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2012/2013 ADMISSION EXAMINATION PAPERPart A Reading (30%)Suggested time: 30 minutes Each question is worth onepoint.PASSAGE ONEA.Public transportation receded into a cultural backwater in the 1950s as prosperousmiddle class people took advantage of cheap gas to put into their vehicles. With access to and use of fossil fuels a growing concern in the climate-changing, post-9/11 world, people are beginning to re-evaluate. And while buses and trains are really on the same team in terms of sustainable transportation—either option a vast improvement over the one-car, one-rider model—outspoken camps have sprung up around each. The two are worth comparing.B.AccessA fixed-rail system will never have the reach of a city bus, which can get just aboutany place there’s a paved road. For folks in some parts if there’s no train nearby, their mass-transit commuting will have to be done by bus.fortStudies suggest that light rail appeals to actual riders in a way that buses do not.Commuters tend to see light rail as more modern, more upscale and safer, with no real possibility of operator error.Rail cars are more spacious, offer more freedom of movement and are easier to board and exit. And the ride is smoother: fewer sharp turns, no potholes, no sudden stops.D.Initial CostBuilding new light rail is stunningly expensive, costing tens of millions of dollars per mile. And anti-light rail types love to massage those numbers into cost comparisons to make bus travel look like a bargain. Of course, those studies tend to ignore the cost of building and maintaining the roads on which buses travel. Still, light rail can’t win this game.E.Operation and Management CostOnce light rail is up and running, both infrastructure and train cars are more durable and less expensive to maintain than a fleet of buses and the roads they use. A rail car can last up to 60 years; a bus can last maybe a quarter of that. Every bus needs one driver, while one driver can pilot a train several cars long. That means a lower payroll. And electricity is cheaper than gas.F.StyleFace it, light rail is kind of cool. Buses are not that cool.G.Resources Used/Environmental ImpactLight-rail trains run on electricity. Much of that is generated by coal, and that’s a nonrenewable resource that leaves an ecological footprint in all stages of itsproduction and use. Yet buses run on petroleum products. There aren’t many people touting fossil fuels as the energy of the future these days.H.VisionOpponents of light rail have created a category of public transportation called Bus Rapid Transit — express buses that travel at higher speeds, with fewer stops, in designated lanes.It’s a project that has been implemented successfully in places and may be integrated into a larger transit package in the future. But dozens of American cities are insisting that light rail be a part of that future.BRT may be forward-thinking, but light rail is a breakthrough, a bold move that seeks to face down our dependence on oil.[Used with permission from the Portland Tribune (Pamplin Media Group). “Bus vs. Light Rail” by Eric Bartels, 13 November 2007.]Vocabulary in ContextBelow are words and phrases from Passage One. Choose the best definition for each underlined word or phrase as it is used in the passage. Mark the letter on the Answer Sheet.1.Paragraph A: …transportation receded into a cultural backwater in the 1950s…A.was talked aboutB.was largely ignoredC.was promotedD.was highlighted2.Paragraph A: …in terms of sustainable transportation…fortableB.economicalC.eco-friendlyD.fashionable3.Paragraph A: …outspoken camps have sprung up…A.vocal supportersB.loud groupsC.thoughtful followersD.open encampments4.Paragraph C: …more modern, more upscale and safer…A.up-to-dateB.elevated from the groundC.appealing to rich people5.Paragraph D: …to massage those numbers…A.changeB.manipulateC.rubD.mix6.Paragraph G: …many people touting fossil fuels as the energy…A.promotingB.criticisingC.buyingD.requesting7.Paragraph H: …in places and may be integrated into a larger…A.may be expanded intoB.may be setup inC.may replaceD.may become part ofComprehensionChoose the best answer and mark the letter on the Answer Sheet.8.Which one of the following statements is a reasonable inference from paragraph A?A.Buses should not be considered an environmentally friendly wayto travel.B.People think driving their cars is environmentally sustainable.C.Trains are a much better public transportation option than buses orprivate cars.D.The popularity and use of public transportation has come fullcircle.9.By discussing the comfort level passengers of light-rail trains feel, the authorassumes thatA.bus riders are people who prefer tradition over modernity.B.bus rides are usually rougher than light-rail train rides.C.bus drivers may skip over stops when their buses are full.D.bus riders do not actually enjoy riding buses.10.From the author’s discussion of the operation and management cost of both the busand light-rail systems, it can be argued thatA.buses cost more than rail cars to operate.B.buses can reach more destinations than light rail.C.light-rail drivers are more expensive to hire than bus drivers.D.light-rail cars break down more often than buses.11.Which of the following would be a reasonable inference about the author’s viewson the initial cost comparison between buses and light rail?A.People who like to take light rail will not mind its high initial cost.B.The initial cost of building light rail is actually lower than settingup bus travel.C.Bus travel advocates do not give an accurate portrayal of theinitial cost of bus travel.D.The initial cost of building a bus system is much lower thanexperts suggest.12.When comparing the sustainability of either a light-rail or a bus system, the authorsuggests thatA.light rail is much more environmentally friendly.B.the bus system is much more environmentally friendly.C.both light-rail and bus systems have a positive environmentalimpact.D.neither light-rail nor bus systems use renewable energies.13.Which of the following according to the article is not a form of “fossil fuel”?A.CoalB.GasC.ElectricityD.Petroleum14.Which of the following attributes does NOT apply to buses?A.FlexibilityB.DurabilityC.SustainabilityD.Lower initial cost15.What does the writer suggest that people are re-evaluating?e of fossil fuelsB.Climate changeC.Paved roadsD.Public transportation16.Which of the following sentences is closest in meaning to this quotation fromparagraph B?“For folks in some parts if there’s no train nearby, their mass-transit commuting will have to be done by bus.”A.Since there are no good trains, buses are a better option.B.Since buses are easy for commuting, taking the trains isunnecessary.C.As reaching train stations is difficult, buses are the only option.D.Trains can never beat buses in terms of connectivity.17.The writer suggests in paragraph H that Bus Rapid TransitA.is out-dated.B.cannot be implemented.C.is not as revolutionary as light rail.D.saves more money than light rail.PASSAGE TWOA.It’s hard to imagine why anyone would object to clean and green windturbines—especially when you compare them to dirty coal-fired plants and risky nuclear ones. Some people worry that because wind is very variable, we might suddenly lose all of our electricity and find ourselves plunged into a “blackout” if we rely on it too much.B.The reality of wind is quite different. Wherever you live, your power comes froma complex grid, or network, of highly interconnected power-generating unitsranging from giant power plants to individual wind turbines. Utility companies are highly adept at balancing power generated in many different places, in many different ways, to match the total power demand as it varies from hour to hour and day to day. The power from any one wind turbine will fluctuate as the wind rises and falls, but the total power produced by thousands of turbines, widely dispersed across an entire country, is much more regular and predictable. While it’s true that you might need 1,000 wind turbines to produce as much power as a giant coal or nuclear plant, it’s also true that if a single wind turbine fails or stops turning, it causes only 1/1000th (0.1 percent) of the disruption you get when a coal or nuclear plant fails (which happens more often than you might think). It’s also worth bearing in mind that wind is extremely predictable several days in advance so it’s easy for power planners to take account of its variability as they figure out how to make enough power to meet expected demands.C.Opponents of wind power have even suggested that it might be counter-productive,because we’d still need to have backup coal or nuclear plants or some way of storing wind-generated electricity for those times when there’s not enough wind blowing. That would certainly be true if we made all our energy from one, single mega-sized wind turbine—but we don’t! In reality, even countries that have large supplies of wind energy have plenty of other sources of power too. Denmark, for example, makes 20 percent of its electricity—and meets 43 percent of its peak load—with wind. As long as wind power is making less than half of a country’s total energy, the variability of the wind is not a problem.Vocabulary in ContextBelow are words and phrases from Passage Two. Choose the best definition for eachunderlined word or phrase as it is used in the passage. Mark the letter on the Answer Sheet.18.Paragraph A: …. clean and green…A.green in colourB.naturalC.economicalD.non-polluting19.Paragraph A: …them to dirty coal-fired plants…A.unprofitableB.filthyC.not cleanD.pollution causing20.Paragraph B: Utility companies are highly adept at balancing power…A.very quickB.extremely skilfulpletely uselessD.very professional21.Paragraph B: …one wind turbine will fluctuate as…A.go up and down suddenlyB.move from side to sideC.vibrate quicklyD.drop suddenly22.Paragraph B: It’s also worth bearing in mind that…A.noticingB.rememberingC.observingD.reminding23.Paragraph C: …single mega-sized wind turbine…rgeB.very largeC.extremely largeD.infinitely largeComprehensionChoose the best answer and mark the letter on the Answer Sheet.24.The writer’s main point isA.wind turbines are more efficient than other power sources.B.wind energy cannot provide a country’s energy.C.wind turbines can provide up to 43 percent of a country’s energy.D.wind energy output can be managed effectively.25.Why does the writer suggest that failure of a wind turbine is not as damaging as thefailure of a coal or nuclear power plant?A.One turbine only contributes a small amount to the output.B.Utility companies have good plans for balancing output.C.Utility companies do not use mega-sized turbines.D.One turbine’s output depends on the direction of the wind.26.The writer suggests that problems with the wind are easily overcome whenA.energy can be stored when the turbine is too hot.B.backup power plants are built in other locations.C.the turbines are spread out across a wide area.D.20 percent of energy is produced by turbines.27.The writer feels that utility companies can use wind power becauseA.wind power is not only clean but green.B.the wind is usually blowing somewhere.C.turbines do not need to produce much power.D.other power plants often fail and cause blackouts.28.Based on paragraph A, the author probably believes that some people’s fears of theunreliability of wind powerA.is real.B.has happened.C.will happen.D.may be groundless.29.The writer’s attitude to people who oppose wind power is generallyA.negative.B.neutral.C.positive.D.uninterested.30.In paragraph B, the writer suggests thatA.wind turbines never fail.B.coal plants fail quite often.C.it is hard to predict the weather.D.nuclear plants are not necessary.Part B Grammar (30%)Each question is worth one point. Suggested time: 30 minutes Verb Tenses / Verb FormsFrom the choices provided, select the tense/form of the verb that best completes the sentence. Mark the letter on the Answer Sheet.People Turn a Blind Eye to the BlindIt never ceases to amaze me how uncaring and selfish this world 1. Are there any compassionate people left in this universe? They seem to be few and far between.Earlier today I 2 on my way home from grocery shopping. As I pulled my shopping cart behind me, I revelled in the warm weather and the snowless sidewalks for the first time in three weeks.I nearly reached the corner where the sidewalk ended and the street began when I 3 across to the opposite side of the street to see a blind man 4 his white cane from side to side. His cane moved frantically from the sidewalk to the curb where snow 5 up high. He was getting more frustrated by the minute, as he stood there moving his cane back and forth trying to find the place to cross.I looked at the traffic on the street, 6 that no one was even slowing down, or stopping to help this blind man who 7 to cross the street.Inside I felt 8 at this fast-paced world, where no one has the time or inclination to stop what they were doing to give aid to this helpless man.My heart went out to him and so I decided to cross the street and help him. I reached him as he was swishing his cane dangerously close to the street. He yelled something out that I could not decipher.I told him that I 9 him cross the street. He took my hand and told me that he wanted to cross the street and stay on the main street to go to the small plaza.commandment in the Bible states what we need to practise with our fellow humans, “Thou shalt love thy neighbour as thyself.” We are not loving our neighbours when we see them in distress and just walk or drive on by.11 someone else other than ourselves means that we 12 the hands of love, compassion, and empathy to someone less fortunate than ourselves.[Used with permission from a Creative Commons 3.0 licence. “People Turn a Blind Eye to the Blind” by Catharine Leona Joy Minter Parks, 29 September 2011.]1. A. became B. will become C. is becoming D. will have become2. A. am B. have been C. had been D. was3. A. was looking B. looked C. have been looking D. look4. A. to swish B. swish C. swished D. swishing5. A. was piling B. piled C. was piled D. were piled6. A. noting B. to note C. being noted D. noted7. A. tried B. had tried C. was trying D. would try8. A. disgusting B. disgusted C. disgusts D. to disgust9. A. had helped B. helped C. would help D. was helping10. A. kept B. keeps C. keep D. had kept11. A. Helped B. Helps C. Help D. Helping12. A. were stretching B. have stretched C. stretches D. were stretched UsageSelect the choices that would best complete the passage. Mark the letter on the Answer Sheet.How to Keep Chickens as PetsThere are many breeds of chickens. Some are better for laying; some are fancier 13 appearance, and some chicken breeds are 14 than others, making them suited for pets.The Orpington is a good all-round bird, suited for 15 and as pets. The Sussexand Rhode Island Chickens are also suited for all purposes. The Silkie Chickens and Cochin are 16 birds generally kept as pets or for eggs, and they make terrific parents if you do have a rooster.Chickens come in different sizes. Bantam chickens are smaller and 17 great pets in a limited space. Some chicken breeds only come in bantam size, 18 others only come in standard sizes. A few come in both.If you want eggs, you will note that some breeds lay more than others, with most hens producing 4 – 6 eggs a week.Typically, white hens lay white eggs and brown hens lay brown eggs. Some breeds even lay colourful green/blue eggs. It is actually the colour of 19 bird’s ear that determines what colour eggs it will lay; egg colour has 20 to do with nutrition.Most hens start laying eggs at 5 months of age and only lay during the spring, summer, and early fall. They molt and stop laying for the winter. A few breeds lay year 21, while others 22 a break. Chickens can be induced to lay at other times by providing artificial light but their bodies do need to rest. As they get older, they lay fewer eggs.Laying hens need a special ration 23 is high in protein and calcium. They can also be given extra calcium in the form of oyster shell or actual crushed egg shells.24 their proper diet, chickens should be given some chicken scratch (a corn mixture) every day, and can be given some kitchen leftovers such as old bananas, ends of brown bread, apples, and so forth. They should not be given onions. Offering scratch and other treats is a good way to make your birds friendly.Chicken should also be given grit to help with digestion and should always have fresh water.If eggs are not removed, some hens become broody and will sit on them to hatch out chicks, but not all hens have this habit. It takes 21 days for chicken eggs to hatch. Only fertile eggs will hatch. 25 there is no rooster, the eggs are not fertile.If you are collecting eggs for eating, you will have to check in the morning and again at noon and refrigerate any eggs you gather.[Used with permission from a Creative Commons 3.0 licence. “How to Keep Chickens as Pets” by Brenda Nelson, 6 October 2011.]13. A. by B. with C. in D. at14. A. friend B. friends C. friendly D. friendlier15. A. lay B. laying C. lie D. lying16. A. ornament B. ornamented C. ornamental D. ornamentally17. A. make B. suit C. turn D. keep18. A. while B. and C. despite D. even19. A. an B. the C. any D. some20. A. anything B. something C. everything D. nothing21. A. in B. around C. within D. round22. A. take B. give C. live D. make23. A. , in that B. in which C. that D. ,which24. A. Except B. In addition to C. Because D. As long as25. A. As B. Although C. However D. IfSentence completionChoose from the choices provided and complete the following sentences in the best way. Mark the letter on the Answer Sheet.26. Forty years ago car safety did not exist and thousands died on the roads _____.Some passengers survived the crash but _____ burn to death in the resulting fire.A.per annual … wouldB.each annual … usuallyC.every year … wouldD.each yearly … usually27. Suzie: Do you miss _____?Denise: No, not at all. I’d rather _____ here.A.he being around … not had himB.him being around … not have himC.he be around … not having himD.him be around … not to have him28. Suddenly, there was absolute silence. Neither the women nor anyone else _____.I supposed they should either charge these women _____ let them go.A.were going to speak ... or as wellB.was going to speak … and alsoC.were going to speak … and thenD.was going to speak … or else29. _____ one British child in four is born into poverty _____ a disgrace.A.When … isB.Which … areC.If … areD.That … is30. Peter came in, _____.A.more excited than anyone had seen him before.B.more exciting than anyone had seen him before.C.more excitement than someone had seen him before.D.more excite than someone had seen him before.Part C Writing (40%)Suggested time: 60minutesTo plan: 5 – 10 minutesTo write: 40 – 45 minutesTo check: 5 minutes Instructions:Choose ONE topic and write at least 300 words. Put the letter (A, B or C) of your choice on the Answer Booklet. The writing topics are designed to give you an opportunity to demonstrate your ability to write clearly and effectively. You should try to produce the best essay possible in the time allotted. Your essay will be judged on the following:∙Logical development of ideas, including an introduction, a body and a conclusion∙Clear expression of ideas supported with specific evidence and concrete examples∙Appropriate choice of vocabulary∙Correct and varied sentence structure∙Correct spelling, grammar and punctuationWriting TopicsA.Many schools in Asia are beginning to actively address the problem of bullies,people who use their strength or power to frighten or hurt other people. In your opinion, how should this issue be addressed?B.Taking music lessons is very common nowadays, but why do we need to studymusic?C.Advertising is now a very big business, but it is not always ethical, oftenencouraging people to buy things they do not really need. How do you view this issue?End of Examination Paper2012/2013 MODEL ANSWERPart A. Reading Part B. Grammar1. B 16. C 1. C 16. C2. C 17. C 2. D 17. A3. A 18. D 3. B 18. A4. C 19. D 4. D 19. B5. B 20. B 5. C 20. D6. A 21. A 6. A 21. D7. D 22. B 7. C 22. A8. D 23. C 8. B 23. C9. B 24. D 9. C 24. B10. A 25. A 10. C 25. D11. C 26. C 11. D 26. C12. D 27. B 12. B 27. B13. C 28. D 13. C 28. D14. B 29. A 14. D 29. D15. D 30. B 15. B 30. A2011/2012 ADMISSION EXAMINATION PAPERPart AReading (30%)Suggested time: 40 minutesEach question is worth two points.PASSAGE ONEA.When I first met Mark Zuckerberg, he seemed as much a visitor to his surroundingsas I was. It was earlier this summer, in Facebook's boardroom in Palo Alto, and it was clear Zuckerberg hadn't spent a lot of time there. He wondered aloud to his media aide why we were meeting in such a big and off-putting formal space. His comments caught me off-guard. I expected a guy who has become as rich and famous as Zuckerberg to more fully embrace it. And then I thought, "Of course he feels awkward about his surroundings. He's only 23 years old."B.It's been like that from the beginning for Zuckerberg. Ever since he startedFacebook out of his Harvard dormitory room four years ago, he has been scrambling to keep up with epic growth in his and the company's fame and fortune.The last year has been particularly remarkable. Users have quadrupled while employees and revenues have tripled. Zuckerberg was mocked briefly in 2006 for turning down a near $1-billion buyout from Yahoo. Now, there is talk that Google and Microsoft both want to buy a chunk of or all of Facebook for a valuation exceeding $10 billion. Meanwhile, in bars and at cocktail parties, Silicon Valley people ask "Do you think he's more like Steve Jobs or Bill Gates?"C.Another round of Silicon Valley hype, you say? Perhaps. It does defy a certain logicthat a 23-year-old might be worth – based on his 30% stake in Facebook – $3 billion. But the facts are these: Facebook is the hottest social networking company on the planet right now. And two very smart companies – Google and Microsoft – along with most of Silicon Valley believe that Facebook, or its kind of technology, is going to completely change the way you use the Internet in five years. Is that worth $5 billion? $10 billion? $15 billion? I don't know, but I know it's worth a lot.D.When I first met Zuckerberg, I hadn't figured that out. Sure, MySpace – owned byRupert Murdoch's News Corp. – had more than 100 million users, and Facebook had 40 million. But these were all teenagers sharing party pictures online, right? At their best, the two websites seemed like a more technologically advanced version of Internet chat rooms. At worst, they were a hangout for scammers and sexualE.It all sounds way too complicated for ordinary people to understand until you hearZuckerberg explain it. Boiled down, it goes like this: Humans get their informationfrom two places – from mainstream media or some other centralized organization such as a church, and from their network of family, friends, neighbours and colleagues. We've already digitized the first. Almost every news organization has a website now. What Zuckerberg is trying to do with Facebook is digitize the second.F.Think about what this means. Right now, the interactions among friends,neighbours and colleagues – a.k.a. word of mouth – is still analogue. You go to a cocktail party, and a friend tells you about this incredible restaurant he's found. You ask a few other friends to confirm that data and eventually two things happen: You go to the restaurant regularly, and the place becomes a favourite in town. Now imagine that information automatically pushed out to all your friends, tested, verified and returned to you in 24 hours, and you have Zuckerberg's vision for Facebook.[Source: Adapted from Fred Vogelstein, “The Facebook Revolution,” Los Angeles Times, 7 October 2007.]Vocabulary in ContextBelow are words and phrases from reading Passage One. Choose the best definition for each underlined word or phrase as it is used in the passage. Mark the letter on the Answer Sheet.1.Paragraph A: …in such a big and off-putting formal space.A.unpleasantB.upstagingC.removingD.replacing2.Paragraph B: Zuckerberg was mocked briefly in 2006...A.congratulatedB.praisedC.persuadedD.ridiculed3.Paragraph C: …Silicon Valley hype...A.optimismB.pessimismC.exaggerationD.explanation4.Paragraph E: Boiled down, it goes like this:A.evaporatedB.simplifiedC.elaboratedD.moreoverComprehensionChoose the best answer and mark the letter on the Answer Sheet.5.According to the passage, Silicon Valley people consider Mark Zuckerberg…A.a fool.B. a visitor.C. a visionary innovator.D.a person obsessed with fame and fortune.6.According to the passage, what important function is Facebook trying toaccomplish?A.Create more games and apps for users.B.Put the opinions of everyone you know onto the internet.C.Add an e-mail function.D.Put every news organization onto the internet.7.The main purpose of the reading passage is…A.to convince people to use Facebook.B.to describe the enormous potential of Facebook.C.to estimate the value of Facebook.D.to compare Facebook to Apple and Microsoft.PASSAGE TWOA.Tired? Lethargic? In dire need of 40 winks? Join the club. But how to boost ourenergy levels without putting in too much effort? I finally accepted the urgent need to sort out my energy levels when the clocks went back last year. The days were suddenly short, drab, dark. I snored through the alarm every morning, then kick-started myself with strong coffee. By midday, I'd be working out ways to fit ina sneaky nap. In the evening, I'd drink wine to wind down, before sliding into bedwith a laptop, promising myself sleep by midnight at the latest, then Skyping friends, ordering groceries and reading tomorrow's papers until past 2am. It didn't seem stupid at the time. Of course it didn't – my mind was in a permanent tired yet over-stimulated fog. And anyway, everyone I knew was the same.B.I came to my first conclusion early. The main reason we're all so incrediblyexhausted is – sorry to blind you with science – we're not getting enough sleep.Obvious, perhaps, but also not so obvious. We all seem fully aware that we need, for example, eight hours, but always get five, yet we do nothing constructive about it. I think the reason for that is that getting good sleep requires sacrifice and strong willpower.。
澳門四高校聯合入學考試（語言科及數學科）模擬試題及參考答案中文正卷第一部分語文知識與篇章閱讀（60%）本部分全部為單項選擇題，共30題，每題2分。
請將答案填在答題紙上。
一. 語文基礎知識（20題，共40分）1.下列詞語中的劃線字，讀音完全相同的一組是：A.差別差錯差強人意B.否則否定否極泰來C.樂意樂曲樂不思蜀D.蛇年蛇足虛與委蛇2.下列各組詞語中，沒有錯別字的一項是：A.肄意盤桓殺氣騰騰伏首稱臣B.瞻養環佩溯流而上挺而走險C.蹉跎幅員觥籌交錯珠光寶氣D.委瑣樸實跋山陟水渙然一新3.下列各句中的劃線成語，使用恰當的一項是：A.雖然交通事故的發生率已經每況愈下，但我們仍不能有絲毫大意。
B.王氏三兄弟從香港來到了澳門，他們齊心協力，抱成一團，開闢了事業的新天地，可謂三人成虎啊！C.“書山有路勤為徑”，在知識爆炸的今天，我們更要努力攀登書山，而不能高山仰止。
D.在現代社會生活中，電視和電腦對我們來說幾乎是不可或缺的。
4.下列關於“六書”的解釋，正確的一項是：A.風、雅、頌、賦、比、興B.象形、指事、會意、形聲、轉注、假借C.《詩》、《書》、《禮》、《易》、《樂》、《春秋》D.甲骨文、金文、篆文、隸書、楷書、行書5.下列各句，語言運用得體的一項是：A.可否勞您把行李送到我的府上？B.現將敝人的大作付梓，以就正於讀者。
C.老先生說得有道理，受教受教！D.您這麼客氣，這禮物我只好笑納了。
6.下列各句，沒有語病的一項是：A.澳門已於2012年1月起實施新控煙法，大部分食肆、公園及碼頭等公共場所全面禁煙。
B.隨著資訊技術的不斷發展和進步，使我們可以通過社交服務網站與朋友保持更加直接和方便的聯繫，擴大交際範圍。
C.在遭遇本賽季的五連敗後，湖人隊的處境令人堪憂。
D.生物入侵就是指那些本來不屬於某一生態系統，但通過某種方式被引入到這一生態系統，然後定居、擴散、暴發危害的物種。
7.依次填入下列句子劃線處的關聯詞語，最恰當的一項是：做哪種學問，總不外乎“擺事實、講道理”六個字。
绝密★启用前2013年中华人民共和国普通高等学校联合招收华侨、港澳地区、台湾省学生入学考试数学试题一、选择题：本大题共12小题，每小题5分，共60分。
在每小题给出的四个选项中，只有一项是符合题目要求的，请把所选出的字母填在题后的括号内。
1.若多项式32x x c -+有因式1,x -则c =______A.–3B.–1C.1D.32.z=-i 22设，z=-i 22设，则│z │=_____A.2B.1C.D.3.斜率为k (k >0)的直线沿x 轴的正方向平移5个单位，平移后的直线与原直线之间的距离为4，则k=____A.53 B.43 C.34 D.354.设f （x ）=x 2–2x –3在(a,+∞)上为增函数.则a 的取值范围为_____A.[1,+∞)B.(–∞,3]C.[–1,+∞)D.(–∞,–3]5.已知tan x =221aa -，其中常数()0,,cos =___a x π∈则A ．221a a -+ B.221a a + C.2211a a -+ D.2211a a -++6.3位男同学与2位女同学排成一列，其中女同学相邻的不同排法共有______A.48种B.36种C.24种D.18种7.已知向量,OA OB 不共线，1,3BM BA = 则向量OM =_____A.1433OA OB -B.2133OA OB +C.1233OA OB -D.1233OA OB+8.焦点为(2，0)，准线为x=–1的抛物线方程为_____A.263y x =-+B.263y x =+C.263y x =--D.263y x =-9.等比数列的前n 项和,,,nn s ab c a b c =+其中为常数，则______A.a+b=0B.b+c=0C.a+c=0D.a+b+c=010.3种颇色的卡片各5张，从中随机抽取3张，则3张卡片颜色相同的概率为____A.691 B.1291 C.8273 D.1627311.设函数f （x ）=cos(sin x ).则下列结论正确的是_____A.f （x ）的定义域是[–1,1]B.f （x ）的值域是[–1,1]C.f （x ）是奇函数D.f （x ）是周期为π的函数12.把正方形ABCD 沿对角线AC 折起，当以A,B,C,D 为项点的三棱锥体积最大时，直线BD 和平面ABC 所成的大小为_____A.30。
2006/2007 學年入學考試試題甲、作文（50%）請於下列兩題中選一題作文，字數不得少於600 字。
1. 根據自己的親身體驗，展開“愛在澳門＂的話題。
題目可另擬。
2. 談選舉文化。
題目可另擬。
【注意】題目是文章的眼睛。
可根據文章內容擬一個貼切精彩的題目。
乙、語文知識（20%）請將答案填在答案表上。
1. 細讀下列句子：日本京都的飲食文化被受推祟，遊客來到這裏，在遊覽名寺古殺外，總不會忘記停下步伐，吃一道菜，渴一口茶。
句中共有多少個錯別字？A. 2 個B. 3 個C. 4 個2. 細看下列兩個句子：（1）有些市民為了圖個涼快，不把門窗關好，梁上君子輕易就能溜門入戶。
（2）她立志長大後要當白衣天使。
“梁上君子＂和“白衣天使＂二語所屬的修辭格為：A. 借代B. 比喻C. 比擬3. 見於信封上的開啟語，下列哪一項為正確？（1）敬啟（2）臺啟（3）親啟（4）鈞啟A. 只有（1）、（2）及（3）B. 只有（2）、（3）及（4）C. 以上皆正確4. 下列三句均為澳門文化活動的主題句。
其中平仄最協調（符合格律句式）的是：A. 錦繡中華圖片展B. 粉墨春秋戲曲展C. 光影百態藝術展5. 下列的陳述，哪一項為不正確？A. 《史記》是中國第一部紀傳體歷史著作。
B. 歐陽修晚年退居，自稱“吾集古錄一千卷，藏書一萬卷，有琴一張，有棋一局，而常置酒一壺，吾老於其間，是為六一。
”C. 吳敬梓《儒林外史》以清代中葉為背景，小說以揭露科舉制度的弊端為中心。
6. 下列與五四新文學相關的陳述，哪一項為正確？（1）聞一多主張新詩應具有建築美、繪畫美、音樂美。
（2）創造社和文學研究會是五四時期的重要文學團體。
（3）胡適、徐志摩和梁實秋等人曾在上海創辦《新月》雜誌，倡導自由主義的文藝。
（4）魯迅曾經出版一本名為《中國小說史略》的專著。
A. 只有（1）及（2）B. 只有（1）、（2）及（3）C. 以上皆正確7. 細讀下列引文：“臣聞客有過主人者，見其竃直突，傍有積薪，客曰：｀更為曲突，遠徙其薪，不者且有火患。
2011 年普通高等学校招生全国统一考试数学理试题（全国卷，含答案）本试卷分第Ⅰ卷 ( 选择题 ) 和第Ⅱ卷 ( 非选择题 ) 两部分。
第Ⅰ卷 1 至 2 页。
第Ⅱ卷 3 至 4 页。
考试结束后，将本试卷和答题卡一并交回。
第Ⅰ卷注意事项：1．答题前， 考生在答题卡上务必用直径0.5 毫米黑色墨水签字笔将自己的姓名、准考证号填写清楚，并贴好条形码。
请认真核准条形码上的准考证号、姓名和科目。
2．每小题选出答案后，用 2B 铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用 橡皮擦干净后，再选涂其他答案标号，在试题卷上作答无效。
．．．．．．．．．．3．第Ⅰ卷共 l2 小题，每小题 5 分，共 60 分。
在每小题给出的四个选项中，只有一项是 符合题目要求的。
一、选择题(1) 复数 z 1i ， z 为 z 的共轭复数，则 zz z 1（ A ） 2i（ B ） i（ C ） i（ D ） 2i【答案】 B(2) 函数 y 2 x( x 0) 的反函数为（ A ） yx 2( x R)（ B ）4（ C ）y 4x 2( x R)（ ）Dyx 2( x 0)4y 4x 2 ( x 0) 【答案】 B(3) 下面四个条件中，使 a b 成立的充分而不必要的条件是（ A ） a ＞b 1（ B ） a ＞b 1（C ） a 2＞ b 2（ D ） a 3＞ b 3【答案】 A(4) 设 S n 为等差数列a n 的前 n 项和，若 a 1 1，公差 d2 ， S k 2 S k 24 ，则 k（ A ） 8 （B ） 7（ C ） 6（ D ） 5【答案】 D(5) 设函数 f ( x) cos x(0) ，将 yf ( x) 的图像向右平移个单位长度后，所得的图3像与原图像重合，则的最小值等于（ A ）1（B ） 3（C ） 6（ D ） 93【答案】 C(6) 已知直二面角l , 点 A ， AC l , C 为垂足 , B ， BD l , D 为垂足．若 AB2, AC BD 1，则 D 到平面 ABC 的距离等于2 (B) 36 (D) 1(A)3 (C)33【答案】 CA(7) 某同学有同样的画册 2 本，同样的集邮册 3 本，从中取出 4 本赠送给 4 位朋友每位朋友 1 本，则不同的赠送方法共有(A) 4 种(B)10 种(C)18 种(D)20 种lD【答案】 BCB E(8) 曲线 y e 2 x1在点 (0,2) 处的切线与直线 y 0 和 y x 围 成的三角形的面积为(A)1(B)1 (C)2 (D)1323【答案】 A(9) 设 f ( x) 是周期为 2 的奇函数，当 0x 1 时， f (x)2x(1 x) , 则 f (5 )11112(A) -(B)(C)(D)2442【答案】 A(10) 已知抛物线C ： y 24x 的焦点为 F ，直线 y2x 4 与 C 交于 A ， B 两点．则cos AFB(A)4(B)3 (C)3 (D)4 5555【答案】 D(11) 已知平面 α截一球面得圆 M ，过圆心 M 且与 α 成 600 二面角的平面 β 截该球面得圆 N .若该球面的半径为 4，圆 M 的面积为 4 ，则圆 N 的面积为(A) 7 (B) 9(C)11(D)13【答案】 D(12) r r rr rr r 1 rr r rr设向量 a ， b ， c 满足 | a | | b |1， agb， ac,bc60 ，则 | c | 的最大值2等于(A) 2 (B)3(c)2(D) 1【答案】 AB绝密★启用前2011 年普通高等学校招生全国统一考试ACD理科数学 ( 必修 +选修 II)第Ⅱ卷注意事项：1 答题前，考生先在答题卡上用直径0． 5 毫米黑色墨水签字笔将自己的姓名、准考证号填写清楚，然后贴好条形码。
2011-2012(3)数分IV---答案Page 1 of 7华南农业大学期末考试试卷（A 卷）2011-2012学年第 2学期 考试科目： 数学分析IV 考试类型：（闭卷）考试 考试时间： 120 分钟学号 姓名 年级专业一、填空题（本大题共8小题，每小题3分，共24分） 1、级数n u ∑收敛，则lim n n u →∞=02、111123234(1)(2)n n n ++++=⨯⨯⨯⨯⨯+⨯+143、叙述函数项级数1()n n u x ∞=∑的一致收敛定义：设{}()n S x 是函数项级数1()n n u x ∞=∑的部分和函数列。
若{}()n S x 在数集D 上一致收敛于函数()S x ，则称函数项级数 在D 上一致收敛于函数()S x . 4、设()n R x 为函数项级数()n u x∑的余项，则()n u x ∑在数集D 上一致收敛于()S x 的充要条件是（余项法则）__________________0)()(sup lim )(sup lim =-=∈∞→∈∞→x S x S x R n Dx n n Dx n5、叙述傅里叶级数收敛定理:若以π2为周期的函数)(x f 在区间] , [ππ-上按段光滑 , 则在每一点x ∈] , [ππ- , f 的Fourier 级数 收敛于f 在点x 的左、右极限的算术平均值 , 即Page 2 of 7=-++2)0()0(x f x f ∑∞=++10 sin cos 2n n n nx b nx a a其中n a 和n b 为函数f 的Fourier 系数.6、级数(1)1()1n nn x-+∑的收敛域为),0[)2,(+∞⋃--∞7、把()f x x = 在（0, 2）内展开成正弦级数（写出展开式）x = _______________________________________________________.8、1220lim 1y yy dx x y +→=++⎰4π.二、解答题（本大题共8个小题，共64分）9、（满分6分）判别级数1213nn n ∞=-∑的收敛性，并求级数的和. 解: 解: 因为12131133333n n n n n nn n n n n a --++==-=- 2231223341(1)()()()3333333n n nn n S -+=-+-+-++-113nn +=-1lim lim(1)13n nn n n S S →∞→∞+==-=所以原级数收敛，且和为1.装订线Page 1 of 7Page 1 of 712、（满分6分）判断函数项级数 ∑∞=+-121sin )1(n n n nx的一致收敛性并说明理由.13、（满分10分）已知幂级数1nn nx∞=∑（1）求收敛半径、收敛区间、收敛域；（3分） （2）求和函数；（4分）（3）求数项级数12n n n∞=∑的和.（3分）14、（满分6分）求函数2()xt F x e dt -=⎰ 的幂级数展开式.Page 2 of 715、（满分6分）把函数0,50,()3,05x f x x -≤<⎧=⎨≤<⎩ 展开成傅里叶级数.16、（满分6分）设22()x xy x F x e dy -=⎰，求().F x 'Page 3 of 7三、证明题（本大题共2小题，共12分）17、(满分6分)设正项级数∑∞=1n n x 收敛，证明级数∑∞=12n n x 也收敛也收敛.18、(满分6分)设()n u x ∑（n =1,2…）是[,]a b 上的单调函数，证明：若()n u a ∑ 与()n u b ∑都绝对收敛，则()n u x ∑在[,]a b 上绝对且一致收敛。
绝密★启用前2011年中华人民共和国普通高等学校 联合招收华侨、港澳地区、台湾省学生入学考试数 学一、选择题：本大题共12小题；每小题5分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
（1）已知tan cot 0θθ+<，那么角θ是 （ ）（A ）第一或第二象限角 （B ）第三或第四象限角（C ）第一或第三象限角（D ）第二或第四象限角（2） 设1111ABCD A B C D -是棱长为1的正方体，则四面体11ACB D 的体积是（ ）（A ）12（B ）13（C ）14（D ）16（3） 在△ABC 中，角A B C 、、的分别为a b c 、、，若222a cb =+-，则B ＝（ ）（A ）6π（B ）3π（C ）6π或56π （D ）3π或23π （4） 若复数z 的虚部不为零，且310z z ++=，则（ ）（A ）1z <（B ）1z =（C ）1z < <（D ）z（5）若2log 3a =，4log 6b =，6log 9c =，则 （ ）（A ）a b c ==（B ）a b c <<（C ）b c a <<（D ）c b a <<（6）在四面体ABCD 中，AB =1，则二面角A CD B --的余弦值为（ ）（A ）13-（B ）0（C ）13（D ）12（7）设数列{}n a 的前n 项和1121n S n =-+，则n a = （ ） （A ）121n - （B ） 121n + （C ）1(21)(21)n n -+ （D ）2(21)(21)n n -+（8）圆的直角坐标方程为22((1)4x y -+-=，在以原点为极点，x 轴正半轴为极轴的极坐标系中，该圆的方程为 （ ） （A ）2ρ=（B ）54cos()((,])366πππρθθ=-∈-（C ）24cos()((,])633πππρθθ=-∈-（D ）4cos ((,])22ππρθθ=∈-（9）函数11(1)1y x x =+ >-+的反函数为 （ ）（A ）11(1)1y x x =+ >- （B ）11(1)1y x x =+ >-+ （C ）11(1)1y x x =- >-+（D ）11(1)1y x x =- >- （10）设1F ,2F 为双曲线2222:1x y C a b-=的两个焦点，P 为C 上一点，若△12F F P 是等腰直角三角形，则C的离心率为 （ ）（A （B （C ）1 （D ）12+ （11）若函数2,1,(),1x x f x ax b x ⎧ ≤=⎨+ >⎩ 在1x =处可导，则a b -= （ ）（A ）3（B ）2（C ）1（D ）0（12）点D E F 、、是△ABC 内三点，满足AD DE BE EF CF FD =， =， =， 设AF AB AC λμ=+ ， 则,)λμ =( （ ）（A ）42(,)77 （B ）14(,)77（C ）41(,)77（D ）24(,)77二、填空题：本大题共6小题；每小题5分.（13）若关于x 的方程320x x ax -+=有重根，则a =____________________． （14）已知两条直线,m n ，两个平面,αβ，给出四个命题： ①若m ∥n ,m α⊥，则n α⊥ ②若α∥β,,m n αβ⊂⊂，则m ∥n ③若m ∥α,m β⊥，则αβ⊥④若αβ⊥,m ∥α，则m β⊥其中正确命题的序号是____________________．（15）设等比数列{}n a 的各项都为正数，前n 项和为n S ．若627S S =，则其公比为____________________． （16）在空间直角坐标系O xyz -中，经过点(2,1,1)P 且与直线310,32210x y z x y z -++=⎧⎨--+=⎩垂直的平面方程为____________________．（17）若多项式()p x 满足(1)1,(2)3p p = = ，则()p x 被232x x -+除所得的余式为_______________． （18）设有4张不同的卡片，若有放回地抽取4次，每次随机抽取一张，则恰好有两张卡片未被抽到的概率为____________________．三、解答题：本大题共4小题；每小题15分．解答应写出文字说明，证明过程或演算步骤． （19）设函数()232f x x x =-++．（Ⅰ）把()f x 写成分段函数，并求()f x 的最小值； （Ⅱ）解不等式()5f x <．（20）设△ABC 为锐角三角形．证明（Ⅰ）sin sin 1cos A B C +>+；（Ⅱ）2sin sin sin A B C <++（21）设抛物线2:4x C y =与直线:1l y kx =+交于A B 、两点，P 为抛物线在这两点的切线的交点．（Ⅰ）当1k =时，求点P 的坐标； （Ⅱ）当k 变化时，求点P 的轨迹．（22）数列{}n a 的前n 项和为n S ，满足111,n n a a S n += -=． （1）写出｛a n ｝的前三项（2）设b n=S n +n+1，证明｛b n ｝是等比数列 （3）求｛a n ｝的通项公式2011年港澳台联考数学真题答案一、选择题：1—5：DBACD 6—10：ADCDC 11—12：AB 二、填空题：13．104或 14．①③ 1516．857280x y z ++-= 17．21x - 18．2164三、解答题19．解：（Ⅰ）当2x <-时，()32(2)13f x x x x =--+=-； 当322x -≤≤时，()32(2)5f x x x x =-++=-； 当32x >时，()23231f x x x x =-++=-； 所以13()531xf x x x -⎧⎪=-⎨⎪-⎩，故()f x 的最小值为72．（Ⅱ）当2x <-时，4()51353f x x x <⇔-<⇒>-，这与2x <-矛盾； 当322x -≤≤时，()5550f x x x <⇔-<⇒>，此时解为302x <≤； 当32x >时，()53152f x x x <⇔-<⇒<，此时解为322x <<． 综上所述，()5f x <的解为02x <<．20．解：（Ⅰ）1cos 1cos()1sin sin cos cos C A B A B A B +=-+=+-，1cos sin sin (1sin )(1sin )cos cos C A B A B A B +--=---，因为A ，B 都是锐角，所以cos A ，cos B 均大于0，所以1cos sin sin 0C A B +--<， 所以sin sin 1cos A B C +>+．（Ⅱ）因为sin sin 1cos A B C +>+，所以sin sin sin 1cos sin 2A B C C C ++>++>．为证明sin sin sin A B C ++≤3C π≥， 由于sin sin 2sincos 2cos 222A B A B C A B +-+=≤，所以sin sin sin sin 2cos 2C A B C C ++≤+， sin 2cos=sin[()]2cos[()]233626C C C C ππππ++-++-1=)]2cos()][sin()]2sin()]3262326C C C C ππππ-+-+--- 注意到=cos()]2cos()3326C C ππ-+-≤，sin()]2sin()0326C C ππ---≤，因此sin 2cos22C C +≤，sin sin sin 2A B C ++≤ 21．解：设l 与抛物线的两交点坐标分别为(,)A A A x y ，(,)B B B x y ，且A B x x <．（Ⅰ）当1k =时，直线l ：1y x =+代入抛物线方程，得214x x =+，则2A x =-2B x =+ 过A ，B 的抛物线的两条切线方程为：:()2A A A A x l y y x x -=-，:()2B B B B xl y y x x -=-，联立解得2,1x y ==-，所以(2,1)P -．（Ⅱ）将l 与C的方程联立，解得2(A x k =，2(B x k =+，将中两切线联立，解得2,1x k y ==-，所以点P 的轨迹方程为：:1P l y =-．22．解：（Ⅰ）由11a =，1n n a S n +-=，可得22a =，35a =．（Ⅱ）由1n n a S n +-=得1()n n n S S S n +--=，即122(1)n n S n S n +++=++，即12n nb b +=，所以{}n b 是（Ⅲ）由（Ⅱ）得1111(11)232n n n S n S --++=++=⨯，1321n n S n -=⨯--．当2n ≥时，2211321321n n n n a S n n n ---=+-=⨯-+-=⨯-，当1n =时，1n a =不适合上式．所以 21,13212n n n a n -=⎧=⎨⨯-≥⎩，． 第3题解析：方法1：估值法，31z z =+，311z z z -≤≤+，可以估计C 正确方法2：三次方程若只有一个实数解，则必有两个共轭复根，设三个根依次为z1，z2，z3，不妨设z3为实数，则由韦达定理， 1231z z z =-，则22121231z z z z z ===-， 构造函数3()1f x x x =++，易知3()1f x x x =++在R 上单调递增，由(1)10f -=-<，13()028f -=>可知3()1f x x x =++在1(1,)2--存在零点，且零点唯一，故3112z -<<-， 22121231(1,2)z z z z z ===-∈，所以1z < <。
港澳联考试卷真题数学最新一、选择题（每题3分，共30分）1. 若函数\( f(x) = 2x^2 - 3x + 1 \)，求\( f(-1) \)的值。
A. 0B. 4C. 6D. 82. 已知三角形ABC的内角A、B、C的度数分别为60°、45°和75°，求边AB的长度，假设边AC=2。
A. \( \sqrt{2} \)B. \( \sqrt{3} \)C. \( 2\sqrt{3} \)D. \( 3\sqrt{2} \)3. 圆的方程为\( (x-2)^2 + (y+3)^2 = 16 \)，求圆心到直线\( x - y + 5 = 0 \)的距离。
A. 3B. 4C. 5D. 64. 已知\( \sin(\alpha + \beta) = \frac{3}{5} \)，\( \cos(\alpha + \beta) = -\frac{4}{5} \)，且\( \alpha \)在第二象限，求\( \sin(\alpha) \)的值。
A. \( \frac{3}{5} \)B. \( -\frac{3}{5} \)C. \( \frac{4}{5} \)D. \( -\frac{4}{5} \)5. 一个等差数列的首项为3，公差为2，求第10项的值。
A. 23B. 27C. 29D. 316. 已知函数\( y = \log_2(x) \)，求其导数。
A. \( \frac{1}{x} \)B. \( \frac{1}{2x} \)C. \( \frac{2}{x} \)D. \( \frac{x}{2} \)7. 一个直角三角形的斜边长为5，一条直角边长为3，求另一条直角边的长度。
A. 2B. 4C. \( 2\sqrt{2} \)D. \( 4\sqrt{2} \)8. 已知\( a \)和\( b \)是方程\( x^2 - 5x + 6 = 0 \)的两个根，求\( a^2 + b^2 \)的值。
绝密★启用前2011年中华人民共和国普通高等学校 联合招收华侨、港澳地区、台湾省学生入学考试数 学一、选择题：本大题共12小题；每小题5分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
（1）已知tan cot 0θθ+<，那么角θ是 （ ）（A ）第一或第二象限角 （B ）第三或第四象限角（C ）第一或第三象限角（D ）第二或第四象限角（2） 设1111ABCD A B C D -是棱长为1的正方体，则四面体11ACB D 的体积是（ ）（A ）12（B ）13（C ）14（D ）16（3） 在△ABC 中，角A B C 、、的分别为a b c 、、，若222a cb =+-，则B ＝（ ）（A ）6π（B ）3π（C ）6π或56π （D ）3π或23π （4） 若复数z 的虚部不为零，且310z z ++=，则（ ）（A ）1z <（B ）1z =（C ）1z < <（D ）z（5）若2log 3a =，4log 6b =，6log 9c =，则 （ ）（A ）a b c ==（B ）a b c <<（C ）b c a <<（D ）c b a <<（6）在四面体ABCD 中，AB =1，则二面角A CD B --的余弦值为（ ）（A ）13-（B ）0（C ）13（D ）12（7）设数列{}n a 的前n 项和1121n S n =-+，则n a = （ ） （A ）121n - （B ） 121n + （C ）1(21)(21)n n -+ （D ）2(21)(21)n n -+（8）圆的直角坐标方程为22((1)4x y -+-=，在以原点为极点，x 轴正半轴为极轴的极坐标系中，该圆的方程为 （ ） （A ）2ρ=（B ）54cos()((,])366πππρθθ=-∈-（C ）24cos()((,])633πππρθθ=-∈-（D ）4cos ((,])22ππρθθ=∈-（9）函数11(1)1y x x =+ >-+的反函数为 （ ）（A ）11(1)1y x x =+ >- （B ）11(1)1y x x =+ >-+ （C ）11(1)1y x x =- >-+（D ）11(1)1y x x =- >- （10）设1F ,2F 为双曲线2222:1x y C a b-=的两个焦点，P 为C 上一点，若△12F F P 是等腰直角三角形，则C的离心率为 （ ）（A （B （C ）1 （D ）12+ （11）若函数2,1,(),1x x f x ax b x ⎧ ≤=⎨+ >⎩ 在1x =处可导，则a b -= （ ）（A ）3（B ）2（C ）1（D ）0（12）点D E F 、、是△ABC 内三点，满足AD DE BE EF CF FD =， =， =， 设AF AB AC λμ=+ ， 则,)λμ =( （ ）（A ）42(,)77 （B ）14(,)77（C ）41(,)77（D ）24(,)77二、填空题：本大题共6小题；每小题5分.（13）若关于x 的方程320x x ax -+=有重根，则a =____________________． （14）已知两条直线,m n ，两个平面,αβ，给出四个命题： ①若m ∥n ,m α⊥，则n α⊥ ②若α∥β,,m n αβ⊂⊂，则m ∥n ③若m ∥α,m β⊥，则αβ⊥④若αβ⊥,m ∥α，则m β⊥其中正确命题的序号是____________________．（15）设等比数列{}n a 的各项都为正数，前n 项和为n S ．若627S S =，则其公比为____________________． （16）在空间直角坐标系O xyz -中，经过点(2,1,1)P 且与直线310,32210x y z x y z -++=⎧⎨--+=⎩垂直的平面方程为____________________．（17）若多项式()p x 满足(1)1,(2)3p p = = ，则()p x 被232x x -+除所得的余式为_______________． （18）设有4张不同的卡片，若有放回地抽取4次，每次随机抽取一张，则恰好有两张卡片未被抽到的概率为____________________．三、解答题：本大题共4小题；每小题15分．解答应写出文字说明，证明过程或演算步骤． （19）设函数()232f x x x =-++．（Ⅰ）把()f x 写成分段函数，并求()f x 的最小值； （Ⅱ）解不等式()5f x <．（20）设△ABC 为锐角三角形．证明（Ⅰ）sin sin 1cos A B C +>+；（Ⅱ）2sin sin sin A B C <++（21）设抛物线2:4x C y =与直线:1l y kx =+交于A B 、两点，P 为抛物线在这两点的切线的交点．（Ⅰ）当1k =时，求点P 的坐标； （Ⅱ）当k 变化时，求点P 的轨迹．（22）数列{}n a 的前n 项和为n S ，满足111,n n a a S n += -=． （1）写出｛a n ｝的前三项（2）设b n=S n +n+1，证明｛b n ｝是等比数列 （3）求｛a n ｝的通项公式2011年港澳台联考数学真题答案一、选择题：1—5：DBACD 6—10：ADCDC 11—12：AB 二、填空题：13．104或 14．①③ 1516．857280x y z ++-= 17．21x - 18．2164三、解答题19．解：（Ⅰ）当2x <-时，()32(2)13f x x x x =--+=-； 当322x -≤≤时，()32(2)5f x x x x =-++=-； 当32x >时，()23231f x x x x =-++=-； 所以13()531xf x x x -⎧⎪=-⎨⎪-⎩，故()f x 的最小值为72．（Ⅱ）当2x <-时，4()51353f x x x <⇔-<⇒>-，这与2x <-矛盾； 当322x -≤≤时，()5550f x x x <⇔-<⇒>，此时解为302x <≤； 当32x >时，()53152f x x x <⇔-<⇒<，此时解为322x <<． 综上所述，()5f x <的解为02x <<．20．解：（Ⅰ）1cos 1cos()1sin sin cos cos C A B A B A B +=-+=+-，1cos sin sin (1sin )(1sin )cos cos C A B A B A B +--=---，因为A ，B 都是锐角，所以cos A ，cos B 均大于0，所以1cos sin sin 0C A B +--<，所以sin sin 1cos A B C +>+．（Ⅱ）因为sin sin 1cos A B C +>+，所以sin sin sin 1cos sin 2A B C C C ++>++>．为证明sin sin sin A B C ++≤3C π≥，由于sin sin 2sincos 2cos 222A B A B C A B +-+=≤，所以sin sin sin sin 2cos 2CA B C C ++≤+， sin 2cos=sin[()]2cos[()]233626C C C C ππππ++-++-1)]2cos()][sin()]2sin()]3262326C C C C ππππ-+-+---注意到=cos()]2cos()3326C C ππ-+-≤，sin()]2sin()0326C C ππ---≤，因此sin 2cos 22C C +≤，sin sin sin 2A B C ++≤21．解：设l 与抛物线的两交点坐标分别为(,)A A A x y ，(,)B B B x y ，且A B x x <．（Ⅰ）当1k =时，直线l ：1y x =+代入抛物线方程，得214x x =+，则2A x =-2B x =+ 过A ，B 的抛物线的两条切线方程为：:()2A A A A x l y y x x -=-，:()2B B B B xl y y x x -=-，联立解得2,1x y ==-，所以(2,1)P -．（Ⅱ）将l 与C的方程联立，解得2(A x k =，2(B x k =+，将中两切线联立，解得2,1x k y ==-，所以点P 的轨迹方程为：:1P l y =-．22．解：（Ⅰ）由11a =，1n n a S n +-=，可得22a =，35a =．（Ⅱ）由1n n a S n +-=得1()n n n S S S n +--=，即122(1)n n S n S n +++=++，即12n nb b +=，所以{}n b 是（Ⅲ）由（Ⅱ）得1111(11)232n n n S n S --++=++=⨯，1321n n S n -=⨯--．当2n ≥时，2211321321n n n n a S n n n ---=+-=⨯-+-=⨯-，当1n =时，1n a =不适合上式．所以 21,13212n n n a n -=⎧=⎨⨯-≥⎩，． 第3题解析：方法1：估值法，31z z =+，311z z z -≤≤+，可以估计C 正确方法2：三次方程若只有一个实数解，则必有两个共轭复根，设三个根依次为z1，z2，z3，不妨设z3为实数，则由韦达定理， 1231z z z =-，则22121231z z z z z ===-， 构造函数3()1f x x x =++，易知3()1f x x x =++在R 上单调递增，由(1)10f -=-<，13()028f -=>可知3()1f x x x =++在1(1,)2--存在零点，且零点唯一，故3112z -<<-， 22121231(1,2)z z z z z ===-∈，所以1z < <。
