x +-=或123x x+-=，故方程12f x a x ⎛⎫+-= ⎪⎝⎭的实数根个数为7； ⑤当01a <<时，1420x x -<+-<或1324x x<+-<， 故方程12f x a x ⎛⎫+-= ⎪⎝⎭的实数根个数为2； ⑥当0a =时，120x x +-=或1324x x<+-<， 故方程12f x a x ⎛⎫+-= ⎪⎝⎭的实数根个数为3； ⑦当0a <时，123x x+->， 故方程12f x a x ⎛⎫+-= ⎪⎝⎭的实数根个数为2；【点睛】本题考查了求零点的个数，考查了数形结合的思想以及分类讨论的思想，属于难题.4．已知函数()221,0log1,0x x f x x x ⎧+≤⎪=⎨->⎪⎩，则方程()()22210f x f x a -+-=的根的个数可能为（ ） A ．2 B ．6 C ．5 D ．4【答案】ACD 【分析】先画出()f x 的图象，再讨论方程()()22210f x f x a -+-=的根，求得()f x 的范围，再数形结合，得到答案. 【详解】画出()f x 的图象如图所示：令()t f x =，则22210t t a -+-=，则24(2)a ∆=-，当0∆=，即22a =时，1t =，此时()1f x =，由图1y =与()y f x =的图象有两个交点，即方程()()22210f x f x a -+-=的根的个数为2个，A 正确；当>0∆时，即22a <时，212t a =-，则2022a <-≤故211212a <+-≤212121a ≤-<，当212t a =-2()12f x a =--(1,1)∈-，则x 有2解， 当212t a =-t (1,2]∈，则x 有3解；若t (2,12]∈+，则x 有2解，故方程()()22210f x f x a -+-=的根的个数为5个或4个，CD 正确；故选：ACD 【点睛】本题考查了函数的根的个数问题，函数图象的画法，考查了分类讨论思想和数形结合思想，难度较大.5．已知定义域为R 的奇函数()f x ，满足22,2()2322,02x f x x x x x ⎧>⎪=-⎨⎪-+<≤⎩，下列叙述正确的A ．存在实数k ，使关于x 的方程()f x kx =有7个不相等的实数根B ．当1211x x -<<<时，恒有12()()f x f x >C ．若当(0,]x a ∈时，()f x 的最小值为1，则5[1,]2a∈ D ．若关于x 的方程3()2f x =和()f x m =的所有实数根之和为零，则32m =- 【答案】AC 【分析】根据奇函数()()f x f x -=-，利用已知定义域的解析式，可得到对称区间上的函数解析式，然后结合函数的图象分析各选项的正误，即可确定答案 【详解】函数是奇函数，故()f x 在R 上的解析式为：222,22322,20()0,022,022,223x x x x x f x x x x x x x ⎧<-⎪+⎪----≤<⎪⎪==⎨⎪-+<≤⎪⎪>⎪-⎩绘制该函数的图象如所示：对A ：如下图所示直线1l 与该函数有7个交点，故A 正确；对B ：当1211x x -<<<时，函数不是减函数，故B 错误； 对C ：如下图直线2:1l y =，与函数图交于5(1,1),(,1)2， 故当()f x 的最小值为1时有5[1,]2a ∈，故C 正确对D ：3()2f x =时，函数的零点有136x =、21x =+、21x =-； 若使得其与()f x m =的所有零点之和为0， 则32m =-或38m =-，如图直线4l 、5l ，故D 错误故选：AC 【点睛】本题考查了分段函数的图象，根据奇函数确定对称区间上函数的解析式，进而根据函数的图象分析命题是否成立6．已知函数()()23,03,0x x x f x f x x ⎧--<⎪=⎨-≥⎪⎩，以下结论正确的是（ ）A ．()f x 在区间[]4,6上是增函数 B ．()()220204f f -+=C ．若函数()y f x b =-在(),6-∞上有6个零点()1,2,3,4,5,6i x i =，则619ii x==∑D ．若方程()1f x kx =+恰有3个实根，则{}11,13k ⎛⎫∈-- ⎪⎝⎭【答案】BCD 【分析】根据()f x 在[2-，0]上的单调性判断A ，根据(2020)(2)f f =-判断B ，根据图象的对称性判断C ，根据直线1y kx =+与()y f x =的图象有3个交点判断D ． 【详解】解：由题意可知当3x -时，()f x 是以3为周期的函数， 故()f x 在[4，6]上的单调性与()f x 在[2-，0]上的单调性相同， 而当0x <时，239()()24f x x =-++，()f x ∴在[2-，0]上不单调，故A 错误；又(2020)(2)2f f =-=，故(2)(2020)4f f -+=，故B 正确； 作出()y f x =的函数图象如图所示：由于()y f x b =-在(,6)-∞上有6个零点，故直线y b =与()y f x =在(,6)-∞上有6个交点，不妨设1i i x x +<，1i =，2，3，4，5， 由图象可知1x ，2x 关于直线32x =-对称，3x ，4x 关于直线32x =对称，5x ，6x 关于直线92x=对称，∴613392229222iix==-⨯+⨯+⨯=∑，故C正确；若直线1y kx=+经过点(3,0)，则13k=-，若直线1y kx=+与23(0)y x x x=--<相切，则消元可得：2(3)10x k x+++=，令0∆=可得2(3)40k+-=，解得1k=-或5k=-，当1k=-时，1x=-，当5k=-时，1x=（舍)，故1k=-．若直线1y kx=+与()y f x=在(0,3)上的图象相切，由对称性可得1k=．因为方程()1f x kx=+恰有3个实根，故直线1y kx=+与()y f x=的图象有3个交点，113k∴-<<-或1k=，故D正确．故选：BCD．【点睛】本题考查了函数零点与函数图象的关系，考查函数周期性、对称性的应用，属于中档题．7．设函数g(x)=sinωx(ω＞0)向左平移5πω个单位长度得到函数f(x)，已知f(x)在[0，2π]上有且只有5个零点，则下列结论正确的是（）A．f(x)的图象关于直线2xπ=对称B．f(x)在(0，2π)上有且只有3个极大值点，f(x)在(0，2π)上有且只有2个极小值点C．f(x)在(0,)10π上单调递增D．ω的取值范围是[1229,510)【答案】CD【分析】利用正弦函数的对称轴可知，A不正确；由图可知()f x在(0,2)π上还可能有3个极小值点，B 不正确；由2A B x x π≤<解得的结果可知，D 正确；根据()f x 在3(0,)10πω上递增，且31010ππω<，可知C 正确. 【详解】依题意得()()5f x g x πω=+sin[()]5x πωω=+sin()5x πω=+， 2T πω=，如图：对于A ，令52x k ππωπ+=+，k Z ∈，得310k x ππωω=+，k Z ∈，所以()f x 的图象关于直线310k x ππωω=+(k Z ∈)对称，故A 不正确； 对于B ，根据图象可知，2A B x x π≤<，()f x 在(0,2)π有3个极大值点，()f x 在(0,2)π有2个或3个极小值点，故B 不正确， 对于D ，因为5522452525A x T ππππωωωω=-+=-+⨯=，22933555B x T ππππωωωω=-+=-+⨯=，所以2429255πππωω≤<，解得1229510ω≤<，所以D 正确；对于C ，因为1123545410T ππππωωωω-+=-+⨯=，由图可知()f x 在3(0,)10πω上递增，因为29310ω<<，所以33(1)0101010πππωω-=-<，所以()f x 在(0,)10π上单调递增，故C 正确；故选：CD. 【点睛】本题考查了三角函数的相位变换，考查了正弦函数的对称轴和单调性和周期性，考查了极值点的概念，考查了函数的零点，考查了数形结合思想，属于中档题.8．设函数cos2cos2()22x x f x -=-，则（ ） A ．()f x 在0,2π⎛⎫⎪⎝⎭单调递增B ．()f x 的值域为33,22⎡⎤-⎢⎥⎣⎦ C ．()f x 的一个周期为π D ．4f x π⎛⎫+ ⎪⎝⎭的图像关于点,04π⎛⎫ ⎪⎝⎭对称【答案】BC 【分析】根据余弦函数及指数函数的单调性，分析复合函数的单调区间及值域，根据周期定义检验所给周期，利用函数的对称性判断对称中心即可求解. 【详解】令cos2t x =，则12222ttt t y -=-=-，显然函数12222t t tty -=-=-为增函数，当0,2x π⎛⎫∈ ⎪⎝⎭时，cos2t x =为减函数， 根据复合函数单调性可知，()f x 在0,2π⎛⎫⎪⎝⎭单调递减， 因为cos2[1,1]t x =∈-， 所以增函数12222ttt ty -=-=-在cos2[1,1]t x =∈-时，3322y -≤≤， 即()f x 的值域为33,22⎡⎤-⎢⎥⎣⎦； 因为cos2()cos2(cos2c )os222)(2()2x x x x x x f f πππ+-+-=-=+-=，所以()f x 的一个周期为π，因为sin 2sin 2224x x f x π-⎛⎫+=- ⎪⎝⎭，令sin 2sin 22(2)xx h x --=， 设(,)P x y 为sin 2sin 22(2)xx h x --=上任意一点，则(,)2P x y π'--为(,)P x y 关于,04π⎛⎫⎪⎝⎭对称的点， 而sin 2(sin 2())22sin 2sin 2()22222x x x x h y x y πππ-----=-==≠--，知点(,)2P x y π'--不在函数图象上，故()h x 的图象不关于点,04π⎛⎫⎪⎝⎭对称，即4f x π⎛⎫+ ⎪⎝⎭的图像不关于点,04π⎛⎫ ⎪⎝⎭对称.故选：BC 【点睛】本题主要考查了余弦函数的性质，指数函数的性质，复合函数的单调性，考查了函数的周期性，值域，对称中心，属于难题.9．定义在R 上的函数()(),()22(2)f x x g x g x x g x =+=--+--,若()f x 在区间[1,)-+∞上为增函数,且存在20t -<<,使得(0)()0f f t ⋅<.则下列不等式一定成立的是( )A ．21(1)()2f t t f ++> B ．(2)0()f f t ->> C ．(2)(1)f t f t +>+D ．(1)()f t f t +>【答案】ABC 【分析】先由()(),()22(2)f x x g x g x x g x =+=--+--推出()f x 关于1x =-对称，然后可得出B 答案成立，对于答案ACD ，要比较函数值的大小，只需分别看自变量到对称轴的距离的大小即可 【详解】因为()(),()22(2)f x x g x g x x g x =+=--+--所以(2)2(2)2()22()()f x x g x x g x x g x x f x --=--+--=--+++=+= 所以()f x 关于1x =-对称，所以(0)(2)f f =- 又因为()f x 在区间[1,)-+∞上为增函数，20t -<< 所以(0)(2)()f f f t =-> 因为(0)()0f f t ⋅<所以()0,(2)(0)0f t f f <-=> 所以选项B 成立因为2231120224t t t ⎛⎫++-=++> ⎪⎝⎭所以21t t ++比12离对称轴远 所以21(1)()2f t t f ++>，所以选项A 成立 因为()()2232250t t t +-+=+>所以32t t +>+，所以2t +比1t +离对称轴远 所以(2)(1)f t f t +>+，即C 答案成立因为20t -<<，所以()()222123t t t +-+=+符号不定 所以2t +，1t +无法比较大小，所以(1)()f t f t +>不一定成立 所以D 答案不一定成立 故选：ABC 【点睛】本题考查的是函数的性质，由条件得出()f x 关于1x =-对称是解题的关键.10．高斯是德国著名数学家、物理学家、天文学家、大地测量学家，近代数学奠基者之一.高斯被认为是历史上最重要的数学家之一，并享有“数学王子”之称.有这样一个函数就是以他名字命名的：设x ∈R ，用[]x 表示不超过x 的最大整数，则[]()f x x =称为高斯函数，又称为取整函数.如：(2.3)2f =，( 3.3)4f -=-.则下列正确的是（ ） A ．函数()f x 是R 上单调递增函数B ．对于任意实数a b ，，都有()()()f a f b f a b +≤+ C ．函数()()g x f x ax =-（0x ≠）有3个零点，则实数a 的取值范围是34434532⎛⎤⎡⎫⋃ ⎪⎥⎢⎝⎦⎣⎭，， D ．对于任意实数x ，y ，则()()f x f y =是1x y -<成立的充分不必要条件 【答案】BCD 【分析】取反例可分析A 选项，设出a ，b 的小数部分，根据其取值范围可分析B 选项，数形结合可分析C 选项，取特殊值可分析D 选项． 【详解】解：对于A 选项，()()1 1.21f f ==，故A 错误；对于B 选项，令[]a a r =+，[](,b b q r =+q 分别为a ，b 的小数部分)， 可知[]01r a a =-<，[]01q b b =-<，[]0r q +≥， 则()[][][][][][][]()()f a b a b r q a b r q a b f a f b ⎡⎤+=+++=++++=+⎣⎦，故B 错误；对于C 选项，可知当1k x k ≤<+，k Z ∈时，则()[]f x x k ==， 可得()f x 的图象，如图所示：函数()()()0g x f x ax x =-≠有3个零点，∴函数()f x 的图象和直线y ax =有3个交点，且()0,0为()f x 和直线y ax =必过的点，由图可知，实数a 的取值范围是][3443,,4532⎛⎫⋃⎪⎝⎭，故C 正确；对于D 选项，当()()f x f y =时，即r ，q 分别为x ，y 的小数部分，可得01r ≤<，01q ≤<，[][]101x y x r y q r q -=+--=-<-=；当1x y -<时，取0.9x =-，0.09y =，可得[]1x =-，[]0y =，此时不满足()()f x f y =，故()()f x f y =是1x y -<成立的充分不必要条件，故D 正确； 故选：BCD ． 【点睛】本题考查函数新定义问题，解答的关键是理解题意，转化为分段函数问题，利用数形结合思想；二、导数及其应用多选题11．已知函数()xf x e =，()1ln22x g x =+的图象与直线y m =分别交于A 、B 两点，则（ ）A ．AB 的最小值为2ln2+B ．m ∃使得曲线()f x 在A 处的切线平行于曲线()g x 在B 处的切线C ．函数()()f x g x m -+至少存在一个零点D ．m ∃使得曲线()f x 在点A 处的切线也是曲线()g x 的切线 【答案】ABD 【分析】求出A 、B 两点的坐标，得出AB 关于m 的函数表达式，利用导数求出AB 的最小值，即可判断出A 选项的正误；解方程()12ln 2m f m g e -⎛⎫''= ⎪⎝⎭，可判断出B 选项的正误；利用导数判断函数()()y f x g x m =-+的单调性，结合极值的符号可判断出C 选项的正误；设切线与曲线()y g x =相切于点()(),C n g n ，求出两切线的方程，得出方程组，判断方程组是否有公共解，即可判断出D 选项的正误.进而得出结论. 【详解】令()xf x e m ==，得ln x m =，令()1ln22x g x m =+=，得122m x e -=，则点()ln ,A m m 、122,m B e m -⎛⎫⎪⎝⎭，如下图所示：由图象可知，122ln m AB e m -=-，其中0m >，令()122ln m h m em -=-，则()1212m h m em-'=-，则函数()y h m '=单调递增，且102h ⎛⎫'= ⎪⎝⎭，当102m <<时，0h m，当12m >时，0h m.所以，函数()122ln m h m e m -=-在10,2⎛⎫ ⎪⎝⎭上单调递减，在1,2⎛⎫+∞⎪⎝⎭上单调递增， 所以，min 112ln 2ln 222AB h ⎛⎫==-=+⎪⎝⎭，A 选项正确； ()x f x e =，()1ln 22x g x =+，则()x f x e '=，()1g x x'=，曲线()y f x =在点A 处的切线斜率为()ln f m m '=，曲线()y g x =在点B 处的切线斜率为1212122m m g e e --⎛⎫'=⎪⎝⎭， 令()12ln 2m f m g e -⎛⎫''= ⎪⎝⎭，即1212m m e -=，即1221m me -=， 则12m =满足方程1221m me -=，所以，m ∃使得曲线()y f x =在A 处的切线平行于曲线()y g x =在B 处的切线，B 选项正确；构造函数()()()1ln22xx F x f x g x m e m =-+=-+-，可得()1x F x e x'=-， 函数()1xF x e x '=-在()0,∞+上为增函数，由于120F e e ⎛⎫'=< ⎪⎝⎭，()110F e -'=>，则存在1,12t ⎛⎫∈⎪⎝⎭，使得()10t F t e t '=-=，可得ln t t =-，当0x t <<时，()0F x '<；当x t >时，()0F x '>.()()min 1111ln ln ln 2ln 22222t t t F x F t e m e t m t m t ∴==-+-=-++-=+++-13ln 2ln 2022m m >+-=++>，所以，函数()()()F x f x g x m =-+没有零点，C 选项错误；设曲线()y f x =在点A 处的切线与曲线()y g x =相切于点()(),C n g n ， 则曲线()y f x =在点A 处的切线方程为()ln ln my m ex m -=-，即()1ln y mx m m =+-，同理可得曲线()y g x =在点C 处的切线方程为11ln 22n y x n =+-， 所以，()111ln ln 22m nn m m ⎧=⎪⎪⎨⎪-=-⎪⎩，消去n 得()11ln ln 202m m m --++=，令()()11ln ln 22G x x x x =--++，则()111ln ln x G x x x x x-'=--=-， 函数()y G x '=在()0,∞+上为减函数，()110G '=>，()12ln 202G '=-<，则存在()1,2s ∈，使得()1ln 0G s s s'=-=，且1s s e =. 当0x s <<时，()0G x '>，当x s >时，()0G x '<.所以，函数()y G x =在()2,+∞上为减函数，()5202G =>，()17820ln 202G =-<， 由零点存在定理知，函数()y G x =在()2,+∞上有零点， 即方程()11ln ln 202m m m --++=有解. 所以，m ∃使得曲线()y f x =在点A 处的切线也是曲线()y g x =的切线. 故选：ABD. 【点睛】本题考查导数的综合应用，涉及函数的最值、零点以及切线问题，计算量较大，属于难题.12．已知函数()f x 对于任意x ∈R ，均满足()()2f x f x =-.当1x ≤时()ln ,01,0x x x f x e x <≤⎧=⎨≤⎩，若函数()()2g x m x f x =--，下列结论正确的为（ ）A ．若0m <，则()g x 恰有两个零点B ．若32m e <<，则()g x 有三个零点 C ．若302m <≤，则()g x 恰有四个零点 D ．不存在m 使得()g x 恰有四个零点 【答案】ABC 【分析】设()2h x m x =-，作出函数()g x 的图象，求出直线2y mx =-与曲线()ln 01y x x =<<相切以及直线2y mx =-过点()2,1A 时对应的实数m 的值，数形结合可判断各选项的正误. 【详解】由()()2f x f x =-可知函数()f x 的图象关于直线1x =对称. 令()0g x =，即()2m x f x -=，作出函数()f x 的图象如下图所示：令()2h x m x =-，则函数()g x 的零点个数为函数()f x 、()h x 的图象的交点个数，()h x 的定义域为R ，且()()22h x m x m x h x -=--=-=，则函数()h x 为偶函数，且函数()h x 的图象恒过定点()0,2-，当函数()h x 的图象过点()2,1A 时，有()2221h m =-=，解得32m =.过点()0,2-作函数()ln 01y x x =<<的图象的切线， 设切点为()00,ln x x ，对函数ln y x =求导得1y x'=， 所以，函数ln y x =的图象在点()00,ln x x 处的切线方程为()0001ln y x x x x -=-， 切线过点()0,2-，所以，02ln 1x --=-，解得01x e=，则切线斜率为e ， 即当m e =时，函数()y h x =的图象与函数()ln 01y x x =<<的图象相切. 若函数()g x 恰有两个零点，由图可得0m ≤或m e =，A 选项正确； 若函数()g x 恰有三个零点，由图可得32m e <<，B 选项正确； 若函数()g x 恰有四个零点，由图可得302m <≤，C 选项正确，D 选项错误. 故选：ABC. 【点睛】方法点睛：利用导数解决函数零点问题的方法：（1）直接法：先对函数求导，根据导数的方法求出函数的单调区间与极值，根据函数的基本性质作出图象，然后将问题转化为函数图象与x 轴的交点问题，突出导数的工具作用，体现了转化与化归思想、数形结合思想和分类讨论思想的应用； （2）构造新函数法：将问题转化为研究两函数图象的交点问题；（3）参变量分离法：由()0f x =分离变量得出()a g x =，将问题等价转化为直线y a =与函数()y g x =的图象的交点问题.13．对于函数()2ln 1f x x ax x a =+--+，其中a R ∈，下列4个命题中正确命题有（ ）A ．该函数定有2个极值B ．该函数的极小值一定不大于2C ．该函数一定存在零点D ．存在实数a ，使得该函数有2个零点【答案】BD 【分析】求出导函数，利用导数确定极值，结合零点存在定理确定零点个数． 【详解】函数定义域是(0,)+∞，由已知2121()2x ax f x x a x x+-'=+-=，280a ∆=+>，2210x ax +-=有两个不等实根12,x x ，但12102x x =-<，12,x x 一正一负．由于定义域是(0,)+∞，因此()0f x '=只有一个实根，()f x 只有一个极值，A 错；不妨设120x x <<，则20x x <<时，()0f x '<，()f x 递减，2x x >时，()0f x '>，()f x 递增．所以2()f x 是函数的极小值．222210x ax +-=，22212x a x -=，22222()ln 1f x x ax x a =+--+＝222222222222212112ln 12ln 2x x x x x x x x x -+---+=-+--+，设21()2ln 2g x x x x x =-+--+，则22111()22(1)(2)g x x x x x x'=-+-+=-+， 01x <<时，()0g x '>，()g x 递增，1x >时，()0g x '<，()g x 递减，所以()g x 极大值＝(1)2g =，即()2g x ≤，所以2()2f x ≤，B 正确； 由上可知当()f x 的极小值为正时，()f x 无零点．C 错；()f x 的极小值也是最小值为2222221()2ln 2f x x x x x =-+--+， 例如当23x =时，173a =-，2()0f x <，0x →时，()f x →+∞，又2422217171714()21()03333f e e e e e =--++=-+>（217()3e >， 所以()f x 在(0,3)和(3,)+∞上各有一个零点，D 正确． 故选：BD ． 【点睛】思路点睛：本题考查用导数研究函数的极值，零点，解题方法是利用导数确定函数的单调性，极值，但要注意在函数定义域内求解，对零点个数问题，注意结合零点存在定理，否则不能确定零点的存在性．14．设函数()ln f x x x =，()212g x x =，给定下列命题，其中正确的是（ ） A ．若方程()f x k =有两个不同的实数根，则1,0k e⎛⎫∈- ⎪⎝⎭； B ．若方程()2kf x x =恰好只有一个实数根，则0k <；C ．若120x x >>，总有()()()()1212m g x g x f x f x ->-⎡⎤⎣⎦恒成立，则m 1≥；D ．若函数()()()2F x f x ag x =-有两个极值点，则实数10,2a ⎛⎫∈ ⎪⎝⎭． 【答案】ACD 【分析】利用导数研究函数的单调性和极值，且将题意转化为()y f x =与y k =有两个不同的交点，即可判断A 选项；易知1x =不是该方程的根，当1x ≠时，将条件等价于y k =和ln xy x=只有一个交点，利用导数研究函数的单调性和极值，从而可推出结果，即可判断B 选项；当120x x >>时，将条件等价于1122()()()()mg x f x mg x f x ->-恒成立，即函数()()y mg x f x =-在(0,)+∞上为增函数，通过构造新函数以及利用导数求出单调区间，即可求出m 的范围，即可判断C 选项；2()ln (0)F x x x ax x =->有两个不同极值点，根据导数的符号列出不等式并求解，即可判断D 选项. 【详解】解：对于A ，()f x 的定义域(0,)+∞，()ln 1f x x '=+， 令()0f x '>，有ln 1x >-，即1x e>， 可知()f x 在1(0,)e 单调递减，在1+e∞（，）单调递增，所以极小值等于最小值， min 11()()f x f e e∴==-，且当0x →时()0f x →，又(1)0f =，从而要使得方程()f x k =有两个不同的实根，即()y f x =与y k =有两个不同的交点，所以1(,0)k e∈-，故A 正确； 对于B ，易知1x =不是该方程的根，当1x ≠时，()0f x ≠，方程2()kf x x =有且只有一个实数根，等价于y k =和ln xy x=只有一个交点， 2ln 1(ln )-'=x y x ，又0x >且1x ≠， 令0y '>，即ln 1x >，有x e >， 知ln xy x=在0,1（）和1e （，）单减，在+e ∞（，）上单增， 1x =是一条渐近线，极小值为e ,由ln xy x=大致图像可知0k <或=k e ，故B 错误；对于C ，当120x x >>时，[]1212()()()()m g x g x f x f x ->-恒成立， 等价于1122()()()()mg x f x mg x f x ->-恒成立， 即函数()()y mg x f x =-在(0,)+∞上为增函数， 即()()ln 10y mg x f x mx x =-''--'=≥恒成立，即ln 1+≥x m x在(0,)+∞上恒成立， 令ln 1()x r x x +=，则2ln ()xr x x -'=，令()0r x '>得ln 0x <，有01x <<，从而()r x 在(0,1)上单调递增，在(1,)+∞上单调递减， 则max ()(1)1r x r ==，于是m 1≥，故C 正确；对于D ，2()ln (0)F x x x ax x =->有两个不同极值点， 等价于()ln 120F x x ax +-'==有两个不同的正根， 即方程ln 12x a x+=有两个不同的正根， 由C 可知，021a <<，即102a <<，则D 正确. 故选：ACD.【点睛】关键点点睛：本题考查导数的应用，利用导数研究函数的单调性和极值，以及利用导数解决函数的零点问题和恒成立问题从而求参数范围，解题的关键在于将零点问题转化成两个函数的交点问题，解题时注意利用数形结合，考查转化思想和运算能力．15．在数学中，布劳威尔不动点定理是拓扑学里一个非常重要的不动点定理，它得名于荷兰数学家鲁伊兹布劳威尔（L.E.Brouwer ）简单的讲就是对于满足一定条件的连续函数()f x ，存在一个点0x ，使得()00f x x =，那么我们称该函数为“不动点”函数，而称0x 为该函数的一个不动点，依据不动点理论，下列说法正确的是（ ） A ．函数()sin f x x =有3个不动点B ．函数2()(0)f x ax bx c a =++≠至多有两个不动点C ．若定义在R 上的奇函数()f x ，其图像上存在有限个不动点，则不动点个数是奇数D ．若函数()x f x e x a =+-[0,1]上存在不动点，则实数a 满足l a e ≤≤（e 为自然对数的底数） 【答案】BCD 【分析】根据题目中的定义，结合导数、一元二次方程的性质、奇函数的性质进行判断即可. 【详解】令()sin g x x x =-，()1cos 0g x x '=-≥， 因此()g x 在R 上单调递增，而(0)0g =，所以()g x 在R 有且仅有一个零点， 即()f x 有且仅有一个“不动点”，A 错误；0a ≠，20ax bx c x ∴++-=至多有两个实数根，所以()f x 至多有两个“不动点”，B 正确；()f x 为定义在R 上的奇函数，所以(0)0f =，函数()-y f x x =为定义在R 上的奇函数，显然0x =是()f x 的一个“不动点”，其它的“不动点”都关于原点对称，个数和为偶数， 因此()f x 一定有奇数个“不动点”，C 正确；因为()f x 在[0,1]存在“不动点”，则()f x x =在[0,1]有解，x =⇒2x a e x x =+-在[0,1]有解，令2()xm x e x x =+-，()12x m x e x '=+-，令()12x n x e x '=+-，()20x n x e '=-=，ln 2x =，()n x 在(0,ln 2)单调递减，在(ln 2,1)单调递增，∴min ()(ln 2)212ln 232ln 20n x n ==+-=->， ∴()0m x '>在[0,1]恒成立，∴()m x 在[0,1]单调递增，min ()(0)1m x m ==，max ()(1)m x m e ==，∴1a e ≤≤，D 正确，. 故选：BCD 【点睛】方法点睛：新定义题型的特点是：通过给出一个新概念，或约定一种新运算，或给出几个新模型来创设全新的问题情景，要求考生在阅读理解的基础上，依据题目提供的信息，联系所学的知识和方法，实现信息的迁移，达到灵活解题的目的.遇到新定义问题，应耐心读题，分析新定义的特点，弄清新定义的性质，按新定义的要求，“照章办事”，逐条分析、验证、运算，使问题得以解决.16．经研究发现：任意一个三次多项式函数32()(0)f x ax bx cx d a =+++≠的图象都只有一个对称中心点()()00,x f x ，其中0x 是()0f x ''=的根，()'f x 是()f x 的导数，()f x ''是()'f x 的导数.若函数32()f x x ax x b =+++图象的对称点为(1,2)-，且不等式(ln 1)x e e mx x -+32()3ef x x x e x ⎡⎤≥--+⎣⎦对任意(1,)x ∈+∞恒成立，则（ ）A ．3a =B ．1b =C ．m 的值可能是e -D ．m 的值可能是1e-【答案】ABC 【分析】求导得()62f x x a ''=+，故由题意得()1620f a ''=-+=-，()1112f a b -=-+-+=，即3,1a b ==，故()3231f x x x x =+++.进而将问题转化为()1ln 1e x x e x e m x --++<+，由于1x e x >+，故ln ln 1ee x x x x e e x e x --+=≥-+，进而得()1ln ln 1ln 1e x x e x e e x ee x x --++--≥=-++，即m e ≤-，进而得ABC 满足条件.【详解】由题意可得()1112f a b -=-+-+=，因为()2321x ax f x =++'，所以()62f x x a ''=+，所以()1620f a ''=-+=-，解得3,1a b ==，故()3231f x x x x =+++.因为1x >，所以()()32ln []13xeee mx xf x x x e x -+≥--+等价于()1ln 1e x x e x e m x --++≤+. 设()()10xg x e x x =-->，则()10xg x e '=->，从而()g x 在()0,∞+上单调递增.因为()00g =，所以()0g x >，即1x e x >+， 则ln ln 1ee x xxx e e x e x --+=≥-+（当且仅当x e =时，等号成立），从而()1ln ln 1ln 1e x x e x e e x e e x x --++--≥=-++，故m e ≤-.故选：ABC. 【点睛】本题解题的关键在于根据题意得()3231f x x x x =+++，进而将不等式恒成立问题转化为()1ln 1e x x e x e m x --++≤+恒成立问题，再结合1x e x >+得ln ln 1ee x xxx e e x e x --+=≥-+，进而得m e ≤-.考查运算求解能力与化归转化思想，是难题.17．设函数()()1x af x a x a =->的定义域为()0,∞+，已知()f x 有且只有一个零点，下列结论正确的有（ ） A ．a e =B ．()f x 在区间()1,e 单调递增C ．1x =是()f x 的极大值点D ．()f e 是()f x 的最小值【答案】ACD 【分析】()f x 只有一个零点，转化为方程0x a a x -=在(0,)+∞上只有一个根，即ln ln x ax a=只有一个正根．利用导数研究函数ln ()xh x x=的性质，可得a e =，判断A ，然后用导数研究函数()x e f x e x =-的性质，求出()'f x ，令()0f x '=，利用新函数确定()'f x 只有两个零点1和e ，并证明出()'f x 的正负，得()f x 的单调性，极值最值．判断BCD ． 【详解】()f x 只有一个零点，即方程0x a a x -=在(0,)+∞上只有一个根，x a a x =，取对数得ln ln x a a x =，即ln ln x ax a=只有一个正根． 设ln ()x h x x =，则21ln ()x h x x-'=，当0x e <<时，()0h x '>，()h x 递增，0x →时，()h x →-∞，x e >时，()0h x '<，()h x 递减，此时()0h x >，max 1()()h x h e e==． ∴要使方程ln ln x ax a =只有一个正根．则ln 1a a e =或ln 0a a<，解得a e =或0a <，又∵1a >，∴a e =．A 正确；()x e f x e x =-，1()x e f x e ex -'=-，1()0x e f x e ex -'=-=，11x e e x --=，取对数得1(1)ln x e x -=-，易知1x =和x e =是此方程的解．设()(1)ln 1p x e x x =--+，1()1e p x x-'=-，当01x e <<-时，()0p x '>，()p x 递增，1x e >-时，()0p x '<，()p x 递减，(1)p e -是极大值，又(1)()0p p e ==， 所以()p x 有且只有两个零点，01x <<或x e >时，()0p x <，即(1)ln 1e x x -<-，11e x x e --<，1e x ex e -<，()0f x '>，同理1x e <<时，()0f x '<，所以()f x 在(0,1)和(,)e +∞上递增，在(1,)e 上递减，所以极小值为()0f e =，极大值为(1)f ，又(0)1f =，所以()f e 是最小值．B 错，CD 正确． 故选：ACD ． 【点睛】关键点点睛：本题考用导数研究函数的零点，极值，单调性．解题关键是确定()'f x 的零点时，利用零点定义解方程，1()0xe f x e ex-'=-=，11x e e x --=，取对数得1(1)ln x e x -=-，易知1x =和x e =是此方程的解．然后证明方程只有这两个解即可．18．已知函数()e sin xf x a x =+，则下列说法正确的是（ ）A ．当1a =-时，()f x 在0,单调递增B ．当1a =-时，()f x 在()()0,0f 处的切线为x 轴C ．当1a =时，()f x 在()π,0-存在唯一极小值点0x ，且()010f x -<<D ．对任意0a >，()f x 在()π,-+∞一定存在零点 【答案】AC 【分析】结合函数的单调性、极值、最值及零点，分别对四个选项逐个分析，可选出答案. 【详解】对于A ，当1a =-时，()e sin xf x x =-，()e cos xf x x '=-，因为()0,x ∈+∞时，e 1,cos 1xx >≤，即0fx，所以()f x 在0,上单调递增，故A 正确；对于B ，当1a =-时，()e sin x f x x =-，()e cos xf x x '=-，则()00e sin01f =-=，()00e cos00f '=-=，即切点为0,1，切线斜率为0，故切线方程为1y =，故B 错误；对于C ，当1a =时，()e sin xf x x =+，()e cos xf x x '+=，()e sin xf x x '=-'，当()π,0x ∈-时，sin 0x <，e 0x >，则()e sin 0xx f x -'=>'恒成立，即()e cos x f x x '+=在()π,0-上单调递增，又ππ22ππe cos e 220f --⎛⎫⎛⎫'-=-= ⎪ ⎪⎝⎭⎝⎭+>，3π3π443π3πe cos e 442f --⎛⎫⎛⎫'-=-= ⎪ ⎪⎝⎭⎝-⎭+，因为123π3π421e e 2e ---⎛⎫=<⎪⎭< ⎝，所以3π43πe 024f -⎛⎫'-= ⎪-⎭<⎝，所以存在唯一03ππ,42x ⎛⎫∈-- ⎪⎝⎭，使得()00f x '=成立，所以()f x 在()0π,x -上单调递减，在()0,0x 上单调递增，即()f x 在()π,0-存在唯一极小值点0x ，由()000e cos 0xf x x +'==，可得()000000πe sin cos sin 4x f x x x x x ⎛⎫=+=-+=- ⎪⎝⎭，因为03ππ,42x ⎛⎫∈-- ⎪⎝⎭，所以0π3ππ,44x ⎛⎫-∈-- ⎪⎝⎭，则()00π4f x x ⎛⎫=- ⎪⎝⎭()1,0∈-，故C 正确；对于选项D ，()e sin xf x a x =+，()π,x ∈-+∞，令()e sin 0xf x a x =+=，得1sin ex x a -=， ()sin ex xg x =，()π,x ∈-+∞，则()πcos sin 4e e x xx x x g x ⎛⎫- ⎪-⎝⎭'==， 令0g x ，得πsin 04x ⎛⎫-= ⎪⎝⎭，则ππ4x k =+()1,k k ≥-∈Z ，令0g x，得πsin 04x ⎛⎫-> ⎪⎝⎭，则π5π2π,2π44x k k ⎛⎫∈++ ⎪⎝⎭()1,k k ≥-∈Z ，此时函数()g x 单调递减， 令0g x，得πsin 04x ⎛⎫-< ⎪⎝⎭，则5π9π2π,2π44x k k ⎛⎫∈++ ⎪⎝⎭()1,k k ≥-∈Z ，此时函数()g x 单调递增， 所以5π2π4x k =+()1,k k ≥-∈Z 时，()g x 取得极小值，极小值为5π5π2π2π445π5π2π5π4s 42in si πe e 4n k k g k k ++⎛⎫ ⎪⎛⎫⎝⎭== ⎪⎝⎭++()1,k k ≥-∈Z ， 在()g x 的极小值中，3π4sin 3π45π5π42π4eg g -⎛⎫⎛⎫=-= ⎪ ⎪⎝⎭⎝+⎭-最小，当3ππ,4x ⎛⎫∈-- ⎪⎝⎭时，()g x 单调递减，所以函数()g x的最小值为3π3π445πsin 3π144eg --⎛⎫-==- ⎪⎝⎭，当3π411a--<-时，即3π40a -<<时，函数()g x 与1=-y a无交点，即()f x 在()π,-+∞不存在零点，故D 错误.故选：AC. 【点睛】本题考查利用导数研究函数的极值、零点、最值，及切线方程的求法，考查学生的推理能力与计算求解能力，属于难题.19．当1x >时，()41ln ln 3k x x x x --<-+恒成立，则整数k 的取值可以是（ ）. A ．2-B ．1-C ．0D ．1【答案】ABC 【分析】将()41ln ln 3k x x x x --<-+，当1x >时，恒成立，转化为13ln ln 4x k x x x ⎛⎫<++ ⎪⎝⎭，.当1x >时，恒成立，令()()3ln ln 1xF x x x x x=++>，利用导数法研究其最小值即可. 【详解】因为当1x >时，()41ln ln 3k x x x x --<-+恒成立，所以13ln ln 4x k x x x ⎛⎫<++ ⎪⎝⎭，当1x >时，恒成立，令()()3ln ln 1xF x x x x x=++>， 则()222131ln 2ln x x x F x x x x x---'=-+=. 令()ln 2x x x ϕ=--， 因为()10x x xϕ-'=>，所以()x ϕ在()1,+∞上单调递增. 因为()10ϕ<，所以()0F x '=在()1,+∞上有且仅有一个实数根0x ， 于是()F x 在()01,x 上单调递减，在()0,x +∞上单调递增， 所以()()000min 00ln 3ln x F x F x x x x ==++.（*） 因为()1ln 3309F -'=<，()()21ln 22ln 4401616F --'==>，所以()03,4x ∈，且002ln 0x x --=， 将00ln 2x x =-代入（*）式， 得()()0000min 00023121x F x F x x x x x x -==-++=+-，()03,4x ∈. 因为0011t x x =+-在()3,4上为增函数， 所以713,34t ⎛⎫∈ ⎪⎝⎭，即()min 1713,41216F x ⎛⎫∈ ⎪⎝⎭. 因为k 为整数，所以0k ≤. 故选：ABC 【点睛】本题主要考查函数与不等式恒成立问题，还考查了转化化归的思想和运算求解的能力，属于较难题.20．（多选题）已知函数31()1x x xe x f x e x x⎧<⎪=⎨≥⎪⎩，，，函数()()g x xf x =，下列选项正确的是（ ）A ．点(0,0)是函数()f x 的零点B ．12(0,1),(1,3)x x ∃∈∈，使12()()f x f x >C ．函数()f x 的值域为)1e ,-⎡-+∞⎣D ．若关于x 的方程[]2()2()0-=g x ag x 有两个不相等的实数根，则实数a 的取值范围是222e e,(,)e 82⎛⎤+∞ ⎥⎝⎦ 【答案】BC 【分析】根据零点的定义可判断A ；利用导数判断出函数在()0,1、()1,3上的单调性性，求出各段上的值域即可判断B ；利用导数求出函数的最值即可判断C ；利用导数求出函数的最值即可判断D. 【详解】对于选项A ，0是函数()f x 的零点，零点不是一个点，所以A 错误. 对于选项B ，当1x <时，()(1)xf x x e '=+，可得， 当1x <-时，()f x 单调递减； 当11x -<<时，()f x 单调递增； 所以，当01x <<时， 0()<<f x e ，当1x >时，4(3)()x e x f x x-'=， 当13x <<时，()f x 单调递减； 当3x >时，()f x 单调递增；()y f x =图像所以，当13x <<时， 3()27e f x e << ，综上可得，选项B 正确；对于选项C ，min 1()(1)f x f e=-=-，选项C 正确. 对于选项D ，关于x 的方程[]2()2()0-=g x ag x 有两个不相等的实数根⇔关于x 的方程()[()2]0-=g x g x a 有两个不相等的实数根 ⇔关于x 的方程()20-=g x a 有一个非零的实数根⇔函数()y g x =与2y a =有一个交点，且0x ≠，22,1(),1x xx e x g x e x x⎧<⎪=⎨≥⎪⎩当1x <时，/2()(2)=+xg x e x x ，当x 变化时，'()g x ，()g x 的变化情况如下：极大值24(2)g e -=，极小值(0)0g =，当1≥x 时，3(2)'()e x g x x -=当x 变化时，'()g x ，()g x 的变化情况如下：极小值(2)4e g =，()y g x =图像综上可得，22424<<e a e 或2a e >，a 的取值范围是222e e,(,)e 82⎛⎫+∞ ⎪⎝⎭，D 不正确.故选：BC 【点睛】本题考查了利用导数求函数的最值，利用导数研究方程的根，考查了转化与化归的思想，属于难题.三、三角函数与解三角形多选题21．如图，已知函数()sin()f x A x ωϕ=+（其中0A >，0>ω，||2πϕ≤）的图象与x轴交于点,A B ，与y 轴交于点C ，2BC BD =，,||23OCB OA π∠==，221||3AD =.则下列说法正确的有（ ）A ．()f x 的最小正周期为12B ．6πϕ=-。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
2013届高三单选复习题(1)Class_____________ Name_______________1. The expansion of Versailles began in the 1660s, ________ Louis XIV was king.A. wereB. whenC. asD. which2.With so many workers _______ off, the British government knew it was time that it had to do something.A. to layB. to be laidC. laidD. laying3.I appreciate the saying: Life is like a long race________ we complete with others to go beyond ourselves.A. whyB. whatC. thatD. where4.It was not until dark _______ he found what he thought was the correct way to solve the problem.A. thatB. whenC. asD. which5. Do me a favour------__________ me the Readers’ Digest, will you?A. passingB. to passC. passD. by passing6. It seems water ________ from this tap for some time. We’ll have to take it apart to put it right.A. had leakedB. is leakingC. leaksD. has been leaking7.----- I thought you were going to call on me last night.------Sorry, I ________. But I had to finish the report.A. would B did C. would like to D. would have8. After ten years of hard work, she changed a lot and looked different from _______she used to be.A. thatB. whomC. whatD. who9. John ________ in the woods near his home in Milkovica when a bear attacked him from behind.A. was huntingB. had huntedC. huntedD. has been hunting10. ______ our school uniforms, all of us feel a sense of pride being a student of this school.A. WearB. To wearC. WearingD. Wore11. English is a language that many people around world ________ not speak perfectly but at least ________ understand.A. may; canB. would; mightC. will; mustD. could; might12.It remains a mystery________ the world is going to end on Dec. 21st, 2012, which seems to be the end of the Mayan calendar.A. ifB. whetherC. thatD. when13. He _______ to go to Beijing today, but he postponed the trip when he heard that there would be a downpour at noon.A. was intendingB. would intendC. had intendedD. intended14. ------Did you hear about a teacher----Zhang Lili who saved the kids from being run over by a school bus?------Yes. What do you think most people _____ if they were in a similar situation?A. will doB. will have doneC. would doD. would have done15. Despite the rule ________ mobile phones are forbidden in class, my deskmate can’t help playing phone games occasionally.A. whichB. whatC. thatD. where16. I have promised that my daughter_______ get a new electronic dictionary on her next birthday.A. shouldB. mustC. shallD. would17. ________ global temperature rising, the UN Climate Conference was held in Cancun, Mexico last year.A. PretendedB. PreventingC. Having pretendedD. To pretend18. The new CRH train between Beijing and Shanghai _______ speed has been limited to 300 km/h focuses more on the safety of the passengers.A. whereB. whoseC. thatD. which19. The headmaster will not permit the change in the course, nor _______ it a thought.A. does he even giveB. he even givesC. will he even giveD. he will even give20. New technologies have made ________ possible to turn out new products faster and at a lower cost.A. thatB. thisC. oneD. it21. There is little doubt in your mind that he is innocent, ________?A. is thereB. isn’t thereC. is heD. isn’t he22. It suddenly occurred to him ______ he had left his keys in the office.A. whetherB. whereC. whichD. that23. The basketball coach, as well as his team, _______ interviewed shortly after the match for their outstanding performance.A. wereB. wasC. isD. are24. If my car ________ more reliable, I would have driven to Lhasa instead of flying last summer.A. wasB. had beenC. should beD. would be25. If you’re buying today’s newspaper from the stand, could you get ______ for me?A. oneB. suchC. thisD. that26. Close the door of fear behind you, and you ____the door of faith open before you.A. sawB. have seenC. will seeD. are seeing27. Maria has written two novels, and both of ______ have been made into television.A. thatB. themC. whichD. what28. The children were jumping on the new sofa, ______ I had paid a large amount of money the day before.A. whichB. whereC. for whichD. with which29.Bicycling is a good exercise; ________, it does not pollute the air.A. neverthelessB. besidesC. otherwiseD. therefore30. Hot ________the night air was, we slept deeply because we were so tired after the long journey.A. althoughB. asC. whileD. however2013届高三单选复习题(2)Class_____________ Name_______________1. Mark could refuse to answer _______ questions, but he never said no to his father’s questions.A. someone else’sB. anyone else’sC. anyoneD. no one2. ------ Are you surprised at my improvement on the tests, Dad?------Yes. I _______ you would get such high marks.A. didn’t expectB. wouldn’t expectC. don’t expectD. haven’t expected3. If I criticize someone, I will do it with great patience as if I were the one ________.A. to criticizeB. criticizingC. having criticizingD. being criticized4. The detective inspected the room for fingerprints, wondering if someone ______ the room.A. enteredB. entersC. had enteredD. has entered5. It’s her cleverness not her appearance ______ makes it difficult for her to work with others.A. whatB. asC. whichD. that6. How close parents are to their children ________ an influence on the character of the child.A. haveB. hasC. havingD. to have7. Children should be taught to leave things ________they can find them again.A. whereB. whenC. thenD. there8. The village students brought ______ they could----- a sack of ground meal or a pig to pay for the tuition.A. wheneverB. whereverC. howeverD. whatever9. Denis has made it known that he _______much of his collection to the nation when he retires.A. has donatedB. is to be donatedC. is to donateD. donates10. In the past few months, many practice exams _________ to sharpen the students’examination skills.A. have heldB. have been heldC. are heldD. are being held11. People in many places, ________ had been pulled down by estate developers, were not paid enough money.A. their housesB. whose housesC. which housesD. of whom houses12. _________ in 1898, Beijing University is one of the most famous universities in the world.A. Being foundedB. It was foundedC. FoundedD. Having founded13. Remember that you can reach success if you actually love what you________.A. have doneB. didC. had doneD. are doing14. _______ our life is like, we should be brave to face it.A. WhateverB. HoweverC. WhicheverD. Whenever15. -----Could you tell me how to get to the station?------Well, this is the road ______ the station.A. ledB. led toC. leading toD. leading16. Before you quit your job, _________ how your family would feel about your decision.A. considerB. consideringC. to considerD. considered17. -----What happened to the postman?------I don’t know. He _________ around here for a long time.A. didn’t seeB. wasn’t seenC. doesn’t seeD. hasn’t been seen18. As we all know, it is the media such as the Internet and TV that keep us _______ with the latest news from all over the world.A. informingB. informC. informedD. to be informed19. We’re having a meeting in half an hour. The decision _________ at the meeting will influence the future of our company.A. to be madeB. being madeC. madeD. having been made20. I’m wondering ____ he expects will win the English Talent Competition next year.A. whoB. whetherC. thatD. what21. ------You didn’t go the party last night, did you?------I do wish I ________ there.A. wasB. wereC. had beenD. went22. I have only completed one-third of the work, so the rest_________ to be done next week.A. haveB. hadC. areD. is23. ________ excited his parents most that he had passed the entrance exam and was admitted to his dream college.A. ThatB. WhatC. WhichD. It24. I love my school. Growing in the garden in front of our classroom________ the flowers of different kinds.A. isB. areC. wasD. were25.There happened to ________ a chance to go travelling because our grade allowed us students half a month off school.A. isB. haveC. getD. be26. -----How much do you know about the 3D film technology?-----A little. Not until _______the hot movie Avatar _______ some about it.A. did I see; did I begin to learnB. I saw; I began to learnC. I saw; did I begin to learnD. did I see; I began to learn27. Do you expect ________ to be a possibility that we shall be able to afford the particular furniture we need?A. itB. thereC. thatD. one28. South of our school and the stadium _______, known as Taozi Lake.A. lie a lakeB. does a lake lieC. lies a lakeD. do a lake lie29. It is only when you nearly lose someone _______ you become fully conscious of how much you value them.A. whichB. whenC. thatD. who30. -----What about the two pairs of glasses?------Well, this pair is not so good for me and, er, __________.A. neither is that pairB. neither that pair isC. so is that pairD. so that pair is2013届高三单选复习题(3)Class_____________ Name_______________1. Helping others is a habit, ________ you can learn even at an early age.A. itB. thatC. whatD. one2. The Hengxin Square is located in________ used to be our canteen.A. whatB. whereC. whichD. the place3. Mr. Li is very happy because the clothes made in his factory have never been ______.A. popularB. more popularC. most popularD. the most popular4. He is writing a novel, so he shuts himself up, _______ to receive guests.A. refusesB. to refuseC. refusingD. refused5. Only when I read the Frog a second time _______ to appreciate the writer’s magic realism.A. did I beginB. I beganC. had I begunD. I have begun6. I have told you the truth. ______ I keep repeating it?A. MustB. CanC. MayD. Will7. The girl arranged to have piano lessons at the training centre with her sister ________ she would stay for an hour.A. whereB. whoC. whichD. what8. Bob would have helped us yesterday but he _______.A. is busyB. had been busyC. has been busyD. was busy9.The fact has worried the people across the world_______ the earth is becoming warmer and warmer these years.A. whatB. whichC. thatD. where10.The international agreement, _______ to help people kick off the habit of smoking, was signed two years ago.A. intendedB. intendingC. intendsD. to intend11. Peter was so excited ________he received an invitation from his friend to visit Chongqing.A. whenB. whereC. whyD. that12. Being exposed to loud music too much________ caused hearing loss in some teenagers.A. isB. hasC. areD. have13. ________ everything a shot because you never know what will change your life.A. GivingB. To giveC. GiveD. Given14. By the time you have completed the essential training, you ________ exposed to every new feature of the course.A. areB. will have beenC. have beenD. will be15. If nature does not provide man with the necessary material, it is the laboratory ________ he will turn to for it.A. whereB. thatC. whichD. what16. Some women ________ a good salary in a job instead of staying home, but they decided not to work for the sake of the family.A. must makeB. should have madeC. would makeD. could have made17. I’m really hungry. Let’s eat at _________ restaurant has a free table.A. whicheverB. whateverC. whichD. what18.Turn on the television or open a magazine and you _______ advertisements showing happy families.A. will often seeB. often seeC. are often seeingD. have often seen19. -----You’ve got your flat furnished, haven’t you?------Yes. I _______ some used furniture at the Sunday Market and it was a real bargain.A. will buyB. have boughtC. had boughtD. bought20. ________ the green hills are there, one need not worry about firewood.A. Even ifB. WhileC. UnlessD. As long as21. _______with a sudden job loss, would you consider it as a failure, or an opportunity for a new start in your career?A. FacingB. FacedC. To faceD. Face22.The development of China’s economy _______ since the 80s of the last century.A. has been increasingB. had increasedC. is increasingD. increased23. Whenever a natural disaster happens, we should offer ________ help we can to the victims.A. howeverB. whateverC. wheneverD. whichever24. The weather in the south is generally warm, but it _______be very cold sometimes.A. mayB. shallC. willD. can25.The food, _______ good, was soon sold out when it was taken to the market.A. tastedB. tastingC. being tastedD. having tasted26. ------Where did you get to know the famous writer?-------It was on the farm _______ we used to work together.A. whereB. whichC. thatD. /27. ________ your letter, I would have set off two days ago.A. If I could have receivedB. If I receivedC. Should I receiveD. Had I received28. _______ on the mirrior, and you’ll find little drops of water on the glass.A. BlowingB. To blowC. BlowD. If you blow29. Kelly, as well as her little son, ________ present at the meeting last Friday.A. wasB. areC. isD. were30. What an unforgettable experience! I’ll write it down ________ it is still fresh in my memory.A. beforeB. whileC. so thatD. until。