澳门大学2011-2012入学考试数学A卷

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澳门大学入学英文考试 2011~2012&2012~2013

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.。

澳门四高校联合入学考试语言科及数学科

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。

港澳台联考数学真题及答案PDF版

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。

澳门大学中文入学考试2006年至2013年考试真题

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).doc

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

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。

2011年港澳台联考数学真题(含答案)

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 < <。

澳门大学近五年入学考试数学试题分析

解题过程援圆摇近五年试题分布
我们把近五年各年的试题涵盖的内容列在表员中援表员数据表明试题涵盖了高中数学的主要内容袁如幂尧指尧对函数袁三角函数袁不等式袁数列袁复数袁立体几何袁解析几何袁排列组合袁二项式定理袁概率统计等援
表员摇各年试题内容所对应的题号
考查内容
圆园园怨
年份圆园园愿圆园园苑圆园园远圆园园缘
员圆
员圆员圆员圆
猿摇主要特征猿援员摇问题的综合性强袁出题者便以子问题的形式来降低问题的难度
尽管澳门大学入学考试题目只要求学生答员园道袁也没有内地高考前面的选择和填空类的题袁而一个问题很少只考一个知识点袁所以多数问题的综合性较强袁为降低问题的难度和综合程度袁出题者便设计了一系列的子问题帮助学生一步一步地得到问题的解答援如附录中圆园园怨年的第圆袁源袁愿袁怨袁员园袁员员袁员圆题等袁圆园园苑年的第怨题子问题的个数居然达缘个援另外袁对一些需要较高数学变形尧作图技巧的问题袁题目也给出相关的提示袁以降低难度袁如附录中圆园园怨年的第员员题援
分类喳员袁愿札袁喳圆袁苑札袁喳猿袁远札袁喳源袁缘札和喳怨袁员园札援在前四类
中袁每一类最多取一个袁而后再根据所取的数有几个来
自全四类渊圆袁猿袁源个冤进行计算得所求概率院
恒等式及其性质冤
解三角形渊余弦定理冤
怨
怨
员员
苑
圆
苑
愿圆袁愿怨
续表
考查内容
年份圆园园怨圆园园愿圆园园苑圆园园远圆园园缘
不等式渊重要不等式的应用尧分式
不等式尧对数不等式尧指数不等式尧源
猿员袁源袁愿圆
员
高次不等式冤

港澳联考试卷真题数学最新

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。

澳门大学测试题库及答案

澳门大学测试题库及答案一、单选题（每题2分，共20分）1. 澳门大学位于哪个地区？A. 香港B. 澳门C. 台湾D. 深圳答案：B2. 澳门大学成立于哪一年？A. 1981年B. 1991年C. 1989年D. 1999年答案：A3. 澳门大学的主要教学语言是什么？A. 英语B. 葡萄牙语C. 粤语D. 普通话答案：D4. 澳门大学的校训是什么？A. 博学、审问、慎思、明辨、笃行B. 求实创新C. 厚德博学D. 知行合一答案：A5. 澳门大学的校徽颜色是什么？A. 蓝色和白色B. 红色和黄色C. 绿色和白色D. 黑色和金色答案：A6. 澳门大学提供哪些学位课程？A. 学士、硕士和博士B. 学士和硕士C. 学士和博士D. 硕士和博士答案：A7. 澳门大学有多少个学院？A. 8个B. 10个C. 12个D. 15个答案：C8. 澳门大学的学生总数大约是多少？A. 5000人B. 10000人C. 15000人D. 20000人答案：B9. 澳门大学的图书馆藏书量是多少？A. 100万册B. 200万册C. 300万册D. 400万册答案：B10. 澳门大学是否提供海外交流项目？A. 是B. 否答案：A二、多选题（每题3分，共15分）1. 澳门大学提供以下哪些学科领域的课程？A. 人文学科B. 社会科学C. 工程学D. 医学E. 法学答案：A, B, C, D, E2. 澳门大学的校园设施包括哪些？A. 图书馆B. 体育场馆C. 学生宿舍D. 实验室E. 艺术中心答案：A, B, C, D, E3. 澳门大学的学生可以参加哪些课外活动？A. 学术研究B. 社团活动C. 志愿服务D. 体育竞赛E. 文化交流答案：A, B, C, D, E4. 澳门大学的国际合作包括哪些方面？A. 学生交换B. 教师互访C. 联合研究D. 学术会议E. 国际研讨会答案：A, B, C, D, E5. 澳门大学的学生可以获得哪些奖学金？A. 学术奖学金B. 体育奖学金C. 艺术奖学金D. 社区服务奖学金E. 领导力奖学金答案：A, B, C, D, E三、判断题（每题1分，共10分）1. 澳门大学是澳门地区唯一的综合性大学。

2009-2010,2008-2009学年澳门大学入学试试题(数学B)

2009/2010學年入學考試試題 ADMISSION EXAMINATION PAPER第一部份 Part IWrite your answers in the space provided for each question. Answers written elsewhere will not be marked.將答題步驟及答案寫在每題所提供的空間內將答題步驟及答案寫在每題所提供的空間內，，寫在該空間以外的答案不會被評分評分。

Part I1. (a) (3 marks) Solve the following equation for x :(3 分) 對以下方程求解x ： x x =−+2122(b) (3 marks) Let 23)(2−−=x x f . For what values of x is )(x f a real number? (3 分)設 23)(2−−=x x f 。

求所有使)(x f 為實數的 x 值。

2. (4 marks) Express )1)(1(2522++++x x x x as sum of partial fractions. (4 分)將)1)(1(2522++++x x x x 化為部分分式和。

3. (6 marks) The following data show the selling prices of 9 models of mobile phones: (6 分) 以下數據所示為9款不同型號手提電話的售價:$2,130 $3,250 $4,760 $1,800 $2,770 $6,050 $2,340 $1,980 $1,560 Find the (a) mean, (b) median, and (c) standard deviation of the set of data listed above.求該組數據的(a)平均數，(b)中位數，(c)標準差。

2013澳门特别行政区大学数学试卷

1、在边长为a厘米的正方形上剪下一个最大的圆，这个圆与正方形的周长比是（）。

2、如果关于x的方程x2﹣2x+k=0（k为常数）有两个不相等的实数根，那么k的取值范围是_________ ．
3、已知反比例函数y= （k是常数，k≠0），在其图象所在的每一个象限内，y的值随着x的值的增大而增大，那么这个反比例函数的解析式是_________ （只需写一个）．
4、综合运用。

1、甲乙两个商场出售洗衣机，一月份甲商场共售出980台，比乙商场多售出1/6，甲商场比乙商场多售出多少台？
2、农机厂计划生产800台，平均每天生产44台，生产了10天，余下的任务要求8天完成，平均每天要生产多少台？
3、一间教室要用方砖铺地。

用边长是3分米的正方形方砖，需要960块，如果改用边长为2分米的正方形方砖，需要多少块？（用比例解）
5、已知有向图G=(V,E)，其中V={V1,V2,V3,V4,V5,V6,V7}，E={<V1,V2>,<V1,V3>,<V1,V4>,<V2,V5>,<V3,V5>,<V3,V6>,<V4,V6>,<V5,V7>,<V6,V7>}
写出G的拓扑排序的结果。

G拓扑排序的结果是：V1、V2、V4、V3、V5、V6、V7。

港澳台高三数学上学期入学考试试题

港澳台2017届高三数学上学期入学考试试题一、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。

请将答案填在题后括号内。

1.若一个圆柱的侧面展开图是一个正方形,则这个圆柱的全面积与侧面积的比为（）A ．ππ221+B ．ππ41+C ．ππ21+ D ．ππ21+ 2。

若0a b >>，则下列不等式不成立．．．的是（ ) A ．11a b < B ．||||a b > C ．ab b a 2>+ D ．b a ⎪⎭⎫ ⎝⎛>⎪⎭⎫ ⎝⎛21213。

已知函数()()()246060x x x f x x x ⎧-+≥⎪=⎨+<⎪⎩,则满足()()1f x f >的x 取值范围是（） A.()()3 13 -+∞，，B. ()()3 12 -+∞，，C. ()()1 13 -+∞，， D 。

()() 31 3-∞-，， 4．圆0204222=-+-+y x y x 截直线0125=+-c y x 所得弦长为8,则C 的值为（ )A 10B -68C 12D 10或-685．已知ΔABC 和点M 满足错误!＋错误!＋错误!＝0.若存在实数m 使得错误!＋错误!＝m 错误!成立，则m ＝( ）A ．2B ．3C ．4D ．5 6．如果方程x 2－4ax +3a 2=0的一根小于1，另一根大于1，那么实数a 的取值范围是（）A 113a << B 1a > C 13a < D 1a =7．将x y cos =的图象上的所有点的纵坐标不变，横坐标缩小到原来的一半，然后再将图象沿x 轴负方向平移4π个单位，则所得图象的解析式为（）（A)x y sin = （B ）x y 2sin -= （C)cos 24y x π⎛⎫=+ ⎪⎝⎭ （D)cos 24xy π⎛⎫=+ ⎪⎝⎭8．数列a n ＝错误!，其前n 项之和为错误!,则在平面直角坐标系中，直线（n ＋1)x ＋y ＋n ＝0在y 轴上的截距为（） A ．－10 B ．－9 C ．10 D ．99。

2010年港澳台高数A卷(2011级民间参考答案)

武汉大学2010——2011第一学期高等数学C1期末试题（港澳台A 卷）民间参考答案（不能保证全对仅供研讨）许祐玮承制廖川为刘猥琐许祐玮廖俊供稿一、计算下列各题（5分每小题，共30分）：⑴)n n →∞=0.5； ⑵2112lim()11x x x →---=0.5； ⑶ 0sin lim 1cos x x x x →-=2； ⑷ln x xdx ⎰=0.5X^2lnX-0.25X^2+C ；⑸sin )aa x dx -+⎰=pai ；（6）10⎰=2-2ln2 二、解答下列各题（7分每小题，共56分）：1、若2()1x ax f x b x⎧+⎪=⎨+⎪⎩ 11x x ≤> 在1x =可导，求,a b 之值？a=b= -3 2、讨论21sin ()0x f x x ⎧⎪=⎨⎪⎩ 00x x ≠= 在0x =的连续性与可导性。

连续、可导 3、求(cos sin )x y e x x =+在0x =的切线与法线方程。

切线y=2X+1 法线Y= -0.5X+14、求2(1)arctan y x x =+的导数与微分。

Y’=1+2XarctanX Dy=(1+2XarctanX)dx5、求()x f x xe -=的凹凸区间及拐点。

拐点（2，2/e^2）(-无穷，2)上凸，（2，+无穷）上凹6、若21()(x f x t t dt -=⎰，求'()f x ，并计算(1)f 。

(1)f =2/3 '()f x =2X^5-2X^3根号1+X^47、若120()()1x f x f x d x x =-+⎰，求10(),()f x f x d x ⎰。

Ln2/4 fx=X/(1+X^2)-(ln2)/48、求曲线22x y =与直线4y x =-所围图形的面积。

18三、（6分）证明：若()f x 在[,]a b 连续，在(,)a b 二阶可导，而且()()()2a b f a f f b +==；则在(,)a b 内至少有一点ξ，使得 "()0f ξ=。

港澳生高考数学试卷及答案

一、选择题（每小题5分，共50分）1. 已知函数f(x) = x^3 - 3x + 2，则f(x)的图像大致为：A. 图像在x轴上单调递增B. 图像在x轴上单调递减C. 图像有极大值和极小值D. 图像有拐点2. 下列哪个数是无理数？A. √2B. 3C. 0.1010010001...D. 2/33. 在直角坐标系中，点A(2,3)关于直线y=x的对称点为：A. (2,3)B. (3,2)C. (-2,-3)D. (-3,-2)4. 已知等差数列{an}的前三项分别为1, 3, 5，则该数列的公差为：A. 1B. 2C. 3D. 45. 在三角形ABC中，∠A=45°，∠B=30°，则∠C的度数为：A. 45°B. 60°C. 75°D. 90°6. 下列哪个函数是奇函数？A. f(x) = x^2B. f(x) = x^3C. f(x) = |x|D. f(x) = x^47. 已知复数z = 3 + 4i，则|z|的值为：A. 5B. 7C. 9D. 128. 在直角坐标系中，直线y = 2x + 1与y轴的交点为：A. (0,1)B. (1,0)C. (0,-1)D. (-1,0)9. 下列哪个方程的解集为空集？A. x^2 + 1 = 0B. x^2 - 1 = 0C. x^2 + 4 = 0D. x^2 - 4 = 010. 已知函数f(x) = ax^2 + bx + c在x=1时取得极值，则：A. a=0B. b=0C. a+b=0D. a+b+c=0二、填空题（每小题5分，共50分）11. 已知等比数列{an}的首项为2，公比为3，则第5项an=______。

12. 在直角坐标系中，点P(3,4)到原点O的距离为______。

13. 函数f(x) = (x-1)^2 - 4在x=______时取得最小值。

14. 等差数列{an}的前10项和为100，第5项为5，则公差d=______。

100澳门-数学1..

1 0 0
學年度海外聯合招生考試試題
科目：科目：數學（數學（一類組）一類組）（澳門）澳門）一、選擇題：(一題 4 分，共 80 分)
1. 設多項式(polynomial)f(x)=ax6−7x4+5x− 13，其中 a 為非零的實數，試求 f(3)−f(−3)的值？ (A)−30 (B)0 (C)30 (D)2 13 (E)無法確定(與 a 的值有關)。 1 −π −π π π 2. 下面四點 A(cos 7 ,sin 7 )、B(−cos 7 ,sin7 )、C(log1081,log109)、D(log281,−log29)中，有幾個點與(3,−2)在同一個象限？ (A)0 個點 (B)1 個點 (C)2 個點 (D)3 個點 (E)4 個點。 3. 有一學童將同樣大小的正方體積木堆積如下圖，由上往下數，第一層堆一個，第二層堆三個，第三層堆六個，依此規律依次遞增，試問第 20 層共有多少個積木？ (A) 191 (B) 195 (C) 199 (D) 200 (E) 210。 4. 在坐標平面上，有兩個點 A(1,−2)、B(−2,2)，平面上與 A 點距離為 3 且與 B 點距離(distance)為 5 的點所成的圖形為下列哪一個選項？ (A)一條直線 (B)一個圓 (C)一個點 (D)二個點 (E)滿足條件的點不存在。 5. 圓(circle)O 的圓心為(2,−3)，A(3,−1)為圓 O 上的一點，試求以 A 為切點的切線 (tangent line)方程式？ −1 −1 1 (A) y+1=2(x−3) (B) y+1= 2 (x−3) (C) y+1= 2 (x−3) (D) y+1=−2(x−3) (E) y−3= 2 (x+1)。 6. 設 P(1,4)，Q(2,5)為坐標平面上兩點，試問下列哪一點與 P、Q 所成的三角形面積最小？ (A) (0, 0) (B) (6, 6) (C) (−8, −8) (D) (6,8) (E) (8, 6) 。 a x ，若 f(a)−f(b)=8，則 b 的值等於多少？

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r 1 r r 1 r 1 expansion of (1 x) n . Show that for 1 r n 1 , Cn 2Cn Cn Cn 2 .
among the three balls drawn, there is exactly 1 red ball?
。
(6 分)
(a)
1 證明 cos B 。 2
(4 分)
(4 分)
(b) 若 b 19 ， a c 5 及 a c ，求 a 和 c 的值。
2. 解不等式 ( x 1) | x 3 | 21 。
(7 分)
7. 一袋中有紅球 3 個和白球 7 個。
r 是在 (1 x) n 的展開式中 x r 的係 3. (a) 設 n 和 r 為整數， 0 r n ，及 Cn
(d) Show that | AB |2 (e) Let m
16(1 m 2 )(1 m 2 ) . m4
(3 marks)
8. Fig. I A N D
1 . If C is the point on the x-axis such that the area of ABC is 12, 2 (5 marks)
(b) 求 m 的取值範圍。 (c) 以 m 表 ( x1 x2 ) 2 。
16(1 m 2 )(1 m 2 ) (d) 證明 | AB | 。 m4
2
(3 分)
(e) 設 m
1 。若 C 是 x-軸上一點，使得 ABC 的面積為 12，求點 C。 2 (5 分)
12. (a) 把複數
(2 marks)
(3 marks) (b) In the expansion of (1 ax) , the coefficients of x and x
n
(ii) If balls are drawn with replacement, what is the probability that, among the three balls drawn, there is exactly 1 red ball? (2 marks)
(ii) 若 3 個球是以取後放回方式抽出，恰有 1 個紅球的概率是多少? (2 分) (b) 若以取後放回方式隨機抽球兩次，每次兩個球，4 個球中恰有 2 個紅球
的概率是多少?
4. 設 {an } 為等差數列。 (a) 設 bn
a1 a2 an ， n 1,2, 。證明 n
P a s t E x a m i n a t i o n P a p e r s 2 0 1 0 / 2 0 11 , 2 0 11 / 2 0 1 2
Syllabus
2012/2013
(b) 推導出對任意正整數 n， n(n 1)(n 2)(3n 1) 可被 24 整除。 (2 分)
(a) 證明 CM AE 。 (b) 證明 AMN 和 AEB 是相似三角形。從而求 | MN | 。 (c) 求三棱錐 C AMN 的體積。 (3 分) (4 分) (4 分)
(b) 求由曲線 y 5 x 2 與直線 y x 1 所包圍的區域的面積。(6 分)
a b b 11. (a) 因式分解行列式 b a b 。 b b a (b) 設 a 為實數。已知以 x, y, z 為未知量的方程組:
find the point C.
10. (a) A right circular cylinder has base radius x and volume 54 . Let S ( x) be the M C E B In Figure I, ABC DEF is a right triangular prism with | AD | 2 . ABC is an equilateral triangle with side length 1. Let M be the midpoint of AB, N be the point on AE such that MN AE . (a) Show that CM AE . (3 marks) F surface area (including the two bases) of the cylinder. 54 (i) Show that S ( x) 2 x 2 , x 0 . x (ii) Find d 2S dS . and dx 2 dx (2 marks) (2 marks)
(b) If a1 a2 a20 320 and a2 a3 a22 399 , find the general term of {an } . (5 marks)
5. (a) Prove by mathematical induction that for any positive integer n, 12 2 22 3 n 2 (n 1) 1 n(n 1)(n 2)(3n 1) . 12 (5 marks)
(5 分)
(d) 求面 ACE 與面 ABE 所成的二面角，答案以 arctan 表示。 (5 分)
9. 設 L 為過點 P(1,0) 的一條直線，其斜率為 m (m 0) 。直線 L 與拋物線
y 2 4 x 相交於兩不同的點 A( x1 , y1 ) 和 B( x2 , y2 ) 。
(a) 證明 x1 和 x2 為方程 m x (2m 4) x m 0 的根。
(iii) 由此，或用其他方法，求方程 (*) 的五個根，答案以 tan 表示。 (3 分)
和拐點標出來。
(iv) 若 1 x 6 ，求 S ( x) 的最大值。
(5 分)
(1 分)
全卷完
64
65
P a s t E x a m i n a t i o n P a p e r s 2 0 1 0 / 2 0 11 , 2 0 11 / 2 0 1 2
(1 i )102 以 a ib 形式表示。 (1 3i ) 2011
(7 分) 5 tan 10 tan 3 tan 5 。 1 10 tan 2 5 tan 4
(b) (i) 用棣美弗定理，或其他方法，證明 tan 5
10. (a) 一底半徑為 x 的正圓柱，其體積為 54 。設該圓柱的表面面積 (包括上、下兩底)為 S ( x) 。 54 (i) 證明 S ( x) 2 x 2 ， x 0 。 x (ii) 求 d 2S dS 及。 dx dx 2 (2 分) (2 分)
A N
D
M C
F E
B
62
63
P a s t E x a m i n a t i o n P a p e r s 2 0 1 0 / 2 0 11 , 2 0 11 / 2 0 1 2
Syllabus
2012/2013
如圖 I，直三棱柱 ABC DEF 的側棱長為 2， ABC 是等邊三角形，其邊長為 1。設 M 為 AB 的中點，N 為 AE 上一點，且 MN AE 。
66
67
P a s t E x a m i n a t i o n P a p e r s 2 0 1 0 / 2 0 11 , 2 0 11 / 2 0 1 2
Syllabus
2012/2013
Section II. Answer any 3 questions. Each carries 16 marks.
(a) 現隨機抽球三次，每次一個球。 (i) 若 3 個球是以取後不放回方式抽出，恰有 1 個紅球的概率是多少? (2 分)
r 1 r r 1 r 1 2Cn Cn Cn 數。證明對於 1 r n 1 ， Cn 2 。
(3 分) (b) 在 (1 ax) n 的展開式中， x 和 x 2 的係數分別為 24 及 252，求 a 和 n 的值。 (5 分)
2 2 2 2
ax y z 1 ( E ) x ay z a 。 2 x y az a
求 a 的各值使得方程組 (E)
(1 分) (3 分) (4 分)
(i) 有唯一解 ; (ii) 有無限多解 ; (iii) 無解。 (c) 設 a 2 。解方程組 (E) 。 (6 分) (5 分)
1 (a) Show that cos B . 2
பைடு நூலகம்
(b) If b 19 , a c 5 and a c , find the values of a and c. (4 marks) 2. Solve the inequality ( x 1) | x 3 | 21 . (7 marks) 7. There are 3 red balls and 7 white balls in a bag.
(4 分)
{bn } 是等差數列。 (3 分)
第二部分:任擇三題作答，每題十六分。
(b) 若 a1 a2 a20 320 及 a2 a3 a22 399 ，求數列 {an } 的通項公
8.
式。
(5 分)
圖I
5. (a) 用數學歸納法，證明對任意正整數 n，
12 2 2 2 3 n 2 (n 1) 1 n(n 1)(n 2)(3n 1) 。 (5 分) 12
Syllabus
2012/2013
(b) Deduce that for any positive integer n, n(n 1)(n 2)(3n 1) is divisible by
2011/2012 ADMISSION EXAMINATION PAPER
24.

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港澳生高考数学试卷及答案

100澳门-数学1..