2018版 江苏高考预测试题(三)
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江苏省南京市2018届高三年级第三次模拟考试英语2018.05.03第一部分听力 (共两节,满分20分)做题时,先将答案标在试卷上。
录音内容结束后,你将有两分钟的时间将试卷上的答案转涂到答题卡上。
第一节(共5小题;每小题1分,满分5分)听下面5段对话。
每段对话后有一个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。
听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1Why does the man want to leave?A . The food is toobad.B The music is too loud C. The service is too slow.2What is the woman?A.A nurseB. A. teacherC. A clerk3.What does the man mean?A .He missed the endof the game.B. He got home a fewminutes late.c. He watched the gamefive minutes.4Where does the conversation probably take place?A.In a shop.B. At the cinema C .On a bus.5.How long did the woman stay in Chicago?A. 6 yearsB. I2 years.C.23 years第二节(共15小题;每小题1分,满分15分)听下面5段对话或独白。
每段对话或独白后有几个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。
听每段对话或独白前,你将有时间阅读各个小题,每小题5秒钟;听完后,各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听第6段材料,回答第6、7题。
2018年普通高校招生全国统一考试冲刺预测·江苏卷(三)语文注意事项:1.本试卷共160分,考试时间150分钟。
2.答题前,考生务必用直径0.5毫米黑色墨水签字笔将密封线内项目填写清楚。
3.考生作答时,请用直径0.5毫米黑色墨水签字笔在答题卡上各题的答题区域内作答,超出答...题区域书写的答案无效..........,.在试题卷、草稿纸上作答无效.............。
语文Ⅰ试题一、语言文字运用(15分)1.在下列文字横线处依次填入词语,最恰当的一组是 (3分) ()从屈辱到崛起、从到独立富强,经过67年的风雨前行,如今屹立在世界东方的,是一个生机盎然的中国。
从温饱不足、欺凌到成为世界经济的新引擎、全球治理的主要参与者,经过67年的 ,如今铺陈在世界面前的,是一幅瑰丽无比的中国画卷。
A.积重难返倍受栉风沐雨B.积贫积弱备受栉风沐雨C.积重难返备受风雨飘摇D.积贫积弱倍受风雨飘摇2.下列句子中,没有使用比喻手法的一项是 (3分) ()A.我们呼唤,在现实生活中能有更多像鲁迅先生这样的人,为了民族的未来而思考,而奋斗。
B.内无余钱剩米,外无豪友强援,衣食不继,生计成忧,在生存和生活两方面,唐伯虎已被逼至悬崖边。
C.一条大河从村边奔腾而去,雪白的浪花激荡涌起,宛如白玉般地迸溅开来,滋润了整个村子。
D.这些带着本乡土产去贩卖的车子,往往成群成帮,队伍拉得老长,道上飞扬的尘土是他们的旗号。
3.下列对联,最适合祝贺老师70岁寿辰的一联是 (3分) ()A.碧桃献岁宜家受福花甲逢春获寿延年B.为学有宗古稀成庆诲人无倦恩重及门C.乐道安贫音容宛在因材施教手泽犹存D.执掌教坛垂七十载载培桃李满三千株4.下列语句中,语言表达得体的一项是 (3分) ()A.“这算得了什么,以后要是再有困难,可以继续到府上来找我。
”孙大款慷慨地说。
B.程一鸣教授将自已的学术专著送给爱徒王斌,他在扉页上写下“王斌同学惠存”的字样。
试题习题、尽在百度江苏省普通高等学校招生考试高三模拟测试卷(十三)英语本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分.满分120分,考试时间120分钟.第Ⅰ卷(选择题共85分)第一部分:听力(共两节,满分20分)第一节(共5小题;每小题1分,满分5分)听下面5段对话.每段对话后有一个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置.听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题.每段对话仅读一遍.()1. Where are the speakers?A. At home.B. In a restaurant.C. In a hotel.()2. What does the boy mean?A. Nancy has left the TV on.B. He forgot to turn off the TV.C. Nancy remembered turning off the TV.()3. What does the woman advise the man to do?A. Go to the post office.B. Call the post office.C. Contact the mail carrier.()4. Which word can best describe the man?A. Hardworking.B. Dishonest.C. Humorous.()5. What can we learn from the conversation?A. The man is unhappy.B. The woman is very helpful.C. Mr. Barkley is disappointed.第二节(共15小题;每小题1分,满分15分)听下面5段对话或独白.每段对话或独白后有几个小题,从题中所给的A、B、C三个项中选出最佳选项,并标在试卷的相应位置.听每段对话或独白前,你将有时间阅读各个小题,每小题5秒钟;听完后,各小题给出5秒钟的作答时间.每段对话或独白读两遍.听第6段材料,回答第6、7题.()6. Where are the woman's children studying?A. At a school nearby.B. At a private school.C. At a public school.仔细审题、认真作答.试题习题、尽在百度()7. What can we learn about the woman?A. She is new here.B. She works in a school.C. She has lost her way.听第7段材料,回答第8至10题.()8. What can we learn about Pamela?A. She must be the man's pet.B. She must be the man's friend.C. She must be the man's daughter.()9. What did the man use to be?A. A doctor.B. A boss.C. A professor.()10. What is the man going to do?A. To board a train.B. To get on an airplane.C. To catch the early bus.听第8段材料,回答第11至13题.()11. What was the woman's original plan?A. To study in a law school.B. To work as a lawyer abroad.C. To go abroad for further study.()12. Why did the woman change her mind?A. She found it was a trick to her.B. She found it unwise to go abroad.C. She thought it would cost her too much.()13. What do the speakers decide to do?A. Keep in touch.B. Have dinner today.C. Make a call tonight.听第9段材料,回答第14至16题.()14. In what field does the woman want to work after graduation?A. Law.B. Medicine.C. Management.()15. What does the man think is the key to one's success?A. Interest.B. Ambitions.C. A backup plan.()16. What can we learn about the woman?A. She hasn't found a job up to now.B. She has no ambition and feels down.C. She will accept her father's suggestion.听第10段材料,回答第17至20题.()17. What is the first news headline about?A. Street violence.B. Personal safety.C. Student's health.仔细审题、认真作答.试题习题、尽在百度()18. Why did some parents gather at schools in Glasgow?A. To participate in school activities.B. To call for better primary education.C. To prevent the close-down of schools.()19. What are the litter pickers doing?A. Collecting private rubbish.B. Having a one-day break.C. Cleaning up after themselves.()20. Which teams will play in the European Cup Final?A. AC Milan and Barcelona.B. Barcelona and Liverpool.C. Liverpool and AC Milan.第二部分:英语基础知识运用(共两节,满分35分)第一节:单项填空(共15小题;每小题1分,满分15分)请认真阅读下面各题,从题中所给的A、B、C、D四个选项中,选出最佳选项. ()21. Different cultural features of ethnic groups are ________ one another and work out a melody.A. in tune withB. in parallel withC. in contrast toD. in response to()22. ________ an increase in foreign legal conflicts, China is expected to see the number continue to rise.A. To witnessB. Being witnessedC. WitnessedD. Having witnessed()23. At the end of the historic area, Wilmington displayed its ________ as a working port city: large ware-houses and a few other dated office buildings.A. achievementB. reputationC. characterD. standard()24. —Do you think I'm a good surfer?—Of course! I ________ you earlier. You made it look so easy, graceful even.A. am watchingB. was watchingC. have watchedD. had watched()25. So far, only one man has ________ a theory that seems to fit all the facts.A. come up withB. put up withC. lined up withD. caught up with()26. —Your car should be ready next Tuesday.仔细审题、认真作答.试题习题、尽在百度—We were ________ hoping you'd be able to do it by this Friday.A. stillB. ratherC. alwaysD. even()27. Many thought that after starring in the immensely popular drama, Nirvana in Fire, Hu Ge would ________ and actively seek new roles.A. make a mountain out of a molehillB. have too many irons in the fireC. strike while the iron is hotD. put the cart before the horse()28. We work during the week, but weekends and evenings are usually ________.A. vacant B. casual C. empty D. clear()29. Passion is passion and it doesn't matter ________ it's directed. Exactly, it can be coins or sports or politics.A. whyB. howC. whetherD. where()30. Different tastes among tourists from outside the mainland ________ the list of the country's attractions.A. topB. shapeC. leadD. show()31. It wasn't easy having my friends talk about their freshman years ________ I wasn't a part of.A. whomB. whenC. thatD. what()32. The desk that ________ clean so I could do homework was always surrounded with bowls of bad milk, old magazines and so on.A. may have beenB. would have beenC. must have beenD. should have been()33. He ________ whether to set aside the minor differences, then he did.A. debatedB. predictedC. plottedD. calculated()34. How could I lie to her ________ she lived for the truth, whether it was found in music or people?A. unlessB. whenC. whileD. though()35. —Mum, look at my shoes. I need a new pair.—________. I bought them for you only a week ago!A. You betB. You said itC. You don't sayD. You name it第二节:完形填空(共20小题;每小题1分,满分20分)仔细审题、认真作答.试题习题、尽在百度请认真阅读下面短文,从短文后各题所给的A、B、C、D四个选项中,选出最佳选项. Human growth is a process of experimentation, trial, and error eventually leading to wisdom. Each time you choose to trust yourself and take action, you can never quite be certain how the situation will __36__.Sometimes you are victorious, and sometimes you become disappointed. The __37__ experiments, however, are no less valuable than the experiments that finally prove successful; in fact, you __38__ learn more from your “failures”than you do from your __39__. If you havemade what you think to be a mistake or failed to live up to your own __40__,you will most likely put up a barrier between your essence and the part of you that is the alleged(声称的) wrong-doer.However, viewing past actions as __41__ implies guilt and blame, and it is not possible tolearn anything meaning while you are engaged in blaming. __42__,forgiveness is required when you are severely judging yourself. Forgiveness is the act of erasing an __43__ debt. There are four kinds of forgiveness.The first is beginner forgiveness for yourself.The second of forgiveness is beginner forgiveness for another.The third kind of forgiveness is __44__ forgiveness of yourself. This is for serious misbehaviors, the ones you carry with deep __45__. When you do something that violates your own values and principles, you create a gap between your standards and your actual __46__.In such a case, you need to work very hard at __47__ yourself for these deeds so that you can close this gap. This does not __48__ that you should rush to forgive yourself or shouldn't feel regret, __49__ taking pleasure in these feelings for a prolonged period of time is not healthy.The __50__ and perhaps most difficult one is the advanced forgiveness of another.At some time of our life, you may have been severely wronged or hurt by another person tosuch a degree that forgiveness seems __51__.However, harboring anger and revenge fantasies only keeps you __52__ in victimhood.Under such a circumstance, you should force yourself to see the bigger picture. By so doing, you will be able to __53__ the focus away from the anger and resentment.It is only through forgiveness that you can erase wrongdoing and __54__ the memory. Whenyou can __55__ release the situation, you may come to see it as a necessary part of your growth.仔细审题、认真作答.试题习题、尽在百度()36. A. turn out B. turn up C. break up D. break out()37. A. important B. engaged C. failed D. successful()38. A. obviously B. necessarily C. continuously D. usually()39. A. success B. failure C. fault D. benefit()40. A. ability B. expectations C. belief D. experiences()41. A. mistakes B. victories C. experiments D. fantasies()42. A. Still B. Therefore C. Instead D. However()43. A. absurd B. original C. emotional D. unusual()44. A. ordinary B. advanced C. alternative D. certain()45. A. wisdom B. mercy C. injury D. shame()46. A. thought B. approach C. behavior D. purpose()47. A. punishing B. forgiving C. blaming D. praising()48. A. mean B. prove C. reflect D. represent()49. A. and B. or C. but D. so()50. A. uncertain B. premier C. next D. last()51. A. essential B. valuable C. impossible D. unavoidable()52. A. trapped B. located C. lost D. occupied()53. A. drive B. drag C. put D. shift()54. A. keep B. refresh C. weaken D. clean()55. A. naturally B. finally C. definitely D. initially第三部分:阅读理解(共15小题;每小题2分,满分30分)请认真阅读下列短文,从短文后各题所给的A、B、C、D四个选项中,选出最佳选项. A5 Secrets of Web Travel SitesBooking a trip on an online travel site is convenient, but comes with its own set of problems.1. They know who's on a Mac and who's on a PC and who's going to spend more.仔细审题、认真作答.试题习题、尽在百度Last year, US travel research company Orbitz tracked people's online activities to test outwhether Mac users spend more on travel than PC users. On average, Mac users lay out US$20—30 more per night on hotels and go for more stars, according to the Wall Street Journal. As a result, online travel sites show these users more expensive travel options first. To avoid inadvertently paying more, sort results by price.2. Their software doesn't always hook up to the hotel's system.A guaranteed reservation is almost impossible to come by anywhere—but the risk of yourflight or hotel being overbooked increases with third-party providers. The middle-man's software isn't immune to system errors, so always call the hotel or airline to make sure your booking was processed.3. Don't be fooled by packages: Often, they're low-end items grouped together.Ever notice how travel sites recommend a hotel, a rental car, and tour package all in one click? These deals usually feature travel that no one wants, like flights with multiple layovers. Check the fine print.4. You could miss out on loyalty points.Third-party providers can get between you and frequent flyer miles or points. Many hotel loyalty programmes don't recognise external sites, others award only minimum points and exclude special offers, like double points on hotel stays.5. Once your trip is purchased, you're on your own.An online travel agency can't provide assistance the same way an agent can if a flight is cancelled or a room is substandard. Basically, when you arrive at the airport or hotel, you're just another client who booked at the lowest rate.()56. Which of the following is TRUE?A. Third-party providers can ensure your reservation.B. Mac users are likely to spend more money than PC users.C. An online travel agency functions the same as an agent.D. Packages usually provide travelers with satisfactory programmes.()57. What's the purpose of the passage?A. To encourage readers to book a trip on an online travel site.B. To make an advertisement about several travel sites online.仔细审题、认真作答.试题习题、尽在百度C. To convince readers not to book a trip on an online travel site.D. To warn readers of some problems with booking trips online.BWant to add some hours to your day? OK, you probably can't change the fabric of time. But anew study suggests that the way you feel about your goal can change your concept of time and that some simple strategies could make you feel less rushed.In a series of experiments, Jordan Etkin, a professor of marketing at Duke, and her co-authors, Loannis Evangelidis and Jennifer Aaker, looked at what happens when people see theirgoals as conflicting with one another. In one, they asked some participants to list two of their goals that they felt were in conflict, and others simply to list two of their goals. Those who were forced to think about conflicting aims felt more time pressure than those who weren't. In anotherexperiment, the researchers gave participants a similar prompt regarding goal conflict, but this time measured their anxiety levels as well as their attitudes toward time. They found that participants who thought about conflicting goals had more anxiety than those who didn't, and that this, in turn, led to feelings of being short on time.“Stress and anxiety and time pressure are closely linked concepts,” D. Etkin explained. “When we feel more stress and anxiety in relation to our personal goals, that manifests(表现) asa sense of having less time.”Technological advances that allow people to do lots of things at once may increase thefeeling of goal conflict, she said.“I think the easier it is for us to try to deal with a lot of these things at the same time,”she said, “the more opportunity there is for us to feel this conflict between our goals.”She isn't the first to suggest that actual busyness isn't the only thing that can make us feelbusy. At the Atlantic, Derek Thompson wrote that “as a country, we're working less than we did in the 1960s and 1980s”. He offered a number of possible reasons some Americans still feel so overworked, including “the fluidness(不固定性) of work and leisure”. As he put it:“The idea that work begins and ends at the office is wrong. On the one hand, flexibility isnice. On the other, mixing work and leisure together creates an always-on expectation that makes it hard for white-collar workers to escape the shadow of work responsibilities.”And Brigid Schulte writes in her 2014 book Overwhelmed: How to Work, Love, and Play仔细审题、认真作答.试题习题、尽在百度When No One Has the Time that some researchers believe “time has no sharp edges. What often matters more than the activity we're doing at a moment in time, they have found, is how we feel about it. Our_concept_of_time_is,_indeed,_our_reality.”Fortunately, Dr. Etkin and her team did find ways of making us feel better about time—or, at least, of reducing the negative influence of goal conflict. When participants performed a breathing exercise that reduced their anxiety, the impact of such conflict on their perception of time was less pronounced. Reframing anxiety as excitement (by reading the phrase “I am excited!”aloud several times) had a similar effect.Breathing and reframing may not solve everyone's time problems—Ms. Schulte writes thatsome Americans are indeed working more than they used to. She cites the work of the sociologists Michael Hout and Caroline Hanley, who have “found that working parents combined put in 13 more hours a week on the job in 2000 than they did in 1970. That's 676 hours of additionally paid work a year for a family. And that's on top of all the unpaid hours spent caring for children and keeping the house together.”Sometimes, we may feel short on time because we actually are. However, Dr. Etkin believes her findings suggest we may “have the ability to influence our experience of time more than we think we do”.“We're all going to have times in our lives when our goals seem to be in more conflict than others,”she said. But with techniques like the ones her team tested, “we really can help ourselves feel like we have more time.”()58. What makes people feel rushed today?A. Goal conflict.B. High pressure.C. Too much expectation.D. Lack of exercise.()59. Which of the following statements is TRUE according to the passage?A. Most people are having less work to do nowadays.B. People under a lot of stress have a better sense of time.C. Technological advances allow people to feel less stressed.D. The flexibility of work increases white-collar workers' pressure.()60. The underlined sentence “Our concept of time is, indeed, our reality.”means________.A. we should make full use of time仔细审题、认真作答.试题习题、尽在百度B. we value time more than the way we liveC. we can feel better about time if we want toD. we don't have the time to enjoy life in realityC“Over the years the unthinkable has become thinkable and today we sense we are close to being able to alter human heredity(遗传).”These were the words of David Baltimore of the California Institute of Technology, on December 1st, when he opened a three-day meeting in Washington to discuss the morality and use of human gene editing. Dr Baltimore is an old hand at these sorts of discussions, for he was also a participant in the Asilomar conference, in 1975, which brought scientists together to discuss a safe way of using the then-new technology of recombinant DNA, and whose recommendations influenced a generation of biotechnology researchers.Four decades on, the need for a similar sort of chin-wag has arisen. The InternationalSummit on Human Gene Editing has been held by the national scientific academies of three countries —America, Britain and China. They are particularly concerned about whether gene editing should be used to make heritable changes to the human germ line, something Dr Baltimore described as a deep and troubling question. Like those of Asilomar, the conclusions of this meeting will not be binding. But the hope is that, again like Asilomar, a mixture of common sense and peer pressure will create a world in which scientists are trusted to regulate themselves, rather than having politicians and civil servants do it for them. The meeting is being held against a backdrop of rapid scientific advance. Since 2012 research into a new, easy-to-use editing tool called CRISPR-Cas9 has blossomed. This technique involves a piece of RNA (a chemical messenger, which can be used to recognise a target section of DNA) and an enzyme(酶) called a nuclease that can snip unwanted genes out and paste new ones in.Public interest was aroused in April, when Chinese scientists announced they had editedgenes in non-viable(无活力的) human embryos, and again in November when British researchers said they had successfully treated a one-year-old girl who had leukaemia(白血病), using gene-edited T-cells. T-cells are part of the immune system that attack, among other things, tumour cells. The researchers altered T-cells from a healthy donor to encourage them to recognise and kill the patient's cancer, to make them immune to her leukaemia drug, and to ensure仔细审题、认真作答.试题习题、尽在百度they did not attack her healthy cells.In another recent development, a firm called Edit as Medicine, which is based in Cambridge, Massachusetts, has said it hopes, in 2017, to start human clinical trials of CRISPR-Cas9 as a treatment for a rare genetic form of blindness known as Leber congenital amaurosis(伯氏先天性黑蒙). Though other companies are already testing gene-editing therapies, these employ older,clunkier forms of the technology that seem likely to have less commercial potential. Moreover, researchers at the Broad Institute, also in Cambridge, said this week that they had made changes to CRISPR-Cas9 which greatly reduce the rate of editing errors —one of the main obstacles to the technique's medical use.On the subject of germ-line editing, Eric Lander, the Broad's head, told the meeting itwould be useful only in rare cases and said it might be a good idea to “exercise caution”before making permanent changes to the gene pool. The need for caution is advice that might also be heeded by those pursuing work in animals other than people, and in plants —subjects not being covered by the summit.()61. Which of the following is TRUE about CRISPR-Cas9?A. It has fewer side effects.B. It can modify human gene.C. It can protect immune system.D. It has less commercial potential.()62. The underlined word “chin-wag”in Paragraph 2 can be replaced by________.A. discussionB. negotiationC. argumentD. comparison()63. What can be inferred from the passage?A. Dr. Baltimore started his research on modifying gene in 1975.B. Scientists' opinions about the use of gene editing are consistent.C. CRISPR-Cas9 has been applied to cure Leber congenital amaurosis.D. More research should be made before the technology comes into wide use.()64. This passage is most probably a ________.A. science fictionB. scientific reportC. conference summaryD. commercial advertisementDBefore the law sits a gatekeeper. To this gatekeeper comes a man from the country who asks仔细审题、认真作答.试题习题、尽在百度to gain entry into the law. But the gatekeeper says that he cannot grant him entry at the moment.The man thinks about it and then asks if he will be allowed to come in sometime later on. “It is possible,”says the gatekeeper, “but not now.”①The gate to the law stands open, as always, and the gatekeeper walks to the side, so the man bends over in order to see through the gate intotheinside.Whenthegatekeepernoticesthat,helaughsandsays:“If_it_tempts_you_so_much,_try_going_inside_in_spite_of_my_prohibition._But_take_note._I_a m_powerful._And_I_am_only_the_most_lowly_gatekeeper._But_from_room_to_room_stand_gat ekeepers,_each_more_powerful_than_the_other._I_cannot_endure_even_one_glimpse_of_the_third.”The man from the country has not expected such difficulties: the law should always be accessible for everyone, he thinks, but as he now looks more closely at the gatekeeper in his fur coat, at his large pointed nose and his long, thin, black Tartar's beard, he decides that it would be better to wait until he gets permission to go inside. The gatekeeper gives him a stool and allows him to sit down at the side in front of the gate. There he sits for days and years. He makes many attempts to be let in, and he wears the gatekeeper out with his requests. The gatekeeper often interrogates him briefly, questioning him about his homeland and many other things, but they are indifferent questions, the kind great men put, and at the end he always tells him once more that he cannot let him inside yet. The man, who has equipped himself with many things for his journey, spends everything, no matter how valuable, to win over the gatekeeper. The latter takes it all but, as he does so, says, “I am taking this only so that you do not think you have failed to do anything.”②During the many years the man observes the gatekeeper almost continuously. He forgets the other gatekeepers, and this first one seems to him the only barrier for entry into the law. He curses the unlucky circumstance, in the first years thoughtlessly and out loud; later, as he grows old, he only mumbles to himself. He becomes childish and, since in the long years studying the gatekeeper he has also come to know the fleas(跳蚤) in his fur collar, he even asks the fleas to help him persuade the gatekeeper. Finally his eyesight grows weak, and he does not know whether things are really darker around him or whether his eyes are merely deceiving him. But he recognizes now in the darkness a ray of light which breaks out of the gateway to the law. Now he no longer has much time to live.仔细审题、认真作答.试题习题、尽在百度Before his death he gathers in his head all his experiences of the entire time up into onequestion which he has not yet put to the gatekeeper. He waves to him, since he can no longer liftup his stiffening body. The gatekeeper has to bend way down to him, for the great difference has changed things considerably to the disadvantage of the man. ③“You are insatiable(不知足的).”“Everyone strives after the law,”says the man, “so how is it that in these many yearsno one except me has requested entry?”The gatekeeper sees that the man is already dying and,in order to reach his diminishing sense of hearing, he shouts at him, “Here no one else can gain entry, since this entrance was assigned only to you. I'm going now to close it.”④()65. Which can best describe the man from the country?A. Brave but innocent.B. Loyal but ridiculous.C. Tolerant but stubborn.D. Trustworthy but childish.()66. What is the implied meaning of the underlined sentences?A. Anyone who breaks the law will get severe punishment.B. It's next to impossible for people to gain entry into the law.C. The gatekeepers are powerful enough to defend the law.D. All the gatekeepers take full responsibility for obeying the law.()67. The sentence “What do you still want to know now?”asks the gatekeeper. canbe put in ________.A. ①B. ②C. ③D. ④()68. Which of the following is TRUE?A. The gatekeeper is actually the symbol of responsibility.B. All efforts made by the man from the country are in vain.C. The man from the country finally gains access into the law.D. A close relationship is formed between the gatekeeper and the man.()69. Why is the man from the country eager to have access to the law continuously?A. Because he is anxious to explore the nature of law.B. Because no one can gain entry into the law except him.C. Because the gatekeeper promises him entry into the law.D. Because he knows how to take advantage of the gatekeeper.()70. What may be the title of the novel?仔细审题、认真作答.试题习题、尽在百度A. Before the LawB. Above the LawC. A Countryman's LifeD. A Gatekeeper's Duty第Ⅱ卷(非选择题共35分)第四部分:任务型阅读(共10小题;每小题1分,满分10分)请认真阅读下面短文,并根据所读内容在文章后表格中的空格里填入一个最恰当的单词.注意:每个空格只填1个单词.Family structure is the core of any culture. A major function of the family is to socialize new members of a culture. As children are raised in a family setting, they learn to become members ofthe family as well as members of the larger culture. The family provides the model for all other relationships in society. Through the observations and modeling of the behavior of other family members, children learn about the family and society including the values of the culture. Familystructure and their inherent relationships and obligations are a major source of cultural difference. The family is the center of most traditional Asians' lives. Many people worry about their families' welfare, reputation, and honor. Asian families are often extended, including several generations related by blood or marriage living in the same home. An Asian person's misdeeds are not blamed just on the individual but also on the family—including the dead ancestors. Traditional Chinese, among many other Asians, respect their elders and feel a deep sense ofduty toward them. Children repay their parents' sacrifices by being successful and supporting them in old age. This is accepted as a natural part of life in China. In contrast, taking care of aged parents is often viewed as tremendous burden in the United States, where aging and family support are not honored highly.The Vietnamese family consists of people currently alive as well as the spirits of the dead andof the as-yet unborn. Any decisions or actions are done from family considerations, not individual desires. People's behavior is judged on whether it brings shame or pride to the family. Vietnamese children are trained to rely on their families, to honor elderly people, and to fear foreigners. Many Vietnamese think that their actions in this life will influence their status in the next life.Fathers in traditional Japanese families are typically strict and distant. Japanese college students in one study said they would tell their fathers just about as much as they would tell a total stranger. The emotional and communication barrier between children and fathers in Japan appears 仔细审题、认真作答.试题习题、尽在百度very strong after children have reached a certain age.Although there has been much talk about “family values”in the United States, the family is not a usual frame of reference for decisions in U.S. mainstream culture. Family connections are not so important to most people. Dropping the names of wealthy or famous people the family knows is done in the United States, but it is not viewed positively. More important is a person's own individual “track record”of personal achievement.Thus, many cultural differences exist in family structures and values. In some cultures, thefamily is the center of life and the main frame of reference for decisions. In other cultures, the individuals, not the family, is primary. In some cultures, the family's reputation and honor depend on each person's actions; in other cultures, individuals can act without permanently affecting the family life. Some cultures value old people, while other cultures look down on them.—Adapted from R. L. Oxford & R. C. Scarcella, “A Few Family Structures and Values Around the Globe”。
2018年高考物理原创押题预测卷03【江苏卷】物理·参考答案【必做题】 10.(8分)(1)0.47(2分) 0.70(2分) (2)0.34(1分) 大于(1分) (3)不需要(2分) 11.(10分)(1)大(1分) ×100(1分) (2)2π4Rd ρ(2分) (3)①0.600(1分) ②1880(1分) ③(2分) ④偏大(2分)【选做题】 12.【选做题】A .[选修3–3](12分) (1)AD (4分)(2)先增大后减小(2分) 先减小后增大(2分) (3)①由理想气体的状态方程A AB BA Bp V p V T T =B .[选修3–4](12分) (1)BC (4分)(2)下凹(2分) 衍射图样(2分)(3)①P 质点经过4T达到负向最大位移,此刻有+y 方向的最大加速度 由图2可知,质点振动的周期T =0.4 s故质点P 第一次有+y 方向的最大加速度需经过的时间0.1s t =(2分) ②PQ 两点间距离14PQ x n λ⎛⎫=+ ⎪⎝⎭(n=0,1,2,……)解得:15m/s v = 下落时间110.5s v t g== 弹起时速度大小为v 2,则根据动能定理可得:22212mgh mv =解得:26m/s v = 学/科*-+网 上升的时间220.6s v t g== 运动员从自由下落到弹起到最高这段时间内,所受重力的冲量大小 012()900N s G I mg t t t =++=⋅(2分)②取向上为正方向,由动量定理有:000G Ft I -=- 代入数据解得F =2 250 N (2分) 13.(15分)(1)两个粒子在圆形磁场中运动的轨迹如图所示(1分)由几何关系可知:因为MQ NQ =,两个粒子做圆周运动的圆心在同一条直线M 1N 1K ,经过M 点的粒子进入磁场运动到P 点的时间是经过N 点的粒子进入磁场运动到P 点的时间的2倍,可知11120M N P ∠=︒,160N KP ∠=︒;轨迹圆的半径与圆形磁场的半径相等(1分) 由向心力公式:2mv qvB R=(1分)解得:粒子的比荷q v m RB=(1分) (2)N 点的纵坐标o(1cos60)2N R y R =-=,所以N 点坐标(0,2R)(2分) M 点的纵坐标o 3(1cos60)2N R y R =+=,所以M 点坐标(0,32R )(2分) (3)带电粒子运动的轨迹如图所示(1分)带电粒子在磁场做圆周运动的周期2π2πR mT v qB==经过N 点的粒子在圆形磁场的运动时间3116t T =经过N 点的粒子在三、四象限磁场的运动时间4223t T =(1分)1234t t t t +=+(1分)以上解得12B B =(1分) 14.(16分)(3)滑块沿斜面向下滑行的过程中,由牛顿第二定律和运动学公式有: 3sin cos mg mg ma θμθ-=(1分) 2132v a x =(1分)解得:滑块到达斜面底端的速度1m/s v =(1分) 滑块在传送带向左滑行的距离2110.5m 2v x a '==(1分) 滑块从斜面滑下后距离A 点的最近距离 4.5m d L x '=-=(1分)(4)滑块最终会停到B 点,因为滑块第一次从斜面滑到传送带的速度小于传送带的速度,所以以后从斜面滑到传送带的速度都小于传送带的速度,所以滑块从斜面滑到传送带的速度等于滑块从传送带上滑行到斜面的速度,所以动能没损失,由能量守恒定律: 21(cos )2mg L mv μθ'=(1分)解得:滑块在斜面滑行的总路程L '=3.125 m (2分) 15.(16分)(1)设在0~2t 0内线圈中感应电动势的大小为20110ΔΔ2nB L E n t t Φ==(1分) 产生的感应电流为:201102nB L E I R Rt ==(1分) 通过的电荷量为:q =I 1·(2t 0)(1分)联立解得:20nB L q R=(2分)(2)在t 0时,由图可知,012B B =(1分) 则ad 边所受安培力22011304n B LF nB I L Rt ==(2分)。
绝密★启用前|试题命制中心2018年高考原创押题预测卷03【江苏卷】语文I试题(考试时间:150分钟试卷满分:160分)注意事项:1.本试卷共6页,包含选择题(第1题~第7题,共7题),非选择题(第8题~第20题,共13题)两部分,本卷满分为160分,考试时间为150分钟。
考试结束后,请将本试卷和答题卡一并交回。
2.答题前,请务必将自己的姓名、准考证号用0.5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置。
3.请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符。
4.作答选择题(第1题~第7题),必须用2B铅笔将答题卡上对应选项的方框涂满、涂黑;如需改动,请用橡皮擦干净后,再选涂其他答案。
作答非选择题,必须用0.5毫米黑色墨水的签字笔在答题卡上的指定位置作答,在其他位置作答一律无效。
一、语言文字运用(15分)1.在下面一段话的空缺处依次填入词语,最恰当的一组是(3分)世界文学璀璨的星空中又一颗巨星了!马尔克斯的去世引发了互联网世界几乎是排山倒海般的缅怀。
但这似乎与逝者没有多大关系,因为真正能打开《百年孤独》沉下心读完全书的人恐怕只是。
而纪念一个作家最好的方式莫过于亲近他的作品,从这个意义上说,通过马尔克斯离世这件事,让人们更加到自己的感情已变得多么空洞苍白。
A.陨落凤毛麟角意识B.陨落沧海一粟意识C.陨灭凤毛麟角认识D.陨灭沧海一粟认识2.下列诗句中,没有使用比喻修辞的一项是(3分)A.战退玉龙三百万,败鳞残甲满天飞。
B.且并水村欹侧过,人间何处不巉岩。
C.霜花强弄春颜色,相吊年光浇大白。
D.人生到处知何似,应似飞鸿踏雪泥。
3.下面是元稹的七言律诗《早春寻李校书》,顺序已经打乱,请选出排列正确的一项(3分)(1)柳枝低作翠栊裙(2)带雾山莺啼尚小(3)江弄琼花散绿纹(4)梅含鸡舌兼红气(5)今朝何事偏相觅(6)款款春风澹澹云(7)穿沙芦笋叶才分(8)撩乱芳情最是君A.(5)(8)(4)(3)(2)(7)(6)(1)B.(6)(4)(3)(1)(2)(5)(7)(8)C.(5)(8)(3)(4)(7)(2)(6)(1)D.(6)(1)(4)(3)(2)(7)(5)(8)4.在下面一段文字横线处填入语句,衔接最恰当的一项是(3分)所谓艺术的生活就是本色的生活。
江苏省南京市、盐城市2018届高三第三次高考模拟考试语文试题(最新版)编制人:__________________审核人:__________________审批人:__________________编制单位:__________________编制时间:____年____月____日序言下载提示:该文档是本店铺精心编制而成的,希望大家下载后,能够帮助大家解决实际问题。
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2018年高三数学预测及最后一讲一、填空题:2018年填空题8-14题总体难度过大. 2018年会控制难度,减少3-4道难题,按6道容易题+6道中等题+2道难题的要求命制.填空题只填结果而不要过程,这个结果可以象做解答题那样,由逻辑推理,计算而得到(演绎推理). 但由于不要过程,也可将一般情形特殊化后再求结果(类比推理),还可从个别事实中归纳出一般性的结论(归纳推理),所以解填空题的基本策略是要在“准”、“巧”、“快”上下功夫巧;解题的要领是:快——运算要快,力戒小题大作;稳——变形要稳,不可操之过急;全——答案要全,力避残缺不齐;活——解题要活,不要生搬硬套;细——审题要细,不能粗心大意.常用的方法有:①直接法,②特例法,③合理猜想法,④图象法. 数学填空题,绝大多数是计算型(尤其是推理计算型)和概念(性质)判断型的试题,应答时必须按规则进行切实的计算或者合乎逻辑的推演和判断。
解题时,要有合理的分析和判断,要求推理、运算的每一步骤都正确无误,还要求将答案表达得准确、完整. 合情推理、优化思路、少算多思将是快速、准确地解答填空题的基本要求.【解法推介】(一)、直接法这是解填空题的基本方法,它是直接从题设条件出发、利用定义、定理、性质、公式等知识,通过变形、推理、运算等过程,直接得到结果.例1.设,)1(,3)1(j m i b i i m a -+=-+=其中i ,j 为互相垂直的单位向量,又)()(b a b a -⊥+,则实数m = .(二)、特殊化法当填空题的结论唯一或题设条件中提供的信息暗示答案是一个定值时,可以把题中变化的不定量用特殊值特殊值(或特殊函数,或特殊角,特殊数列,图形特殊位置,特殊点,特殊方程,特殊模型等)代替,即可以得到正确结果.例2.在△ABC 中,角A 、B 、C 所对的边分别为a 、b 、c 。
若a 、b 、c 成等差数列,则=++CA C A cos cos 1cos cos .例3.一个四棱锥和一个三棱锥恰好可以拼接成一个三棱柱,这个四棱锥的底面为正方形,且底面边长与各侧棱长相等,这个三棱锥的底面边长与各侧棱长也都相等.设四棱锥、三棱锥、三棱柱的高分别为1h ,2h ,h ,则12::h h h =___________.例4.坐标原点为O ,抛物线22y x =与过焦点的直线交于A 、B 两点,则OA OB ∙=34- . (三)、数形结合法对于一些含有几何背景的填空题,若能数中思形,以形助数,则往往可以简捷地解决问题,得出正确的结果.例5.如果不等式x a x x )1(42->-的解集为A ,且}20|{<<⊆x x A ,那么实数a 的取值范围是 .例6.设等差数列{}n a 的前n 项和为n S ,若410S ≥,515S ≤,则5a 的最大值为________.(四)、等价转化法通过“化复杂为简单、化陌生为熟悉”,将问题等价地转化成便于解决的问题,从而得出正确的结果.例7.不等式23+>ax x 的解集为(4,b ),则a= ,b=例8.下列表中的对数值有且仅有一个是错误的:请将错误的一个改正为lg = .(五)、归纳猜想法例9.已知()1(1)()1f nf nf n-+=+(n∈N*),2)1(=f,则f(2018)= _______(六)、几种开放型填空题1:开放型填空题之多选型填空题例10.若干个能唯一确定一个数列的量称为该数列的“基量”。
江苏省普通高等学校招生考试高三模拟测试卷(三)语文附加分(满分40分,考试时间30分钟)一、阅读材料,完成20—22题(10分)20. 用斜线“/”给下面文言文中的画线部分断句。
(限5处)(5分)学者不谋道久矣,然道固不茀废,而圣人之书如日月,卓乎其可求,苟不为刑祸禄利动其心者,则勉之皆可至也。
惟足下力焉而不止,则不必相见以目而后可知其心,相语以言而后可尽其说也。
以所示文求足下之志苟不惑而止则仆将见足下大发于文著于行而质于行事以要其成焉。
(节选自欧阳修《答孙正之侔第一书》)21. 欧阳修的个人成就较高,他创作的《____________》是我国最早的诗话,开后代诗歌理论著作新体裁,他还曾独立修撰了史书《____________》。
(2分)22. 在这段回信的节选文字里,欧阳修向友人孙侔主要表达了哪两层意思?请简要说明。
(3分)________________________________________________________________________ ________________________________________________________________________二、名著阅读题(15分)23. 下列有关名著的说明,不正确的两项是(5分)()()A. 《狂人日记》是一篇表现内心生活的小说,作品采用象征的手法构思了一个“迫害狂”的形象,其语言似杂乱实敏锐,既道出了被压迫者的心声,又象征着新文化的声音。
B. 奥菲莉娅虽然爱慕哈姆莱特,但在父兄卑劣的怀疑和诽谤下,遵从他们的意愿,不与哈姆莱特接近,却又成为他们刺探王子的工具,她所受的宗法家庭的教养和管束决定了她的绝对驯服和无知。
C. 《三国演义》中,袁绍因好大喜功拒绝采纳沮授休养生息的建议,贸然出兵攻打曹操,最终大败;曹操因生性多疑中了诸葛亮的反间计,杀了熟悉水战的蔡瑁、张允,最终在赤壁之战中惨败;诸葛亮因个人感情任用毫无作战经验的马谡为主将,致使街亭失守。
1. {2} 解析:由A ={x|x ≥3,x ∈N },则∁U A ={2}.本题考查了集合补集的概念,属于容易题.2. -5 解析:z =2a 5+a 5i ,|z|=⎝⎛⎭⎫2a 52+⎝⎛⎭⎫a 52=5,则a =-5.本题主要考查复数的模的概念及除法运算等基础知识,属于容易题.3. 32 解析:由a =2,c =3得e =32.本题主要考查双曲线方程中a ,b ,c 之间的关系及离心率的概念,属于容易题.4. 2 解析:由平均数的定义知x =12,再由方差公式得方差为2.本题主要考查平均数的概念及方差公式,属于容易题.5. 9 解析:由a ⊥(a -b )知,a 2=a·b ,即5=x -4,则x =9.本题主要考查向量垂直以及向量数量积的性质与坐标运算,属于容易题.6. 53解析:由题设流程图的循环体执行如下:第1次循环z =2,x =1,y =2;第2次循环z =3,x =2,y =3;第3次循环z =5,x =3,y =5;第3次循环后z =8,此时输出的结果为53.本题考查流程图的基础知识,关键把握每一次循环体执行情况.本题属于容易题.7. (-∞,1] 解析:可由函数的图象得到函数f(x)的值域为(-∞,1].本题主要考查分段函数的图象,属于容易题.8. 16解析:连续2次抛掷一枚骰子共有36种基本事件,则事件“两次向上的数字之和等于7”共有6种,则其发生的概率为16.本题考查用列举法解决古典概型问题,属于容易题.9. 5 解析:三个圆锥的底面周长分别为53π,103π,5π,则它们的半径r 1,r 2,r 3依次为56,53,52,则r 1+r 2+r 3=5.本题考查圆锥的侧面展开图中弧长与底面圆周长的关系.本题属于容易题.10. -3125 解析:由sin θ-2cos θ=-25,sin 2θ+cos 2θ=1,θ是第三象限角,得sinθ=-2425,cos θ=-725,则sin θ+cos θ=-3125.本题考查同角的三角函数关系.本题属于容易题.11. 5或6 解析:由a 5=15,a 10=-10,得d =-5,则a n =40-5n ,T n =3(a n + a n +5)=15(11-2n), 则|T n |取得最小值时的n 的值为5或6.本题考查了等差数列的通项公式以及性质.本题属于中等题.12. 18 解析:由直线l 1和直线l 2将圆分成长度相等的四段弧,r =22,知:直线l 1和直线l 2之间的距离为4,圆心到直线l 1、直线l 2的距离都为2,可得a =22+1,b =1-22,则a 2+b 2=18.本题综合考查了直线和圆的位置关系和点到直线的距离公式.本题属于中等题.13. 12解析:由|sinx|-kx =0有且只有三个根,又0为其中一个根,即y =kx 与y =|sinx|相切,设切点为(x 0,y 0),由导数的几何意义和斜率公式得-cosx 0=y 0x 0,即得tanx 0=x 0,x 0(1+x 20)sin2x 0=x 01+x 20×sin 2x 0+cos 2x 02sinx 0cosx 0=x 01+x 20×tan 2x 0+12tanx 0=12.本题综合考查了函数的图象变换,导数的几何意义和斜率公式,三角变换等内容.本题综合性强,属于难题.14. 4+423 解析:将b =14a 代入y =11-a +21-b =11-a +8a 4a -1,其中14<a<1,求导得y′=1(1-a )2-8(4a -1)2=0,则a =-12+342,代入y =11-a +21-b,得y 的最小值为4+423.本题综合考查了代数式变形,以及利用导数求最值.本题属于难题.15. 解:(1) 由余弦定理知acosB +bcosA =a·a 2+c 2-b 22ac +b·b 2+c 2-a 22bc =2c 22c=c ,(3分)∴ acosB +bcosA c =1,∴ cosC =12.(5分)又C ∈(0,π),C =π3.(7分)(2) ∵ S △ABC =12absinC =23,∴ ab =8.(10分)∵ a +b =6,∴ c 2=a 2+b 2-2abcosC =(a +b)2-3ab =12,(13分) ∴ c =2 3.(14分)16. 证明:(1) 连结AC ,因为E ,F 分别是AB ,BC 的中点,所以EF 是△ABC 的中位线,所以EF ∥AC.(2分)由直棱柱知AA 1平行等于CC 1,所以四边形AA 1C 1C 为平行四边形,所以AC ∥A 1C 1.(5分)所以EF ∥A 1C 1,故A 1,C 1,F ,E 四点共面.(7分)(2) 连结BD ,因为直棱柱中DD 1⊥平面A 1B 1C 1D 1,A 1C 1⊂平面A 1B 1C 1D 1,所以DD 1⊥A 1C 1.(9分)因为底面A 1B 1C 1D 1是菱形,所以A 1C 1⊥B 1D 1.又DD 1∩B 1D 1=D 1,所以A 1C 1⊥平面BB 1D 1D.(11分) 因为OD ⊂平面BB 1D 1D ,所以OD ⊥A 1C 1.又OD ⊥A 1E ,A 1C 1∩A 1E =A 1,A 1C 1 平面A 1C 1FE ,A 1E ⊂平面A 1C 1FE ,所以OD ⊥平面A 1C 1FE.(14分)17. 解:(1) 以AB 所在的直线为x 轴,AB 的中垂线为y 轴,建立如图所示的直角坐标系xOy ,因为AB =2米,所以半圆的半径为1米,则半圆的方程为x 2+y 2=1(-1≤x ≤1,y ≤0).(3分) 因为水深CD =0.4米,所以OD =0.6米. 在Rt △ODM 中,DM =OM 2-OD 2=1-0.62=0.8(米).(5分)所以MN =2DM =1.6米,故渠中水面宽为1.6米.(6分)(2) 为使挖掉的土最少,等腰梯形的两腰必须与半圆相切,设切点为P(cos θ,sin θ)⎝⎛⎭⎫-π2<θ<0是圆弧BC 上的一点,过P 作半圆的切线得如图所示的直角梯形OCFE ,得切线EF 的方程为xcos θ+ysin θ=1.(8分)令y =0,得E ⎝⎛⎭⎫1cos θ,0,令y =-1,得F ⎝ ⎛⎭⎪⎫1+sin θcos θ,-1.设直角梯形OCFE 的面积为S ,则S =(CF +OE)·OC =⎝ ⎛⎭⎪⎫1cos θ+1+sin θcos θ×1=2+sin θcos θ⎝⎛⎭⎫-π2<θ<0. S ′=cos θcos θ-(2+sin θ)(-sin θ)cos 2θ=1+2sin θcos 2θ,令S′=0,解得θ=-π6,当-π2<θ<-π6时,S ′<0,函数单调递减;当-π6<θ<0时,S ′>0,函数单调递增.(12分)所以θ=-π6时,面积S 取得最小值,最小值为 3.此时CF =1+sin ⎝⎛⎭⎫-π6cos ⎝⎛⎭⎫-π6=33,即当渠底宽为233米时,所挖的土最少.(14分)18. 解:(1) 由题意B(0,1),C(0,-1),焦点F(3,0),当直线PM 过椭圆的右焦点F 时,则直线PM 的方程为x 3+y -1=1,即y =33x -1,联立⎩⎨⎧x 24+y 2=1,y =33x -1,解得⎩⎨⎧x =837,y =17,或⎩⎪⎨⎪⎧x =0,y =-1(舍),即M ⎝⎛⎭⎫837,17.(2分)连结BF ,则直线BF :x 3+y1=1,即x +3y -3=0,而BF =a =2,d =⎪⎪⎪⎪837+3·17-312+(3)2=2372=37.(4分) 故S △MBF =12·BF ·d =12·2·37=37.(5分)(2) (解法1)① 设P(m ,-2),且m ≠0,则直线PM 的斜率为k =-1-(-2)0-m=-1m ,则直线PM 的方程为y =-1mx -1,联立⎩⎨⎧y =-1m x -1,x 24+y 2=1,化简得⎝⎛⎭⎫1+4m 2x 2+8m x =0,解得M ⎝ ⎛⎭⎪⎫-8m m 2+4,4-m 2m 2+4,(8分) 所以k 1=4-m 2m 2+4-1-8m m 2+4=-2m 2-8m =14m ,k 2=1-(-2)0-m =-3m ,所以k 1·k 2=-3m ·14m =-34为定值.(10分)② 由①知,PB →=(-m ,3),PM →=(-8m m 2+4-m ,4-m 2m 2+4+2)=⎝ ⎛⎭⎪⎫-m 3-12m m 2+4,m 2+12m 2+4,所以PB →·PM →=(-m ,3)·⎝ ⎛⎭⎪⎫-m 3+12m m 2+4,m 2+12m 2+4 =m 4+15m 2+36m 2+4.(13分)令m 2+4=t >4,故PB →·PM →=(t -4)2+15(t -4)+36t =t 2+7t -8t =t -8t+7.因为y =t -8t+7在t ∈(4,+∞)上单调递增,所以PB →·PM →=t -8t +7>4-84+7=9,即PB →·PM →的取值范围为(9,+∞).(16分)(解法2)① 设点M(x 0,y 0)(x 0≠0),则直线PM 的方程为y =y 0+1x 0x -1,令y =-2,得P ⎝⎛⎭⎫-x 0y 0+1,-2.(7分)所以k 1=y 0-1x 0,k 2=-2-1-x 0y 0+1=3(y 0+1)x 0,所以k 1k 2=y 0-1x 0·3(y 0+1)x 0=3(y 20-1)x 20=3(y 20-1)4(1-y 20)=-34(定值).(10分) ② 由①知,PB →=⎝⎛⎭⎫x 0y 0+1,3,PM →=⎝⎛⎭⎫x 0+x 0y 0+1,y 0+2,所以PB →·PM →=x 0y 0+1⎝⎛⎭⎫x 0+x 0y 0+1+3(y 0+2) =x 20(y 0+2)(y 0+1)2+3(y 0+2) =4(1-y 20)(y 0+2)(y 0+1)2+3(y 0+2)=(7-y 0)(y 0+2)y 0+1.(13分) 令t =y 0+1∈(0,2),则PB →·PM →=(8-t )(t +1)t =-t +8t+7,因为y =-t +8t+7在t ∈(0,2)上单调递减,所以PB →·PM →=-t +8t +7>-2+82+7=9,即PB →·PM →的取值范围为(9,+∞).(16分)19. 解:(1) q =0,a n +1-a n =p·3n -1,∴ a 2=a 1+p =12+p ,a 3=a 2+3p =12+4p.由数列{a n }为等比数列,得⎝⎛⎭⎫12+p 2=12⎝⎛⎭⎫12+4p ,解得p =0或p =1.(3分) 当p =0时,a n +1=a n ,∴ a n =12符合题意;(4分)当p =1时,a n +1-a n =3n -1,∴ a n =a 1+(a 2-a 1)+(a 3-a 2)+…+(a n -a n -1)=12+(1+3+…+3n -2)=12+1-3n -11-3=12·3n -1, ∴ a n +1a n=3符合题意.(6分)(2) (解法1)若p =1,a n +1-a n =3n -1-nq , ∴ a n =a 1+(a 2-a 1)+(a 3-a 2)+…+(a n -a n -1) =12+(1+3+…+3n -2)-[1+2+…+(n -1)]q =12[3n -1-n(n -1)q].(8分)∵ 数列{a n }的最小项为a 4,∴ 对 n ∈N *,有12[3n -1-n(n -1)q]≥a 4=12(27-12q)恒成立,即3n -1-27≥(n 2-n -12)q对 n ∈N *恒成立.(10分)当n =1时,有-26≥-12q ,∴ q ≥136;当n =2时,有-24≥-10q ,∴ q ≥125;当n =3时,有-18≥-6q ,∴ q ≥3; 当n =4时,有0≥0,∴ q ∈R ;(12分)当n ≥5时,n 2-n -12>0,所以有q ≤3n -1-27n 2-n -12恒成立.令c n =3n -1-27n 2-n -12(n ≥5,n ∈N *),有c n +1-c n =2(n 2-2n -12)3n -1+54n (n 2-16)(n 2-9)>0,即数列{c n }为递增数列,∴ q ≤c 5=274.(15分)综上所述,3≤q ≤274.(16分)(解法2)因为p =1,a n +1-a n =3n -1-nq , 又a 4为数列{a n }的最小项,所以⎩⎪⎨⎪⎧a 4-a 3≤0,a 5-a 4≥0,即⎩⎪⎨⎪⎧9-3q ≤0,27-4q ≥0,所以3≤q ≤274.(8分)此时a 2-a 1=1-q <0,a 3-a 2=3-2q <0, 所以a 1>a 2>a 3≥a 4.(10分)当n ≥4时,令b n =a n +1-a n ,b n +1-b n =2·3n -1-q ≥2·34-1-274>0,所以b n +1>b n ,所以0≤b 4<b 5<b 6<…,即a 4≤a 5<a 6<a 7<….(14分)综上所述,当3≤q <274时,a 4为数列{a n }的最小项,即所求q 的取值范围为⎣⎡⎦⎤3,274.(16分)20. 解:(1) 当a =1时,f(x)=e x (2x -1)-x +1,f ′(x)=e x (2x +1)-1,(1分) 由于f′(0)=0,当x ∈(0,+∞)时,e x >1,2x +1>1,∴ f ′(x)>0; 当x ∈(-∞,0)时,0<e x <1,2x +1<1,∴ f ′(x)<0,∴ f(x)在区间(-∞,0)上单调递减,在区间(0,+∞)上单调递增.(4分) (2) ① 由f(x)<0得e x (2x -1)<a(x -1). 当x =1时,不等式显然不成立;当x >1时,a >e x (2x -1)x -1;当x <1时,a <e x (2x -1)x -1.(6分)记g(x)=e x (2x -1)x -1,g ′(x)=e x (2x +1)(x -1)-e x (2x -1)(x -1)2=e x (2x 2-3x )(x -1)2,∴ g(x)在区间(-∞,0)和⎝⎛⎭⎫32,+∞上为增函数,在(0,1)和⎝⎛⎭⎫1,32上为减函数. ∴ 当x >1时,a >g ⎝⎛⎭⎫32=4e 32,当x <1时,a <g(0)=1.(8分)综上所述,所有a 的取值范围为(-∞,1)∪()4e 32,+∞.(9分)② 由①知a <1时,x 0∈(-∞,1), 由f(x 0)<0,得g(x 0)>a ,又g(x)在区间(-∞,0)上单调递增,在(0,1)上单调递减,且g(0)=1>a ,∴ g(-1)≤a ,即a ≥32e ,∴ 32e ≤a <1.(12分)当a >4e 32时,x 0∈(1,+∞),由f(x 0)<0,得g(x 0)<a ,又g(x)在区间⎝⎛⎭⎫1,32上单调递减,在⎝⎛⎭⎫32,+∞上单调递增,且g ⎝⎛⎭⎫32=4e 32<a ,∴ ⎩⎪⎨⎪⎧g (2)<a ,g (3)≥a ,解得3e 2<a ≤5e 32.(15分)综上所述,所有a 的取值范围为⎣⎡⎭⎫32e ,1∪⎝⎛⎦⎤3e 2,5e 32.(16分)21. A. (1) 证明:因为BD =CD ,所以∠BCD =∠CBD. 因为CE 是圆的切线,所以∠ECD =∠CBD.(2分) 所以∠ECD =∠BCD ,所以∠BCE =2∠ECD.因为∠EAC =∠BCE ,所以∠EAC =2∠ECD.(5分)(2) 解:因为BD ⊥AB ,所以AC ⊥CD ,AC =AB.(6分) 因为BC =BE ,所以∠BEC =∠BCE =∠EAC , 所以AC =EC.(7分)由切割线定理得EC 2=AE·BE ,即AB 2=AE·(AE -AB), 即AB 2+2AB -4=0,解得AB =5-1.(10分)B. 解:设M =⎣⎢⎡⎦⎥⎤a b c d ,则⎣⎢⎡⎦⎥⎤a b c d ⎣⎢⎡⎦⎥⎤11=3⎣⎢⎡⎦⎥⎤11=⎣⎢⎡⎦⎥⎤33,故⎩⎪⎨⎪⎧a +b =3,c +d =3.(3分) ⎣⎢⎡⎦⎥⎤a b cd ⎣⎢⎡⎦⎥⎤-1 2=⎣⎢⎡⎦⎥⎤915,故⎩⎪⎨⎪⎧-a +2b =9,-c +2d =15.(6分) 联立以上两方程组解得a =-1,b =4,c =-3,d =6,故M =⎣⎢⎡⎦⎥⎤-1 4-36.(10分)C. 解:由⎩⎪⎨⎪⎧x =t ,y =3t 3,消去t 得曲线C 1的普通方程为y =33x(x ≥0);(3分)由ρ=2,得ρ2=4,得曲线C 2的直角坐标方程是x 2+y 2=4.(6分) 联立⎩⎪⎨⎪⎧y =33x (x ≥0),x 2+y 2=4,解得⎩⎨⎧x =3,y =1.故曲线C 1与C 2的交点坐标为(3,1).(10分)D. (1) 证明:由a >0,有f(x)=⎪⎪⎪⎪x +1a +|x -a| ≥⎪⎪⎪⎪x +1a -(x -a )=1a +a ≥2, 所以f(x)≥2.(4分)(2) 解:f(3)=⎪⎪⎪⎪3+1a +|3-a|. 当a >3时,f(3)=a +1a ,由f(3)<5得3<a <5+212.(6分)当0<a ≤3时,f(3)=6-a +1a ,由f(3)<5得1+52<a ≤3.(8分)综上,a 的取值范围是⎝⎛⎭⎪⎫1+52,5+212.(10分)22. 解:(1) 记“该网民购买i 种商品”为事件A i ,i =2,3,则 P(A 3)=34×23×12=14,P(A 2)=34×23×⎝⎛⎭⎫1-12+34×⎝⎛⎭⎫1-23×12+⎝⎛⎭⎫1-34×23×12=1124,(3分) 所以该网民至少购买2种商品的概率为 P(A 3)+P(A 2)=14+1124=1724.答:该网民至少购买2种商品的概率为1724.(5分)(2) 随机变量η的可能取值为0,1,2,3, P(η=0)=⎝⎛⎭⎫1-34×⎝⎛⎭⎫1-23×⎝⎛⎭⎫1-12=124, 又P(η=2)=P(A 2)=1124,P(η=3)=P(A 3)=14,所以P(η=1)=1-124-1124-14=14.所以随机变量η的概率分布为(8分)故数学期望E(η)=0×124+1×14+2×1124+3×14=2312.(10分)23. 解:(1) 当k =4时,第4层标注数字依次为x 1,x 2,x 3,x 4,第3层标注数字依次为x 1+x 2,x 2+x 3,x 3+x 4,第2层标注数字依次为x 1+2x 2+x 3,x 2+2x 3+x 4,所以x 0=x 1+3x 2+3x 3+x 4.(2分)因为x 0为2的倍数,所以x 1+x 2+x 3+x 4是2的倍数,则x 1,x 2,x 3,x 4四个都取0或两个取0两个取1或四个都取1,所以共有1+C 24+1=8种标注方法.(4分)(2) 当k=11时,第11层标注数字依次为x1,x2,…,x11,第10层标注数字依次为x1+x2,x2+x3,…,x10+x11,第9层标注数字依次为x1+2x2+x3,x2+2x3+x4,…,x9+2x10+x11,以此类推,可得x0=x1+C110x2+C210x3+…+C910x10+x11.(6分)因为C210=C810=45,C310=C710=120,C410=C610=210,C510=252均为3的倍数,所以只要x1+C110x2+C910x10+x11是3的倍数,即只要x1+x2+x10+x11是3的倍数.(8分) 所以x1,x2,x10,x11四个都取0或三个取1一个取0,而其余七个x3,x4, (x9)以取0或1,这样共有(1+C34)×27=640种标注方法.(10分)。
2018年江苏高考预测试题(三)(对应学生用书第137页)(限时:120分钟)参考公式样本数据x 1,x 2,…,x n 的方差s 2=1n ni =1 (x i -x )2,其中x =1n ni =1x i . 棱柱的体积V =Sh ,其中S 是棱柱的底面积,h 是高. 棱锥的体积V =13Sh ,其中S 是棱锥的底面积,h 是高.数学Ⅰ试题一、填空题(本大题共14小题,每小题5分,共70分.请把答案填写在题中模线上)1.已知A ={x |x +1>0},B ={-2,-1,0,1},则(∁R A )∩B =________.{-2,-1} [因为集合A ={x |x >-1},所以∁R A ={x |x ≤-1}, 则(∁R A )∩B ={x |x ≤-1}∩{-2,-1,0,1} ={-2,-1}.]2.若i(x +y i)=3+4i ,x ,y ∈R ,则复数x +y i 的模等于________.5 [因为i(x +y i)=3+4i ,所以x +y i =3+4i i =(3+4i )(-i )i (-i )=4-3i ,故|x +y i|=|4-3i|=42+(-3)2=5.]3.下表是关于青年观众的性别与是否喜欢戏剧的调查数据,人数如表所示:若在“不喜欢戏剧的男性青年观众”的人中抽取了8人,则n 的值为________. 30 [由题意840=n40+10+40+60,解得n =30.]4.如图1所示,在圆心角为直角的扇形OAB 中,分别以OA ,OB 为直径作两个半圆.在扇形OAB 内随机取一点,则此点取自阴影部分的概率是________.图11-2π [设OA =OB =2,如图,由题意得S 弓形AC =S 弓形BC =S 弓形OC ,所以S 空白=S △OAB =12×2×2=2.又因为S 扇形OAB =14×π×22=π,所以S 阴影=π-2.所以P =S 阴影S 扇形OAB =π-2π=1-2π.] 5.在同一直角坐标系中,函数y =sin ⎝ ⎛⎭⎪⎫x +π3(x ∈[0,2π))的图象和直线y =12的交点的个数是________.【导学号:56394125】2 [令y =sin ⎝ ⎛⎭⎪⎫x +π3=12,解得x +π3=π6+2k π,或x +π3=5π6+2k π,k ∈Z ;即x =-π6+2k π,或x =π2+2k π,k ∈Z ; ∴同一直角坐标系中,函数y 的图象和直线y =12 在x ∈[0,2π)内的交点为⎝ ⎛⎭⎪⎫π2,12和⎝ ⎛⎭⎪⎫11π6,12,共2个.]6.如下是一个算法的伪代码,则输出的结果是________.7.现有一根n 节的竹竿,自上而下每节的长度依次构成等差数列,最上面一节长为10 cm ,最下面的三节长度之和为114 cm ,第6节的长度是首节与末节长度的等比中项,则n =________.16 [设对应的数列为{a n },公差为d (d >0).由题意知a 1=10,a n +a n -1+a n -2=114,a 26=a 1a n ,由a n +a n -1+a n -2=114,得3a n -1=114,解得a n -1=38,又(a 1+5d )2=a 1(a n -1+d ),即(10+5d )2=10(38+d ),解得d =2,所以a n -1=a 1+(n -2)d =38,即10+2(n -2)=38,解得n =16.] 8.设α为锐角,若sin ⎝ ⎛⎭⎪⎫α+π6=35,则cos ⎝ ⎛⎭⎪⎫2α-π6=________. 2425[∵0<α<π2,∴π6<α+π6<2π3,-π3<α-π3<π6. ∵sin ⎝ ⎛⎭⎪⎫α+π6=35<32,故α+π6<π3,∴α<π6. ∴cos ⎝ ⎛⎭⎪⎫α+π6=45;又∵-π3<α-π3<π6,sin ⎝ ⎛⎭⎪⎫α+π6=cos ⎣⎢⎡⎦⎥⎤π2-⎝ ⎛⎭⎪⎫α+π6=cos ⎝ ⎛⎭⎪⎫α-π3=35, ∴sin ⎝ ⎛⎭⎪⎫α-π3=-45.cos ⎝ ⎛⎭⎪⎫2α-π6=cos ⎣⎢⎡⎦⎥⎤⎝ ⎛⎭⎪⎫α+π6+⎝ ⎛⎭⎪⎫α-π3=cos ⎝ ⎛⎭⎪⎫α+π6cos ⎝ ⎛⎭⎪⎫α-π3-sin ⎝ ⎛⎭⎪⎫α+π6sin ⎝ ⎛⎭⎪⎫α-π3=45×35+45×35=2425.]9.已知实数x ,y 满足不等式⎩⎨⎧2x -y ≥0,x +y -4≥0,x ≤3,则2x 3+y 3x 2y 的取值范围是________.⎣⎢⎡⎦⎥⎤3,559 [ω=2x 3+y 3x 2y =2x y +y 2x 2.令t =y x ,由图可知13≤t ≤2, 则ω=t 2+2t ,t ∈⎣⎢⎡⎦⎥⎤13,2,令ω′=2t -2t 2=0,则t =1.ω在t ∈⎣⎢⎡⎦⎥⎤13,1上为减函数,在t ∈[1,2]上为增函数,t =1时,ω有最小值3,t =13时,ω有最大值559,故t 的范围为⎣⎢⎡⎦⎥⎤3,559.]10.在平面直角坐标系xOy 中,双曲线E :x 2a 2-y 2b 2=1(a >0,b >0)的左顶点为A ,过双曲线E 的右焦点F 作与实轴垂直的直线交双曲线E 于B ,C 两点,若△ABC 为直角三角形,则双曲线E 的离心率为________.2 [如图,由题意得∠BAC =90°,∠BAF =∠F AC =45°,从而AF =BF .将x =c 代入双曲线方程得y B =b 2a ,AF =a +c ,从而b 2a =a +c ,即b 2=a 2+ac ,则c 2-ac -2a 2=0,即e 2-e -2=0,从而e =2.]图211.如图2,三棱锥S -ABC 中,∠SBA =∠SCA =90°,△ABC 是斜边AB =a 的等腰直角三角形,则以下结论中: ①异面直线SB 与AC 所成的角为90°; ②直线SB ⊥平面ABC ; ③平面SBC ⊥平面SAC ; ④点C 到平面SAB 的距离是12a . 其中正确结论的序号是________.①②③④ [由题意知AC ⊥平面SBC ,故AC ⊥SB ,SB ⊥平面ABC ,平面SBC ⊥平面SAC ,①②③正确;取AB 的中点E ,连接CE ,可证得CE ⊥平面SAB ,故CE 的长度12a 即为C 到平面SAB 的距离,④正确.]12.在△ABC 中,A =30°,AB =3,AC =23,且AD →+2BD →=0,则AC →·CD →=________.-6 [如图所示,△ABC 中,A =30°,AB =3,AC =23,∴cos 30°=323=32, ∴∠ABC =90°, ∴BC =3; 又AD →+2BD →=0,∴A (0,3),D (0,1),C (3,0); ∴AC →=(3,-3),CD →=(-3,1), ∴AC →·CD →=3×(-3)-3×1=-6.]13.已知a ,b 为正实数,函数f (x )=ax 3+bx +2x 在[0,1]上的最大值为4,则f (x )在[-1,0]上的最小值为________.-32 [由a ,b 为正实数,可得函数y =ax 3+bx 的导函数y ′=3ax 2+b >0,即可得函数y =ax 3+bx 在R 上是增函数,由此可得函数f (x )=ax 3+bx +2x 在R 上是增函数,又由函数f (x )=ax 3+bx +2x 在[0,1]上的最大值为f (1)=a +b +2=4,可得a +b =2,∴函数f (x )在[-1,0]上的最小值为f (-1)=-a -b +12=-2+12=-32.]14.由正整数组成的一组数据x 1,x 2,x 3,x 4,其平均数和中位数都是2,且标准差等于1,则这组数据为________.(从小到大排列)1,1,3,3 [假设这组数据按从小到大的顺序排列为x 1,x 2,x 3,x 4, 则⎩⎪⎨⎪⎧x 1+x 2+x 3+x 44=2,x 2+x 32=2,∴⎩⎨⎧x 1+x 4=4,x 2+x 3=4.又s =14[(x 1-2)2+(x 2-2)2+(x 3-2)2+(x 4-2)2] =12(x 1-2)2+(x 2-2)2+(4-x 2-2)2+(4-x 1-2)2 =122[(x 1-2)2+(x 2-2)2] =1,∴(x 1-2)2+(x 2-2)2=2. 同理可求得(x 3-2)2+(x 4-2)2=2.由x 1,x 2,x 3,x 4均为正整数,且(x 1,x 2),(x 3,x 4)均为圆(x -2)2+(y -2)2=2上的点,分析知x 1,x 2,x 3,x 4应为1,1,3,3.]二、解答题(本大题共6小题,共90分.解答时应写出文字说明、证明过程或演算步骤)15.(本小题满分14分)已知△ABC 的内角A ,B ,C 所对的边分别是a ,b ,c ,且满足a =3b cos C . (1)求tan Ctan B 的值;(2)若a =3,tan A =3,求△ABC 的面积.[解] (1)由正弦定理a sin A =b sin B =csin C =2R 及a =3b cos C 可得2R sin A =3×2R sin B cos C ,即sin A =3sin B cos C .∵A +B +C =π,∴sin A =sin(B +C )=3sin B cos C , ∴sin B cos C +cos B sin C =3sin B cos C , ∴cos B sin C =2sin B cos C ,∴cos B sin C sin B cos C =2,故tan Ctan B=2.6分(2)法一:由A +B +C =π,得tan(B +C )=tan(π-A )=-3, 即tan B +tan C1-tan B ·tan C=-3,将tan C =2tan B 代入得3tan B 1-2tan 2B=-3,解得tan B =1或tan B =-12. 根据tan C =2tan B ,得tan C ,tan B 同号, 又tan C ,tan B 同时为负数不合题意, ∴tan B =1,tan C =2,∴sin B =22,sin C =255,sin A =31010, 由正弦定理可得331010=b22,∴b =5, ∴S △ABC =12ab sin C =12×3×5×255=3.法二:由A+B+C=π,得tan(B+C)=tan(π-A)=-3,即tan B+tan C1-tan B·tan C=-3,将tan C=2tan B代入得3tan B1-2tan2B=-3,解得tan B=1或tan B=-12.根据tan C=2tan B得tan C,tan B同号,又tanC,tan B同时为负数不合题意,∴tan B=1,tan C=2.又∵a=3b cos C=3,∴b cos C=1,∴ab cos C=3,∴ab cos C tan C=6,∴S△ABC =12ab sin C=12×6=3. 14分16.(本小题满分14分)如图3,四棱锥E-ABCD中,EA=EB,AB∥CD,AB⊥BC,AB=2CD.图3(1)求证:AB⊥ED;(2)线段EA上是否存在点F,使DF∥平面BCE?若存在,求出EFEA的值;若不存在,说明理由.【导学号:56394126】[解](1)证明:取AB中点O,连接EO,DO、∵EA=EB,∴EO⊥AB.∵AB ∥CD ,AB =2CD , ∴BO ∥CD ,BO =CD .又AB ⊥BC ,∴四边形OBCD 为矩形,∴AB ⊥DO . ∵EO ∩DO =O ,∴AB ⊥平面EOD . ∴AB ⊥ED .6分(2)存在点F ,当F 满足EF EA =12,即F 为EA 中点时,有DF ∥平面BCE . 理由如下:取EB 中点G ,连接CG ,FG ,DF . ∵F 为EA 中点,∴FG ∥AB ,FG =12AB .∵AB ∥CD ,CD =12AB ,∴FG ∥CD ,FG =CD . ∴四边形CDFG 是平行四边形,∴DF ∥CG . ∵DF ⊄平面BCE ,CG ⊂平面BCE , ∴DF ∥平面BCE .14分17.(本小题满分14分)如图4,有一块半径为R 的半圆形空地,开发商计划征地建一个矩形游泳池ABCD 和其附属设施,附属设施占地形状是等腰△CDE ,其中O 为圆心,A ,B 在圆的直径上,C ,D ,E 在圆周上.图4(1)设∠BOC =θ,征地面积记为f (θ),求f (θ)的表达式; (2)当θ为何值时,征地面积最大?[解] (1)连接OE ,OC ,可得OE =R ,OB =R cos θ,BC =R sin θ,θ∈⎝ ⎛⎭⎪⎫0,π2,∴f (θ)=2S 梯形OBCE =R 2(sin θcos θ+cos θ),θ∈⎝ ⎛⎭⎪⎫0,π2.6分(2)求导数可得f ′(θ)=-R 2(2sin θ-1)(sin θ+1), 令f ′(θ)=0,则sin θ=12,∵θ∈⎝ ⎛⎭⎪⎫0,π2,∴θ∈⎝ ⎛⎭⎪⎫0,π6时,f ′(θ)>0,θ∈⎝ ⎛⎭⎪⎫π6,π2时,f ′(θ)<0,∴θ=π6时,f (θ)取得最大,即θ=π6时,征地面积最大.14分18.(本小题满分16分)已知{a n }是公差为d 的等差数列,{b n }是公比为q 的等比数列,q ≠±1,正整数组E =(m ,p ,r )(m <p <r ). (1)若a 1+b 2=a 2+b 3=a 3+b 1,求q 的值;(2)若数组E 中的三个数构成公差大于1的等差数列,且a m +b p =a p +b r =a r +b m ,求q 的最大值.(3)若b n =⎝ ⎛⎭⎪⎫-12n -1,a m +b m =a p +b p =a r +b r =0,试写出满足条件的一个数组E 和对应的通项公式a n .(注:本小问不必写出解答过程)[解] (1)∵a 1+b 2=a 2+b 3=a 3+b 1,∴a 1+b 1q =a 1+d +b 1q 2=a 1+2d +b 1,化为:2q 2-q -1=0,q ≠±1. 解得q =-12.4分(2)a m +b p =a p +b r =a r +b m ,即a p -a m =b p -b r ,∴(p -m )d =b m (q p -m -q r -m ), 同理可得:(r -p )d =b m (q r -m -1).∵m ,p ,r 成等差数列,∴p -m =r -p =12(r -m ),记q p -m =t ,则2t 2-t -1=0,∵q ≠±1,t ≠±1,解得t =-12,即q p -m =-12,∴-1<q <0, 记p -m =α,α为奇数,由公差大于1,∴α≥3.(3)满足题意的数组为E =(m ,m +2,m +3),此时通项公式为:a n =⎝ ⎛⎭⎪⎫-12m-1·⎝ ⎛⎭⎪⎫38n -38m -1,m ∈N *. 例如E =(1,3,4),a n =38n -118.16分19.(本小题满分16分)已知函数f (x )=13x 3-ax +1.(1)若x =1时,f (x )取得极值,求a 的值; (2)求f (x )在[0,1]上的最小值;(3)若对任意m ∈R ,直线y =-x +m 都不是曲线 y =f (x )的切线,求a 的取值范围. [解] (1)因为f ′(x )=x 2-a ,当x =1时,f (x )取得极值,所以f ′(1)=1-a =0,a =1. 又当x ∈(-1,1)时,f ′(x )<0,x ∈(1,+∞)时,f ′(x )>0, 所以f (x )在x =1处取得极小值,即a =1符合题意. 4分(2)当a ≤0时,f ′(x )>0对x ∈(0,1)成立,所以f (x )在[0,1]上单调递增,f (x )在x =0处取最小值f (0)=1, 当a >0时,令f ′(x )=x 2-a =0,x 1=-a ,x 2=a , 当0<a <1时,a <1,x ∈(0,a )时,f ′(x )<0,f (x )单调递减, x ∈(a ,1)时,f ′(x )>0,f (x )单调递增, 所以f (x )在x =a 处取得最小值f (a )=1-2a a3. 当a ≥1时,a ≥1,x ∈[0,1]时,f ′(x )<0,f (x )单调递减, 所以f (x )在x =1处取得最小值f (1)=43-a .综上所述,当a ≤0时,f (x )在x =0处取最小值f (0)=1;当0<a <1时,f (x )在x =a 处取得最小值f (a )=1-2a a3; 当a ≥1时,f (x )在x =1处取得最小值f (1)=43-a .10分(3)因为∀m ∈R ,直线y =-x +m 都不是曲线y =f (x )的切线,所以f ′(x )=x 2-a ≠-1对x ∈R 成立,只要f ′(x )=x 2-a 的最小值大于-1即可, 而f ′(x )=x 2-a 的最小值为f (0)=-a , 所以-a >-1,即a <1. 所以a 的取值范围是(-∞,1).16分20.(本小题满分16分)已知点P (4,4),圆C :(x -m )2+y 2=5(m <3)与椭圆E :x 2a 2+y 2b 2=1(a >b >0)有一个公共点A (3,1),F 1,F 2分别是椭圆的左、右焦点,直线PF 1与圆C 相切.(1)求m 的值与椭圆E 的方程;(2)设Q 为椭圆E 上的一个动点,求AP →·AQ →的取值范围.图5[解] (1)点A 代入圆C 方程,得(3-m )2+1=5. ∵m <3,∴m =1. 圆C :(x -1)2+y 2=5. 设直线PF 1的斜率为k , 则PF 1:y =k (x -4)+4, 即kx -y -4k +4=0. ∵直线PF 1与圆C 相切,∴|k -0-4k +4|k 2+1= 5. 解得k =112或k =12.当k =112时,直线PF 1与x 轴的交点横坐标为3611,不合题意,舍去.当k =12时,直线PF 1与x 轴的交点横坐标为-4, ∴c =4.F 1(-4,0),F 2(4,0).2a =AF 1+AF 2=52+2=62,a =32,a 2=18,b 2=2. 椭圆E 的方程为x 218+y 22=1.10分(2)AP →=(1,3),设Q (x ,y ),AQ →=(x -3,y -1), AP →·AQ →=(x -3)+3(y -1)=x +3y -6. ∵x 218+y 22=1,即x 2+(3y )2=18, 而x 2+(3y )2≥2|x |·|3y |, ∴-18≤6xy ≤18.则(x +3y )2=x 2+(3y )2+6xy =18+6xy 的取值范围是[0,36]. x +3y 的取值范围是[-6,6].∴AP →·AQ →=x +3y -6的取值范围是[-12,0].16分 数学Ⅱ(附加题)21.[选做题](本题包括A 、B 、C 、D 四小题,请选定其中两小题........,并在相应的.....答题区域内作答.........若多做,则按作答的前两小题评分.解答时应写出文字说明、证明过程或演算步骤)图6A .[选修4-1:几何证明选讲](本小题满分10分)如图6,直线AB 为圆的切线,切点为B ,点C 在圆上,∠ABC 的角平分线BE 交圆于点E ,DB 垂直BE 交圆于点D .若设圆的半径为1,BC =3,延长CE 交AB 于点F ,求△BCF 外接圆的半径.【导学号:56394127】[解] 如图,连接DE ,交BC 于点G.由弦切角定理,得∠ABE =∠BCE ,而∠ABE =∠CBE ,故∠CBE =∠BCE ,所以BE =CE .又因为DB ⊥BE ,所以DE 为圆的直径,∠DCE =90°. 由勾股定理可得DB =DC . 因为∠CDE =∠BDE ,DB =DC , 故DG 是BC 边的中垂线,所以BG =32.设DE 的中点为O ,连接BO ,则∠BOG =60°,从而∠ABE =∠BCE =∠CBE =30°,所以CF ⊥BF ,故Rt △BCF 外接圆的半径等于32.10分B .[选修4-2:矩阵与变换](本小题满分10分) 已知矩阵A =⎣⎢⎡⎦⎥⎤1011,B =⎣⎢⎡⎦⎥⎤0 23 2. 求满足条件AM =B 的矩阵M 及曲线C :x 2+y 2=1在矩阵M 对应变换下的曲线方程C ′. [解] 设M =⎣⎢⎡⎦⎥⎤a b c d , AM =⎣⎢⎡⎦⎥⎤1 011⎣⎢⎡⎦⎥⎤a b cd =⎣⎢⎡⎦⎥⎤a b a +c b +d =⎣⎢⎡⎦⎥⎤0 232, 得⎩⎨⎧a =0,a +c =3,b =2,b +d =2,∴a =0,b =2,c =3,d =0.∴M =⎣⎢⎡⎦⎥⎤0 23 0. 设曲线C 上任意一点P (x ,y )在矩阵M 对应的变换作用下变为点P ′(x ′,y ′), 则M ⎣⎢⎡⎦⎥⎤x y =⎣⎢⎡⎦⎥⎤0 23 0⎣⎢⎡⎦⎥⎤x y =⎣⎢⎡⎦⎥⎤2y 3x =⎣⎢⎡⎦⎥⎤x ′y ′, ∴⎩⎨⎧2y =x ′,3x =y ′,即⎩⎪⎨⎪⎧y =x ′2,x =y ′3,代入曲线C :x 2+y 2=1, 得⎝ ⎛⎭⎪⎫x ′22+⎝ ⎛⎭⎪⎫y ′32=1. ∴曲线C ′的方程是x 24+y 29=1.10分C .[选修4-4:坐标系与参数方程](本小题满分10分)在极坐标系中,已知点A ⎝ ⎛⎭⎪⎫2,π2,点B 在直线l :ρcos θ+ρsin θ=0(0≤θ≤2π)上,当线段AB 最短时,求点B 的极坐标.[解] 以极点为原点,极轴为x 轴正半轴,建立平面直角坐标系, 则点A ⎝ ⎛⎭⎪⎫2,π2的直角坐标为(0,2),直线l 的直角坐标方程为x +y =0.AB 最短时,点B 为直线x -y +2=0与直线l 的交点,联立⎩⎨⎧ x -y +2=0,x +y =0,得⎩⎨⎧x =-1,y =1,所以点B 的直角坐标为(-1,1).所以点B 的极坐标为⎝ ⎛⎭⎪⎫2,3π4.10分 D .[选修4-5:不等式选讲](本小题满分10分) 设函数f (x )=⎪⎪⎪⎪⎪⎪x +1a +|x -a |(a >0).若f (3)<5,求a 的取值范围. [解] f (3)=⎪⎪⎪⎪⎪⎪3+1a +|3-a |.当a >3时,f (3)=a +1a ,由f (3)<5,得3<a <5+212. 当0<a ≤3时,f (3)=6-a +1a , 由f (3)<5,得1+52<a ≤3.综上,a 的取值范围是⎝ ⎛⎭⎪⎫1+52,5+212.10分[必做题](第22题,第23题,每题10分,共20分.解答时应写出文字说明、证明过程或演算步骤)22.(本小题满分10分)已知正三棱柱ABC -A 1B 1C 1中,AB =2,AA 1=3,点D 为AC 的中点,点E 在线段AA 1上.图7(1)当AE ∶EA 1=1∶2时,求证:DE ⊥BC 1;(2)是否存在点E ,使二面角D -BE -A 等于60°,若存在,求AE 的长;若不存在,请说明理由.[解] (1)证明:连接DC 1,因为ABC -A 1B 1C 1为正三棱柱,所以△ABC 为正三角形,又因为D 为AC 的中点,所以BD ⊥AC ,又平面ABC ⊥平面ACC 1A 1,所以BD ⊥平面ACC 1A 1,所以BD ⊥DE . 因为AE ∶EA 1=1∶2,AB =2,AA 1=3,所以AE =33,AD =1, 所以在Rt △ADE 中,∠ADE =30°,在Rt △DCC 1中,∠C 1DC =60°,所以∠EDC 1=90°,即ED ⊥DC 1,所以ED ⊥平面BDC 1,BC 1⊂平面BDC 1,所以ED ⊥BC 1. 4分(2)假设存在点E 满足条件,设AE =h .取A 1C 1的中点D 1,连接DD 1,则DD 1⊥平面ABC ,所以DD 1⊥AD ,DD 1⊥BD ,分别以DA ,DB ,DD 1所在直线为x ,y ,z 轴建立空间直角坐标系D -xyz ,则A (1,0,0),B (0,3,0), E (1,0,h ),所以DB →=(0,3,0),DE →=(1,0,h ),AB →=(-1,3,0),AE →=(0,0,h ), 设平面DBE 的一个法向量为n 1=(x 1,y 1,z 1), 则⎩⎪⎨⎪⎧n 1·DB →=0,n 1·DE →=0,即⎩⎨⎧3y 1=0,x 1+hz 1=0,令z 1=1, 得n 1=(-h,0,1),同理,平面ABE 的一个法向量为n 2=(x 2,y 2,z 2), 则⎩⎪⎨⎪⎧n 2·AB →=0,n 2·AE →=0,即⎩⎨⎧-x 2+3y 2=0,hz 2=0.令y 2=1,得 n 2=(3,1,0).所以cos 〈n 1,n 2〉=|-3h |h 2+1·2=cos 60°=12.解得h =22<3,故存在点E ,当AE =22时,二面角D -BE -A 等于60°.10分23.(本小题满分10分)已知(x +2)n =a 0+a 1(x -1)+a 2(x -1)2+…+a n (x -1)n (n ∈N *).(1)求a 0及S n = ni =1a i ; (2)试比较S n 与(n -2)3n +2n 2的大小,并说明理由.[解] (1)令x =1,则a 0=3n ,令x =2,则 ni =0a i =4n ,所以S n = ni =1a i =4n -3n . 2分(2)要比较S n 与(n -2)3n +2n 2的大小,只要比较4n 与(n -1)3n +2n 2的大小. 当n =1时,4n >(n -1)3n +2n 2,当n =2或3时,4n <(n -1)3n +2n 2, 当n =4时,4n <(n -1)3n +2n 2, 当n =5时,4n >(n -1)3n +2n 2.猜想:当n ≥5时,4n >(n -1)3n +2n 2.下面用数学归纳法证明: ①由上述过程可知,当n =5时,结论成立.②假设当n =k (k ≥4,k ∈N *)时结论成立,即4k >(k -1)3k +2k 2,两边同乘以4,得4k +1>4[(k -1)3k +2k 2]=k 3k +1+2(k +1)2+[(k -4)3k +6k 2-4k -2],而(k -4)3k +6k 2-4k -2=(k -4)3k +6(k 2-k -2)+2k +10=(k -4)3k +6(k -2)(k +1)+2k +10>0,所以4k +1>[(k +1)-1]3k +1+2(k +1)2, 即n =k +1时结论也成立.8分由①②可知,当n ≥5时,4n >(n -1)3n +2n 2成立.综上所述,当n =1时,S n >(n -2)3n +2n 2;当n =2或3或4时,4n <(n -1)3n +2n 2,S n <(n -2)3n +2n 2; 当n ≥5时,S n >(n -2)3n +2n 2.10分。