2011年真题(解析版)[1]
2011年考研数学一试卷真题及答案解析
2011年考研数一真题及答案解析一、选择题1、 曲线()()()()4324321----=x x x x y 的拐点是（ ）（A ）（1，0） （B ）（2，0） （C ）（3，0） （D ）（4，0）【答案】C 【考点分析】本题考查拐点的判断。
直接利用判断拐点的必要条件和第二充分条件即可。
【解析】由()()()()4324321----=x x x x y 可知1,2,3,4分别是()()()()23412340y x x x x =----=的一、二、三、四重根，故由导数与原函数之间的关系可知(1)0y '≠，(2)(3)(4)0y y y '''===(2)0y ''≠，(3)(4)0y y ''''==，(3)0,(4)0y y ''''''≠=，故（3，0）是一拐点。
2、 设数列{}n a 单调减少，0lim =∞→n n a ，()∑===n k k n n a S 12,1 无界，则幂级数()11nn n a x ∞=-∑的收敛域为（ ） （A ） (-1，1] （B ） [-1，1) （C ） [0，2) （D ）(0，2]【答案】C 【考点分析】本题考查幂级数的收敛域。
主要涉及到收敛半径的计算和常数项级数收敛性的一些结论，综合性较强。
【解析】()∑===n k k n n a S 12,1 无界，说明幂级数()11nn n a x ∞=-∑的收敛半径1R ≤；{}n a 单调减少，0lim =∞→nn a ，说明级数()11nn n a ∞=-∑收敛，可知幂级数()11nn n a x ∞=-∑的收敛半径1R ≥。
因此，幂级数()11nn n a x ∞=-∑的收敛半径1R =，收敛区间为()0,2。
又由于0x =时幂级数收敛，2x =时幂级数发散。
2011年考研英语真题及答案解析
2011年考研英语(一)真题Section I Use of EnglishDirections:Read the following text. Choose the best word(s) for ea ch numbered blank and mark [A], [B], [C] or [D] on ANSWER S HEET 1. (10 points)Ancient Greek philosopher Aristotle viewed laughter as “a bodily exercise precious to health.” But _____some cla ims to the contrary, laughing probably has little influence on physical filness Laughter does _____short-term changes in the function of the heart and its blood vessels, ____ he art rate and oxygen consumption But because hard laughter i s difficult to ____, a good laugh is unlikely to have _____ benefits the way, say, walking or jogging does.____, instead of straining muscles to build them, as ex ercise does, laughter apparently accomplishes the ____, stu dies dating back to the s indicate that laughter. muscles, Such bodily reaction might conceivably help____the effe cts of psychological stress.Anyway,the act of laughing prob ably does produce other types of ______feedback,that improve an individual’s emotional state. ______one classical the ory of emotion,our feelings are partially rooted _______ ph ysical reactions. It was argued at the end of the 19th cent ury that humans do not cry ______they are sad but they beco me sad when te tears begin to flow.Although sadness also _______ tears,evidence suggests t hat emotions can flow _____ muscular responses.In an experi ment published in 1988,social psychologist Fritz.1．[A]among [B]except [C]despite [D]like2．[A]reflect [B]demand [C]indicate [D]produce3．[A]stabilizing [B]boosting [C]impairing [D]determinin g4．[A]transmit [B]sustain [C]evaluate [D]observe5．[A]measurable [B]manageable [C]affordable [D]renewabl e6．[A]In turn [B]In fact [C]In addition [D]In brief7．[A]opposite [B]impossible [C]average [D]expected8．[A]hardens [B]weakens [C]tightens [D]relaxes9．[A]aggravate [B]generate [C]moderate [D]enhance10．[A]physical [B]mental [C]subconscious [D]internal11．[A]Except for [B]According to [C]Due to [D]As for12．[A]with [B]on [C]in [D]at13．[A]unless [B]until [C]if [D]because14．[A]exhausts [B]follows [C]precedes [D]suppresses15．[A]into [B]from [C]towards [D]beyond16．[A]fetch [B]bite [C]pick [D]hold17．[A]disappointed [B]excited [C]joyful [D]indifferent 18．[A]adapted [B]catered [C]turned [D]reacted19．[A]suggesting [B]requiring [C]mentioning [D]supposin g20．[A]Eventually [B]Consequently [C]Similarly [D]Conver selySection II Reading ComprehensionPart ADirections:Read the following four texts. Answer the questions bel ow each text by choosing [A], [B], [C] or [D]. Mark your an swers on ANSWER SHEET 1. (40 points)Text 1The decision of the New York Philharmonic to hire Alan Gilbert as its next music director has been the talk of the classical-music world ever since the sudden announcement o f his appointment in 2009. For the most part, the response has been favorable, to say the least. “Hooray! At last!” wrote Anthony Tommasini, a sober-sided classical-music crit ic.One of the reasons why the appointment came as such a s urprise, however, is that Gilbert is comparatively little k nown. Even Tommasini, who had advocated Gilbert’s appointm ent in the Times, calls him “an unpretentious musician wit h no air of the formidable conductor about him.” As a desc ription of the next music director of an orchestra that has hitherto been led by musicians like Gustav Mahler and Pier re Boulez, that seems likely to have struck at least some T imes readers as faint praise.For my part, I have no idea whether Gilbert is a great conductor or even a good one. To be sure, he performs an im pressive variety of interesting compositions, but it is not necessary for me to visit Avery Fisher Hall, or anywhere e lse, to hear interesting orchestral music. All I have to do is to go to my CD shelf, or boot up my computer and downlo ad still more recorded music from iTunes.Devoted concertgoers who reply that recordings are no s ubstitute for live performance are missing the point. For t he time, attention, and money of the art-loving public, cla ssical instrumentalists must compete not only with opera ho uses, dance troupes, theater companies, and museums, but al so with the recorded performances of the great classical mu sicians of the 20th century. There recordings are cheap, av ailable everywhere, and very often much higher in artistic quality than today’s live performances; moreover, they can be “consumed” at a time and place of the listener’s choo sing. The widespread availability of such recordings has th us brought about a crisis in the institution of the traditi onal classical concert.One possible response is for classical performers to pr ogram attractive new music that is not yet available on rec ord. Gilbert’s own interest in new music has been widely n oted: Alex Ross, a classical-music critic, has described hi m as a man who is capable of turning the Philharmonic into “a markedly different, more vibrant organization.” But wh at will be the nature of that difference? Merely expanding the orchestra’s repertoire will not be enough. If Gilbert and the Philharmonic are to succeed, they must first change the relationship between ’s oldest orchestra and the new audience it hops to attract.21. We learn from Para.1 that Gilbert’s appointment has[A]incurred criticism.[B]raised suspicion.[C]received acclaim.[D]aroused curiosity.22. Tommasini regards Gilbert as an artist who is[A]influential.[B]modest.[C]respectable.[D]talented.23. The author believes that the devoted concertgoers[A]ignore the expenses of live performances.[B]reject most kinds of recorded performances.[C]exaggerate the variety of live performances.[D]overestimate the value of live performances.24. According to the text, which of the following is tr ue of recordings?[A]They are often inferior to live concerts in quality.[B]They are easily accessible to the general public.[C]They help improve the quality of music.[D]They have only covered masterpieces.25. Regarding Gilbert’s role in revitalizing the Philha rmonic, the author feels[A]doubtful.[B]enthusiastic.[C]confident.[D]puzzled.Text 2When Liam McGee departed as president of Bank of Americ a in August, his explanation was surprisingly straight up. Rather than cloaking his exit in the usual vague excuses, h e came right out and said he was leaving “to pursue my goa l of runni ng a company.” Broadcasting his ambition was “v ery much my decision,” McGee says. Within two weeks, he wa s talking for the first time with the board of Hartford Fin ancial Services Group, which named him CEO and chairman on September 29.McGee says leaving without a position lined up gave him time to reflect on what kind of company he wanted to run. It also sent a clear message to the outside world about his aspirations. And McGee isn’t alone. In recent weeks the N o.2 executives at and American Express quit with the expla nation that they were looking for a CEO post. As boards scr utinize succession plans in response to shareholder pressur e, executives who don’t get the nod also may wish to move on. A turbulent business environment also has senior managers cautious of letting vague pronouncements cloud their rep utations.As the first signs of recovery begin to take hold, depu ty chiefs may be more willing to make the jump without a ne t. In the third quarter, CEO turnover was down 23% from a y ear ago as nervous boards stuck with the leaders they had, according to Liberum Research. As the economy picks up, opp ortunities will abound for aspiring leaders.The decision to quit a senior position to look for a be tter one is unconventional. For years executives and headhu nters have adhered to the rule that the most attractive CEO candidates are the ones who must be poached. Says Korn/Fer ry senior partner Dennis Carey:”I can’t think of a single search I’ve done where a board has not instructed me to lo ok at sitting CEOs fi rst.”Those who jumped without a job haven’t always landed in top positions quickly. Ellen Marram quit as chief of Tropi cana a decade age, saying she wanted to be a CEO. It was a year before she became head of a tiny Internet-based commod ities exchange. Robert Willumstad left Citigroup in 2005 with ambitions to be a CEO. He finally took that post at a ma jor financial institution three years later.Many recruiters say the old disgrace is fading for top performers. The financial crisis has made it more acceptabl e to be between jobs or to leave a bad one. “The tradition al rule was it’s safer to stay where you are, but that’s been fundamentally inverted,” says one headhunter. “The p eople who’ve been hurt the worst are those who’ve stayed too long.”26. When McGee announced his departure, his manner can best be described as being[A]arrogant.[B]frank.[C]self-centered.[D]impulsive.27. According to Paragraph 2, senior executives’ quitti ng may be spurred by[A]their expectation of better financial status.[B]their need to reflect on their private life.[C]their strained relations with the boards.[D]their pursuit of new career goals.28. The word “poached” (Line 3, Paragraph 4) most prob ably means[A]approved of.[B]attended to.[C]hunted for.[D]guarded against.29. It can be inferred from the last paragraph that[A]top performers used to cling to their posts.[B]loyalty of top performers is getting out-dated.[C]top performers care more about reputations.[D]it’s safer to stick to the traditional rules.30. Which of the following is the best title for the te xt?[A]CEOs: Where to Go?[B]CEOs: All the Way Up?[C]Top Managers Jump without a Net[D]The Only Way Out for Top PerformersText 3The rough guide to marketing success used to be that yo u got what you p aid for. No longer. While traditional “pai d” media – such as television commercials and print adver tisements – still play a major role, companies today can e xploit many alternative forms of media. Consumers passionat e about a product may create “owned” med ia by sending e-m ail alerts about products and sales to customers registered with its Web site. The way consumers now approach the broa d range of factors beyond conventional paid media.Paid and owned media are controlled by marketers promot ing their own products. For earned media , such marketers a ct as the initiator for users’ responses. But in some case s, one marketer’s owned media become another marketer’s p aid media – for instance, when an e-commerce retailer sell s ad space on its Web site. We define such sold media as ow ned media whose traffic is so strong that other organizatio ns place their content or e-commerce engines within that en vironment. This trend ,which we believe is still in its infancy, effectively began with retailers and travel providers such as airlines and hotels and will no doubt go further. Johnson & Johnson, for example, has created BabyCenter, a s tand-alone media property that promotes complementary and e ven competitive products. Besides generating income, the pr esence of other marketers makes the site seem objective, gi ves companies opportunities to learn valuable information a bout the appeal of other companies’ marketing, and may hel p expand user traffic for all companies concerned.The same dramatic technological changes that have provi ded marketers with more (and more diverse) communications c hoices have also increased the risk that passionate consume rs will voice their opinions in quicker, more visible, and much more damaging ways. Such hijacked media are the opposi te of earned media: an asset or campaign becomes hostage to consumers, other stakeholders, or activists who make negat ive allegations about a brand or product. Members of social networks, for instance, are learning that they can hijack media to apply pressure on the businesses that originally c reated them.If that happens, passionate consumers would try to pers uade others to boycott products, putting the reputation of the target company at risk. In such a case, the company’s response may not be sufficiently quick or thoughtful, and t he learning curve has been steep. Toyota Motor, for example, alleviated some of the damage from its recall crisis earli er this year with a relatively quick and well-orchestrated social-media response campaign, which included efforts to e ngage with consumers directly on sites such as Twitter and the social-news site Digg.31.Consumers may create “earned” media when they are[A] obscssed with online shopping at certain Web sites.[B] inspired by product-promoting e-mails sent to them.[C] eager to help their friends promote quality product s.[D] enthusiastic about recommending their favorite prod ucts.32. According to Paragraph 2,sold media feature[A] a safe business environment.[B] random competition.[C] strong user traffic.[D] flexibility in organization.33. The author indicates in Paragraph 3 that earned med ia[A] invite constant conflicts with passionate consumer s.[B] can be used to produce negative effects in marketin g.[C] may be responsible for fiercer competition.[D] deserve all the negative comments about them.34. Toyota Motor’s experience is cited as an example of[A] responding effectively to hijacked media.[B] persuading customers into boycotting products.[C] cooperating with supportive consumers.[D] taking advantage of hijacked media.35. Which of the following is the text mainly about ?[A] Alternatives to conventional paid media.[B] Conflict between hijacked and earned media.[C] Dominance of hijacked media.[D] Popularity of owned media.Text 4It’s no surprise that Jennifer Senior’s insightful, pr ovocative magazine cover story, “I love My Children, I Hat e My Life,” is arousing much chatter – nothing gets peopl e talking like the suggestion that child rearing is anythin g less than a completely fulfilling, life-enriching experie nce. Rather than concluding that children make parents eith er happy or miserable, Senior suggests we need to redefine happiness: instead of thinking of it as something that can be measured by moment-to-moment joy, we should consider bei ng happy as a past-tense condition. Even though the day-to-day experience of raising kids can be soul-crushingly hard, Senior writes that “the very things that in the moment da mpen our moods can later be sources of intense gratificatio n and delight.”The magazine cover showing an attractive mother holding a cute baby is hardly the only Madonna-and-child image on newsstands this week. There are also stories about newly ad optive – and newly single – mom Sandra Bullock, as well a s the usual “Jennifer Aniston is pregnant” news. Practica lly every week features at least one celebrity mom, or mom-to-be, smiling on the newsstands.In a society that so persistently celebrates procreatio n, is it any wonder that admitting you regret having childr en is equivalent to admitting you support kitten-killing ? It doesn’t seem quite fair, then, to compare the regrets o f parents to the regrets of the children. Unhappy parents r arely are provoked to wonder if they shouldn’t have had ki ds, but unhappy childless folks are bothered with the messa ge that children are the single most important thing in the world: obviously their misery must be a direct result of t he gaping baby-size holes in their lives.Of course, the image of parenthood that celebrity magaz ines like Us Weekly and People present is hugely unrealisti c, especially when the parents are single mothers like Bull ock. According to several studies concluding that parents are less happy than childless couples, single parents are th e least happy of all. No shock there, considering how much work it is to raise a kid without a partner to lean on; yet to hear Sandra and Britney tell it, raising a kid on their “own” (read: with round-the-clock help) is a piece of ca ke.It’s hard to imagine that many people are dumb enough t o want children just because Reese and Angelina make it loo k so glamorous: most adults understand that a baby is not a haircut. But it’s interesting to wonder if the images we see every week of stress-free, happiness-enhancing parentho od aren’t in some small, subconscious way contributing to our own dissatisfactions with the actual experience, in the same way that a small part of us hoped getting “ the Rach el” might make us look just a little bit like Jennifer Ani ston.36.Jennifer Senior suggests in her article that raisinga child can bring[A]temporary delight[B]enjoyment in progress[C]happiness in retrospect[D]lasting reward37.We learn from Paragraph 2 that[A]celebrity moms are a permanent source for gossip.[B]single mothers with babies deserve greater attentio n.[C]news about pregnant celebrities is entertaining.[D]having children is highly valued by the public.38.It is suggested in Paragraph 3 that childless folks[A]are constantly exposed to criticism.[B]are largely ignored by the media.[C]fail to fulfill their social responsibilities.[D]are less likely to be satisfied with their life.39.According to Paragraph 4, the message conveyed by ce lebrity magazines is[A]soothing.[B]ambiguous.[C]compensatory.[D]misleading.40.Which of the following can be inferred from the last paragraph?[A]Having children contributes little to the glamour of celebrity moms.[B]Celebrity moms have influenced our attitude towards child rearing.[C]Having children intensifies our dissatisfaction with life.[D]We sometimes neglect the happiness from child rearin g.Part BDirections:The following paragraph are given in a wrong order. For Questions 41-45, you are required to reorganize these para graphs into a coherent text by choosing from the list A-G t o filling them into the numbered boxes. Paragraphs E and Ghave been correctly placed. Mark your answers on ANSWER SHE ET 1. (10 points)[A] No disciplines have seized on professionalism with as much enthusiasm as the humanities. You can, Mr Menand po ints out, became a lawyer in three years and a medical doct or in four. But the regular time it takes to get a doctoral degree in the humanities is nine years. Not surprisingly, up to half of all doctoral students in English drop out bef ore getting their degrees.[B] His concern is mainly with the humanities: Literatu re, languages, philosophy and so on. These are disciplines that are going out of style: 22% of American college gradua tes now major in business compared with only 2% in history and 4% in English. However, many leading American universit ies want their undergraduates to have a grounding in the ba sic canon of ideas that every educated person should posses. But most find it difficult to agree on what a “general ed ucation” should look like. At Harvard, Mr Menand notes, “t he great books a re read because they have been read”-they form a sort of social glue.[C] Equally unsurprisingly, only about half end up with professorships for which they entered graduate school. The re are simply too few posts. This is partly because univers ities continue to produce ever more PhDs. But fewer student s want to study humanities subjects: English departments aw arded more bachelor’s degrees in 1970-71 than they did 20 years later. Fewer students requires fewer teachers. So, at the end of a decade of theses-writing, many humanities stu dents leave the profession to do something for which they h ave not been trained.[D] One reason why it is hard to design and teach such courses is that they can cut across the insistence by top A merican universities that liberal-arts educations and profe ssional education should be kept separate, taught in differ ent schools. Many students experience both varieties. Altho ugh more than half of Harvard undergraduates end up in law, medicine or business, future doctors and lawyers must stud y a non-specialist liberal-arts degree before embarking on a professional qualification.[E] Besides professionalizing the professions by this s eparation, top American universities have professionalisedthe professor. The growth in public money for academic rese arch has speeded the process: federal research grants rose fourfold between 1960and 1990, but faculty teaching hours f ell by half as research took its toll. Professionalism has turned the acquisition of a doctoral degree into a prerequi site for a successful academic career: as late as third of American professors did not possess one. But the key idea behind professionalisation, argues Mr Menand, is that “the knowledge and skills needed for a particular specialization are transmissible but n ot transferable.”So disciplines ac quire a monopoly not just over the production of knowledge, but also over the production of the producers of knowledg e.[F] The key to reforming higher education, concludes Mr Menand, is to alter the way in which “the prod ucers of kn owledge are produced.”Otherwise, academics will continue t o think dangerously alike, increasingly detached from the s ocieties which they study, investigate and criticize.”Acad emic inquiry, at least in some fields, may need to become l ess exclusi onary and more holistic.”Yet quite how that hap pens, Mr Menand dose not say.[G] The subtle and intelligent little book The Marketpl ace of Ideas: Reform and Resistance in the should be read by every student thinking of applying to take a doctoral de gree. They may then decide to go elsewhere. For something c urious has been happening in American Universities, and Lou is Menand, a professor of English at , captured it skillful ly.G → 41. →42. → E →43. →44. →45.Part CDirections:Read the following text carefully and then translate th e underlined segments into Chinese. Your translation should be written carefully on ANSWER SHEET 2. (10 points) With its theme that “Mind is the master weaver,” creat ing our inner character and outer circumstances, the book A s a Man Thinking by James Allen is an in-depth exploration of the central idea of self-help writing.(46) Allen’s contribution was to take an assumption we all share-that because we are not robots we therefore contr ol our thoughts-and reveal its erroneous nature. Because most of us believe that mind is separate from matter, we thin k that thoughts can be hidden and made powerless; this allo ws us to think one way and act another. However, Allen beli eved that the unconscious mind generates as much action as the conscious mind, and (47) while we may be able to sustai n the illusion of control through the conscious mind alone, in reality we are continually faced with a question: “Why cannot I make myself do this or achieve that? ”Since desire and will are damaged by the presence of th oughts that do not accord with desire, Allen concluded : “ We do not attract what we want, but what we are.” Achievem ent happens because you as a person embody the external ach ievement; you don’t “ get” success but become it. There is no gap between mind and matter.\Part of the fame of Allen’s book is its contention tha t “Circumstances do not make a person, they reveal him.”(48) This seems a justification for neglect of those in nee d, and a rationalization of exploitation, of the superiorit y of those at the top and the inferiority of those at the b ottom.This ,however, would be a knee-jerk reaction to a subtl e argument. Each set of circumstances, however bad, offers a unique opportunity for growth. If circumstances always de termined the life and prospects of people, then humanity wo uld never have progressed. In fat, (49)circumstances seem t o be designed to bring out the best in us and if we feel th at we have been “wronged” then we are unlikely to begin a conscious effort to escape from our situation .Nevertheless, as any biographer knows, a person’s early life and its co nditions are often the greatest gift to an individual.The sobering aspect of Allen’s book is that we have no one else to blame for our present condition except ourselve s. (50) The upside is the possibilities contained in knowin g that everything is up to us; where before we were experts in the array of limitations, now we become authorities of what is possible.Section Ⅲ WritingPart A51. Directions:Write a letter to a friend of yours to1) recommend one of your favorite movies and2) give reasons for your recommendationYour should write about 100 words on ANSWER SHEET 2Do not sign your own name at the end of the leter. User “LI MING” instead.Do not writer the address.(10 points)Part B52. Directions:Write an essay of 160---200 words based on the following drawing. In your essay, you should1) describe the drawing briefly,2) explain it’s intended meaning, and3) give your comments.Your should write neatly on ANSWER SHEET 2. (20 points)2011年考研英语(一)真题参考答案1-5，ACDBA 6-10 CADCB 11-15 BCACA 16-20 BCADB21-25 DBCAA 26-30 CCBDB 31-35 CCBDB 36-40 CBCCC41-45 BDCAE翻译：46、xx的贡献在于提供了我们能分担和揭示错误性质的假设--因为我们不是机器人，因此我们能够控制我们的理想。
2011年国家司法考试真题及解析(卷一)
2011年司法考试真题及答案详解试卷一一、单项选择题.每题所设选项中只有一个正确答案,多选、错选或不选均不得分。
本部分含1—50题，每题1分,共50分。
1.社会主义法治理念借鉴了中国传统法律文化中的“民为邦本”、“法不阿贵”、“和为贵”和西方法治思想中的“人民主权”、“基本人权”、“法律面前人人平等"等文化资源。
关于借鉴中体现的社会主义法治理念基本特征，下列哪一说法是准确的？（）（2011年卷一单选第1题)A.本质的同源性B.彻底的人民性C。
充分的开放性D。
实践基础的相同性【答案】C【考点】社会主义法治理念的基本特征【解析】社会主义法治理念基本特征包括鲜明的政治性、彻底的人民性、系统的科学性和充分的开放性。
选项A、D错误.本质的同源性、实践基础的相同性不属于社会主义法治理念的基本特征，因此，直接予以排除.选项B错误。
彻底的人民性指社会主义法治反映最广大人民的根本利益和共同意志,是党领导人民制定和实施法律，有效治理社会的方式、过程和状态，人民是社会主义法治建设的重要参与者和推动者.题干没有表明这种“借鉴”反映彻底的人民性.选项C正确。
社会主义法治理念借鉴了中国传统法律文化中的“民为邦本”、“法不阿贵"、“和为贵”和西方法治思想中的“人民主权”、“基本人权”、“法律面前人人平等”等文化资源,广泛吸收、兼容并包、与时俱进、不断借鉴和吸收人类法治文明的优秀成果，反映了其具有“充分的开放性”的特征。
2.近年来,政法机关通过“大接访”、“大走访”、“大下访"等做法，通过开门评警、回访信访当事人等形式，倾听群众呼声，了解群众疾苦，为群众排忧解难.关于这些做法的意义，下列哪一表述是不恰当的？（）（2011年卷一单选第2题）A。
政法机关既是执法司法机关,也是群众工作机关B.政法干警既是执法司法工作者,也是群众工作者C。
人民群众是执法主体，法治建设要坚持群众运动D.司法权必须坚持专门机关工作与群众路线相结合【答案】C【考点】执法为民的内涵【解析】执法为民是社会主义法治的本质要求。
2011年考研数学一真题及解析(公式及答案修正版)
A = E 0
知， α1 ,α 2 ,α 3 ,α 4 都是 Α x = 0 的解，且 Α x = 0 的极大线生无关组就是其基础解系，又
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） (D)
α1，α 3
(B)
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α1，α 2，α 3
α 2，α 3，α 4
【答案】 D 【考点分析】本题考查齐次线性方程组的基础解系，需要综合应用秩，伴随矩 阵等方面的知识，有一定的灵活性。
= A 【解析】由 Αx = 0 的基础解系只有一个知 r ( A) = 3 ，所以 r ( A∗ ) = 1 ，又由 A
∫
x
0
π tan tdt 0 ≤ x ≤ 的弧长 s = 4
【考点分析】本题考查曲线弧长的计算，直接代公式即可。
π
4
π
4
【解析】 s =
∫
0
(y )
' 2
dx = tan xdx = sec 2 x − 1dx = tan x − x 04 = 1−
0 0
∫
π
4 2
∫
π
4
π
π
4
10、微分方程 y ′ + y = e − x cos x 满足条件 y (0) = 0 的解为 y = 【答案】 y = sin xe − x 【考点分析】本题考查一阶线性微分方程的求解。先按一阶线性微分方程的求解步骤求出 其通解，再根据定解条件，确定通解中的任意常数。 【解析】原方程的通解为
2011考研数一真题答案及详细解析
所以 x1= -./k二［是极小值点， X2 =.fl..厂二了是极大值点；
由千 f(O)=O, 则 f(x) 的极大值 f (./1..言刁-)>0, J(x) 的极小值 f(- ,/k — 1 ) < 0.
又lim f(x)= +=,lim J(x) = —=,J(O) =0,
工j—00
.,•-•j-0<>
00) e一1 sinx
解 由条件知： P(x)=1,Q(x) =尸cosx'于是微分方程通解为
(J (J y=e-I压）扛 Q(x)eJP<x)d丑'dx +c) =e寸ld工 尸cosx ef1凸 dx +c) (J =e一1 cosxdx +C)=尸(sinx +C),
由y(O)=O得C=O,因此所求特解为
J'(y) , f(y)
a飞 a正
=f
，，(x)lnf(y),
一3一五—= 妇办
J'(x)•
J'(y) f(y)'
a飞
尸(y汀(y) -[f'(y)J 2
ay2 =f(x)
尸(y)
若函数乏 = f位） Inf Cy)在(0,0) 处取得极小值 ， 则
�o, (�'"·"�J'(O)ln::�:
-I f ay co.o> = f(O)• Co) = O,
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=EX•
[DY+(EY) 2 ]
= 叭矿＋矿）
= µ
rJ
2
+矿．
三、解答题
ln(l +x)�
2011年全国考研数学三真题及答案解析
2011年全国硕士研究生入学统一考试数学三试题一、选择题：1～8小题，每小题4分，共32分。
下列每题给出的四个选项中，只有一个选项是符合题目要求的。
请将所选项前的字母填在答题纸指定位置上。
(1) 已知当0x →时，函数()3sin sin3f x x x =-与是k cx 等价无穷小，则(A) 1,4k c == (B) 1,4k c ==- (C) 3,4k c == (D) 3,4k c ==-(2) 已知()f x 在0x =处可导，且(0)0f =,则2330()2()lim x x f x f x x→-= (A) '2(0)f - (B) '(0)f - (C) '(0)f (D) 0 (3) 设{}n u 是数列，则下列命题正确的是(A) 若1nn u∞=∑收敛，则2121()n n n uu ∞-=+∑收敛(B) 若2121()n n n uu ∞-=+∑收敛，则1n n u ∞=∑收敛(C) 若1nn u∞=∑收敛，则2121()n n n uu ∞-=-∑收敛(D) 若2121()n n n uu ∞-=-∑收敛，则1n n u ∞=∑收敛(4) 设40ln(sin )I x dx π=⎰,4ln(cot )J x dx π=⎰,40ln(cos )K x dx π=⎰ 则I ,J ,K 的大小关系是(A) I J K << (B) I K J << (C) J I K << (D) K J I << (5) 设A 为3阶矩阵，将A 的第2列加到第1列得矩阵B ，再交换B 的第2行与第3行得单位矩阵记为1100110001P ⎛⎫ ⎪= ⎪ ⎪⎝⎭，2100001010P ⎛⎫ ⎪= ⎪ ⎪⎝⎭，则A = (A)12P P (B)112P P - (C)21P P (D) 121P P -(6) 设A 为43⨯矩阵,1η, 2η , 3η 是非齐次线性方程组Ax β=的3个线性无关的解，1k ,2k 为任意常数，则Ax β=的通解为(A)23121()2k ηηηη++-(B) 23221()2k ηηηη-+-(C) 23131221()()2k k ηηηηηη++-+-(D) 23221331()()2k k ηηηηηη-+-+-(7) 设1()F x ,2()F x 为两个分布函数，其相应的概率密度1()f x , 1()f x 是连续函数，则必为概率密度的是(A) 12()()f x f x (B)212()()f x F x(C) 12()()f x F x (D) 1221()()()()f x F x f x F x +(8) 设总体X 服从参数λ(0)λ>的泊松分布，11,,(2)n X X X n ≥ 为来自总体的简单随即样本，则对应的统计量111ni i T X n ==∑，121111n in i T X X n n -==+-∑ (A)1212,ET ET DT DT >> (B)1212,ET ET DT DT >< (C)1212,ET ET DT DT <> (D) 1212,ET ET DT DT <<二、填空题：9~14小题，每小题4分，共24分，请将答案写在答题纸指定位置上. (9) 设0()lim (13)xtt f x x t →=+，则'()f x =______.(10) 设函数(1)xy xz y=+，则(1,1)|dz =______.(11) 曲线tan()4y x y e π++=在点(0,0)处的切线方程为______.(12)曲线y =2x =及x 轴所围成的平面图形绕x 轴旋转所成的旋转体的体积______.(13) 设二次型123(,,)T f X X X x Ax =的秩为1，A 中行元素之和为3，则f 在正交变换下x Qy =的标准型为______.(14) 设二维随机变量(,)X Y 服从22(,;,;0)N μμσσ，则2()E XY =______. 三、解答题：15－23小题，共94分.请将解答写在答题纸指定的位置上.解答应写出文字说明、证明过程或演算步骤.(15) (本题满分10分)求极限0x →.(16) (本题满分10分)已知函数(,)f u v 具有连续的二阶偏导数，(1,1)2f =是(,)f u v 的极值，[](),(,)z f x y f x y =+。
2011年考研英语真题答案及解析
2011年考研英语真题答案及解析2011年全国硕士研究生招生考试英语（一）答案详解Section I Use of English一、文章题材结构分析文章出自2009年4月的《科学美国人》（Scientific American）,作者Steve Ayan,原文题目为How Humor Makes You Friendlier,Sexier：幽默如何使你更加有人缘且性感。
文章主要探讨了笑的作用以及情感和肌肉反应之间的相互关系。
第一段由古希腊哲学家亚里士多德的观点引出“笑是有益于健康的身体运动”。
第二、三段承接上文，阐述了笑能放松肌肉，从而帮助减轻心理紧张的程度。
第四段以在1988年公布的一项实验为例论证了情绪是肌肉反应的结果，笑这一行为可以使心情好转。
二、试题解析1.[A]among在……之中[B]except除了[C]despite尽管[D]like像，如同【答案】[C]【考点】上下文逻辑关系+介词辨析【解析】第一段第一句意思是：古希腊哲学家亚里士多德把笑看作是“有益于健康的身体运动”，由连词but可知，第二句与第一句形成语义转折，即一些人提出相反的观点：笑不利于身体健康。
第二句逗号之后又提出：笑可能对身体健康几乎没有影响，这是对前两种观点的否定，由此判断第二句的句内逻辑是转折关系，[A]、[B]、[C]、[D]四个选项中只有[C]despite“尽管”表示转折，所以是正确答案。
2.[A]reflect反映[B]demand要求[C]indicate表明，预示[D]produce产生，引起【答案】[D]【考点】上下文语义衔接+动词辨析【解析】上下文语境是“笑确实能对心血管功能短期的改变”，具体说明笑对身体产生的影响。
所选动词要与后面的changes构成动宾关系，并且带有“发生……作用，产生……效果”的含义。
四个选项中[A]reflect“反映”，[B]demand“要求”，[C]indicate“表明，暗示”，[D]produce“产生”，只有[D]选项“产生、引起”符合本句语境，所以是正确答案。
2011年普通高等学校招生全国统一考试(全国卷Ⅰ)-精校解析版
绝密★启用前2011年普通高等学校招生全国统一考试英语本试卷分第一卷（选择题）和第二卷（非选择题）两部分。
第一卷1至14页。
第二卷15至16页。
考试结束后，将本试卷和答题卡一并交回。
第一卷注意事项：1. 答题前，考生在答题卡上务必用直径0. 5毫米黑色墨水签字笔将自己的姓名、准考证号填写清楚，并贴好条形码。
请认真核准条形码上的准考证号、姓名和科目。
2. 每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案标号，在试题卷上作答无效。
第一部分听力（共两节，满分30分）做题时，先将答案标在试卷上。
录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。
第一节（共5小题，每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
例：How much is the shirt?A. ￡19.15.B. ￡9.15.C. ￡9.18.答案是B。
1. What does the man like about the play?A. The story.B. The ending.C. The actor.2. Which place are the speakers trying to find?A.A hotel.B.A bank.C. A restaurant.3. At what time will the two speakers meet?A. 5:20.B. 5:10.C.4:40.4. what will the man do ?A. Change the plan.B. Wait for a phone call.C. Sort things out.5. What does the woman want to do ?A. See a film with the man.B. Offer the man some help.C. Listen to some great music.第二节（共15小题：每小题1.5分，满分22.5分）请听下面5段对话。
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Part I Reading Comprehension (35 minutes, 40 points) Passage 1 题型解析
1. What is the main idea of this passage?【主旨题】 2. In the first sentence the author means that_______. 【细节题】 3. According to the expert, a good relationship should be_____. 【细节题】 4. In the third paragraph, the phrase “with the upper hand” means_____. 【词汇题】 5. What is the most important for you to consider when somebody say “I love you” to you?【细节题】
1
2011 年成人高等教育本科毕业生申请学士学位外语考试
【解析】A really good relationship should be about being fair and being equal 【答案】A 4. In the third paragraph, the phrase “with the upper hand” means _______it B. having only one hand C. being active D. being passive 【解析】The one with the upper hand(优势，上风 ) is often the person who takes the initiative(主动). 【答案】C 5. What is the most important for you to consider when somebody say “I love you” to you? A. The intention. B. The place C. The time D. The determination. 【解析】 Intention(意图) is everything. It’s not what is said, but(不是…而是) how it’s said. What it comes down to(归结为) is the sincerity(真诚，诚挚) of the speaker. 【答案】A
习题解析
1. What is the main idea of this passage? A. The importance of “I love you”. B. The meaning of ‘I love you”. C. The time of saying ‘I love you”. D. The place of saying ‘I love you”. 【解析】You must have been troubled by when to say “I love you” because it is one of the greatest puzzles(困惑) in our life. 【答案】C 2. In the first sentence the author means that ________. A. it is easy to say “I love you”. B. it is hard to say “I love you”. C. we have many troubles in our life. D. people usually do not know when to say “I love you”. 【解析】You must have been troubled by when to say “I love you” because it is one of the greatest puzzles(困惑) in our life. 【答案】D 3. According to the expert, a good relationship should be_________. A. fair and equal B. fair and kind C. powerful and equal D. confident and fair
篇章解析
Television has changed the lifestyle(生活方式 ) of people in every individualized(有个性的 ) country in the world. In the United States, where sociologists( 社 会 学 家 ) have studied the effects( 影 响 ), some interesting observations(观察) have been made. ( 必 要 的 ), has become an important part of most people’s lives. It Television, although not essential essential( alters(改变) people’s ways of seeing the world; in many ways, it supports and sustains(维持) modern life. Television has become a baby-sitter, an introducer of conversations, the major transmitter( 传 送 器 ) of culture and a keeper of tradition. Yet when what can be seen on TV in one day is critically( 批判地 ) analyzed, it becomes evident( 明 显 的 ) that television is not a teacher but a sustainer( 支 持 者 ); the poor quality of programming does not elevate( 提高 ) people into greater understanding, but rather maintains and encourages the life as it exists. The primary reason for the lack of quality in American television is related to(和…有关) both the history of TV programming development and the economics( 经济学 ) of TV. Television in America began with( 以 … 开始 ) the radio. Radio companies and their sponsors( 赞 助 商 ) first experimented with( 实 验 ， 体 验 ) television. Therefore, the close relationship which the advertisers had with radio programs became the system for American TV. Sponsors not only paid money for time within programs, but( 不 仅 … 而 且 ) many actually produced the programs. Thus, in American society, television is primarily concerned with( 涉 及 ) reflecting and attracting society rather than( 而 不 是 ) experimenting with new ideas. Advertisers want to attract the largest viewing audience( 观 众 ) possible. To do so requires that the programs be entertaining rather than educational, attractive
知识点总结
� � � � � � go through be bored with depend on set off not…but… come down to 经历 厌倦 依赖，依靠 出发，动身 不是…而是 归结为
Passage 2 题型解析
6. According to the author, American television is poor in quality because ________.【细节题】 7. The second paragraph is mainly about _________.【主旨题】 8. In the author’s view American TV should ________.【细节题】 9. The author believes that television in the United States has become important to most people because ________. 【细节题】 10. The author’s attitude towards American television is ________.【观点态度题】
篇章解析
You must have been troubled by when to say “I love you” because it is one of the greatest puzzles( 困惑 ) in our life. What if you say it first and your partner doesn’t love you back? Or if they do say it, but you don’t feel they mean it? Being the first to declare( 宣布，断言 ) your love can be very nervous( 紧张的 ) and risky( 冒险的 ) and can leave you feeling as vulnerable( 脆弱的 ) as a turtle( 海龟 ) with no shell. But is the person who says it first really in a position of weakness( 缺点 )? Doesn’t it pay to hold back( 退缩 ), play it cool( 抑制住感情，慢慢来 ) and wait until the other half has shown their hand fast? A really good relationship should be about being fair and being equal,” says psychologist(心理学家) Sidney Crown. “But love is seldom equal.” All relationships go through( 经 历 ) power struggles but, he says if a love imbalance( 不 平 衡 ) continues for years, the trouble will set in( 到 来 ). “That feeling of ‘I’ve always loved you more’ may be subverted( 破 坏 ) for a time, but it never goes away completely and it often emerges( 出 现 ) in quarreling.” In love, at least, the silent, withholding( 克 制 的 ) type is not always the most powerful. “The strongest one in a relationship is often the person who feels confident( 有 信 心 的 ) enough to talk about their ( 临床医学家 ) Paula feelings,” says educational psychologist Ingrid Collins. Psychosexual( 性心理的 ) therapist therapist( Hall agrees, “The one with the upper hand(优势， 上风) is often the person who takes the initiative(主动). In fact, the person who says ‘I love you’ first may also be the one who says ‘I’m bored with( 厌 倦 ) you’ first. Hall believes that much depends on( 依赖，依靠 ) how “I love you’ is said and the motivation( 动机 ) of the person saying it. “Is it said when they’re drunk? Is it said before their partner sets off(出发， 动身) on holiday, and what it really means is ‘Please don’t be unfaithful(不忠诚的 ) to me’? By saying ‘I love you’, they really saying ‘Do you love me? If so, wouldn’t it just be more honest to say that. Collins agrees that intention( 意图 ) is everything. “It’s not what is said, but(不是…而是) how it’s said. What it comes down to(归结为) is the sincerity(真诚，诚挚) of the speaker.”