2005年研究生入学考试答案B

中国科学院2005年研究生入学试题《细胞生物学》以及答案一、是非题：20题，共30分1、只有跨细胞膜的主动运输才需要载体蛋白。

2、内吞作用涉及细胞膜凹陷的质膜分离，所为不是主动运输。

3、原核细胞没有细胞内膜系统。

4、细胞定向迁移与微丝有关，与微管无关。

5、将蛋白质用荧光素标记后，就形成了绿色荧光蛋白（Green fluorescence protein）6、Ras是由αβγ三个亚基组成的GTP酶。

7、胞外信号通过跨膜受体才能转换成胞内信号。

8、cAMP应答元件（cAMP-reapinsive element）是启动子上与cAMP结合的DNA 序列。

9、原位杂交（in siru hybridization）技术通常用于细胞内特异DNA 和RNA 的定位及定性。

10、细胞凋亡时，核小体间DNA断裂是由物理、化学因素或病理性刺激引起的。

11、组蛋白H3的甲基化既可为与基因激活，也可为与基因沉默相关。

12、基因组是指细胞中含有遗传信息的所有核酸量。

13、不同生物细胞的细胞周期有差异，而细胞周期的长短主要由于G0期的长短不同所导致。

14、抗癌基因突变能转变成癌基因从而致癌。

15、基因组印记（genomic imprinting）是指基因组中某些基因的甲基化模式。

16、细胞内没有沿中等纤维运动的驱动蛋白（motor protein）17、由于细胞内环境的特点，生物膜只能是脂质双分子层。

18、一个细胞克隆是由单个细胞通过分裂形成的细胞群体。

19、病毒是非细胞形态的生命体，它的复制可在细胞外实现。

20、从细胞匀浆中分离出来微粒体不是一种细胞器。

二，选择题30题，共45分1、下列哪个因素不影响细胞膜的流动性A）膜脂脂肪酸碳链的长度B）膜脂脂肪酸碳链的不饱和度C）膜脂极性基团的极性D）胆固醇2、在被动运输中，自由扩散和协助扩散的主要区别为A）对能量的需求B）运输物质的大小C）运输能力是否饱和D）物质的浓度3、内质网有许多功能，下列哪个不在内质网中发生A）蛋白质合成 B）脂类合成 C）糖合成 D）解毒作用4、经常接触粉尘的人会导致肺部疾病，如粉末引起的矽肺。

绝密★启用前2005年全国硕士研究生入学统一考试 管理类专业学位联考综合试卷考生需知1.选择题的答案需用2B铅笔填涂在答题卡上，其它笔填涂的或做在试卷或其它类型答题卡上的答案无效。

2.其它题一律用蓝色或黑色钢笔或圆珠笔在答题纸上按规定要求作答，凡做在试卷上或未做在制定位置的答案无效。

3.交卷时，请配合监考人员验收，并请监考人员在准考证相应位置签字（作为考生交卷的凭据）。

否则，所产生的一切后果由考生自负。

一．问题求解：第1‐12小题，每小题4分，共48分，下列每题给出的A 、B 、C 、D 、E 五个选项中，只有一项是符合试题要求的，请在答题卡上将所选项的字母涂黑1.甲、乙两个储煤仓的库存煤量之比为10：7.要使这两仓库的库存煤量相等，甲仓库需向乙仓库搬入的煤量占甲仓库库存煤量的A 10%B 15%C 20%D 25%E 30%2.已知队伍排成长度为800米的队伍行军，速度为80米/分，车队首的通讯员以3倍于行军的速度跑步到队尾。

花一分钟传达首长命令后，立即以同样的速度跑回到队首。

在这往返全过程中通讯员所花费的时间为A 6.5分B 7.5分C 8分D 8.5分E 10分3.满足不等式（x+4）（x+6）+3＞0的所以实数x 的集合是A [4,)+∞B (4,)+∞C (,2]-∞-D (,1)-∞-E (,)-∞+∞4. 'f x （）=g(x)，x ∈（a ，b ），已知曲线y=g （x ）的图像如下，则曲线f （x ）的极值点为 A 1C ，3C B 2C ，4C C 1C ，3C ，5C D 2C ，4C ，5CE 以上结论都不正确5.设f（x，y）=222x +y t x e dt ⎰，则N xy f x y =（，） A 22222x +y x x +y e （）（） B 22222x +y xy x +y e （）（）C 822222x +y xy x +y e （）（）D 22222x +y y x +y e （）（）6.过抛物线y= 2-x +4x-3上两点（0，‐3），（3，0）的两条切线与X 轴所围成图形的面积是A 49B 278C 94D 827E 2747.函数f （x ）= t x0e dt 1-t ⎰， 10f x dt ⎰（）的值为A e ‐1B 1‐eC e 1-eD eE 18.已知n 维向量组1α，2α，3α线性无关，1β可由1α，2α，3α线性表示，2β不能被1α，2α，3α线性表示，则下列结论不正确的是A 向量组1α，2α，3α，1β线性相关B 向量组1α，2α，3α，2β线性无关C 向量组1α，2α，3α，1β，2β线性相关D 向量组1α，2α，3α，1β‐2β线性相关E 向量组1α，2α，3α，1β+2β线性无关9.设A=123011abc ⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦，且r （A ）=2，则a A x=0的通集是 A 1k 10a ⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦ B 12k 1b ⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦ C 13k 1c ⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦D 11k 0a ⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦+22k 1b ⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦（注：1k ，2k 为任意常数）10.若P （A ）=1P A B 2⋃（）=0.3，则P （B A ）= A 13 B 25 C 37 D 12 E 5811.以一种检验方法诊断癌症，真患癌症跟未患癌症者被诊断正确的概率分别为0.95和0.90。

2005年全国硕士研究生入学统一考试英语试题Section I Use of EnglishDirections:Read the following text. Choose the best word(s) for each numbered blank and mark [A], [B], [C] or [D] on ANSWER SHEET 1 (10 points)The human nose is an underrated tool. Humans are often thought to be insensitive smellers compared with animals, 1this is largely because, 2animals, we stand upright. This means that our noses are 3to perceiving those smells which float through the air, 4 the majority of smells which stick to surfaces. In fact, 5, we are extremely sensitive to smells, 6we do not generally realize it. Our noses are capable of 7human smells even when these are 8to far below one part in one million.Strangely, some people find that they can smell one type of flower but not another, 9 others are sensitive to the smells of both flowers. This may be because some people do not have the genes necessary to generate 10smell receptors in the nose. These receptors are the cells which sense smells and send 11to the brain. However, it has been found that even people insensitive to a certain smell 12can suddenly become sensitive to it when 13to it often enough.The explanation for insensitivity to smell seems to be that the brain finds it 14to keep all smell receptors working all the time but can 15new receptors if necessary. This may 16explain why we are not usually sensitive to our own smells—we simply do not need to be. We are not 17of the usual smell of our own house, but we 18new smells when we visit someone else’s. The brain finds it be st to keep smell receptors 19for unfamiliar and emergency signals 20the smell of smoke, which might indicate the danger of fire.1. [A] although [B] as [C] but [D] while2. [A] above [B] unlike [C] excluding [D] besides3. [A] limited [B] committed [C] dedicated [D] confined4. [A] catching [B] ignoring [C] missing [D] tracking5. [A] anyway [B] though [C] instead [D] therefore6. [A] even if [B] if only [C] only if [D] as if7. [A] distinguishing [B] discovering [C] determining [D] detecting8. [A] diluted [B] dissolved [C] dispersed [D] diffused9. [A] when [B] since [C] for [D] whereas10. [A] unusual [B] particular [C] unique [D] typical11. [A] signs [B] stimuli [C] messages [D] impulses12. [A] at first [B] at all [C] at large [D] at times13. [A] subjected [B] left [C] drawn [D] exposed14. [A] ineffective [B] incompetent [C] inefficient [D] insufficient15. [A] introduce [B] summon [C] trigger [D] create16. [A] still [B] also [C] otherwise [D] nevertheless17. [A] sure [B] sick [C] aware [D] tired18. [A] tolerate [B] repel [C] neglect [D] notice19. [A] available [B] reliable [C] identifiable [D] suitable20. [A] similar to [B] such as [C] along with [D] aside fromSection II Reading ComprehensionPart ADirections:Read the following four texts. Answer the questions below each text by choosing [A], [B], [C] or D. Mark your answers on ANSWER SHEET 1 (40 points)Text 1Everybody loves a fat pay rise. Yet pleasure at your own can vanish if you learn that a colleague has been given a bigger one. Indeed, if he has a reputation for slacking, you might even be outraged. Such behaviour is regarded as “all too human,” with the underlying assumption that other animals would not be capable of this finely developed sense of grievance. But a study by Sarah Brosnan and Frans de Waal of Emory University in Atlanta, Georgia, which has just been published in Nature, suggests that it is all too monkey, as well.The researchers studied the behaviour of female brown capuchin monkeys. They look cute. They are good-natured, co-operative creatures, and they share their food readily. Above all, like their female human counterparts, they tend to pay much closer attent ion to the value of “goods and services” than males.Such characteristics make them perfect candidates for Dr. Brosnan’s and Dr. de W aal’s study. The researchers spent two years teaching their monkeys to exchange tokens for food. Normally, the monkeys were happy enough to exchange pieces of rock for slices of cucumber. However, when two monkeys were placed in separate but adjoining chambers, so that each could observe what the other was getting in return for its rock, their behaviour became markedly different.In the world of capuchins, grapes are luxury goods (and much preferable to cucumbers). So when one monkey was handed a grape in exchange for her token, the second was reluctant to hand hers over for a mere piece of cucumber. And if one received a grape without having to provide her token in exchange at all, the other either tossed her own token at the researcher or out of the chamber, or refused to accept the slice of cucumber. Indeed, the mere presence of a grape in the other chamber (without an actual monkey to eat it) was enough to induce resentment in a female capuchin.The researchers suggest that capuchin monkeys, like humans, are guided by social emotions. In the wild, they are a co-operative, group-living species. Such co-operation is likely to be stable only when each animal feels it is not being cheated. Feelings of righteous indignation, it seems, are not the preserve of people alone. Refusing a lesser reward completely makes these feelings abundantly clear to other members of the group. However, whether such a sense of fairness evolved independently in capuchins and humans, or whether it stems from the common ancestor that the species had 35 million years ago, is, as yet, an unanswered question.21. In the opening paragraph, the author introduces his topic by ________.[A] posing a contrast[B] justifying an assumption[C] making a comparison[D] explaining a phenomenon22. The statement “it is all too monkey” (Last line, Paragraph l) implies that ________.[A] monkeys are also outraged by slack rivals[B] resenting unfairness is also monkeys’ nature[C] monkeys, like humans, tend to be jealous of each other[D] no animals other than monkeys can develop such emotions23. Female capuchin monkeys were chosen for the research most probably because they are________.[A] more inclined to weigh what they get[B] attentive to researchers’ instructions[C] nice in both appearance and temperament[D] more generous than their male companions24. Dr. Brosnan and Dr. de Waal have eventually found in their study that the monkeys ________.[A] prefer grapes to cucumbers[B] can be taught to exchange things[C] will not be co-operative if feeling cheated[D] are unhappy when separated from others25. What can we infer from the last paragraph?[A] Monkeys can be trained to develop social emotions.[B] Human indignation evolved from an uncertain source.[C] Animals usually show their feelings openly as humans do.[D] Cooperation among monkeys remains stable only in the wild.Text 2Do you remember all those years when scientists argued that smoking would kill us but the doubters insisted that we didn’t know for sure? That the evidence was inconclusive, the science uncertain? That the antismoking lobby was out to destroy our way of life and the government should stay out of the way? Lots of Americans bought that nonsense, and over three decades, some 10 million smokers went to early graves.There are upsetting parallels today, as scientists in one wave after another try to awaken us to the growing threat of global warming. The latest was a panel from the National Academy of Sciences, enlisted by the White House, to tell us that the Earth’s atmosphere is definitely warming and that the problem is largely man-made. The clear message is that we should get moving to protect ourselves. The president of the National Academy, Bruce Alberts, added this key point in the preface to the panel’s report: “Science never has all the answers. But science does provide us with the best available guide to the future, and it is critical that our nation and the world base important policies on the best judgments that science can provide concerning the future consequences of present actions.”Just as on smoking, voices now come from many quarters insisting that the science about globalwarming is incomplete, that it’s OK to keep pouring fumes into the air until we know for sure. This is a dangerous game: by the time 100 percent of the evidence is in, it may be too late. With the risks obvious and growing, a prudent people would take out an insurance policy now.Fortunately, the White House is starting to pay attention. But it’s obvious that a majority of the president’s advisers still don’t take global warming seriously. Instead of a plan of action, they continue to press for more research -- a classic case of “paralysis by analysis.”To serve as responsible stewards of the planet, we must press forward on deeper atmospheric and oceanic research. But research alone is inadequate. If the Administration won’t take the legislative initiative, Congress should help to begin fashioning conservation measures. A bill by Democratic Senator Robert Byrd of West Virginia, which would offer financial incentives for private industry, is a promising start. Many see that the country is getting ready to build lots of new power plants to meet our energy needs. If we are ever going to protect the atmosphere, it is crucial that those new plants be environmentally sound.26. An argument made by supporters of smoking was that ________.[A] there was no scientific evidence of the correlation between smoking and death[B] the number of early deaths of smokers in the past decades was insignificant[C] people had the freedom to choose their own way of life[D] antismoking people were usually talking nonsense27. According to Bruce Alberts, science can serve as ________.[A] a protector[B] a judge[C] a critic[D] a guide28. What does the author mean by “paralysis by analysis” (Last line, Paragraph 4)?[A] Endless studies kill action.[B] Careful investigation reveals truth.[C] Prudent planning hinders progress.[D] Extensive research helps decision-making.29. According to the author, what should the Administration do about global warming?[A] Offer aid to build cleaner power plants.[B] Raise public awareness of conservation.[C] Press for further scientific research.[D] Take some legislative measures.30. The author associates the issue of global warming with that of smoking because ________.[A] they both suffered from the government’s negligence[B] a lesson from the latter is applicable to the former[C] the outcome of the latter aggravates the former[D] both of them have turned from bad to worseText 3Of all the components of a good night’s sleep, dreams seem to be least within our control. In dreams, a window opens into a world where logic is suspended and dead people speak. A century ago, Freud formulated his revolutionary theory that dreams were the disguised shadows of our unconscious desires and fears; by the late 1970s, neurologists had switched to thinking of them as just “mental noise” -- the random byproducts of the neural-repair work that goes on during sleep. Now researchers suspect that dreams are part of the mind’s emotional thermost at, regulating moods while the brain is “off-line.” And one leading authority says that these intensely powerful mental events can be not only harnessed but actually brought under conscious control, to help us sleep and feel better, “It’s your dream,” says Rosalind Cartwright, chair of psychology at Chicago’s Medical Center. “If you don’t like it, change it.”Evidence from brain imaging supports this view. The brain is as active during REM (rapid eye movement) sleep -- when most vivid dreams occur -- as it is when fully awake, says Dr, Eric Nofzinger at the University of Pittsburgh. But not all parts of the brain are equally involved; the limbic system (the “emotional brain”) is especially active, while the prefrontal cortex (the center of intellect and reas oning) is relatively quiet. “We wake up from dreams happy o r depressed, and those feelings can stay with us all day.” says Stanford sleep researcher Dr. William Dement.The link between dreams and emotions shows up among the patients in Cartwright’s clinic. Most people seem to have more bad dreams early in the night, progressing toward happier ones before awakening, suggesting that they are working through negative feelings generated during the day. Because our conscious mind is occupied with daily life we don’t always think about the emotional significance of the day’s events -- until, it appears, we begin to dream.And this process need not be left to the unconscious. Cartwright believes one can exercise conscious control over recurring bad dreams. As soon as you awaken, identify what is upsetting about the dream. Visualize how you would like it to end instead; the next time it occurs, try to wake up just enough to control its course. With much practice people can learn to, literally, do it in their sleep.At the end of the day, there’s probably little reason to pay attention to our dreams at all unless they keep us from sleeping or “we wake up in a panic,”Cartwright says. Terrorism, economic uncertainties and general feelings of insecurity have increased p eople’s anxiety. Those suffering from persistent nightmares should seek help from a therapist. For the rest of us, the brain has its ways of working through bad feelings. Sleep -- or rather dream -- on it and you’ll feel better in the morning.31. Researchers have come to believe that dreams ________.[A] can be modified in their courses[B] are susceptible to emotional changes[C] reflect our innermost desires and fears[D] are a random outcome of neural repairs32. By referring to the limbic system, the author intends to show ________.[A] its function in our dreams[B] the mechanism of REM sleep[C] the relation of dreams to emotions[D] its difference from the prefrontal cortex33. The negative feelings generated during the day tend to ________.[A] aggravate in our unconscious mind[B] develop into happy dreams[C] persist till the time we fall asleep[D] show up in dreams early at night34. Cartwright seems to suggest that ________.[A] waking up in time is essential to the ridding of bad dreams[B] visualizing bad dreams helps bring them under control[C] dreams should be left to their natural progression[D] dreaming may not entirely belong to the unconscious35. What advice might Cartwright give to those who sometimes have bad dreams?[A] Lead your life as usual.[B] Seek professional help.[C] Exercise conscious control.[D] Avoid anxiety in the daytime.Text 4Americans no longer expect public figures, whether in speech or in writing, to command the English language with skill and gift. Nor do they aspire to such command themselves. In his latest book, Doing Our Own Thing: The Degradation of Language and Music and Why We Should, Like, Care, John McWhorter, a linguist and controversialist of mixed liberal and conservative views, sees the triumph of 1960s counter-culture as responsible for the decline of formal English.Blaming the permissive 1960s is nothing new, but this is not yet another criticism against the decline in education. Mr. McWhorter’s academic speciality is language history and change, and he sees the gradual disappearance of “whom,” for example, to be natural and no more regrettable than the loss of the case-endings of Old English.But the cult of the authentic and the personal, “doing our own thing,” has spelt the death of formal speech, writing, poetry and music. While even the modestly educated sought an elevated tonewhen they put pen to paper before the 1960s, even the most well regarded writing since then has sought to capture spoken English on the page. Equally, in poetry, the highly personal, performative genre is the only form that could claim real liveliness. In both oral and written English, talking is triumphing over speaking, spontaneity over craft.Illustrated with an entertaining array of examples from both high and low culture, the trend that Mr. McWhorter documents is unmistakable. But it is less clear, to take the question of his subtitle, why we should, like, care. As a linguist, he acknowledges that all varieties of human language, including non-standard ones like Black English, can be powerfully expressive -- there exists no language or dialect in the world that cannot convey complex ideas. He is not arguing, as many do, that we can no longer think straight because we do not talk proper.Russians have a deep love for their own language and carry large chunks of memorized poetry in their heads, while Italian politicians tend to elaborate speech that would seem old-fashioned to most English-speakers. Mr. McWhorter acknowledges that formal language is not strictly necessary, and proposes no radical education reforms -- he is really grieving over the loss of something beautiful more than useful. We now take our English “on paper plates instead of china.” A shame, perhaps, but probably an inevitable one.36. According to McWhorter, the decline of formal English ________.[A] is inevitable in radical education reforms[B] is but all too natural in language development[C] has caused the controversy over the counter-culture[D] brought about changes in public attitudes in the 1960s37. The word “talking” (Line 6, Paragraph 3) denotes ________.[A] modesty[B] personality[C] liveliness[D] informality38. To which of the following statements would McWhorter most likely agree?[A] Logical thinking is not necessarily related to the way we talk.[B] Black English can be more expressive than standard English.[C] Non-standard varieties of human language are just as entertaining.[D] Of all the varieties, standard English can best convey complex ideas.39. The description of Russians’ love of memorizing poetry shows the author’s ________.[A] interest in their language[B] appreciation of their efforts[C] admiration for their memory[D] contempt for their old-fashionedness40. According to the last paragraph, “paper plates” is to “china” as ________.[A] “temporary” is to “permanent”[B] “radical” is to “conservative”[C] “functional” is to “artistic”[D] “humble” is to “noble”Part BDirections:In the following text, some sentences have been removed. For Questions 41-45, choose the most suitable one from the list A-G to fit into each of the numbered blanks. There are two extra choices, which do not fit in any of the gaps. Mark your answers on ANSWER SHEET 1. (10 points) Canada’s premiers (the leaders of provincial governments), if they have any breath left after complaining about Ottawa at their late July annual meeting, might spare a moment to do something, together, to reduce health-care costs.They’re all groaning about soaring health budgets, the fastest-growing component of which are pharmaceutical costs.41. ________What to do? Both the Romanow commission and the Kirby committee on health care -- to say nothing of reports from other experts -- recommended the creation of a national drug agency. Instead of each province having its own list of approved drugs, bureaucracy, procedures and limited bargaining power, all would pool resources, work with Ottawa, and create a national institution.42. ________But “national”doesn’t have to mean that. “National”could mean interprovincial -- provinces combining efforts to create one body.Either way, one benefit of a “national”organization would be to negotiate better prices, if possible, with drug manufacturers. Instead of having one province -- or a series of hospitals within a province -- negotiate a price for a given drug on the provincial list, the national agency would negotiate on behalf of all provinces.Rather than, say, Quebec, negotiating on behalf of seven million people, the national agency would negotiate on behalf of 31 million people. Basic economics suggests the greater the potential consumers, the higher the likelihood of a better price.43. ________A small step has been taken in the direction of a national agency with the creation of the Canadian Co-ordinating Office for Health Technology Assessment, funded by Ottawa and the provinces. Under it, a Common Drug Review recommends to provincial lists which new drugs should be included. Predictably, and regrettably, Quebec refused to join.A few premiers are suspicious of any federal-provincial deal-making. They (particularly Quebecand Alberta) just want Ottawa to fork over additional billions with few, if any, strings attached. That’s one reason why the idea of a national list hasn’t gone anywhere, while drug costs keep rising fast.44. ________Premiers love to quote Mr. Romanow’s report selectively, especially the parts about more federal money. Perhaps they should read what he had to say about drugs: “A national drug agency would provide governments more influence on pharmaceutical companies in order to constrain the ever-increasing cost of drugs.”45. ________So when the premiers gather in Niagara Falls to assemble their usual complaint list, they should also get cracking about something in their jurisdiction that would help their budgets and patients.[A] Quebec’s resistance to a national agency is provincialist ideology. One of the first advocatesfor a national list was a researcher at Laval University. Quebec’s Drug Insurance Fund has seen its costs skyrocket with annual increases from 14.3 per cent to 26.8 per cent![B] Or they could read Mr. Kirby’s report: “the substantial buying power of such an agencywould strengthen the public prescription-drug insurance plans to negotiate the lowest possible purchase prices from drug companies.”[C] What does “national”mean? Roy Romanow and Senator Michael Kirby recommended afederal-provincial body much like the recently created National Health Council.[D] The problem is simple and stark: health-care costs have been, are, and will continue toincrease faster than government revenues.[E] According to the Canadian Institute for Health Information, prescription drug costs haverisen since 1997 at twice the rate of overall health-care spending. Part of the increase comes from drugs being used to replace other kinds of treatments. Part of it arises from new drugs costing more than older kinds. Part of it is higher prices.[F] So, if the provinces want to run the health-care show, they should prove they can run it,starting with an interprovincial health list that would end duplication, save administrative costs, prevent one province from being played off against another, and bargain for better drug prices.[G] Of course, the pharmaceutical companies will scream. They like divided buyers; they canlobby better that way. They can use the threat of removing jobs from one province to another. They can hope that, if one province includes a drug on its list, the pressure will cause others to include it on theirs. They wouldn’t like a national agency, but self-interest would lead them to deal with it.Part CDirections:Read the following text carefully and then translate the underlined segments into Chinese. Your translation should be written clearly on ANSWER SHEET 2. (10 points)It is not easy to talk about the role of the mass media in this overwhelmingly significant phasein European history. History and news become confused, and one’s impressions tend to be a mixture of skepticism and optimism. 46) Television is one of the means by which these feelings are created and conveyed -- and perhaps never before has it served so much to connect different peoples and nations as in the recent events in Europe. The Europe that is now forming cannot be anything other than its peoples, their cultures and national identities. With this in mind we can begin to analyze the European television scene. 47) In Europe, as elsewhere, multi-media groups have been increasingly successful: groups which bring together television, radio, newspapers, magazines and publishing houses that work in relation to one another. One Italian example would be the Berlusconi group, while abroad Maxwell and Murdoch come to mind.Clearly, only the biggest and most flexible television companies are going to be able to compete in such a rich and hotly-contested market. 48) This alone demonstrates that the television business is not an easy world to survive in, a fact underlined by statistics that show that out of eighty European television networks, no less than 50% took a loss in 1989.Moreover, the integration of the European community will oblige television companies to cooperate more closely in terms of both production and distribution.49) Creating a “European identity” that respects the different cultures and traditions which go to make up the connecting fabric of the Old Continent is no easy task and demands a strategic choice -- that of producing programs in Europe for Europe. This entails reducing our dependence on the North American market, whose programs relate to experiences and cultural traditions which are different from our own.In order to achieve these objectives, we must concentrate more on co-productions, the exchange of news, documentary services and training. This also involves the agreements between European countries for the creation of a European bank for Television Production which, on the model of the European Investments Bank, will handle the finances necessary for production costs. 50) In dealing with a challenge on such a scale, it is no exaggeration to say “Unit ed we stand, divided we fall” -- and if I had to choose a slogan it would be “Unity in our diversity.” A unity of objectives that nonetheless respect the varied peculiarities of each country.Section III WritingPart A51. Directions:Two months ago you got a job as an editor for the magazine Designs & Fashions. But now you find that the work is not what you expected. You decide to quit. Write a letter to your boss, Mr. Wang, telling him your decision, stating your reason (s), and making an apology.Write your letter with no less than 100 words. Write it neatly on ANSWER SHEET 2.Do not sign your own name at the end of the letter; use “Li Ming” instead.You do not need to write the address. (10 points)Part B52. Directions:Write an essay of 160-200 words based on the following drawing. In your essay, you should first describe the drawing, then interpret its meaning, and give your comment on it.You should write neatly on ANSWER SHEET 2. (20 points)2005年全国硕士研究生入学统一考试英语试题答案与解析Section I Use of English一、文章题材结构分析这是一篇科普性说明文，文章主要介绍了人类嗅觉的特点及原因。

2005年全国硕士研究生入学统一考试英语试题Section I: Use of EnglishDirections:Read the following text. Choose the best word(s) for each numbered blank and mark [A], [B], [C] or [D] on ANSWER SHEET 1 (10 points)The human nose is an underrated tool. Humans are often thought to be insensitive smellers compared with animals, __1__ this is largely because, __2__ animals, we stand upright. This means that our noses are __3__ to perceiving those smells which float through the air, __4__ the majority of smells which stick to surfaces. In fact, __5__, we are extremely sensitive to smells, __6__ we do not generally realize it. Our noses are capable of __7__ human smells even when these are __8__ to far below one part in one million.Strangely, some people find that they can smell one type of flower but not another, __9__ others are sensitive to the smells of both flowers. This may be because some people do not have the genes necessary to generate __10__ smell receptors in the nose. These receptors are the cells which sense smells and send __11__ to the brain. However, it has been found that even people insensitive to a certain smell __12__ can suddenly become sensitive to it when __13__ to it often enough.The explanation for insensitivity to smell seems to be that brain finds it __14__ to keep all smell receptors working all the time but can __15__ new receptors if necessary. This may __16__ explain why we are not usually sensitive to our own smells we simply do not need to be. We are not __17__ of the usual smell of our own house but we __18__ new smells when we visit someone else’s. The brain finds it best to keep smell receptors __19__ for unfamiliar and emergency signals __20__ the smell of smoke, which might indicate the danger of fire.1. [A] although[B] as[C] but[D] while2. [A] above[B] unlike[C] excluding[D] besides3. [A] limited[B] committed[C] dedicated[D] confined4. [A] catching[B] ignoring[C] missing[D] tracking5. [A] anyway[B] though[C] instead[D] therefore6. [A] even if[B] if only[C] only if[D] as if7. [A] distinguishing[B] discovering[C] determining[D] detecting8. [A] diluted[B] dissolved[C] determining[D] diffused9. [A] when[B] since[C] for[D] whereas10. [A] unusual[B] particular[C] unique[D] typical11. [A] signs[B] stimuli[C] messages[D] impulses12. [A] at first[B] at all[C] at large[D] at times13. [A] subjected[B] left[C] drawn[D] exposed14. [A] ineffective[B] incompetent[C] inefficient[D] insufficient15. [A] introduce[B] summon[C] trigger[D] create16. [A] still[B] also[C] otherwise[D] nevertheless17. [A] sure[B] sick[C] aware[D] tired18. [A] tolerate[B] repel[C] neglect[D] notice19. [A] available[B] reliable[C] identifiable[D] suitable20. [A] similar to[B] such as[C] along with[D] aside fromSection II: Reading ComprehensionPart ADirections:Read the following four texts. Answer the questions below each text by choosing [A], [B], [C] or D. Mark your answers on ANSWER SHEET 1 (40 points)Text 1Everybody loves a fat pay rise. Yet pleasure at your own can vanish if you learn that a colleague has been given a bigger one. Indeed, if he has a reputation for slacking, you might even be outraged. Such behaviour is regarded as “all too human,” with the underlying assumption that other animals would not be capable of this finely developed sense of grievance. But a study by Sarah Brosnan and Frans de Waal of Emory University in Atlanta, Georgia, which has just been published in Nature, suggests that it all too monkey, as well.The researchers studied the behaviour of female brown capuchin monkeys. They look cute. They are good-natured, cooperative creatures, and they share their food tardily. Above all, like their female human counterparts, they tend to pay much closer attention to the value of “goods and services” than males. Such characteristics make them perfect candidates for Dr. Brosnan’s and Dr. de waal’s study. The researchers spent two years teaching their monkeys to exchange tokens for food. Normally, the monkeys were happy enough to exchange pieces of rock for slices of cucumber. However, when two monkeys were placed in separate but adjoining chambers, so that each could observe what the other was getting in return for its rock, their behaviour became markedly different.In the world of capuchins grapes are luxury goods (and much preferable to cucumbers). So when one monkey was handed a grape in exchange for her token, the second was reluctant to hand hers over for a mere piece of cucumber. And if one received a grape without having to provide her token in exchange at all, the other either tossed her own token at the researcher or out of the chamber, or refused to accept the slice of cucumber. Indeed, the mere presence of a grape in the otherchamber (without an actual monkey to eat it) was enough to reduce resentment in a female capuchin.The researches suggest that capuchin monkeys, like humans, are guided by social emotions. In the wild, they are a cooperative, group living species. Such cooperation is likely to be stable only when each animal feels it is not being cheated. Feelings of righteous indignation, it seems, are not the preserve of people alone. Refusing a lesser reward completely makes these feelings abundantly clear to other members of the group. However, whether such a sense of fairness evolved independently in capuchins and humans, or whether it stems from the common ancestor that the species had 35 million years ago, is, as yet, an unanswered question.21. In the opening paragraph, the author introduces his topic by ________.[A] posing a contrast[B] justifying an assumption[C] making a comparison[D] explaining a phenomenon22. The statement “it is all too monkey” (Last line, paragraph l) implies that________.[A] monkeys are also outraged by slack rivals[B] resenting unfairness is also monkeys’ nature[C] monkeys, like humans, tend to be jealous of each other[D] no animals other than monkeys can develop such emotions23. Female capuchin monkeys were chosen for the research most probably becausethey are ________.[A] more inclined to weigh what they get[B] attentive to researchers’ instructions[C] nice in both appearance and temperament[D] more generous than their male companions24. Dr. Brosnan and Dr. de Waal have eventually found in their study that themonkeys ________.[A] prefer grapes to cucumbers[B] can be taught to exchange things[C] will not be cooperative if feeling cheated[D] are unhappy when separated from others25. What can we infer from the last paragraph?[A] Monkeys can be trained to develop social emotions.[B] Human indignation evolved from an uncertain source.[C] Animals usually show their feelings openly as humans do.[D] Cooperation among monkeys remains stable only in the wild.Text 2Do you remember all those years when scientists argued that smoking would kill us but the doubters insisted that we didn’t know for sure? That the evidence was inconclusive, the science uncertain? That the antismoking lobby was out to destroy our way of life and the government should stay out of the way? Lots of Americans bought that nonsense, and over three decades, some 10 million smokers went to early graves.There are upsetting parallels today, as scientists in one wave after another try to awaken us to the growing threat of global warming. The latest was a panel from the National Academy of Sciences, enlisted by the White House, to tell us that the Earth’s atmosphere is definitely warming and that the problem is largely man-made. The clear message is that we should get moving to protect ourselves. The president of the National Academy, Bruce Alberts, added this key point in the preface to the panel’s report: “Science never has all the answers. But science does provide us with the best available guide to the future, and it is critical that out nation and the world base important policies on the best judgments that science can provide concerning the future consequences of present actions.”Just as on smoking, voices now come from many quarters insisting that the science about global warming is incomplete, that it’s Ok to keep pouring fumes into the air until we know for sure. This is a dangerous game: by the 100 percent of the evidence is in, it may be too late. With the risks obvious and growing, a prudent people would take out an insurance policy now.Fortunately, the White House is starting to pay attention. But it’s obvious that a majority of the president’s advisers still don’t take global warming seriously. Instead of a plan of action, they continue to press for more research -- a classic case of “paralysis by analysis”.To serve as responsible stewards of the planet, we must press forward on deeper atmospheric and oceanic research. But research alone is inadequate. If the Administration won’t take the legislative initiative, Congress should help to begin fashioning conservation measures. A bill by Democratic Senator Robert Byrd of West Virginia, which would offer financial incentives for private industry, is a promising start. Many see that the country is getting ready to build lots of new power plants to meet our energy needs. If we are ever going to protect the atmosphere, it is crucial that those new plants be environmentally sound.26. An argument made by supporters of smoking was that ________.[A] there was no scientific evidence of the correlation between smoking anddeath[B] the number of early deaths of smokers in the past decades was insignificant[C] people had the freedom to choose their own way of life[D] antismoking people were usually talking nonsense27. According to Bruce Alberts, science can serve as ________.[A] a protector[B] a judge[C] a critic[D] a guide28. What does the author mean by “paralysis by analysis” (Last line, paragraph 4)?[A] Endless studies kill action.[B] Careful investigation reveals truth.[C] Prudent planning hinders progress.[D] Extensive research helps decision-making.29. According to the author, what should the Administration do about globalwarming?[A] Offer aid to build cleaner power plants.[B] Raise public awareness of conservation.[C] Press for further scientific research.[D] Take some legislative measures.30. The author associates the issue of global warming with that of smoking because________.[A] they both suffered from the government’s negligence[B] a lesson from the latter is applicable to the former[C] the outcome of the latter aggravates the former[D] both of them have turned from bad to worseText 3Of all the components of a good night’s sleep, dreams seem to be least within our control. In dreams, a window opens into a world where logic is suspended and dead people speak. A century ago, Freud formulated his revolutionary theory that dreams were the disguised shadows of our unconscious desires and fears; by the late 1970s, neurologists had switched to thinking of them as just “mental noise” -- the random byproducts of the neural-repair work that goes on during sleep. Now researchers suspect that dreams are part of the mind’s emotional thermostat,regulating moods while the brain is “off-line.” And one leading authority says that these intensely powerful mental events can be not only harnessed but actually brought under conscious control, to help us sleep and feel better, “It’s your dream,” says Rosalind Cartwright, chair of psychology at Chicago’s Medical Center. “If you don’t like it, change it.”Evidence from brain imaging supports this view. The brain is as active during REM (rapid eye movement) sleep -- when most vivid dreams occur -- as it is when fully awake, says Dr, Eric Nofzinger at the University of Pittsburgh. But not all parts of the brain are equally involved; the limbic system (the “emotional brain”) is especially active, while the prefrontal cortex (the center of intellect and reasoning) is relatively quiet. “We wake up from dreams happy or depressed, and those feelings can stay with us all day.” says Stanford sleep researcher Dr. William Dement.The link between dreams and emotions show up among the patients in Cartwright’s clinic. Most people seem to have more bad dreams early in the night, progressing toward happier ones before awakening, suggesting that they are working through negative feelings generated during the day. Because our conscious mind is occupied with daily life we don’t always think about the emotional significance of the day’s events -- until, it appears, we begin to dream.And this process need not be left to the unconscious. Cartwright believes one can exercise conscious control over recurring bad dreams. As soon as you awaken, identify what is upsetting about the dream. Visualize how you would like it to end instead; the next time is occurs, try to wake up just enough to control its course. With much practice people can learn to, literally, do it in their sleep.At the end of the day, there’s probably little reason to pay attention to our dreams at all unless they keep us from sleeping or “we waken up in a panic,” Cartwright says. Terrorism, economic uncertainties and general feelings of insecurity have increased people’s anxiety. Those suffering from persistent nightmares should seek help from a therapist. For the rest of us, the brain has its ways of working through bad feelings. Sleep -- or rather dream -- on it and you’ll feel better in the morning.31. Researchers have come to believe that dreams ________.[A] can be modified in their courses[B] are susceptible to emotional changes[C] reflect our innermost desires and fears[D] are a random outcome of neural repairs32. By referring to the limbic system, the author intends to show ________.[A] its function in our dreams[B] the mechanism of REM sleep[C] the relation of dreams to emotions[D] its difference from the prefrontal cortex33. The negative feelings generated during the day tend to ________.[A] aggravate in our unconscious mind[B] develop into happy dreams[C] persist till the time we fall asleep[D] show up in dreams early at night34. Cartwright seems to suggest that ________.[A] waking up in time is essential to the ridding of bad dreams[B] visualizing bad dreams helps bring them under control[C] dreams should be left to their natural progression[D] dreaming may not entirely belong to the unconscious35. What advice might Cartwright give to those who sometimes have had dreams?[A] Lead your life as usual.[B] Seek professional help.[C] Exercise conscious control.[D] Avoid anxiety in the daytime.Text 4American no longer expect public figures, whether in speech or in writing, to command the English language with skill and gift. Nor do they aspire to such command themselves. In his latest book, Doing Our Own Thing: The Degradation of Language and Music and Why We Should, Like, Care, John McWhorter, a linguist and controversialist of mixed liberal and conservative views, sees the triumph of 1960s counter-culture as responsible for the decline of formal English.Blaming the permissive 1960s is nothing new, but this is not yet another criticism against the decline in education. Mr. McWhorter’s academic speciality is language history and change, and he sees the gradual disappearance of “whom,” for example, to be natural and no more regrettable than the loss of the case-endings of Old English.But the cult of the authentic and the personal, “doing our own thing,” has spelt the death of formal speech, writing, poetry and music. While even the modestly educated sought an elevated tone when they put pen to paper before the 1960s, even the most well regarded writing since then has sought to capture spoken English on the page. Equally, in poetry, the highly personal, performative genre is the only form that could claim real liveliness. In both oral and written English, talking is triumphing over speaking, spontaneity over craft.Illustrated with an entertaining array of examples from both high and lowculture, the trend that Mr. McWhorter documents is unmistakable. But it is less clear, to take the question of his subtitle, why we should, like, care. As a linguist, he acknowledges that all varieties of human language, including non-standard ones like Black English, can be powerfully expressive -- there exists no language or dialect in the world that cannot convey complex ideas. He is not arguing, as many do, that we can no longer think straight because we do not talk proper.Russians have a deep love for their own language and carry large chunks of memorized poetry in their heads, while Italian politicians tend to elaborate speech that would seem old-fashioned to most English-speakers. Mr. McWhorter acknowledges that formal language is not strictly necessary, and proposes no radical education reforms -- he is really grieving over the loss of something beautiful more than useful. We now take our English “on paper plates instead of china.” A shame, perhaps, but probably an inevitable one.36. According to McWhorter, the decline of formal English ________.[A] is inevitable in radical education reforms[B] is but all too natural in language development[C] has caused the controversy over the counter-culture[D] brought about changes in public attitudes in the 1960s37. The word “talking” (Line 6, paragraph 3) denotes ________.[A] modesty[B] personality[C] liveliness[D] informality38. To which of the following statements would McWhorter most likely agree?[A] Logical thinking is not necessarily related to the way we talk.[B] Black English can be more expressive than standard English.[C] Non-standard varieties of human language are just as entertaining.[D] Of all the varieties, standard English can best convey complex ideas.39. The description of Russians’ love of memorizing poetry shows the author’s________.[A] interest in their language[B] appreciation of their efforts[C] admiration for their memory[D] contempt for their old-fashionedness40. According to the last paragraph, “paper plates” is to “china” as ________.年全国硕士研究生入学统一考试英语试题[A] “temporary” is to “permanent”[B] “radical” is to “conservative”[C] “functional” is to “artistic”[D] “humble” is to “noble”Part BDirections:In the following text, some sentences have removed. For Questions 41-45, choose the most suitable one from the list A-G to fit into of the numbered blank there are two extra choices, which do not fit in any of the gaps. Mark your answers on ANSWER SHEET 1. (10 points)Canada’s premiers (the leaders of provincial governments), if they have any breath left after complaining about Ottawa at their late July annual meeting, might spare a moment to do something, together, to reduce health-care costs.They’re all groaning about soaring health budgets, the fastest-growing component of which are pharmaceutical costs.41. ________What to do? Both the Romanow commission and the Kirby committee on health care -- to say nothing of reports from other experts -- recommended the creation of a national drug agency. Instead of each province having its own list of approved drugs, bureaucracy, procedures and limited bargaining power, all would pool resources, work with Ottawa, and create a national institution.42. ________But “national” doesn’t have to mean that. “National” could mean interprovincial -- provinces combining efforts to create one body.Either way, one benefit of a “national” organization would be to negotiate better prices, if possible, with drug manufacturers. Instead of having one province -- or a series of hospitals within a province -- negotiate a price for a given drug on the provincial list, the national agency would negotiate on behalf of all provinces.Rather than, say, Quebec, negotiating on behalf of seven million people, the national agency would negotiate on behalf 31 million people. Basic economics suggests the greater the potential consumers, the higher the likelihood of a better price.43. ________A small step has been taken in the direction of a national agency with the creation of the Canadian Coordinating Office for Health Technology Assessment, funded by Ottawa and the provinces. Under it, a Common Drug Review recommends to provincial lists which new drugs should be included. Predictably, and regrettably, Quebec refused to join.A few premiers are suspicious of any federal-provincial deal-making. They2005年全国硕士研究生入学统一考试英语试题(particularly Quebec and Alberta) just want Ottawa to fork over additional billions with few, if any, strings attached. That’s one reason why the idea of a national list hasn’t gone anywhere while drug costs keep rising fast.44. ________Premiers love to quote Mr. Romanow’s report selectively, especially the parts about more federal money. Perhaps they should read what he had to say about drugs: “A national drug agency would provide governments more influence on pharmaceutical companies in order to constrain the ever-increasing cost of drugs.”45. ________So when the premiers gather in Niagara Falls to assemble their usual complaint list, they should also get cracking about something in their jurisdiction that would help their budgets and patients.[A] Quebec’s resistance to a national agency is provincialist ideology. One ofthe first advocates for a national list was a researcher at Laval University.Quebec’s Drug Insurance Fund has seen its costs skyrocket with annualincreases from 14.3 per cent to 26.8 per cent![B] Or they could read Mr. Kirby’s report: “the substantial buying power ofsuch an agency would strengthen the public prescription-drug insuranceplans to negotiate the lowest possible purchase prices from drugcompanies.”[C] What does “national” mean? Roy Romanow and Senator Michael Kirbyrecommended a federal-provincial body much like the recently createdNational Health Council.[D] The problem is simple and stark: health-care costs have been, are, and willcontinue to increase faster than government revenues.[E] According to the Canadian Institute for Health Information, prescriptiondrug costs have risen since 1997 at twice the rate of overall health-carespending. Part of the increase comes from drugs being used to replaceother kinds of treatments. Part of it arises from new drugs costing morethan older kinds. Part of it is higher prices.[F] So, if the provinces want to run the health-care show, they should prove theycan run it, starting with an interprovincial health list that would endduplication, save administrative costs, prevent one province from beingplayed off against another, and bargain for better drug prices.[G] Of course the pharmaceutical companies will scream. They like dividedbuyers; they can lobby better that way. They can use the threat of removingjobs from one province to another. They can hope that, if one provinceincludes a drug on its list, the pressure will cause others to include it ontheirs. They wouldn’t like a national agency, but self-interest would leadthem to deal with it.Part C年全国硕士研究生入学统一考试英语试题Directions:Read the following text carefully and then translate the underlined segments into Chinese. Your translation should be written clearly on ANSWER SHEET 2. (10 points)It is not easy to talk about the role of the mass media in this overwhelmingly significant phase in European history. History and news become confused, and one’s impressions tend to be a mixture of skepticism and optimism. 46) Television is one of the means by which these feelings are created and conveyed -- and perhaps never before has it served so much to connect different peoples and nations as is the recent events in Europe. The Europe that is now forming cannot be anything other than its peoples, their cultures and national identities. With this in mind we can begin to analyze the European television scene. 47) In Europe, as elsewhere, multi-media groups have been increasingly successful: groups which bring together television, radio newspapers, magazines and publishing houses that work in relation to one another. One Italian example would be the Berlusconi group, while abroad Maxwell and Murdoch come to mind.Clearly, only the biggest and most flexible television companies are going to be able to compete in such a rich and hotly-contested market. 48) This alone demonstrates that the television business is not an easy world to survive in, a fact underlined by statistics that show that out of eighty European television networks no less than 50% took a loss in 1989.Moreover, the integration of the European community will oblige television companies to cooperate more closely in terms of both production and distribution.49) Creating a “European identity” that respects the different cultures and traditions which go to make up the connecting fabric of the Old Continent is no easy task and demands a strategic choice -- that of producing programs in Europe for Europe. This entails reducing our dependence on the North American market, whose programs relate to experiences and cultural traditions which are different from our own.In order to achieve these objectives, we must concentrate more on co-productions, the exchange of news, documentary services and training. This also involves the agreements between European countries for the creation of a European bank for Television Production which, on the model of European Investment Bank, will handle the finances necessary for production costs. 50) In dealing with a challenge on such a scale, it is no exaggeration to say “Unity we stand, divided we fall” -- and if I had to choose a slogan it would be “Unity in our diversity.” A unity of objectives that nonetheless respect the varied peculiarities of each country.Section III: WritingPart A2005年全国硕士研究生入学统一考试英语试题51. Directions:Two months ago you got a job as an editor for the magazine Designs & fashions. But now you find that the word is not what you expected. You decide to quit. Write a letter to your boss, Mr. Wang, telling him your decision, stating your reason (s), and making an apology.Write your letter with no less than 100 words. Write it neatly on ANSWER SHEET 2.Do not sign your own name at the end of the letter; use “Li Ming” instead.You do not need to write the address. (10 points)Part B52. Directions:Write an essay of 160-200 words based on the following drawing. In your essay, you should first describe the drawing, then interpret its meaning, and give your comment on it.You should write neatly on ANSWER SHEET 2. (20 points)年全国硕士研究生入学统一考试英语试题参考答案Section I: Use of English (10 points)1.[C]2.[B]3.[A]4.[C]5.[B]6.[A]7.[D]8.[A]9.[D] 10.[B]11.[C] 12.[A] 13.[D] 14.[C] 15.[D]16.[B] 17.[C] 18.[D] 19.[A] 20.[B] Section II: Reading Comprehension (60 points)Part A (40 points)21.[C] 22.[B] 23.[A] 24.[C] 25.[B]26.[C] 27.[D] 28.[A] 29.[D] 30.[B]31.[A] 32.[C] 33.[D] 34.[D] 35.[A]36.[B] 37.[D] 38.[A] 39.[B] 40.[C]Part B (10 points)41.[E] 42.[C] 43.[G] 44.[F] 45.[B]Part C (10 points)46. 电视是创造和传递感情的手段之一。

2005年全国硕士研究生入学统一考试理工数学二试题详解及评析一、填空题（本题共6小题，每小题4分，满分24分. 把答案填在题中横线上）（1） 设x x y )sin 1(+=，则π=x dy = ______【答】 dx π−.【详解】 dy =()ln(1sin )(1sin )ln(1sin )x x x de x d x x +=++cos ln(1sin )ln(1sin )1sin x x x dx x ⎛⎞=+++⎜⎟+⎝⎠π=x dy=.)(dx dx y ππ−=′（2） 曲线xx y 23)1(+=的斜渐近线方程为______.【答】 23+=x y 【详解】 因为a=32limlim 1,x x y x →+∞== []23)1(lim)(lim 2323=−+=−=+∞→+∞→xxx ax x f b x x ， 于是所求斜渐近线方程为.23+=x y（3）=−−∫1221)2(xx xdx ______【答】4π.【详解】 令t x sin =，则=−−∫1221)2(x xxdx∫−202cos )sin 2(cos sin πdt tt tt =.4)arctan(cos cos 1cos 20202πππ=−=+−∫t ttd（4）微分方程x x y y x ln 2=+′满足91)1(−=y 的解为______.【答】 .91ln 31x x x y −=【详解】 原方程等价为x y x y ln 2=+′，于是通解为 ∫∫+⋅=+∫⋅∫=−]ln [1]ln [2222C xdx x xC dx ex ey dxx dxx =2191ln 31x C x x x +−， 由91)1(−=y 得C=0，故所求解为.91ln 31x x x y −=（5）当0→x 时，2)(kx x =α与x x x x cos arcsin 1)(−+=β是等价无穷小，则k= ______【答】 43.【详解】 200cos arcsin 1lim )()(limkxx x x x x x x −+=→→αβ =)cos arcsin 1(cos 1arcsin lim2x x x kx x x x x ++−+→=k 21143cos 1arcsin lim 20==−+→k xx x x x ， 得.43=k（6）设321,,ααα均为3维列向量，记矩阵),,(321ααα=A ，)93,42,(321321321ααααααααα++++++=B ， 如果1=A ，那么=B . 【答】 2【详解】 由题设，有)93,42,(321321321ααααααααα++++++=B=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡941321111),,(321ααα， 于是有 .221941321111=×=⋅=A B二、选择题（本题共8小题，每小题4分，满分32分. 每小题给出的四个选项中，只有一项符合题目要求，把所选项前的字母填在题后的括号内）（7）设函数n nn xx f 31lim )(+=∞→，则f(x)在),(+∞−∞内(A) 处处可导. (B) 恰有一个不可导点.(C) 恰有两个不可导点. (D) 至少有三个不可导点.【 】【答】 应选（C ）【详解】 先求出f(x)的表达式.()()()()()130101333lim lim 1111,lim lim 11211,1lim lim 11.n nn n nn n nn n n xx x x x x x →∞→∞→∞=+==<=+===⎛⎞=⎜+⎟=>⎜⎟⎝⎠因此，31, 1,(), 1.x f x x x ⎧≤⎪=⎨>⎪⎩由()y f x =的表达式及它的函数图形可知，()f x 在1x =±处不可导（图形是尖点），其余点()f x 均可导，因此选（C ）.（8）设F(x)是连续函数f(x)的一个原函数，""N M ⇔表示“M 的充分必要条件是N”，则必有(A) F(x)是偶函数⇔f(x)是奇函数. （B ） F(x)是奇函数⇔f(x)是偶函数.(C) F(x)是周期函数⇔f(x)是周期函数.(D) F(x)是单调函数⇔f(x)是单调函数.【 】【答】 应选（A ）【详解】 已知，∫+=xC dt t f x F 0)()(若()F x 为奇函数⇒()0xf t dt ∫为偶函数⇒()F x 的全体原函数为偶函数.又若()F x 为偶函数，则()()'F x f x =为奇函数，因此选（A ）.（9）设函数y=y(x)由参数方程⎩⎨⎧+=+=)1ln(,22t y t t x 确定，则曲线y=y(x)在x=3处的法线与x 轴交点的横坐标是(A) 32ln 81+. (B) 32ln 81+−.(C) 32ln 8+−. (D) 32ln 8+.【 】【答】 应选（B ）【详解】 当x=3时，有322=+t t ，得3,1−==t t （舍去，此时y 无意义），于是81221111=++===t t t t dxdy ， 可见过点x=3(此时y=ln2)的法线方程为：)3(82ln −−=−x y ，令y=0, 得其与x 轴交点的横坐标为：32ln 81+,故应(A).（10）设区域}0,0,4),{(22≥≥≤+=y x y x y x D ，f(x)为D 上的正值连续函数，a,b 为常数，则=++∫∫σd y f x f y f b x f a D)()()()((A) πab . (B)π2ab . (C) π)(b a +. (D) π2ba + . 【 】【答】 应选（D ） 【详解】 由轮换对称性，有=++∫∫σd y f x f y f b x f a D)()()()(σd x f y f x f b y f a D∫∫++)()()()(=σd x f y f x f b y f a y f x f y f b x f a D ∫∫+++++)()()()()()()()([21=.2241222ππσb a b a d b a D +=⋅⋅+=+∫∫ 应选(D).（11）设函数∫+−+−++=yx yx dt t y x y x y x u )()()(),(ψϕϕ, 其中函数ϕ具有二阶导数，ψ 具有一阶导数，则必有(A) 2222yux u ∂∂−=∂∂. （B ）2222y u x u ∂∂=∂∂. (C) 222yuy x u ∂∂=∂∂∂. (D)222x u y x u ∂∂=∂∂∂. 【 】【答】 应选（B ）【详解】)()()()(y x y x y x y x xu−−++−′++′=∂∂ψψϕϕ，)()()()(y x y x y x y x yu−+++−′−+′=∂∂ψψϕϕ， )()()()(22y x y x y x y x xu−′−+′+−′′++′′=∂∂ψψϕϕ，)()()()(2y x y x y x y x yx u−′++′+−′′−+′′=∂∂∂ψψϕϕ， )()()()(22y x y x y x y x y u−′−+′+−′′++′′=∂∂ψψϕϕ， 可见有2222yux u ∂∂=∂∂，应选(B).（12）设函数,11)(1−=−x xex f 则 (A) x=0,x=1都是f(x)的第一类间断点. （B ） x=0,x=1都是f(x)的第二类间断点.(C) x=0是f(x)的第一类间断点，x=1是f(x)的第二类间断点. (D) x=0是f(x)的第二类间断点，x=1是f(x)的第一类间断点.【 】【答】 应选（D ）【详解】 由于函数f(x)在x=0,x=1点处无定义，因此是间断点.且 ∞=→)(lim 0x f x ，所以x=0为第二类间断点；0)(lim 1=+→x f x ，1)(lim 1−=−→x f x ， 所以x=1为第一类间断点，故应选(D).（13）设21,λλ是矩阵A 的两个不同的特征值，对应的特征向量分别为21,αα，则1α，)(21αα+A 线性无关的充分必要条件是(A) 01≠λ. (B) 02≠λ. (C) 01=λ. (D) 02=λ.【 】【答】 应选（B ）【详解】 按特征值特征向量定义，有()12121122.A A A ααααλαλα+=+=+1α，)(21αα+A 线性无关⇔0)(21211=++αααA k k ，12,k k 恒为0 ⇔()11212220,k k k λαλα++=12,k k 恒为0 由于不同特征值的特征向量线性无关，所以21,αα线性无关.于是 ⎩⎨⎧==+.0,022121λλk k k 12,k k 恒为0而齐次方程组 ⎩⎨⎧==+.0,022121λλk k k 只有零解⇔ 122100.0λλλ≠⇒≠所以应选（B ）.（14）设A 为n （2≥n ）阶可逆矩阵，交换A 的第1行与第2行得矩阵B, **,B A 分别为A,B 的伴随矩阵，则(A) 交换*A 的第1列与第2列得*B . (B) 交换*A 的第1行与第2行得*B .(C) 交换*A 的第1列与第2列得*B −. (D) 交换*A 的第1行与第2行得*B −.【 】 【答】 应选（C ）【详解】 为书写方便，不妨考查A 为3阶矩阵，因为A 做初等行变换得到B ，所以用初等矩阵左乘A 得到B ，按已知有。

2005年全国硕士研究生入学统一考试数学三试题一、填空题（本题共6小题，每小题4分，满分24分. 把答案填在题中横线上）（1）极限12sinlim 2+∞→x xx x = . （2） 微分方程0=+'y y x 满足初始条件2)1(=y 的特解为______. （3）设二元函数)1ln()1(y x xe z y x +++=+，则=)0,1(dz________.（4）设行向量组)1,1,1,2(，),,1,2(a a ，),1,2,3(a ，)1,2,3,4(线性相关，且1≠a ，则a=_____. （5）从数1,2,3,4中任取一个数，记为X, 再从X ,,2,1 中任取一个数，记为Y , 则}2{=Y P =______.（6）设二维随机变量(X,Y) 的概率分布为 X Y 0 1 0 0.4 a 1 b 0.1已知随机事件}0{=X 与}1{=+Y X 相互独立，则a= ， b= .二、选择题（本题共8小题，每小题4分，满分32分. 每小题给出的四个选项中，只有一项符合题目要求，把所选项前的字母填在题后的括号内）（7）当a 取下列哪个值时，函数a x x x x f -+-=1292)(23恰好有两个不同的零点. (A) 2. (B) 4. (C) 6. (D) 8. [ ] （8）设σd y x I D⎰⎰+=221cos ,σd y x I D ⎰⎰+=)cos(222,σd y x I D⎰⎰+=2223)cos(,其中 }1),{(22≤+=y x y x D ，则(A) 123I I I >>. （B ）321I I I >>.(C) 312I I I >>. (D) 213I I I >>. [ ] （9）设,,2,1,0 =>n a n 若∑∞=1n na发散，∑∞=--11)1(n n n a 收敛，则下列结论正确的是(A)∑∞=-112n n a收敛，∑∞=12n na发散 . （B ）∑∞=12n na收敛，∑∞=-112n n a发散.- 2 -(C))(1212∑∞=-+n n n a a收敛. (D))(1212∑∞=--n n n a a收敛. [ ]（10）设x x x x f cos sin )(+=,下列命题中正确的是(A) f(0)是极大值，)2(πf 是极小值. （B ） f(0)是极小值，)2(πf 是极大值.（C ） f(0)是极大值，)2(πf 也是极大值. (D) f(0)是极小值，)2(πf 也是极小值.[ ]（11）以下四个命题中，正确的是(A) 若)(x f '在（0，1）内连续，则f(x)在（0，1）内有界. （B ）若)(x f 在（0，1）内连续，则f(x)在（0，1）内有界. （C ）若)(x f '在（0，1）内有界，则f(x)在（0，1）内有界.(D) 若)(x f 在（0，1）内有界，则)(x f '在（0，1）内有界. [ ]（12）设矩阵A=33)(⨯ij a 满足T A A =*，其中*A 是A 的伴随矩阵，TA 为A 的转置矩阵. 若131211,,a a a 为三个相等的正数，则11a 为(A)33. (B) 3. (C) 31. (D)3. [ ]（13）设21,λλ是矩阵A 的两个不同的特征值，对应的特征向量分别为21,αα，则1α，)(21αα+A 线性无关的充分必要条件是(A)01=λ. (B) 02=λ. (C) 01≠λ. (D) 02≠λ. [ ]（14） 设一批零件的长度服从正态分布),(2σμN ，其中2,σμ均未知. 现从中随机抽取16个零件，测得样本均值)(20cm x =，样本标准差)(1cm s =，则μ的置信度为0.90的置信区间是(A) )).16(4120),16(4120(05.005.0t t +-(B) )).16(4120),16(4120(1.01.0t t +- (C))).15(4120),15(4120(05.005.0t t +-(D))).15(4120),15(4120(1.01.0t t +- [ ]三 、解答题（本题共9小题，满分94分.解答应写出文字说明、证明过程或演算步骤.）（15）（本题满分8分） 求).111(lim 0x ex xx --+-→ （16）（本题满分8分）梅花香自苦寒来，岁月共理想，人生齐高飞！第 - 3 - 页 共 16 页设f(u)具有二阶连续导数，且)()(),(y x yf x y f y x g +=，求.222222yg y x g x ∂∂-∂∂ （17）（本题满分9分） 计算二重积分σd y xD⎰⎰-+122，其中}10,10),{(≤≤≤≤=y x y x D .（18）（本题满分9分） 求幂级数∑∞=-+12)1121(n nxn 在区间(-1,1)内的和函数S(x).（19）（本题满分8分）设f(x),g(x)在[0，1]上的导数连续，且f(0)=0,0)(≥'x f ,0)(≥'x g .证明：对任何a ]1,0[∈,有⎰⎰≥'+'ag a f dx x g x f dx x f x g 01).1()()()()()(（20）（本题满分13分）已知齐次线性方程组（i ） ⎪⎩⎪⎨⎧=++=++=++,0,0532,032321321321ax x x x x x x x x和（ii ） ⎩⎨⎧=+++=++,0)1(2,03221321x c x b x cx bx x 同解，求a,b, c 的值.（21）（本题满分13分）设⎥⎦⎤⎢⎣⎡=B CC AD T 为正定矩阵，其中A,B 分别为m 阶，n 阶对称矩阵，C 为n m ⨯矩阵. (I) 计算DP P T，其中⎥⎦⎤⎢⎣⎡-=-n mE oC A EP 1； （II ）利用(I)的结果判断矩阵C A C B T1--是否为正定矩阵，并证明你的结论. （22）（本题满分13分）设二维随机变量(X,Y)的概率密度为 .,20,10,0,1),(其他x y x y x f <<<<⎩⎨⎧=求：（I ） (X,Y)的边缘概率密度)(),(y f x f Y X ； （II ） Y X Z -=2的概率密度).(z f Z- 4 -( III ) }.2121{≤≤X Y P （23）（本题满分13分）设)2(,,,21>n X X X n 为来自总体N(0,2σ)的简单随机样本，X 为样本均值，记.,,2,1,n i X X Y i i =-=求：（I ） i Y 的方差n i DY i ,,2,1, =； （II ）1Y 与n Y 的协方差).,(1n Y Y Cov（III ）若21)(n Y Y c +是2σ的无偏估计量，求常数c.梅花香自苦寒来，岁月共理想，人生齐高飞！第 - 5 - 页 共 16 页2005年考研数学（三）真题解析一、填空题（本题共6小题，每小题4分，满分24分. 把答案填在题中横线上）（1）极限12sinlim 2+∞→x xx x = 2 . 【分析】 本题属基本题型，直接用无穷小量的等价代换进行计算即可.【详解】 12s i n l i m2+∞→x x x x =.212lim 2=+∞→x xx x （2） 微分方程0=+'y y x 满足初始条件2)1(=y 的特解为 2=xy . 【分析】 直接积分即可.【详解】 原方程可化为 0)(='xy ，积分得 C xy =， 代入初始条件得C=2，故所求特解为 xy=2.（3）设二元函数)1ln()1(y x xez yx +++=+，则=)0,1(dzdy e edx )2(2++ .【分析】 基本题型，直接套用相应的公式即可. 【详解】)1l n (y xe e xzy x y x +++=∂∂++,yx xe y z y x +++=∂∂+11, 于是 =)0,1(dzdy e edx )2(2++.（4）设行向量组)1,1,1,2(，),,1,2(a a ，),1,2,3(a ，)1,2,3,4(线性相关，且1≠a ，则a= 21. 【分析】 四个4维向量线性相关，必有其对应行列式为零，由此即可确定a. 【详解】 由题设，有=1234123121112aa a 0)12)(1(=--a a , 得21,1==a a ，但题设1≠a ，故.21=a（5）从数1,2,3,4中任取一个数，记为X, 再从X ,,2,1 中任取一个数，记为Y , 则}2{=Y P =4813 . 【分析】 本题涉及到两次随机试验，想到用全概率公式, 且第一次试验的各种两两互不相容的结果即为完备事件组或样本空间的划分.【详解】 }2{=Y P =}12{}1{===X Y P X P +}22{}2{===X Y P X P- 6 -+}32{}3{===X Y P X P +}42{}4{===X Y P X P =.4813)4131210(41=+++⨯ （6）设二维随机变量(X,Y) 的概率分布为X Y 0 1 0 0.4 a 1 b 0.1已知随机事件}0{=X 与}1{=+Y X 相互独立，则a= 0.4 , b= 0.1 .【分析】 首先所有概率求和为1，可得a+b=0.5, 其次，利用事件的独立性又可得一等式，由此可确定a,b 的取值.【详解】 由题设，知 a+b=0.5又事件}0{=X 与}1{=+Y X 相互独立，于是有}1{}0{}1,0{=+===+=Y X P X P Y X X P ， 即 a=))(4.0(b a a ++, 由此可解得 a=0.4, b=0.1二、选择题（本题共8小题，每小题4分，满分32分. 每小题给出的四个选项中，只有一项符合题目要求，把所选项前的字母填在题后的括号内）（7）当a 取下列哪个值时，函数a x x x x f -+-=1292)(23恰好有两个不同的零点.(A) 2. (B) 4. (C) 6. (D) 8. [ B ]【分析】 先求出可能极值点，再利用单调性与极值画出函数对应简单图形进行分析，当恰好有一个极值为零时，函数f(x)恰好有两个不同的零点.【详解】 12186)(2+-='x x x f =)2)(1(6--x x ，知可能极值点为x=1,x=2，且a f a f -=-=4)2(,5)1(，可见当a=4时，函数f(x) 恰好有两个零点，故应选(B). （8）设σd y x I D⎰⎰+=221cos ,σd y x I D ⎰⎰+=)cos(222,σd y x I D⎰⎰+=2223)cos(,其中}1),{(22≤+=y x y x D ，则(A) 123I I I >>. （B ）321I I I >>.(C) 312I I I >>. (D) 213I I I >>. [ A ]【分析】 关键在于比较22y x +、22y x +与222)(y x +在区域}1),{(22≤+=y x y x D 上的大小. 【详解】 在区域}1),{(22≤+=y x y x D 上，有1022≤+≤y x ，从而有2212y x +≥>π≥22y x +≥0)(222≥+y x梅花香自苦寒来，岁月共理想，人生齐高飞！第 - 7 - 页 共 16 页由于cosx 在)2,0(π上为单调减函数，于是22c o s 0y x +≤)c o s (22y x +≤≤222)c o s (y x +因此<+⎰⎰σd y x D22cos<+⎰⎰σd y x D)cos(22σd y x D⎰⎰+222)cos(，故应选(A). （9）设,,2,1,0 =>n a n 若∑∞=1n n a 发散，∑∞=--11)1(n n n a 收敛，则下列结论正确的是 (A)∑∞=-112n n a收敛，∑∞=12n na发散 . （B ）∑∞=12n na收敛，∑∞=-112n n a发散.(C))(1212∑∞=-+n n n a a收敛. (D))(1212∑∞=--n n n a a收敛. [ D ]【分析】 可通过反例用排除法找到正确答案.【详解】 取n a n 1=，则∑∞=1n n a 发散，∑∞=--11)1(n n n a 收敛，但∑∞=-112n n a与∑∞=12n na均发散，排除(A),(B)选项，且)(1212∑∞=-+n n n a a发散，进一步排除(C), 故应选(D).事实上，级数)(1212∑∞=--n n n a a的部分和数列极限存在.（10）设x x x x f cos sin )(+=,下列命题中正确的是(B) f(0)是极大值，)2(πf 是极小值. （B ） f(0)是极小值，)2(πf 是极大值.（C ） f(0)是极大值，)2(πf 也是极大值. (D) f(0)是极小值，)2(πf 也是极小值.[ B ]【分析】 先求出)(),(x f x f '''，再用取极值的充分条件判断即可.【详解】 x x x x x x x f cos sin cos sin )(=-+='，显然 0)2(,0)0(='='πf f ，又 x x x x f s i n c o s)(-=''，且02)2(,01)0(<-=''>=''ππf f ，故f(0)是极小值，)2(πf 是极大值，应选(B).（11）以下四个命题中，正确的是(A) 若)(x f '在（0，1）内连续，则f(x)在（0，1）内有界. （B ）若)(x f 在（0，1）内连续，则f(x)在（0，1）内有界.- 8 -（C ）若)(x f '在（0，1）内有界，则f(x)在（0，1）内有界.(D) 若)(x f 在（0，1）内有界，则)(x f '在（0，1）内有界. [ C ] 【分析】 通过反例用排除法找到正确答案即可. 【详解】 设f(x)=x 1, 则f(x)及21)(xx f -='均在（0，1）内连续，但f(x)在（0，1）内无界，排除(A)、(B); 又x x f =)(在（0，1）内有界，但xx f 21)(='在（0，1）内无界，排除(D). 故应选(C).（12）设矩阵A=33)(⨯ij a 满足TA A =*，其中*A 是A 的伴随矩阵，TA 为A 的转置矩阵. 若131211,,a a a 为三个相等的正数，则11a 为(A)33. (B) 3. (C) 31. (D)3. [ A ]【分析】 题设与A 的伴随矩阵有关，一般联想到用行列展开定理和相应公式：.**E A A A AA ==.【详解】 由TA A =*及E A A A AA ==**，有3,2,1,,==j i A a ij ij ，其中ij A 为ij a 的代数余子式，且032=⇒=⇒=A A AE A AA T或1=A而03211131312121111≠=++=a A a A a A a A ，于是1=A ，且.3311=a 故正确选项为(A). （13）设21,λλ是矩阵A 的两个不同的特征值，对应的特征向量分别为21,αα，则1α，)(21αα+A 线性无关的充分必要条件是(A)01=λ. (B) 02=λ. (C) 01≠λ. (D) 02≠λ. [ D ]【分析】 讨论一组抽象向量的线性无关性，可用定义或转化为求其秩即可. 【详解】 方法一：令 0)(21211=++αααA k k ，则022211211=++αλαλαk k k ， 0)(2221121=++αλαλk k k . 由于21,αα线性无关，于是有⎩⎨⎧==+.0,022121λλk k k当02≠λ时，显然有0,021==k k ，此时1α，)(21αα+A 线性无关；反过来，若1α，)(21αα+A梅花香自苦寒来，岁月共理想，人生齐高飞！第 - 9 - 页 共 16 页线性无关，则必然有02≠λ(,否则，1α与)(21αα+A =11αλ线性相关)，故应选(B).方法二： 由于 ⎥⎦⎤⎢⎣⎡=+=+21212211121101],[],[)](,[λλαααλαλααααA ， 可见1α，)(21αα+A 线性无关的充要条件是.001221≠=λλλ故应选(D).（14） 设一批零件的长度服从正态分布),(2σμN ，其中2,σμ均未知. 现从中随机抽取16个零件，测得样本均值)(20cm x =，样本标准差)(1cm s =，则μ的置信度为0.90的置信区间是(A) )).16(4120),16(4120(05.005.0t t +-(B) )).16(4120),16(4120(1.01.0t t +- (C))).15(4120),15(4120(05.005.0t t +-(D))).15(4120),15(4120(1.01.0t t +- [ C ]【分析】 总体方差未知，求期望的区间估计，用统计量：).1(~--n t ns x μ【详解】 由正态总体抽样分布的性质知，)1(~--n t ns x μ， 故μ的置信度为0.90的置信区间是))1(1),1(1(22-+--n t n x n t nx αα，即)).15(4120),15(4120(05.005.0t t +-故应选(C).三 、解答题（本题共9小题，满分94分.解答应写出文字说明、证明过程或演算步骤.）（15）（本题满分8分）求).111(lim 0xe x x x --+-→【分析】 ""∞-∞型未定式，一般先通分，再用罗必塔法则.【详解】 )1(1lim )111(lim 200x xx x x e x e x x x e x --→-→-+-+=--+ =2201lim x e x x x x -→+-+ =x e x x x 221lim 0-→-+=.2322lim0=+-→x x e （16）（本题满分8分）- 10 -设f(u)具有二阶连续导数，且)()(),(y x yf x y f y x g +=，求.222222yg y x g x ∂∂-∂∂ 【分析】 先求出二阶偏导数，再代入相应表达式即可.【详解】 由已知条件可得)()(2y x f x y f xy x g '+'-=∂∂， )(1)()(242322y xf y y x f xy x y f x y x g ''+''+'=∂∂，)()()(1yxf y x y x f x y f x yg '-+'=∂∂， )()()()(13222222y xf yx y x f y x y x f y x x y f x y g ''+'+'-''=∂∂， 所以 222222yg y x g x ∂∂-∂∂ =)()()(2222y x f y x y x f x y x y f x y ''+''+')()(222y x f y x x y f xy ''-''-=).(2xy f x y ' （17）（本题满分9分） 计算二重积分σd y x D⎰⎰-+122，其中}10,10),{(≤≤≤≤=y x y x D .【分析】 被积函数含有绝对值，应当作分区域函数看待，利用积分的可加性分区域积分即可.【详解】 记}),(,1),{(221D y x y x y x D ∈≤+=，}),(,1),{(222D y x y x y x D ∈>+=，于是σd y x D⎰⎰-+122=⎰⎰-+-1)1(22D dxdy y x ⎰⎰-++2)1(22D dxdy y x=⎰⎰--2021)1(πθrdr r d ⎰⎰-++Ddxdy y x )1(22⎰⎰-+-1)1(22D dxdy y x=8π+⎰⎰⎰⎰---+20102210210)1()1(πθrdr r d dy y x dx =.314-π（18）（本题满分9分） 求幂级数∑∞=-+12)1121(n n x n 在区间(-1,1)内的和函数S(x).梅花香自苦寒来，岁月共理想，人生齐高飞！【分析】幂级数求和函数一般采用逐项求导或逐项积分，转化为几何级数或已知函数的幂级数展开式，从而达到求和的目的.【详解】 设∑∞=-+=12)1121()(n n x n x S ， ∑∞=+=121121)(n n x n x S ，∑∞==122)(n n x x S ，则 )()()(21x S x S x S -=，).1,1(-∈x由于∑∞==122)(n n xx S =221x x -， )1,1(,1))((22121-∈-=='∑∞=x xx xx xS n n , 因此 ⎰-++-=-=xx x x dt t t x xS 022111ln 211)(， 又由于 0)0(1=S ，故.0,1,0,11ln 211)(1=<⎪⎩⎪⎨⎧-++-=x x x x x x S 所以 )()()(21x S x S x S -=.0,1,0,1111ln 212=<⎪⎩⎪⎨⎧---+=x x x x x x （19）（本题满分8分）设f(x),g(x)在[0，1]上的导数连续，且f(0)=0,0)(≥'x f ,0)(≥'x g .证明：对任何a ]1,0[∈,有⎰⎰≥'+'ag a f dx x g x f dx x f x g 010).1()()()()()( 【分析】 可用参数变易法转化为函数不等式证明，或根据被积函数的形式，通过分部积分讨论.【详解】 方法一：设=)(x F ⎰⎰-'+'x g x f dt t g t f dt t f t g 010)1()()()()()(， 则F(x)在[0，1]上的导数连续，并且=')(x F )]1()()[()1()()()(g x g x f g x f x f x g -'='-'，由于]1,0[∈x 时，0)(,0)(≥'≥'x g x f ，因此0)(≤'x F ，即F(x)在[0，1]上单调递减.注意到=)1(F ⎰⎰-'+'1010)1()1()()()()(g f dt t g t f dt t f t g ，而 ⎰⎰⎰'-=='10101010)()()()()()()()(dt t g t f t f t g t df t g dt t f t g=⎰'-10)()()1()1(dt t g t f g f ，故F(1)=0.因此]1,0[∈x 时，0)(≥x F ，由此可得对任何]1,0[∈a ，有⎰⎰≥'+'a g a f dx x g x f dx x f x g 010).1()()()()()(方法二：⎰⎰'-='aa a dx x g x f x f x g dx x f x g 000)()()()()()(=⎰'-adx x g x f a g a f 0)()()()(，⎰⎰'+'a dx x g x f dx x f x g 010)()()()(=⎰⎰'+'-100)()()()()()(dx x g x f dx x g x f a g a f a⎰'+1.)()()()(a dx x g x f a g a f由于]1,0[∈x 时，0)(≥'x g ，因此)()()()(x g a f x g x f '≥'，]1,[a x ∈，⎰⎰-='≥'1010)]()1()[()()()()(a g g a f dx x g a f dx x g x f ，从而 ⎰⎰'+'a dx x g x f dx x f x g 010)()()()().1()()]()1()[()()(g a f a g g a f a g a f =-+≥（20）（本题满分13分）已知齐次线性方程组（i ） ⎪⎩⎪⎨⎧=++=++=++,0,0532,032321321321ax x x x x x xx x和（ii ） ⎩⎨⎧=+++=++,0)1(2,03221321x c x b x cx bx x同解，求a,b, c 的值.梅花香自苦寒来，岁月共理想，人生齐高飞！【分析】 方程组（ii ）显然有无穷多解，于是方程组（i ）也有无穷多解，从而可确定a ，这样先求出（i ）的通解，再代入方程组（ii ）确定b,c 即可.【详解】 方程组（ii ）的未知量个数大于方程个数，故方程组方程组（ii ）有无穷多解.因为方程组（i ）与（ii ）同解，所以方程组（i ）的系数矩阵的秩小于3.对方程组（i ）的系数矩阵施以初等行变换⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-→⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡20011010111532321a a ， 从而a=2. 此时，方程组（i ）的系数矩阵可化为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡→⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡000110101211532321， 故T)1,1,1(--是方程组（i ）的一个基础解系.将1,1,1321=-=-=x x x 代入方程组（ii ）可得2,1==c b 或.1,0==c b当2,1==c b 时，对方程组（ii ）的系数矩阵施以初等行变换，有 ⎥⎦⎤⎢⎣⎡→⎥⎦⎤⎢⎣⎡110101312211， 显然此时方程组（i ）与（ii ）同解.当1,0==c b 时，对方程组（ii ）的系数矩阵施以初等行变换，有⎥⎦⎤⎢⎣⎡→⎥⎦⎤⎢⎣⎡000101202101， 显然此时方程组（i ）与（ii ）的解不相同.综上所述，当a=2,b=1,c=2时，方程组（i ）与（ii ）同解.（21）（本题满分13分）设⎥⎦⎤⎢⎣⎡=B CC AD T 为正定矩阵，其中A,B 分别为m 阶，n 阶对称矩阵，C 为n m ⨯矩阵. (I) 计算DP P T ，其中⎥⎦⎤⎢⎣⎡-=-n mE oC A E P 1； （II ）利用(I)的结果判断矩阵C A C B T 1--是否为正定矩阵，并证明你的结论.【分析】 第一部分直接利用分块矩阵的乘法即可；第二部分是讨论抽象矩阵的正定性，一般用定义.【详解】 (I) 因 ⎥⎦⎤⎢⎣⎡-=-n T mT E A C o E P 1，有 DP P T =⎥⎦⎤⎢⎣⎡--n T m E A C o E 1⎥⎦⎤⎢⎣⎡B C C A T ⎥⎦⎤⎢⎣⎡--n m E o C A E 1 =⎥⎦⎤⎢⎣⎡--C A C B o C A T 1⎥⎦⎤⎢⎣⎡--n m E oC A E 1 =⎥⎦⎤⎢⎣⎡--C A C B o o A T 1. （II ）矩阵C A C B T 1--是正定矩阵.由(I)的结果可知，矩阵D 合同于矩阵.1⎥⎦⎤⎢⎣⎡-=-C A C B o o A M T 又D 为正定矩阵，可知矩阵M 为正定矩阵.因矩阵M 为对称矩阵，故C A C B T 1--为对称矩阵. 对T X )0,,0,0( =及任意的0),,,(21≠=T n y y y Y ，有.0)(),(11>-=⎪⎪⎭⎫ ⎝⎛⎪⎪⎭⎫ ⎝⎛---Y C A C B Y Y X C A C B o o A Y X T T T T T 故C A C B T 1--为正定矩阵. （22）（本题满分13分）设二维随机变量(X,Y)的概率密度为.,20,10,0,1),(其他x y x y x f <<<<⎩⎨⎧= 求：（I ） (X,Y)的边缘概率密度)(),(y f x f Y X ；（II ） Y X Z -=2的概率密度).(z f Z( III ) }.2121{≤≤X Y P 【分析】 求边缘概率密度直接用公式即可；而求二维随机变量函数的概率密度，一般用分布函数法，即先用定义求出分布函数，再求导得到相应的概率密度; 直接用条件概率公式计算即可.【详解】 （I ） 关于X 的边缘概率密度)(x f X =⎰+∞∞-dy y x f ),(=.,10,0,20其他<<⎪⎩⎪⎨⎧⎰x dy x梅花香自苦寒来，岁月共理想，人生齐高飞！=.,10,0,2其他<<⎩⎨⎧x x 关于Y 的边缘概率密度)(y f Y =⎰+∞∞-dx y x f ),(=.,20,0,12其他<<⎪⎩⎪⎨⎧⎰y dx y =.,20,0,21其他<<⎪⎩⎪⎨⎧-y y （II ） 令}2{}{)(z Y X P z Z P z F Z ≤-=≤=，1） 当0<z 时，0}2{)(=≤-=z Y X P z F Z ；2） 当20<≤z 时，}2{)(z Y X P z F Z ≤-= =241z z -; 3) 当2≥z 时，.1}2{)(=≤-=z Y X P z F Z即分布函数为： .2,20,0,1,41,0)(2≥<≤<⎪⎩⎪⎨⎧-=z z z z z z F Z 故所求的概率密度为：.,20,0,211)(其他<<⎪⎩⎪⎨⎧-=z z z f Z （III ） .4341163}21{}21,21{}2121{==≤≤≤=≤≤X P Y X P X Y P （23）（本题满分13分）设)2(,,,21>n X X X n 为来自总体N(0,2σ)的简单随机样本，X 为样本均值，记.,,2,1,n i X X Y i i =-=求：（I ） i Y 的方差n i DY i ,,2,1, =；（II ）1Y 与n Y 的协方差).,(1n Y Y Cov（III ）若21)(n Y Y c +是2σ的无偏估计量，求常数c.【分析】 先将i Y 表示为相互独立的随机变量求和，再用方差的性质进行计算即可；求1Y 与n Y 的协方差),(1n Y Y Cov ，本质上还是数学期望的计算，同样应注意利用数学期望的运算性质；估计21)(n Y Y c +，利用其数学期望等于2σ确定c 即可.【详解】 由题设，知)2(,,,21>n X X X n 相互独立，且),,2,1(,02n i DX EX i i ===σ，.0=X E （I ）∑≠--=-=n ij j i i i X n X n D X X D DY ]1)11[()(=∑≠+-nij j i DX n DX n 221)11(=.1)1(1)1(222222σσσn n n n n n -=-⋅+-（II ） )])([(),(111n n n EY Y EY Y E Y Y Cov --= =)])([()(11X X X X E Y Y E n n --= =)(211X X X X X X X E n n +--=211)(2)(X E X X E X X E n +- =22121)(][20X E X D X X X E n n j j +++-∑==.112222σσσn n n -=+-（III ）)(])([121n n Y Y cD Y Y c E +=+=)],(2[121n Y Y Cov DY DY c ++ =222)2(2]211[σσσ=-=--+-c n n n n n n n c ，故 .)2(2-=n nc。

2005年全国硕士研究生入学统一考试数学(一)试卷一、填空题(本题共6小题,每小题4分,满分24分.把答案填在题中横线上)(1)曲线122+=x x y 的斜渐近线方程为 _____________.(2)微分方程x x y y x ln 2=+'满足91)1(-=y 的解为____________.(3)设函数181261),,(222z y x z y x u +++=,单位向量}1,1,1{31=n ,则)3,2,1(nu∂∂=.________.(4)设Ω是由锥面22y x z +=与半球面222y x R z --=围成的空间区域,∑是Ω的整个边界的外侧,则⎰⎰∑=++zdxdy ydzdx xdydz ____________.(5)设123,,ααα均为3维列向量,记矩阵123(,,)=A ααα,123123123(,24,39)=++++++B ααααααααα,如果1=A ,那么=B .(6)从数1,2,3,4中任取一个数,记为X , 再从X ,,2,1 中任取一个数,记为Y , 则}2{=Y P =____________.二、选择题(本题共8小题,每小题4分,满分32分.每小题给出的四个选项中,只有一项符合题目要求,把所选项前的字母填在题后的括号内)(7)设函数n n n x x f 31lim )(+=∞→,则()f x 在),(+∞-∞内(A)处处可导 (B)恰有一个不可导点(C)恰有两个不可导点 (D)至少有三个不可导点(8)设()F x 是连续函数()f x 的一个原函数,""N M ⇔表示"M 的充分必要条件是",N 则必有(A)()F x 是偶函数()f x ⇔是奇函数 (B)()F x 是奇函数()f x ⇔是偶函数(C)()F x 是周期函数()f x ⇔是周期函数 (D)()F x 是单调函数()f x ⇔是单调函数(9)设函数⎰+-+-++=yx y x dt t y x y x y x u )()()(),(ψϕϕ, 其中函数ϕ具有二阶导数,ψ 具有一阶导数,则必有(A)2222y ux u ∂∂-=∂∂(B)2222yu x u ∂∂=∂∂(C)222yu y x u ∂∂=∂∂∂(D)222x uy x u ∂∂=∂∂∂ (10)设有三元方程ln e 1xz xy z y -+=,根据隐函数存在定理,存在点(0,1,1)的一个邻域,在此邻域内该方程(A)只能确定一个具有连续偏导数的隐函数(,)z z x y = (B)可确定两个具有连续偏导数的隐函数(,)x x y z =和(,)z z x y = (C)可确定两个具有连续偏导数的隐函数(,)y y x z =和(,)z z x y = (D)可确定两个具有连续偏导数的隐函数(,)x x y z =和(,)y y x z =(11)设21,λλ是矩阵A 的两个不同的特征值,对应的特征向量分别为12,αα,则1α,12()+A αα线性无关的充分必要条件是(A)01≠λ (B)02≠λ (C)01=λ (D)02=λ(12)设A 为(2)n n ≥阶可逆矩阵,交换A 的第1行与第2行得矩阵**.,B A B 分别为,A B 的伴随矩阵,则(A)交换*A 的第1列与第2列得*B (B)交换*A 的第1行与第2行得*B(C)交换*A 的第1列与第2列得*-B (D)交换*A 的第1行与第2行得*-B(13)设二维随机变量(,)X Y 的概率分布为已知随机事件}0{=X 与}1{=+Y X 相互独立,则(A)0.2,0.3a b == (B)0.4,0.1a b == (C)0.3,0.2a b == (D)0.1,0.4a b ==(14)设)2(,,,21≥n X X X n 为来自总体(0,1)N 的简单随机样本,X 为样本均值,2S 为样本方差,则(A))1,0(~N X n (B)22~()nS n χ(C))1(~)1(--n t SXn (D)2122(1)~(1,1)nii n X F n X=--∑三 、解答题(本题共9小题,满分94分.解答应写出文字说明、证明过程或演算步骤) (15)(本题满分11分)设}0,0,2),{(22≥≥≤+=y x y x y x D ,]1[22y x ++表示不超过221y x ++的最大整数. 计算二重积分⎰⎰++Ddxdy y x xy .]1[22(16)(本题满分12分) 求幂级数∑∞=--+-121))12(11()1(n n n x n n 的收敛区间与和函数()f x .(17)(本题满分11分)如图,曲线C 的方程为()y f x =,点(3,2)是它的一个拐点,直线1l 与2l 分别是曲线C 在点(0,0)与(3,2)处的切线,其交点为(2,4).设函数()f x 具有三阶连续导数,计算定积分⎰'''+32.)()(dx x f x x(18)(本题满分12分)已知函数()f x 在[0,1]上连续,在(0,1)内可导,且(0)0,(1)1f f ==. 证明:(1)存在),1,0(∈ξ 使得ξξ-=1)(f .(2)存在两个不同的点)1,0(,∈ζη,使得.1)()(=''ζηf f(19)(本题满分12分)设函数)(y ϕ具有连续导数,在围绕原点的任意分段光滑简单闭曲线L 上,曲线积分24()22Ly dx xydyx y φ++⎰的值恒为同一常数.(1)证明:对右半平面0x >内的任意分段光滑简单闭曲线,C 有24()202Cy dx xydyx yφ+=+⎰.(2)求函数)(y ϕ的表达式.(20)(本题满分9分)已知二次型21232221321)1(22)1()1(),,(x x a x x a x a x x x f +++-+-=的秩为2.(1)求a 的值；(2)求正交变换x y =Q ,把),,(321x x x f 化成标准形. (3)求方程),,(321x x x f =0的解.(21)(本题满分9分)已知3阶矩阵A 的第一行是c b a c b a ,,),,,(不全为零,矩阵12324636k ⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦B (k 为常数),且=AB O ,求线性方程组0x =A 的通解.(22)(本题满分9分)设二维随机变量(,)X Y 的概率密度为(,)f x y =1001,02x y x <<<<其它求:(1)(,)X Y 的边缘概率密度)(),(y f x f Y X . (2)Y X Z -=2的概率密度).(z f Z(23)(本题满分9分)设)2(,,,21>n X X X n 为来自总体(0,1)N 的简单随机样本,X 为样本均值,记.,,2,1,n i X X Y i i =-=求:(1)i Y 的方差n i DY i ,,2,1, =. (2)1Y 与n Y 的协方差1Cov(,).n Y Y2005年考研数学一真题解析一、填空题（本题共6小题，每小题4分，满分24分. 把答案填在题中横线上）（1）曲线122+=x x y 的斜渐近线方程为 .4121-=x y【分析】 本题属基本题型，直接用斜渐近线方程公式进行计算即可.【详解】 因为a=212lim )(lim22=+=∞→∞→x x x x x f x x ， []41)12(2lim)(lim -=+-=-=∞→∞→x x ax x f b x x ，于是所求斜渐近线方程为.4121-=x y （2）微分方程x x y y x ln 2=+'满足91)1(-=y 的解为.91ln 31x x x y -=. 【分析】直接套用一阶线性微分方程)()(x Q y x P y =+'的通解公式：⎰+⎰⎰=-])([)()(C dx e x Q e y dxx P dx x P ， 再由初始条件确定任意常数即可.【详解】 原方程等价为x y xy ln 2=+'， 于是通解为 ⎰⎰+⋅=+⎰⋅⎰=-]ln [1]ln [2222C xdx x xC dx ex ey dxx dxx =2191ln 31x C x x x +-， 由91)1(-=y 得C=0，故所求解为.91ln 31x x x y -=（3）设函数181261),,(222z y x z y x u +++=，单位向量}1,1,1{31=n ，则)3,2,1(nu∂∂=33. 【分析】 函数u(x,y,z)沿单位向量γβαcos ,cos ,{cos =n}的方向导数为：γβαcos cos cos zu y u x u n u ∂∂+∂∂+∂∂=∂∂ 因此，本题直接用上述公式即可.【详解】 因为3x x u =∂∂，6y y u =∂∂，9zz u =∂∂，于是所求方向导数为)3,2,1(nu ∂∂=.33313131313131=⋅+⋅+⋅ （4）设Ω是由锥面22y x z +=与半球面222y x R z --=围成的空间区域，∑是Ω的整个边界的外侧，则⎰⎰∑=++zdxdy ydzdx xdydz 3)221(2R -π. 【分析】本题∑是封闭曲面且取外侧，自然想到用高斯公式转化为三重积分，再用球面（或柱面）坐标进行计算即可.【详解】⎰⎰∑=++zdxdy ydzdx xdydz ⎰⎰⎰Ωdxdydz 3=.)221(2sin 3320402R d d d R⎰⎰⎰-=πππθϕϕρρ （5）设321,,ααα均为3维列向量，记矩阵),,(321ααα=A ，)93,42,(321321321ααααααααα++++++=B ， 如果1=A ，那么=B 2 .【分析】 将B 写成用A 右乘另一矩阵的形式，再用方阵相乘的行列式性质进行计算即可.【详解】 由题设，有)93,42,(321321321ααααααααα++++++=B=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡941321111),,(321ααα， 于是有 .221941321111=⨯=⋅=A B（6）从数1,2,3,4中任取一个数，记为X, 再从X ,,2,1 中任取一个数，记为Y , 则}2{=Y P =4813. 【分析】 本题涉及到两次随机试验，想到用全概率公式, 且第一次试验的各种两两互不相容的结果即为完备事件组或样本空间的划分.【详解】 }2{=Y P =}12{}1{===X Y P X P +}22{}2{===X Y P X P +}32{}3{===X Y P X P +}42{}4{===X Y P X P =.4813)4131210(41=+++⨯ 二、选择题（本题共8小题，每小题4分，满分32分. 每小题给出的四个选项中，只有一项符合题目要求，把所选项前的字母填在题后的括号内）（7）设函数n nn xx f 31lim )(+=∞→，则f(x)在),(+∞-∞内(A) 处处可导. (B) 恰有一个不可导点.(C) 恰有两个不可导点. (D) 至少有三个不可导点. [ C ] 【分析】 先求出f(x)的表达式，再讨论其可导情形. 【详解】 当1<x 时，11lim )(3=+=∞→n nn xx f ；当1=x 时，111lim )(=+=∞→n n x f ；当1>x 时，.)11(lim )(3133x xx x f nnn =+=∞→即.1,11,1,,1,)(33>≤≤--<⎪⎩⎪⎨⎧-=x x x x x x f 可见f(x)仅在x=1±时不可导，故应选(C).（8）设F(x)是连续函数f(x)的一个原函数，""N M ⇔表示“M 的充分必要条件是N ”，则必有(A) F(x)是偶函数⇔f(x)是奇函数. （B ） F(x)是奇函数⇔f(x)是偶函数.(C) F(x)是周期函数⇔f(x)是周期函数.(D) F(x)是单调函数⇔f(x)是单调函数. [ A ] 【分析】 本题可直接推证，但最简便的方法还是通过反例用排除法找到答案.【详解】 方法一：任一原函数可表示为⎰+=xC dt t f x F 0)()(，且).()(x f x F ='当F(x)为偶函数时，有)()(x F x F =-，于是)()1()(x F x F '=-⋅-'，即 )()(x f x f =--，也即)()(x f x f -=-，可见f(x)为奇函数；反过来，若f(x)为奇函数，则⎰xdt t f 0)(为偶函数，从而⎰+=xC dt t f x F 0)()(为偶函数，可见(A)为正确选项.方法二：令f(x)=1, 则取F(x)=x+1, 排除(B)、(C); 令f(x)=x, 则取F(x)=221x , 排除(D); 故应选(A).（9）设函数⎰+-+-++=yx yx dt t y x y x y x u )()()(),(ψϕϕ, 其中函数ϕ具有二阶导数，ψ 具有一阶导数，则必有(A) 2222y u x u ∂∂-=∂∂. （B ） 2222yu x u ∂∂=∂∂. (C) 222y uy x u ∂∂=∂∂∂. (D) 222x u y x u ∂∂=∂∂∂. [ B ] 【分析】 先分别求出22x u ∂∂、22yu∂∂、y x u ∂∂∂2，再比较答案即可.【详解】 因为)()()()(y x y x y x y x xu--++-'++'=∂∂ψψϕϕ，)()()()(y x y x y x y x yu-+++-'-+'=∂∂ψψϕϕ， 于是 )()()()(22y x y x y x y x x u-'-+'+-''++''=∂∂ψψϕϕ，)()()()(2y x y x y x y x yx u-'++'+-''-+''=∂∂∂ψψϕϕ， )()()()(22y x y x y x y x yu-'-+'+-''++''=∂∂ψψϕϕ， 可见有2222yu x u ∂∂=∂∂，应选(B). （10）设有三元方程1ln =+-xzey z xy ，根据隐函数存在定理，存在点(0,1,1)的一个邻域，在此邻域内该方程(A) 只能确定一个具有连续偏导数的隐函数z=z(x,y).(B) 可确定两个具有连续偏导数的隐函数x=x(y,z)和z=z(x,y). (C) 可确定两个具有连续偏导数的隐函数y=y(x,z)和z=z(x,y).(D) 可确定两个具有连续偏导数的隐函数x=x(y,z)和y=y(x,z). [ D ]【分析】 本题考查隐函数存在定理，只需令F(x,y,z)=1ln -+-xzey z xy , 分别求出三个偏导数y x z F F F ,,，再考虑在点(0,1,1)处哪个偏导数不为0，则可确定相应的隐函数.【详解】 令F(x,y,z)=1ln -+-xzey z xy , 则z e y F xzx +='， yz x F y -='，x e y F xzz +-='ln ，且 2)1,1,0(='x F ，1)1,1,0(-='y F ，0)1,1,0(='z F . 由此可确定相应的隐函数x=x(y,z)和y=y(x,z). 故应选(D).（11）设21,λλ是矩阵A 的两个不同的特征值，对应的特征向量分别为21,αα，则1α，)(21αα+A 线性无关的充分必要条件是(A) 01≠λ. (B) 02≠λ. (C) 01=λ. (D) 02=λ. [ B ] 【分析】 讨论一组抽象向量的线性无关性，可用定义或转化为求其秩即可. 【详解】 方法一：令 0)(21211=++αααA k k ，则022211211=++αλαλαk k k ， 0)(2221121=++αλαλk k k . 由于21,αα线性无关，于是有 ⎩⎨⎧==+.0,022121λλk k k当02≠λ时，显然有0,021==k k ，此时1α，)(21αα+A 线性无关；反过来，若1α，)(21αα+A 线性无关，则必然有02≠λ(,否则，1α与)(21αα+A =11αλ线性相关)，故应选(B).方法二： 由于 ⎥⎦⎤⎢⎣⎡=+=+21212211121101],[],[)](,[λλαααλαλααααA ，可见1α，)(21αα+A 线性无关的充要条件是.001221≠=λλλ故应选(B).（12）设A 为n （2≥n ）阶可逆矩阵，交换A 的第1行与第2行得矩阵B, **,B A 分别为A,B 的伴随矩阵，则(A) 交换*A 的第1列与第2列得*B . (B) 交换*A 的第1行与第2行得*B .(C) 交换*A 的第1列与第2列得*B -. (D) 交换*A 的第1行与第2行得*B -. [C ]【分析】 本题考查初等变换的概念与初等矩阵的性质，只需利用初等变换与初等矩阵的关系以及伴随矩阵的性质进行分析即可.【详解】 由题设，存在初等矩阵12E （交换n 阶单位矩阵的第1行与第2行所得），使得 B A E =12，于是 12*11212*12***12*)(E A E E A E A A E B -=⋅===-，即*12*B E A -=,可见应选(C).（13）设二维随机变量(X,Y) 的概率分布为 X Y 0 1 0 0.4 a 1 b 0.1已知随机事件}0{=X 与}1{=+Y X 相互独立，则(A) a=0.2, b=0.3 (B) a=0.4, b=0.1(C) a=0.3, b=0.2 (D) a=0.1, b=0.4 [ B ] 【分析】 首先所有概率求和为1，可得a+b=0.5, 其次，利用事件的独立性又可得一等式，由此可确定a,b 的取值.【详解】 由题设，知 a+b=0.5又事件}0{=X 与}1{=+Y X 相互独立，于是有}1{}0{}1,0{=+===+=Y X P X P Y X X P ， 即 a=))(4.0(b a a ++, 由此可解得 a=0.4, b=0.1, 故应选(B).（14）设)2(,,,21≥n X X X n 为来自总体N(0,1)的简单随机样本，X 为样本均值，2S 为样本方差，则(A) )1,0(~N X n (B) ).(~22n nS χ(C) )1(~)1(--n t SXn (D) ).1,1(~)1(2221--∑=n F X X n n i i [ D ] 【分析】 利用正态总体抽样分布的性质和2χ分布、t 分布及F 分布的定义进行讨论即可.【详解】 由正态总体抽样分布的性质知，)1,0(~10N X n nX =-，可排除(A); 又)1(~0-=-n t SXn nS X ，可排除(C); 而)1(~)1(1)1(2222--=-n S n S n χ，不能断定(B)是正确选项.因为 ∑=-n i in X X222221)1(~),1(~χχ，且∑=-ni i n X X 222221)1(~)1(~χχ与相互独立，于是).1,1(~)1(1122212221--=-∑∑==n F XX n n XX ni ini i故应选(D).三 、解答题（本题共9小题，满分94分.解答应写出文字说明、证明过程或演算步骤.） （15）（本题满分11分） 设}0,0,2),{(22≥≥≤+=y x y x y x D ，]1[22y x ++表示不超过221y x ++的最大整数. 计算二重积分⎰⎰++Ddxdy y x xy .]1[22 【分析】 首先应设法去掉取整函数符号，为此将积分区域分为两部分即可.【详解】 令 }0,0,10),{(221≥≥<+≤=y x y x y x D ， }0,0,21),{(222≥≥≤+≤=y x y x y x D .则⎰⎰++Ddxdy y x xy ]1[22=⎰⎰⎰⎰+122D D xydxdy xydxdy dr r d dr r d ⎰⎰⎰⎰+=20213132cos sin 2cos sin ππθθθθθθ=.834381=+ （16）（本题满分12分） 求幂级数∑∞=--+-121))12(11()1(n n n x n n 的收敛区间与和函数f(x).【分析】 先求收敛半径，进而可确定收敛区间. 而和函数可利用逐项求导得到.【详解】 因为11)12()12()12)(1(1)12)(1(lim=+--⨯+++++∞→n n n n n n n n n ，所以当21x <时，原级数绝对收敛，当21x >时，原级数发散，因此原级数的收敛半径为1，收敛区间为（－1,1）记 121(1)(),(1,1)2(21)n nn S x x x n n -∞=-=∈--∑，则 1211(1)(),(1,1)21n n n S x x x n -∞-=-'=∈--∑，122211()(1),(1,1)1n n n S x x x x ∞--=''=-=∈-+∑. 由于 (0)0,(0)0,S S '==所以 201()()arctan ,1xxS x S t dt dt x t '''===+⎰⎰2001()()arctan arctan ln(1).2x x S x S t dt tdt x x x '===-+⎰⎰又21221(1),(1,1),1n nn x xx x ∞-=-=∈-+∑ 从而 22()2()1x f x S x x =++2222arctan ln(1),(1,1).1x x x x x x=-++∈-+ （17）（本题满分11分）如图，曲线C 的方程为y=f(x)，点(3,2)是它的一个拐点，直线1l 与2l 分别是曲线C 在点(0,0)与(3,2)处的切线，其交点为(2,4). 设函数f(x)具有三阶连续导数，计算定积分⎰'''+32.)()(dx x f x x【分析】 题设图形相当于已知f(x)在x=0的函数值与导数值，在x=3处的函数值及一阶、二阶导数值.【详解】 由题设图形知，f(0)=0, 2)0(='f ; f(3)=2, .0)3(,2)3(=''-='f f 由分部积分，知⎰⎰⎰+''-''+=''+='''+330302232)12)(()()()()()()(dx x x f x f x x x f d x x dx x f x x=dx x f x f x x f d x ⎰⎰'+'+-='+-3330)(2)()12()()12(=.20)]0()3([216=-+f f（18）（本题满分12分）已知函数f(x)在[0，1]上连续，在(0,1)内可导，且f(0)=0,f(1)=1. 证明： （I ）存在),1,0(∈ξ 使得ξξ-=1)(f ；（II ）存在两个不同的点)1,0(,∈ζη，使得.1)()(=''ζηf f【分析】 第一部分显然用闭区间上连续函数的介值定理；第二部分为双介值问题，可考虑用拉格朗日中值定理，但应注意利用第一部分已得结论.【详解】 （I ） 令x x f x F +-=1)()(，则F(x)在[0，1]上连续，且F(0)=-1<0, F(1)=1>0,应用零点定理，存在),1,0(∈ξ 使得0)(=ξF ，即ξξ-=1)(f .（II ） 在],0[ξ和]1,[ξ上对f(x)分别应用拉格朗日中值定理，知存在两个不同的点)1,(),,0(ξζξη∈∈，使得0)0()()(--='ξξηf f f ，ξξζ--='1)()1()(f f f于是 .1111)(1)()()(=-⋅-=--⋅=''ξξξξξξξξζηf f f f （19）（本题满分12分）设函数)(y ϕ具有连续导数，在围绕原点的任意分段光滑简单闭曲线L 上，曲线积分⎰++Ly x xydydx y 4222)(ϕ的值恒为同一常数.（I ）证明：对右半平面x>0内的任意分段光滑简单闭曲线C ，有022)(42=++⎰Cyx xydydx y ϕ；（II ）求函数)(y ϕ的表达式.【分析】 证明（I ）的关键是如何将封闭曲线C 与围绕原点的任意分段光滑简单闭曲线相联系，这可利用曲线积分的可加性将C 进行分解讨论；而（II ）中求)(y ϕ的表达式，显然应用积分与路径无关即可.【详解】 （I ）如图，将C 分解为：21l l C +=，另作一条曲线3l=++⎰Cy x xydydx y 4222)(ϕ-++⎰+314222)(l l y x xydydx y ϕ022)(3242=++⎰+l l y x xydydx y ϕ.（II ） 设2424()2,22y xyP Q x yx yϕ==++，,P Q 在单连通区域0x >内具有一阶连续偏导数，由（Ⅰ）知，曲线积分24()22Ly dx xydyx y ϕ++⎰在该区域内与路径无关，故当0x >时，总有Q Px y∂∂=∂∂. 24252422422(2)4242,(2)(2)Q y x y x xy x y y x x y x y ∂+--+==∂++ ①243243242242()(2)4()2()()4().(2)(2)P y x y y y x y y y y y y x y x y ϕϕϕϕϕ'''∂+-+-==∂++ ② 比较①、②两式的右端，得435()2,()4()2.y y y y y y y ϕϕϕ'=-⎧⎨'-=⎩ 由③得2()y y c ϕ=-+，将()y ϕ代入④得 535242,y cy y -= 所以0c =，从而2().y y ϕ=-（20）（本题满分9分）已知二次型21232221321)1(22)1()1(),,(x x a x x a x a x x x f +++-+-=的秩为2.（I ） 求a 的值；（II ） 求正交变换Qy x =，把),,(321x x x f 化成标准形； （III ） 求方程),,(321x x x f =0的解.【分析】 （I ）根据二次型的秩为2，可知对应矩阵的行列式为0，从而可求a 的值；（II ）是常规问题，先求出特征值、特征向量，再正交化、单位化即可找到所需正交变换； （III ）利用第二步的结果，通过标准形求解即可.【详解】 （I ） 二次型对应矩阵为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-++-=200011011a a a a A ， 由二次型的秩为2，知 020011011=-++-=aa a a A ，得a=0. （II ） 这里⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=200011011A ， 可求出其特征值为0,2321===λλλ. 解 0)2(=-x A E ，得特征向量为：⎪⎪⎪⎭⎫⎝⎛=⎪⎪⎪⎭⎫ ⎝⎛=100,01121αα，解 0)0(=-x A E ，得特征向量为：.0113⎪⎪⎪⎭⎫ ⎝⎛-=α由于21,αα已经正交，直接将21,αα，3α单位化，得：③ ④⎪⎪⎪⎭⎫⎝⎛-=⎪⎪⎪⎭⎫ ⎝⎛=⎪⎪⎪⎭⎫ ⎝⎛=01121,100,01121321ηηη令[]321ααα=Q ，即为所求的正交变换矩阵，由x=Qy ，可化原二次型为标准形：),,(321x x x f =.222221y y + （III ） 由),,(321x x x f ==+222122y y 0，得k y y y ===321,0,0（k 为任意常数）.从而所求解为：x=Qy=[]⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-==⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡0003321c c k k ηηηη，其中c 为任意常数. （21）（本题满分9分）已知3阶矩阵A 的第一行是c b a c b a ,,),,,(不全为零，矩阵⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=k B 63642321（k 为常数），且AB=O, 求线性方程组Ax=0的通解.【分析】 AB=O, 相当于告之B 的每一列均为Ax=0的解，关键问题是Ax=0的基础解系所含解向量的个数为多少，而这又转化为确定系数矩阵A 的秩.【详解】 由AB=O 知，B 的每一列均为Ax=0的解，且.3)()(≤+B r A r（1）若k 9≠, 则r(B)=2, 于是r(A)1≤, 显然r(A)1≥, 故r(A)=1. 可见此时Ax=0的基础解系所含解向量的个数为3-r(A)=2, 矩阵B 的第一、第三列线性无关，可作为其基础解系，故Ax=0 的通解为：2121,,63321k k k k k x ⎪⎪⎪⎭⎫ ⎝⎛+⎪⎪⎪⎭⎫ ⎝⎛=为任意常数.(2) 若k=9，则r(B)=1, 从而.2)(1≤≤A r1） 若r(A)=2, 则Ax=0的通解为：11,321k k x ⎪⎪⎪⎭⎫⎝⎛=为任意常数.2） 若r(A)=1,则Ax=0 的同解方程组为：0321=++cx bx ax ,不妨设0≠a ,则其通解为2121,,1001k k a c k a b k x ⎪⎪⎪⎪⎪⎭⎫ ⎝⎛-+⎪⎪⎪⎪⎪⎭⎫ ⎝⎛-=为任意常数.（22）（本题满分9分）设二维随机变量(X,Y)的概率密度为 .,20,10,0,1),(其他x y x y x f <<<<⎩⎨⎧=求：（I ） (X,Y)的边缘概率密度)(),(y f x f Y X ； （II ）Y X Z -=2的概率密度).(z f Z【分析】 求边缘概率密度直接用公式即可；而求二维随机变量函数的概率密度，一般用分布函数法，即先用定义求出分布函数，再求导得到相应的概率密度.【详解】 （I ） 关于X 的边缘概率密度)(x f X =⎰+∞∞-dy y x f ),(=.,10,0,20其他<<⎪⎩⎪⎨⎧⎰x dy x=.,10,0,2其他<<⎩⎨⎧x x关于Y 的边缘概率密度)(y f Y =⎰+∞∞-dx y x f ),(=.,20,0,12其他<<⎪⎩⎪⎨⎧⎰y dx y=.,20,0,21其他<<⎪⎩⎪⎨⎧-y y （II ） 令}2{}{)(z Y X P z Z P z F Z ≤-=≤=， 1） 当0<z 时，0}2{)(=≤-=z Y X P z F Z ；2） 当20<≤z 时，}2{)(z Y X P z F Z ≤-= =241z z -; 3) 当2≥z 时，.1}2{)(=≤-=z Y X P z F Z即分布函数为： .2,20,0,1,41,0)(2≥<≤<⎪⎩⎪⎨⎧-=z z z z z z F Z故所求的概率密度为：.,20,0,211)(其他<<⎪⎩⎪⎨⎧-=z z z f Z （23）（本题满分9分）设)2(,,,21>n X X X n 为来自总体N(0,1)的简单随机样本，X 为样本均值，记.,,2,1,n i X X Y i i =-=求：（I ） i Y 的方差n i DY i ,,2,1, =； （II ）1Y 与n Y 的协方差).,(1n Y Y Cov【分析】 先将i Y 表示为相互独立的随机变量求和，再用方差的性质进行计算即可；求1Y 与n Y 的协方差),(1n Y Y Cov ，本质上还是数学期望的计算，同样应注意利用数学期望的运算性质.【详解】 由题设，知)2(,,,21>n X X X n 相互独立，且),,2,1(1,0n i DX EX i i ===，.0=X E（I ）∑≠--=-=ni j j i i i X n X n D X X D DY ]1)11[()(=∑≠+-nij ji DXnDX n 221)11(=.1)1(1)1(222n n n n n n -=-⋅+- （II ） )])([(),(111n n n EY Y EY Y E Y Y Cov --= =)])([()(11X X X X E Y Y E n n --==)(211X X X X X X X E n n +--=211)(2)(X E X X E X X E n +-=22121)(][20X E X D X X X E n nj j +++-∑==.112nn n -=+-。

专业课真题详细解析(05年-09年)北京交通大学2005年硕士研究生入学考试试卷考试科目:管理学原理一、单项选择题（每题2分，共40分）1.现年32岁的李先生是某大型企业集团的总裁助理，工作十分出色，最近被提拔为集团生产总公司的总经理，从而从一个参谋角色转变为独立部门的直线管理负责人,在李先生近日参与的几项活动中，你认为以下哪一项最有可能与他的领导职能无关？(）A.与下属讨论对生产工作目标的认识B.与各分公司经理协商生产计划的落实情况C。

与某大学商讨有关未来技术合作事宜D。

召集公司有关部门的只能人员开联谊会，激励他们相互协作【参考答案】C【分析】A为计划,B为控制，D为激励。

C为作业工作,因此答案选C。

管理工作与作业工作.作业工作是指在组织中专门从事某项具体生产业务活动和专门技术工作的人员所进行的工作，他们大多位于一线，直接从事生产与技术工作；管理工作则是为作业工作提供服务的活动，从本质上讲,就是通过他人并使他人同自己一起去完成组织的目标和任务.2。

泰勒主张在企业中实行职能工长制，这一组织形式违反了：（）A。

分工原则 B。

权责对等原则 C。

统一指挥原则 D。

管理幅度原则【参考答案】C【分析】职能制组织缺点.容易形成多头领导,消弱统一指挥.3。

在现代管理理论学派中，哪一学派认为在企业管理中，没有什么一成不变、普遍使用的“最佳的”管理理论和方法？A。

管理过程学派 B。

行为科学学派 C。

系统管理学派 D.权变理论学派【参考答案】D【分析】权变理论观点。

该理论认为，并没有万能的、固定不变的有效领导类型，某种领导方式在实际工作中是否有效主要取决于具体的情景和场合,应当根据情境之不同而采取不同的领导方式,方位有效.没有最好的领导模式，只有最合适的领导模式。

4。

大邱庄在用人上总结出一条经验:大材小用，一般没用;小材大用,一般可用，这一现象说明：（）A。

人员的素质并不是起决定性作用的B.在乡镇企业中，高级人才的竞争力不如普通人C.学历并不是最重要的,重要的是真才实学和工作干劲D。

目录1.05年北师大物理类各方向2.05年长光所3.05年东南大学4.05年中科大5.05年南京大学6.05年华中科大7.05年吉林大学（原子所）8.05年四川大学（原子与分子）9.05年北京理工10.05年河北理工11.05年长春理工北京师范大学2005年招收硕士研究生入学考试试题专业:物理类各专业科目代号:459研究方向:各方向考试科目:量子力学[注意]答案写在答题纸上，写在试题上无效。

1.(20分)一个电子被限制在一维谐振子势场中，活动范围求激发电子到第一激发态所需要的能量（用ev表示）（，，）提示：谐振子能量本征函数可以写成2.（30分）一个电子被限制在二维各向同性谐振子势场中（特征频率为）。

（1）写出其哈密顿量，利用一维谐振子能级公式找到此电子的能级公式和简并度。

（2）请推导电子的径向运动方程。

并讨论其在时的渐近解。

提示：极坐标下3．（50分）两个质量为的粒子，被禁闭在特征频率为的一维谐振子势场中，彼此无相互作用（此题中波函数无须写出具体形式）：（1）如果两个粒子无自旋可分辨，写出系统的基态（两个都在自己的基态）和第一激发能级（即一个在基态，另一个在第一激发态）的波函数和能量（注意简并情形）。

（10分）（2）如果两个粒子是不可分辨的无自旋波色子，写出系统的基态和第一激发态的能量和波函数。

如果粒子间互作用势为，计算基态能级到一级微扰项。

（15分）（3分）如果两个粒子是不可分辨的自旋1/2粒子，写出基态能级和波函数（考虑自旋）。

如果粒子间互作用能为，计算基态能量。

（15分）（4）同（3），解除势阱，两个粒子以左一右飞出。

有两个探测器分别（同时）测量它们的y方向自旋角动量。

请问测量结果为两电子自旋反向的几率是多少？（10分）4．（30分）中心力场中电子自旋与轨道角动量存在耦合能。

总角动量，是的共同本征态。

现有一电子处于态，且。

（1）在一基近似下，可用代替，请问电子的能量与态差多少？（2）请计算该电子产生的平均磁矩，并由此计算在z方向均匀磁场B中电子的能量改变多少？（），当，，当，5．（20分）一个定域（空间位置不动）的电子（自旋1/2）处于z方向强磁场中。

2005年全国硕士研究生入学统一考试英语试题Directions:Read the following text. Choose the best word(s) for each numbered blank and mark [A], [B], [C] or [D] on ANSWER SHEET 1 (10 points)The human nose is an underrated tool. Humans are often thought to be insensitive smellers compared with animals, 1 this is largelybecause, 2animals, we stand upright. This means that our noses are 3 to perceiving those smells which float through the air, 4 the majority of smells which stick to surfaces. In fact, 5 , we are extremely sensitive to smells, 6 we do not generally realize it. Our noses are capable of 7 human smells even when these are 8 to far below one part in one million. Strangely, some people find that they can smell one type of flower but not another, 9 others are sensitive to the smells of both flowers. This may be because some people do not have the genes necessary togenerate 10 smell receptors in the nose. These receptors are the cells which sense smells and send 11to the brain. However, it has been found that even people insensitive to a certain smell12 can suddenly become sensitive to it when 13to it often enough.The explanation for insensitivity to smell seems to be that brain findsit 14 to keep all smell receptors working all the time but can 15 new receptors if necessary. Thismay 16 explain why we are not usually sensitive to our own smells—we simply do not need to be. We are not 17 of the usual smell ofour own house, but we 18 new smells when we visit someone else’s. The brain finds it best to keep smell receptors 19 for unfamiliar and emergency signals 20 the smell of smoke, which might indicate the danger of fire.1.[A] although [B] as [C] but [D] while2.[A] above [B] unlike [C] excluding [D] besides3.[A] limited [B]committed [C] dedicated [D] confined4.[A] catching [B]ignoring [C] missing [D] tracking5.[A] anyway [B]though [C] instead [D] therefore 6.[A] even if [B] if only [C] only if [D] as if7.[A]distinguishing [B]discovering [C] determining [D] detecting8.[A] diluted [B]dissolved [C] dispersed [D] diffused9.[A] when [B] since [C]for [D] whereas10.[A] unusual [B]particular [C] unique [D] typical11.[A] signs [B] stimuli [C] messages [D] impulses12.[A] at first [B] at all [C] at large [D] at times13.[A] subjected [B]left [C] drawn [D] exposed14.[A] ineffective [B] incompetent [C] inefficient [D] insufficient15.[A] introduce [B]summon [C] trigger [D] create16.[A] still [B] also [C] otherwise [D] nevertheless17.[A] sure [B] sick [C] aware [D] tired18.[A] tolerate [B]repel [C] neglect [D] notice19.[A] available [B]reliable [C] identifiable [D] suitable20.[A] similar to [B] suchas [C] along with [D] aside fromSection II Reading Comprehension Part ADirections:Read the following four texts. Answer the questions below each text by choosing [A], [B], [C] or [D]. Mark your answers on ANSWER SHEET 1.(40 points)Text 1Everybody loves a fat pay rise. Yet pleasure at your own can vanish if you learn that a colleague has been given a bigger one. Indeed, if he has a reputation for slacking, you might even be outraged. Such behaviour is regarded as “all too human”, with the underlying assumption that other animals would not be capable of this finely developed sense of grievance. But a study by Sarah Brosnan and Frans de Waal of Emory University in Atlanta, Georgia, which has justbeen published in Nature, suggests that it is all too monkey, as well.The researchers studied the behaviour of female brown capuchin monkeys. They look cute. They are good-natured, co-operative creatures, and they share their food readily. Above all, like their female human counterparts, they tend to pay much closer attention to the value of “goods and services” than males. Such characteristics make them perfect candidates for Dr. Brosnan’s and Dr. de Waal’s study. The researchers spent two years teaching their monkeys to exchange tokens for food. Normally, the monkeys were happy enough to exchange pieces of rock for slices of cucumber. However, when two monkeys were placed in separatebut adjoining chambers, so that each could observe what the other was getting in return for its rock, their behaviour became markedly different.In the world of capuchins grapes are luxury goods (and much preferableto cucumbers). So when one monkey was handed a grape in exchange for her token, the second was reluctant to hand hers over for a mere piece of cucumber. And if one received a grape without having to provide her token in exchange at all, the other either tossed her own token at the researcher or out of the chamber, or refused to accept the slice of cucumber. Indeed, the mere presence of a grape in the other chamber (without an actual monkey to eat it) was enough to induce resentment in a female capuchin. The researchers suggest that capuchin monkeys, like humans, are guided by social emotions. In the wild,they are a co-operative, group-living species. Such co-operation is likely to be stable only when each animal feels it is not being cheated. Feelings of righteous indignation, it seems, are not the preserve of people alone. Refusing a lesser reward completely makes these feelings abundantly clear to other members of the group. However, whether such a sense of fairness evolved independently in capuchins and humans, or whether it stems from the common ancestor that the species had 35 million years ago, is, as yet, an unanswered question.21. In the opening paragraph, the author introduces his topic by________.[A] posing acontrast[B] justifying an assumption [C] making acomparison[D] explaining a phenomenon22. The statement “it is all too monkey” (Last line, Para graph l) implies that ________.[A] monkeys are also outraged by slack rivals [B] resenting unfairness is also monkeys’ nature [C] monkeys, like humans, tend to be jealous of each other[D] no animals other than monkeys can develop such emotions23. Female capuchin monkeys were chosen for the research most probably because theyare ________.[A] more inclined to weigh what they get [B] attentive to researchers’ instructions[C] nice in both appearance and temperament [D] more generous than their male companions24. Dr. Brosnan and Dr. de Waal have eventually found in their study that the monkeys ________.[A] prefer grapes tocucumbers[B] can be taught to exchange things[C] will not be co-operative if feeling cheated [D] are unhappy when separated from others25. What can we infer from the last paragraph?[A] Monkeys can be trained to develop social emotions.[B] Human indignation evolved from an uncertain source. [C] Animals usually show their feelings openly as humans do. [D] Cooperation among monkeys remains stable only in the wild.Text 2Do you remember all those years when scientists argued that smoking would kill us but the doubters insisted that we didn’t know for sure? That the evidence was inconclusive, the science uncertain? That the antismoking lobby was out to destroy our way of life and the government should stay out of the way? Lots of Americans bought that nonsense, and over three decades, some 10 million smokers went to early graves. There are upsetting parallels today, as scientists in one wave after another try to awaken us to the growing threat of global warming. The latest was a panel from theNational Academy of Sciences, enlisted by the White House, to tell us that the Earth’s atmosphere is definitely warming and that the problem is largely man-made. The clear message is that we should get moving to protect ourselves. The president of the National Academy, Bruce Alberts, added this key point in the preface to the panel’s report: “Science never has all the answers. But science does provide us with the best available guide to the future, and it is critical that our nation and the world base important policies on the best judgments that science can provide concerning the future consequences of present actions.”Just as on smoking, voices now come from many quarters insisting that the science about global warming is incomplete, that it’s OK to keep pouring fumes into the air until we know for sure. This is a dangerous game: by the time 100 percent of the evidence is in, it may be too late. With the risks obvious and growing, a prudent people would take out an insurance policy now. Fortunately, the White House is starting to pay at tention. But it’s obvious that a majority of the president’s advisers still don’t take global warming seriously. Instead of a plan of action, they continue to press for more research—a classic case of “paralysis by analysis”.To serve as responsible stewards of the planet, we must press forward on deeper atmospheric and oceanic research. But research alone is inadequate. If the Administration won’t take the legislative initiative, Congress should help to begin fashioning conservation measures. A bill by Democratic Senator RobertByrd of West Virginia, which would offer financial incentives for private industry, is a promising start. Many see that the country is getting ready to build lots of new power plants to meet our energy needs. If we are ever going to protect the atmosphere, it is crucial that those new plants be environmentally sound.26. An argument made by supporters of smoking was that ________. [A] there was no scientific evidence of the correlation between smoking and death[B] the number of early deaths of smokers in the past decades was insignificant[C] people had the freedom to choose their own way of life[D] antismoking people were usually talking nonsense 27. According to Bruce Alberts, science can serve as ________. [A] a protector [B] a judge [C] a critic [D] a guide28. What does the author mean by “paralysis by analysis” (Last line, Paragraph 4)?[A] Endless studies killaction. [B] Careful investigation reveals truth. [C] Prudent planning hinders progress. [D] Extensive research helpsdecision-making.29. According to the author, what should the Administration do about global warming?[A] Offer aid to build cleaner power plants. [B] Raise public awareness of conservation.[C] Press for further scientific research. [D] Take some legislative measures.30. The author associates the issue of global warming with that of smoking because ______.[A] they both suffered from the government’s negligence[B] a lesson from the latter is applicable to the former[C] the outcome of the latter aggravates the former [D] both of them have turned from bad to worseText 3Of all the components of a good night’s sleep, drea ms seem to be least within our control. In dreams, a window opens into a world where logic is suspended and dead people speak. A century ago, Freud formulated his revolutionary theory that dreams were the disguised shadows of our unconscious desires and fears; by the late 1970s, neurologists had switched to thinking of them as just “mental noise”—the random byproducts of theneural-repair work that goes on during sleep. Now researchers suspect that dreams are part of the mind’s emotional thermostat, regulating moods while the brain is “off-line.” And one leading authority says that these intensely powerful mental events can be not only harnessed but actually brought under conscious control, to help us sleep and feel better. “It’s your dream,” says Rosalind Cartwright, chair of psychology at Chicago’s Medical Center. “If you don’t like it, change it.”Evidence from brain imaging supports this view. The brain is asactive during REM (rapid eye movement) sleep—when most vivid dreams occur—as it is when fully awake, says Dr. Eric Nofzinger at the University of Pittsburgh. But not all parts of the brain are equally involved; the limbic system (the “emotional brain”) is especially active, while the prefrontal cortex (the center of intellect and reasoning) isrelativ ely quiet. “We wake up from dreams happy or depressed, and those feelings can stay with us all day.” says Stanford sleep researcher Dr. William Dement.The link between dreams and emotions shows up among the patients in Cartwright’s clinic. Most people seem to have more bad dreams early in the night, progressing toward happier ones before awakening, suggesting that they are working through negative feelings generated during the day. Because our conscious mind is occupied with daily life we don’t always think about the emotional significance of the day’s events—until, it appears, we begin to dream.And this process need not be left to the unconscious. Cartwright believes one can exercise conscious control over recurring bad dreams. As soon as you awaken, identify what is upsetting about the dream. Visualize how you would like it to end instead; the next time it occurs, try to wake up just enough to control its course. With much practice people can learn to, literally, do it in their sleep.At the end of the da y, there’s probably little reason to pay attention to our dreams at all unless they keep us from sleeping or “we wake up in a panic,” Cartwright says. Terrorism,economic uncertainties and general feelings of insecurity have increased people’s anxiety. Tho se suffering from persistent nightmares should seek help from a therapist. For the rest of us, the brain has its ways of working through bad feelings. Sleep—or rather dream—on it and you’ll feel better in the morning.31. Researchers have come to believe that dreams ________. [A] can be modified in theircourses [B] are susceptible to emotional changes [C] reflect our innermost desires and fears [D] are a random outcome of neural repairs 32. By referring to the limbic system, the author intends to show________. [A] its function in ourdreams [B] the mechanism of REM sleep[C] the relation of dreams to emotions [D] its difference from the prefrontal cortex 33. The negative feelings generated during the day tend to ________. [A] aggravate in our unconscious mind [B] develop into happy dreams[C] persist till the time we fallasleep [D] show up in dreams early at night34. Cartwright seems to suggest that ________.[A] waking up in time is essential to the ridding of bad dreams[B] visualizing bad dreams helps bring them under control[C] dreams should be left to their natural progression[D] dreaming may not entirely belong to the unconscious35. What advice might Cartwright give to those who sometimes have bad dreams?[A] Lead your life asusual. [B] Seek professional help.[C] Exercise consciouscontrol. [D] Avoid anxiety in the daytime.Text 4Americans no longer expect public figures, whether in speech or in writing, to command the English language with skill and gift. Nor do they aspire to such command themselves. In his latest book, Doing Our Own Thing: The Degradation of language and Music and Why We Should Like, Care, John McWhorter, a linguist and controversialist of mixed liberal and conservative views, sees the triumph of 1960scounter-culture as responsible for the decline of formal English.Blaming the permissive 1960s is nothing new, but this is not yet another criticism against the decline in education. Mr. McWhorter’s academic speciality is language history and change, and he sees the g radual disappearance of “whom”,for example, to be natural and no more regrettable than the loss of the case-endings of Old English.But the cult of the authentic and the personal, “doing our own thing”, has spelt the death of formal speech, writing, poetry and music. While even the modestly educated sought an elevated tone when they put pento paper before the 1960s, even the most well regarded writing since then has sought to capture spoken English on the page. Equally, in poetry, the highly personal, performative genre is the only form that could claim real liveliness. In both oral and writtenEnglish, talking is triumphing over speaking, spontaneity over craft. Illustrated with an entertaining array of examples from both high and low culture, the trend that Mr. McWhorter documents is unmistakable. But it is less clear, to take the question of his subtitle, why we should, like, care. As a linguist, he acknowledges that all varieties of human language, including non-standard ones like Black English, can be powerfully expressive—there exists no language or dialect in the world that cannot convey complex ideas. He is not arguing, as many do, that we can no longer think straight because we do not talk proper.Russians have a deep love for their own language and carry large chunks of memorized poetry in their heads, while Italian politicians tend to elaborate speech that would seem old-fashioned to mostEnglish-speakers. Mr. McWhorter acknowledges that formal language is not strictly necessary, and proposes no radical education reforms—he is really grieving over the loss of something beautiful more than useful. We now take our English “on paper plates instead of china”. A shame, perhaps, but probably an inevitable one.36. According to McWhorter, the decline of formal English ________.[A] is inevitable in radical education reforms[B] is but all too natural in language development[C] has caused the controversy over the counter-culture[D] brought about changes in public attitudes in the 1960s37. The word “talking” (Line 6, Paragraph 3) denotes ________. [A]modesty[B] personality[C]liveliness[D] informality38. To which of the following statements would McWhorter most likely agree? [A] Logical thinking is not necessarily related to the way we talk.[B] Black English can be more expressive than standard English. [C] Non-standard varieties of human language are just as entertaining. [D] Of all the varieties, standard English can best convey complex ideas.39. The description of Russians’ love of memorizing poetry shows the author’s ________.[A] interest in theirlanguage[B] appreciation of their efforts[C] admiration for theirmemory [D] contempt for their old-fashionedness40. According to the last paragraph, “paper plates” is to “china” as________.[A] “temporary” is to“permanent”[B] “radical” is to “conservative”[C] “functional” is to“artistic”[D] “humble” is to “noble”Part BDirections:In the following text, some sentences have been removed. For Questions 41-45, choose the most suitable one from the list A-G to fit into each of the numbered blanks. There are two extra choices, which do not fit in any of the gaps. Mark your answers on ANSWER SHEET 1. (10 points) Canada’s premiers (the leaders of provincial governments), if they have any breath left after complaining about Ottawa at their late July annual meeting, might spare a moment to do something, together, to reduce health-care costs.They’re all groaning about soaring health budgets, the fastest-growing component of which are pharmaceutical costs.(41) ____________What to do? Both the Romanow commission and the Kirby committee on health care—to say nothing of reports from other experts—recommended the creation of a national drug agency. Instead of each province having its own list of approved drugs, bureaucracy, procedures and limited bargaining power, all would pool resources, work with Ottawa, and create a national institution.(42) _____________But “national” doesn’t have to mean that. “National” could mean interprovincial—provinces combining efforts to create one body.Either way, one benefit of a “national” organization would be to negotiate better prices, if possible, with drug manufacturers. Instead of having one province—or a series of hospitals within a province—negotiate a price for a given drug on the provincial list, the national agency would negotiate on behalf of all provinces.Rather than, say, Quebec, negotiating on behalf of seven million people, the national agency would negotiate on behalf of 31 million people. Basic economics suggests the greater the potential consumers, the higher the likelihood of a better price. (43) _____________A small step has been taken in the direction of a national agency with the creation of the CanadianCo-ordinating Office for Health Technology Assessment, funded by Ottawa and the provinces. Under it, a Common Drug Review recommends to provincial lists which new drugs should be included. Predictably, and regrettably, Quebec refused to join.A few premiers are suspicious of any federal-provincial deal-making. They (particularly Quebec and Alberta) just want Ottawa to fork over additional billions with few, if any, strings attached. That’s one reason why the idea of a national list hasn’t gone anywhere, while drug costskeep rising fast.(44) _____________Premiers love to quote Mr. Romanow’s report selectively, especially the parts about more federal money. Perhaps they should read what he had to say about drugs: “A national drug agency would provide governments more influence on pharmaceutical companies in order to constrain theever-increasing cost of drugs.”(45) _____________So when the premiers gather in Niagara Falls to assemble their usual complaint list, they should also get cracking about something in their jurisdiction that would help their budgets and patients.[A] Quebec’s resistance to a national agency is provincialist ideology. One of the first advocates for a national list was a researcher at Laval University. Quebec’s Drug Insurance Fund has seen its costs skyrocket with annual increases from 14.3 per cent to 26.8 per cent![B] Or they could read Mr. Kirby’s report: “the substantial buying power of such an agency would strengthen the public prescription-drug insurance plans to negotiate the lowest possible purchase prices from drug companies.”[C] What does “national” mean? Roy Romanow and Senator Michael Kirby recommended a federal-provincial body much like the recently created National Health Council.[D] The problem is simple and stark: health-care costs have been, are, and will continue to increase faster than government revenues.[E] According to the Canadian Institute for Health Information, prescription drug costs have risensince 1997 at twice the rate of overall health-care spending. Part of the increase comes from drugs being used to replace other kinds of treatments. Part of it arises from new drugs costing more than older kinds. Part of it is higher prices.[F] So, if the provinces want to run the health-care show, they should prove they can run it, starting with an interprovincial health list that would end duplication, save administrative costs, prevent one province from being played off against another, and bargain for better drug prices.[G] Of course, the pharmaceutical companies will scream. They like divided buyers; they can lobby better that way. They can use the threat of removing jobs from one province to another. They can hope that, if one province includes a drug on its list, the pressure will cause others toinclude it on theirs. They wouldn’t like a national agency, butself-interest would lead them to deal with it.Part CDirections:Read the following text carefully and then translate the underlined segments into Chinese. Your translation should be written clearly on ANSWER SHEET 2. (10 points) It is not easy to talk about the role of the mass media in this overwhelmingly significant phase in European history. History and news become confused, and one’s impressions tend to be a mixture of skepticism and optimism.(46)Television is one of the means by which these feelings are created and conveyed—and perhaps never before has it served so much toconnect different peoples and nations as in the recent events in Europe. The Europe that is now forming cannot be anything other than its peoples, their cultures and national identities. With this in mind we can begin to analyze the European television scene. (47) In Europe, as elsewhere, multi-media groups have been increasingly successful; groups which bring together television, radio, newspapers, magazines and publishing houses that work in relation to one another. One Italian example would be the Berlusconi group, while abroad Maxwell and Murdoch come to mind.Clearly, only the biggest and most flexible television companies are going to be able to compete in such a rich and hotly-contested market. (48) This alone demonstrates that the television business is not an easy world to survive in, a fact underlined by statistics that show that out of eighty European television networks, no less than 50% took a loss in 1989. Moreover, the integration of the European community will oblige television companies to cooperate more closely in terms of both production and distribution.(49) Creating a “European identity” that respects the different cultures and traditions which go to make up the connecting fabric of the Old Continent is no easy task and demands a strategic choice—that of producing programs in Europe for Europe. This entails reducing our dependence on the North American market, whose programs relate to experiences and cultural traditions which are different from our own.In order to achieve these objectives, we must concentrate more onco-productions, the exchange of news, documentary services and training. This also involves the agreements between European countries for thecreation of a European bank for Television Production which, on the model of the European Investments Bank, will handle the finances necessary for production costs. (50)In dealing with a challenge on such a scale, it is no exaggeration to s ay, “United we stand, divided we fall”—and if I had to choose a slogan it would be “Unity in our diversity.” A unity of objectives that nonetheless respect the varied peculiarities of each country. Section III WritingPart A51. Directions: Two months ago you got a job as an editor for the magazine Designs & Fashions. But now you find that the work is not what you expected. You decide to quit. Write a letter to your boss, Mr. Wang, telling him your decision, stating your reason(s), and making an apology.Write your letter with no less than 100 words. Write it neatly on ANSWER SHEET 2. Do not sign your own name at the end of the letter; use “Li Ming” instead. You do not need to write the address. (10 points)Part B52. Directions:Write an essay of 160-200 words based on the following drawing. In your essay, you should first describe the drawing, then interpret itsmeaning, and give your comment on it.You should write neatly on ANSWER SHEET 2. (20 points)。