2000~2004年研究生入学考试试题

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研究生英语一2000-2004真题翻译和作文详解

考研翻译的命题原则:1、所选择的体裁偏向于专业领域的学术文献2、所选择的话题偏向文科、社会科学领域3、划线的长度为30个单词左右，总长度为150个单词考研翻译的评分标准=翻译标准=检查译文标准准确：大意相同通顺：说人话（准确是通顺的前提）完整：要成句翻译的方法：直接为主（直接翻译），适当意译（把意思说出来）（一句话4分钟）考研翻译的步骤：1、通读全句，查找连接（when，and）2、分析成分，划分意群（前两步骤1分钟）3、选择词义，适当草稿(看1分钟就动笔写)读：多读汉语4、调整通顺，书写译文（次序调整，词义选择）碰到生词：造句，填空，根据前后句遇到多义词：同义替换Part ⅢEnglish-Chinese Translation(2000)Directions:Read the following passage carefully and then translate the underlined segments into Chinese. Your translation must be written neatly on ANSWER SHEET 2. (15 points) Governments throughout the world act on the assumption that the welfare of their people depends largely on the economic strength and wealth of the community. 31）Under modern conditions, this requires varying measures of centralized control and hence the help of specialized scientists such as economists and operational research experts. 32）Furthermore, it is obvious that the strength of a country’s economy is directly bound up with the efficiency of its agriculture and industry, and that this in turn rests upon the efforts of scientists and technologists of all kinds. It also means that governments are increasingly compelled to interfere in these sectors in order to step up production and ensure that it is utilized to the best advantage. For example, they may encourage research in various ways, including the setting up of their own research centers; they may alter the structure of education, or interfere in order to reduce the wastage of natural resources or tap resources hitherto unexploited; or they may cooperate directly in the growing number ofinternational projects related to science, economics and industry. In any case, all such interventions are heavily dependent on scientific advice and also scientific and technological manpower of all kinds.33）Owing to the remarkable development in mass-communications, people everywhere are feeling new wants and are being exposed to new customs and ideas, while governments are often forced to introduce still further innovations for the reasons given above. At the same time, the normal rate of social change throughout the world is taking place at a vastly accelerated speed compared with the past. For example, 34）in the early industrialized countries of Europe the process of industrialization—with all the far-reaching changes in social patterns that followed—was spread over nearly a century, whereas nowadays a developing nation may undergo the same process in a decade or so. All this has the effect of building up unusual pressures and tensions within the community and consequently presents serious problems for the governments concerned. 35）Additional social stresses may also occur because of the population explosion or problems arising from mass migration movements—themselves made relatively easy nowadays by modern means of transport. As a result of all these factors, governments are becoming increasingly dependent on biologists and social scientists for planning the appropriate programs and putting them into effect. ［390 words］Part ⅢEnglish-Chinese Translation一、核心词汇注释act on*1.按……行动，奉行例：act on principles 根据原则办事 2.对……起作用，影响例：The music acted stirringly on the emotions of the audience. 音乐使观众情绪激动。

中国人民大学2004年硕士生入学考试试题(2)

中国人民大学2004年硕士生入学考试试题招生专业：政治经济学、网络经济学考试科目：政治经济学和西方经济学政治经济学部分一、说明马克思的货币流通规律理论与西方传统货币数量论的异同。

（15分）二、说明劳动生产率的变化对不同部门产品比价关系的影响。

（15分）三、说明资本主义经济中平均利润率下降趋势及阻碍这种下降的因素。

（20分）四、试述深化国有资产管理体制改革的方向及其理论依据。

（25分）西方经济学部分一、名词解释（每个名词5分，共20分）1．低档物品2．古典二分法3．奥肯定律4．边际产品价值二、问答题（35分）1．简述生产要素最优组合条件与利润最大化条件的关系。

（10分）2．如何从价格-消费曲线推导出消费者的需求曲线？（10分）3．在货币政策效果问题上，凯恩斯主义、货币主义和新古典宏观经济学的观点有什么不同？为什么不同？（15分）三、计算题（每小题10分，共20分）1．已知消费者对某种商品的需求函数为Q=100－2p，写出相应的总收益函数和边际收益函数。

在什么价格水平上，需求价格弹性系数为1？2．已知W国的宏观经济可以用下列一组方程式来描述：消费函数：C=120+0.8y (1)投资函数：I=50-200r (2)收入恒等式：Y=C+I (3)货币需求函数：L=（0.5Y-500r）P (4)其中，C为消费，Y为国民收入，I为投资，r为利率，P为价格总水平，L为货币需求。

（1）如果在2003年，W国的价格总水平为2，货币供应量为500。

试写出W国的IS 曲线和LM曲线方程。

（2）写出W国的总需求函数。

（3）W国的宏观经济均衡时国民收入和利率分别是多少？参考答案：中国人民大学2004年硕士生入学考试试题招生专业：政治经济学、网络经济学考试科目：政治经济学和西方经济学政治经济学部分一、说明马克思的货币流通规律理论与西方传统货币数量论的异同。

（15分）答：马克思货币流通规律理论是以完全的金币流通为假设条件，他认为，商品价格取决于商品的价值和黄金的价值，而价值取决于生产过程，所以商品是带有价格进入流通的，商品价格有多大，就需要有多少金币来实现它，商品和货币交换后，商品退出流通，黄金却留在流通之中可以使另外的商品得以出售，从而实现一定数量的金，流通几次，就可使相应倍数价格的商品出售，因此有：执行流通手段职能的货币量=商品价格总额/同名货币的流通次数。

2000年全国硕士研究生入学统一考试数学一、二、三、四试题完整版附答案解析及评分标准

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2004年研究生入学考试英语试题

Section Ⅰ Listening Comprehension Part A(每题1分，共20分)Directions: This section is designed to test your ability to understand spoken English. You will hear a selection of recorded materials and you must answer the questions that accompany them. There are three parts in this section, Part A, Part B, and Part C. Remember, you should first put down your answers in your test booklet. At the end of the listening comprehension section, you will have five minutes to transfer all your answers from your test booklet to ANSWER SHEET I. Now look at Part A in your test booklet. Part A Directions: For Quesstions1-5,you will hear a talk about Boston Museum of Fine Art. While you listen, fill out the table with the information you have heard. Some of the information has been given to you in the table. Write only 1 word or number in each numbered box. You will hear the recording twice. You now have 25 seconds to read the table below.(5 points) 1、Geography of BelgiumThree main regions coastal plaincentral plateau Highest 1 （本题分值：1分）【正确答案】 highlands 2、altitude of the coastal plain 2 m （本题分值：1分）【正确答案】 20 3、Climate near the sea 3 humid （本题分值：1分）【正确答案】 mild 4、Particularly rainy months of the years 4 April （本题分值：1分）【正确答案】 November 5、Average temperatures in July in Brussels low 13℃ high 5 ℃ （本题分值：1分）【正确答案】 22 Section Ⅰ Part B(每题1分，共5分)Directions: For Questions 6-10,you will hear an interview with Mr. Saffo from the Institute for the Future. While you listen, complete the sentences or answer the questions. Use not more than 3 words for each answer. You will hear the recording twice. You now have 25 seconds to read the sentences and questions below. ( 5 points ) 6、What is Saffo according to himself? （本题分值：1分）【正确答案】 A (technology)forecaster 7、The Institute for the Future provides services to private companies and （本题分值：1分）【正确答案】 government agencies 8、The Institute believes that to think systematically about the long-range future is （本题分值：1分）【正确答案】 (a)meaningful(exercise) 9、To succeed in anything, one should be flexible, curious and （本题分值：1分）【正确答案】 open to change 10、What does Saffo consider to be essential to the work of a team? （本题分值：1分） Section Ⅰ Part C（共三节，满分10分） Directions: You will hear three pieces of recorded material. Before listening to each one, you will have time to read the questions related to it. While listening, answer each question by choosing A,B,C or D . After listening, you will have time to check your answers. You will hear each piece once only. ( 10 points ) Questions 11-13 are based on the following talk about naming newborns. You now have 15 seconds to read questions 11-13. 11、What do we often do with the things we love? （本题分值：1分）【正确答案】 D A.Ask for their names. babies after them. C.Put down their names. D.Choose names for them. 12、 The unpleasant meaning of an old family name is often overlooked if （本题分值：1分）【正确答案】 B A. the family tree is fairly limited. B. the family tie is strong enough. C.the name is commonly used. D.nobody in the family complains. 13、 Several months after a baby's birth, its name will （本题分值：1分）【正确答案】 C A.show the beauty of its own. B.develop more associations. C.lose the original meaning. D.help form the baby's personality. Questions 14-16 are based on the biography of Bobby Moore, an English soccer player. You now have 15 seconds to read Questions 14-16. 14. How many matches did Moore play during his professional career? （本题分值：1分）【正确答案】 D A. 90. B .108. C.180. D. 668. 15、In 1964, Bobby Moore was made （本题分值：1分）【正确答案】 A A.England's footballer of the year. B.a soccer coach in West Germany. C.a medalist for his sportsmanship. D.a number of the Order of the British Empire. 16、After Moore retired from playing, the first thing he did was （本题分值：1分）【正确答案】 C A.editing Sunday Sport. B.working for Capital Radio. C.managing professional soccer teams. D.developing a sports marketing company. Questions 17-20 are based on the on the city of Belfast. You now have 20 seconds to read Questions 17-20. 17. Belfast has long been famous for its （本题分值：1分）【正确答案】 B A. oil refinery. B. linen textiles. C.food products. D. deepwater port. 18、Which of the following does Belfast chiefly export? （本题分值：1分）【正确答案】 A A. Soap. B. Grain. C.Steel. D.Tobacco. 19、When was Belfast founded? （本题分值：1分）【正确答案】 A A. In 1177. B. In 1315. C.In the 16th century. D. In the 17th century. 20、 What happened in Belfast in the late 18th century? （本题分值：1分）【正确答案】 C A. French refugees arrived. B. The harbor was destroyed. C.Shipbuilding began to flourish. D.The city was taken by the English. Section II Use of English（满分10分） 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) Many theories concerning the causes of juvenile delinquency (crimes committed by young people) focus either on the individual or on society as the major contributing influence. Theories (21)[] on the individual suggest that children engage in criminal behavior (22)[] they were not sufficiently penalized for previous misdeeds or that they have learned criminal behavior through (23)[] with others. Theories focusing on the role of society that children commit crimes in (24)[] to their failure to rise above their socioeconomic status (25)[] as a rejection of middle-class values. Most theories of juvenile delinquency have focused on children from disadvantaged families, (26)[] the fact that children from wealthy homes also commit crimes. The latter may commit crimes (27)[] lack of adequate parental control. All theories, however, are tentative and are (28)[] to criticism. Changes in the social structure may indirectly (29)[] juvenile crime rates. For example, changes in the economy that (30) [] to fewer job opportunities for youth and rising unemployment (31)[] make gainful employment increasingly difficult to obtain. The resulting discontent may in (32)[] lead more youths into criminal behavior. Families have also(33)[] changes these years. More families consist of one parent households or two working parents;(34)[], children are likely to have less supervision at home (35)[] was common in the traditional family (36)[]. This lack of parental supervision is thought to be an influence on juvenile crime rates. Other (37)[] causes of offensive acts include frustration or failure in school, the increased (38)[] of drugs and alcohol, and the growing (39)[] of child abuse and child neglect. All these conditions tend to increase the probability of a child committing a criminal act, (40)[] a direct causal relationship has not yet been established. 21、（本题分值：0.5分）【正确答案】 C ［注释］"很多有关少年犯罪原因的理论，要么把个⼈当成主要的影响因素，要么把社会当成主要的影响因素。

华东师范大学2004年攻读硕士研究生入学试题

华东师范大学2 00 4 年攻读硕士研究生入学试题考试科目：语言基础招生专业：语言学及应用语言学（对外汉语教学与实践、翻译理论与实践、社会语言学）第一部分语言学概论与现代汉语（120 分）一、填空题（10 分）1、汉语的语素从 _______ 看有单音节语素、双音节语素和多音节语素；从_____________ 看有自由语素、半自由语素和不自由语素。

2、现代汉语的五种基本句法结构是______ 、________ 、________ 、 ________、________ 。

3、“对面走过来几个人”的主语是：__________________ 。

4、句子可以根据不同的标准来分类，根据结构特点分出来的句子叫__________，根据表达功能分出来的叫 _______ 。

5、“简直把人气坏了” 、“这鬼天气把人冻死了”的补语属于______ 补语。

二、判断正误（10 分）正确的在括号内打V,不用说明理由；错误的在括号内打X,并说明理由，不说明理由的不给分。

1、音素是按语音的物理性质划分出来的最小的语音单位,音位是从生理性质和社会属性划分出来的最小语音单位。

（）2、“笔直”、“清凉”、“轻视”三个合成词的构造方式相同。

（）3、我们可以说“很舒服” ,因为“舒服”是形容词,不可以说“很出发” ,以为“出发”是动词。

所以,程度副词“很”不能修饰所有的动词。

（）4、“他这个人太没意思了！”和“太没意思了,他这个人！”属于同一句型。

（）5、语体的差别主要表现在语体风格上,在用词上没有什么差异。

（）6、“他身体不好大家都知道。

”这句话的主语是“他” 。

（）7、用“关于”组成的介宾短语做状语,可以放在主语前,也可以放在主语后。

（）8、“‘书'以类聚”这句话运用了仿词的修辞方式。

（）只有走到最后的考研人才知道什么叫考研,只有经历过对自己目标的坚定才知道什么叫不放弃。

19、“你来得正是时候。

”中的“的”是 _____ 词。

2004年全国硕士研究生入学统一考试数学(一)试题及答案解析

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全国硕士研究生入学统一考试数学二真题2000年

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全国硕士研究生入学统一考试数学二真题2000年
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2004年真题+解析

2004年硕士研究生入学考试政治试题答案及解析一、单项选择题1.唯物史观认为，人类的第一个历史活动是A.吃喝穿住B.物质生活资料的生产C.人的自觉意识活动D.结成社会关系【答案】 B【解析】本题考查的知识点是对唯物史观关于社会生产在社会赖以存在和发展中的地位和作用的确认。

地理环境、人口因素、生产实践都是社会存在和发展的必要的物质生活条件，都是不可缺少的。

其中“物质生活资料的生产是人类社会赖以存在和发展的物质基础，是人类历史的前提，是人类的第一个历史活动；社会生产实践制约着整个社会经济生活、政治生活和精神生活过程。

根据这一基本理论分析题中所给定的四个选项：“吃喝穿住”必须以生产实践为前提；“人的自觉意识活动”属于人的精神生活过程，也是由人的生产实践活动所制约的；人与人之间所“结成的社会关系”项也不是从来就有的，恰恰是在人们的生产实践活动中所形成的。

所以正确选项为B项。

2.20世纪50年代，北大荒人烟稀少、一片荒凉。

由于人口剧增，生产力水平低下，吃饭问题成为中国面临的首要问题，于是人们不得不靠扩大耕地面积增加粮食产量，经过半个世纪的开垦，北大荒成了全国闻名的“北大仓”。

然而由于过度开垦已经造成了许多生态问题。

现在，黑龙江垦区全面停止开荒，退耕还“荒”。

这说明A.人与自然的和谐最终以恢复原始生态为归宿B.人们改造自然的一切行为都会遭到“自然界的报复”C.人在自然界面前总是处于被支配的地位D.人们应合理地调节人与自然之间的物质变换【答案】 D【解析】本题考查的知识点是对唯物史观关于人类社会与自然界的协调发展的理解和掌握。

唯物史观认为，社会发展是一个人类与自然协调发展的过程，自然史和人类史彼此相互制约，一旦人与自然的和谐关系遭到破坏，社会的发展就会出现灾难性后果。

此外，社会发展还是一个合目的性和合规律性的统一过程。

人类在推动社会发展的过程中，应该把发展科学技术与生产力和保护生态环境有机地统一起来，把人类生活需要的内在尺度与生态环境规律的外在尺度有机地结合起来，提高人类利用自然的科学性与道德性，协调人类改造自然的行动，调整好人类改造自然的方向，建立起人与自然的全面和谐的关系，以利于我们星球的繁荣和人类自身的发展。

中国科学院2000-2004年博士入学部分考题18份

五、思考题（20分）：
你支持还是反对克隆人？理由是什么？如何避免克隆技术被滥用？
中科院遗传与发育生物学研究所2000-2001年细胞生物学（博士）
2000年
一、名词解释（每词3分，共30分）
1．着丝粒 6. 核骨架
2．微管 7. 核糖体
3．溶酶体 8. 细胞的程序死亡
8．细胞编程性死亡又称细胞凋亡是细胞的一种基本生命现象，请阐述细胞凋亡的生物学意义及主要生物化学特征。
2001年博士学位研究生入学考试
生物化学试题
1.请阐明蛋白质间最重要的原子相互作用。（15分）
2. 蛋白质的测活是蛋白纯化过程中的重要组成部分，可以从哪些方面来考虑建立一个快速、简便、定量的测活方法。（15分）
二、真核生物的基因表达控制（control of gene expression）和信号传导（signal transduction）有密切的关系，请举出一个你熟悉的例子分别说明这两个概念的含义及其联系。
三、目前已经有一些现成的软件用来预测基因组全序列中的基因。为了设计这些软件，你觉得哪些关于基因和基因组的分子遗传学知识是必须的？请说明理由。
9、二酰基甘油是蛋白激酶C的（）。
10、常染色质的英文是（）。
三、论述题（每题10分，共20分）：
1、细胞凋亡的生物学意义
2、磷脂酰肌醇信号通路
四、综合题（每题10分，共20分）：
1、给你一株动物体细胞，你如何验证该株细胞的发育全能性？
2、如何研究一个基因在细胞及发育中的功能？
中科院遗传与发育生物学研究所2003年遗传学（博士）
一、今年是DNA双螺旋模型发表五十周年。请回答以下问题（20分）：

2000-2004年考研英语真题及解析

2000年全真试题Part ⅠClose T estDirections：For each numbered blank in the following passage, there are four choices marked ［A］, ［B］, ［C］and ［D］. Choose the best one and mark your answer on ANSWER SHEET 1 by blackening the corresponding letter in the brackets with a pencil. (10 points)①If a farmer wishes to succeed, he must try to keep a wide gap between his consumption and his production. ②He must store a large quantity of grain 1 consuming all his grain immediately. ③He can continue to support himself and his family 2 he produces a surplus. ④He must use this surplus in three ways: as seed for sowing, as an insurance 3 the unpredictable effects of bad weather and as a commodity which he must sell in order to 4 old agricultural implements and obtain chemical fertilizers to 5 the soil. ⑤He may also need money to construct irrigation 6 and improve his farm in other ways. ⑥If no surplus is available, a farmer cannot be 7 . ⑦He must either sell some of his property or 8 extra funds in the form of loans. ⑧Naturally he will try to borrow money at a low 9 of interest, but loans of this kind are not 10 obtainable. ［139 words］1.［A］other than ［B］as well as ［C］instead of ［D］more than2.［A］only if ［B］much as ［C］long before ［D］ever since3.［A］for ［B］against ［C］of ［D］towards4.［A］replace ［B］purchase ［C］supplement ［D］dispose5.［A］enhance ［B］mix ［C］feed ［D］raise6.［A］vessels ［B］routes ［C］paths ［D］channels7.［A］self-confident ［B］self-sufficient［C］self-satisfied ［D］self-restrained8.［A］search ［B］save ［C］offer ［D］seek9.［A］proportion ［B］percentage ［C］rate ［D］ratio10.［A］genuinely ［B］obviously ［C］presumably ［D］frequentlyPart ⅡReading ComprehensionDirections:Each of the passages below is followed by some questions. For each question there are four answers marked ［A］, ［B］, ［C］and ［D］. Read the passages carefully and choose the best answer to each of the questions. Then mark your answer on ANSWER SHEET 1 by blackening the corresponding letter in the brackets with a pencil. (40 points)Passage 1①A history of long and effortless success can be a dreadful handicap, but, if properly handled, it may become a driving force. ②When the United States entered just such a glowing period after the end of the Second World War, it had a market eight times larger than anycompetitor, giving its industries unparalleled economies of scale. ③Its scientists were the world s best; its workers the most skilled. ④(11)America and Americans were prosperous beyond the dreams of the Europeans and Asians whose economies the war had destroyed.①It was inevitable that this primacy should have narrowed as other countries grew richer. ②Just as inevitably, the retreat from predominance proved painful. ③By the mid-1980s Americans had found themselves at a loss over their fading industrial competitiveness. ④Some huge American industries, such as consumer electronics, had shrunk or vanished in the face of foreign competition. ⑤By 1987 there was only one American television maker left, Zenith. ⑥(Now there is none: Zenith was bought by South Korea’s LG Electronics in July.) ⑦（12）Foreign-made cars and textiles were sweeping into the domestic market. America’s machine-tool industry was on the ropes. ⑧For a while it looked as though the making of semiconductors, which America had invented and which sat at the heart of the new computer age, was going to be the next casualty.①All of this caused a crisis of confidence. ②Americans stopped taking prosperity for granted. ③They began to believe that their way of doing business was failing, and that their incomes would therefore shortly begin to fall as well. ④The mid-1980s brought one inquiry after another into the causes of America’s industrial decline. ⑤Their sometimes sensational findings were filled with warnings about the growing competition from overseas.①How things have changed! ②In 1995 the United States can look back on five years of solid growth while Japan has been struggling. ③（14）Few Americans attribute this solely to such obvious causes as a devalued dollar or the turning of the business cycle. ④Self-doubt has yielded to blind pride. ⑤“American industry has changed its structure, has gone on a diet, has learnt to be more quick-witted,”according to Richard Cavanaugh, executive dean of Harvard’s Kennedy School of Government. ⑥“It makes me proud to be an American just to see how our businesses are improving their productivity,”says Stephen Moore of the Cato Institute, a think-tank in Washington, DC. ⑦And William Sahlman of the Harvard Business School believes that people will look back on this period as “a golden age of business management in the United States.”［429 words］11. The U.S. achieved its predominance after World War II because.［A］it had made painstaking efforts towards this goal［B］its domestic market was eight times larger than before［C］the war had destroyed the economies of most potential competitors［D］the unparalleled size of its workforce had given an impetus to its economy12. The loss of U.S. predominance in the world economy in the 1980s is manifested in the fact that the American.［A］TV industry had withdrawn to its domestic market［B］semiconductor industry had been taken over by foreign enterprises［C］machine-tool industry had collapsed after suicidal actions［D］auto industry had lost part of its domestic market13. What can be inferred from the passage?［A］It is human nature to shift between self-doubt and blind pride.［B］Intense competition may contribute to economic progress.［C］The revival of the economy depends on international cooperation.［D］A long history of success may pave the way for further development.14. The author seems to believe the revival of the U.S. economy in the 1990s can be attributed to the.［A］turning of the business cycle ［B］restructuring of industry［C］improved business management ［D］success in educationPassage 2①（15）Being a man has always been dangerous. ②There are about 105 males born for every 100 females, but this ratio drops to near balance at the age of maturity, and among 70-year-olds there are twice as many women as men. ③But the great universal of male mortality is being changed. ④Now, boy babies survive almost as well as girls do. ⑤This means that, for the first time, there will be an excess of boys in those crucial years when they are searching for a mate. ⑥More important, another chance for natural selection has been removed. ⑦Fifty years ago, the chance of a baby (particularly a boy baby) surviving depended on its weight. A kilogram too light or too heavy meant almost certain death. ⑧Today it makes almost no difference. Since much of the variation is due to genes, one more agent of evolution has gone.①There is another way to commit evolutionary suicide: stay alive, but have fewer children.②Few people are as fertile as in the past. ③Except in some religious communities, very few women have 15 children. ④Nowadays the number of births, like the age of death, has become average. ⑤Most of us have roughly the same number of offspring. ⑥（16）Again, differences between people and the opportunity for natural selection to take advantage of it have diminished.⑦India shows what is happening. The country offers wealth for a few in the great cities and poverty for the remaining tribal peoples. ⑧The grand mediocrity of today—everyone being the same in survival and number of offspring—means that natural selection has lost 80% of its power in upper-middle-class India compared to the tribes.For us, this means that evolution is over; the biological Utopia has arrived. ②Strangely, it has involved little physical change. ③No other species fills so many places in nature. ④But in the past 100, 000 years—even the past 100 years—our lives have been transformed but our bodies have not. ⑤（17）We did not evolve, because machines and society did it for us. ⑥Darwin had a phrase to describe those ignorant of evolution: they “look at an organic being as a savage looks at a ship, as at something wholly beyond his comprehension.”⑦No doubt we will remember a 20th century way of life beyond comprehension for its ugliness. But however amazed our descendants may be at how far from Utopia we were, they will look just like us.［406 words］15. What used to be the danger in being a man according to the first paragraph?［A］A lack of mates. ［B］A fierce competition.［C］A lower survival rate. ［D］A defective gene.16. What does the example of India illustrate?［A］Wealthy people tend to have fewer children than poor people.［B］Natural selection hardly works among the rich and the poor.［C］The middle class population is 80% smaller than that of the tribes.［D］India is one of the countries with a very high birth rate.17. The author argues that our bodies have stopped evolving because.［A］life has been improved by technological advance［B］the number of female babies has been declining［C］our species has reached the highest stage of evolution［D］the difference between wealth and poverty is disappearing18. Which of the following would be the best title for the passage?［A］Sex Ratio Changes in Human Evolution.［B］Ways of Continuing Man’s Evolution.［C］The Evolutionary Future of Nature.［D］Human Evolution Going Nowhere.Passage 3①（20）When a new movement in art attains a certain fashion, it is advisable to find out what its advocates are aiming at, for, however farfetched and unreasonable their principles may seem today, it is possible that in years to come they may be regarded as normal. ②With regard to Futurist poetry, however, the case is rather difficult, for whatever Futurist poetry may be—even admitting that the theory on which it is based may be right—it can hardly be classed as Literature.①This, in brief, is what the Futurist says: for a century, past conditions of life have been conditionally speeding up, till now we live in a world of noise and violence and speed. ②Consequently, our feelings, thoughts and emotions have undergone a corresponding change. ③（21）This speeding up of life, says the Futurist, requires a new form of expression. ④We must speed up our literature too, if we want to interpret modern stress. ⑤We must pour out a large stream of essential words, unhampered by stops, or qualifying adjectives, or finite verbs. ⑥Instead of describing sounds we must make up words that imitate them; we must use many sizes of type and different colored inks on the same page, and shorten or lengthen words at will.①Certainly their descriptions of battles are confused. ②But it is a little upsetting to read in the explanatory notes that a certain line describes a fight between a Turkish and a Bulgarian officer on a bridge off which they both fall into the river —and then to find that the line consists of the noise of their falling and the weights of the officers: “Pluff! Pluff! A hundred and eighty-five kilograms.”①（22）This, though it fulfills the laws and requirements of Futurist poetry, can hardly be classed as Literature. ②All the same, no thinking man can refuse to accept their first proposition: that a great change in our emotional life calls for a change of expression. ③The whole question is really this: have we essentially changed?［334 words］19. This passage is mainly.［A］ a survey of new approaches to art［B］ a review of Futurist poetry［C］about merits of the Futurist movement［D］about laws and requirements of literature20. When a novel literary idea appears, people should try to.［A］determine its purposes ［B］ignore its flaws［C］follow the new fashions ［D］accept the principles21. Futurists claim that we must.［A］increase the production of literature［B］use poetry to relieve modern stress［C］develop new modes of expression［D］avoid using adjectives and verbs22. The author believes that Futurist poetry is.［A］based on reasonable principles［B］new and acceptable to ordinary people［C］indicative of a basic change in human nature［D］more of a transient phenomenon than literaturePassage 4①（23）Aimlessness has hardly been typical of the postwar Japan whose productivity and social harmony are the envy of the United States and Europe. ②But increasingly the Japanese are seeing a decline of the traditional work-moral values. ③Ten years ago young people were hardworking and saw their jobs as their primary reason for being, but now Japan has largely fulfilled its economic needs, and young people don’t know where they should go next.①The coming of age of the postwar baby boom and an entry of women into the male-dominated job market have limited the opportunities of teen-agers who are already questioning the heavy personal sacrifices involved in climbing Japan’s rigid social ladder to good schools and jobs. ②In a recent survey, it was found that only 24.5 percent of Japanese students were fully satisfied with school life, compared with 67.2 percent of students in the United States. ③In addition, far more Japanese workers expressed dissatisfaction with their jobs than did their counterparts in the 10 other countries surveyed.①While often praised by foreigners for its emphasis on the basics, Japanese education tends to stress test taking and mechanical learning over creativity and self-expression. ②（25）“Those things that do not show up in the test scores—personality, ability, courage or humanity—are completely ignored,”says Toshiki Kaifu, chairman of the ruling Liberal Democratic Party’s education committee. ③“Frustration against this kind of thing leads kids to drop out and run wild.”④Last year Japan experienced 2，125 incidents of school violence, including 929 assaults on teachers. ⑤Amid the outcry, many conservative leaders are seeking a return to the prewar emphasis on moral education. ⑥Last year Mitsuo Setoyama, who was then education minister, raised eyebrows when he argued that liberal reforms introduced by the American occupation authorities after World War II had weakened the ―Japanese morality of respect for parents.‖①（26）But that may have more to do with Japanese life-styles. ②“In Japan,”says educator Y oko Muro, “it’s never a question of whether you enjoy your job and your life, but only how much you can endure.”③With economic growth has come centralization; fully 76 percent of Japan’s 119 million citizens live in cities where community and the extended family have been abandoned in favor of isolated, two-generation households. ④Urban Japanese have long endured lengthy commutes (travels to and from work) and crowded living conditions, but as the old group and family values weaken, the discomfort is beginning to tell. ⑤In the past decade, the Japanese divorce rate, while still well below that of the United States, has increased by more than 50 percent, and suicides have increased by nearly one-quarter.［447 words］23. In the Westerners’ eyes, the postwar Japan was.［A］under aimless development ［B］ a positive example［C］ a rival to the West ［D］on the decline24. According to the author, what may chiefly be responsible for the moral decline of Japanese society?［A］Women’s participation in social activities is limited.［B］More workers are dissatisfied with their jobs.［C］Excessive emphasis has been placed on the basics.［D］The life-style has been influenced by Western values.25. Which of the following is true according to the author?［A］Japanese education is praised for helping the young climb the social ladder.［B］Japanese education is characterized by mechanical learning as well as creativity.［C］More stress should be placed on the cultivation of creativity.［D］Dropping out leads to frustration against test taking.26. The change in Japanese life-style is revealed in the fact that.［A］the young are less tolerant of discomforts in life［B］the divorce rate in Japan exceeds that in the U.S.［C］the Japanese endure more than ever before［D］the Japanese appreciate their present lifePassage 5①（27）If ambition is to be well regarded, the rewards of ambition—wealth, distinction, control over one’s destiny—must be deemed worthy of the sacrifices made on ambition’s behalf. ②If the tradition of ambition is to have vitality, it must be widely shared; and it especially must be highly regarded by people who are themselves admired, the educated not least among them. ③（28）In an odd way, however, it is the educated who have claimed to have given up on ambition as an ideal. ④What is odd is that they have perhaps most benefited from ambition—if not always their own then that of their parents and grandparents. ⑤There is a heavy note of hypocrisy in this, a case of closing the barn door after the horses have escaped—with the educated themselves riding on them.①Certainly people do not seem less interested in success and its signs now than formerly. ②Summer homes, European travel, BMWs—the locations, place names and name brands may change, but such items do not seem less in demand today than a decade or two years ago.③（29）What has happened is that people cannot confess fully to their dreams, as easily and openly as once they could, lest they be thought pushing, acquisitive and vulgar. ④Instead, we are treated to fine hypocritical spectacles, which now more than ever seem in ample supply: the critic of American materialism with a Southampton summer home; the publisher of radical books who takes his meals in three-star restaurants; the journalist advocating participatory democracy in all phases of life, whose own children are enrolled in private schools. ⑤For such people and many more perhaps not so exceptional, the proper formulation is, “Succeed at all costs but avoid appearing ambitious.”①The attacks on ambition are many and come from various angles; its public defenders are few and unimpressive, where they are not extremely unattractive. ②As a result, the support for ambition as a healthy impulse, a quality to be admired and fixed in the mind of the young, is probably lower than it has ever been in the United States. ③This does not mean that ambition is at an end, that people no longer feel its stirrings and promptings, but only that, no longer openly honored, it is less openly professed. ④Consequences follow from this, of course, some of which are that ambition is driven underground, or made sly. ⑤Such, then, is the way things stand: on the left angry critics, on the right stupid supporters, and in the middle, as usual, the majority of earnest people trying to get on in life. ［431 words］27. It is generally believed that ambition may be well regarded if.［A］its returns well compensate for the sacrifices［B］it is rewarded with money, fame and power［C］its goals are spiritual rather than material［D］it is shared by the rich and the famous28. The last sentence of the first paragraph most probably implies that it is.［A］customary of the educated to discard ambition in words［B］too late to check ambition once it has been let out［C］dishonest to deny ambition after the fulfillment of the goal［D］impractical for the educated to enjoy benefits from ambition29. Some people do not openly admit they have ambition because.［A］they think of it as immoral［B］their pursuits are not fame or wealth［C］ambition is not closely related to material benefits［D］they do not want to appear greedy and contemptible30. From the last paragraph the conclusion can be drawn that ambition should be maintained.［A］secretly and vigorously ［B］openly and enthusiastically［C］easily and momentarily ［D］verbally and spirituallyPart ⅢEnglish-Chinese TranslationDirections:Read the following passage carefully and then translate the underlined segments into Chinese. Y our translation must be written neatly on ANSWER SHEET 2. (15 points)Governments throughout the world act on the assumption that the welfare of their people depends largely on the economic strength and wealth of the community. 31）Under modern conditions, this requires varying measures of centralized control and hence the help of specialized scientists such as economists and operational research experts. 32）Furthermore, it is obvious that the strength of a country’s economy is directly bound up with the efficiency of its agriculture and industry, and that this in turn rests upon the efforts of scientists and technologists of all kinds. It also means that governments are increasingly compelled to interfere in these sectors in order to step up production and ensure that it is utilized to the best advantage. For example, they may encourage research in various ways, including the setting up of their own research centers; they may alter the structure of education, or interfere in order to reduce the wastage of natural resources or tap resources hitherto unexploited; or they may cooperate directly in the growing number of international projects related to science, economics and industry. In any case, all such interventions are heavily dependent on scientific advice and also scientific and technological manpower of all kinds.33）Owing to the remarkable development in mass-communications, people everywhere are feeling new wants and are being exposed to new customs and ideas, while governments are often forced to introduce still further innovations for the reasons given above. At the same time, the normal rate of social change throughout the world is taking place at a vastly accelerated speed compared with the past. For example, 34）in the early industrialized countries of Europe the process of industrialization—with all the far-reaching changes in social patterns that followed—was spread over nearly a century, whereas nowadays a developing nation may undergo the same process in a decade or so. All this has the effect of building up unusual pressures and tensions within the community and consequently presents serious problems for the governments concerned. 35）Additional social stresses may also occur because of the population explosion or problems arising from mass migration movements—themselves made relatively easy nowadays bymodern means of transport. As a result of all these factors, governments are becoming increasingly dependent on biologists and social scientists for planning the appropriate programs and putting them into effect. ［390 words］Section ⅣWriting(15 points)36.Directions:A. Study the following two pictures carefully and write an essay of at least 150 words.B. Y our essay must be written neatly on ANSWER SHEET 2.C. Y our essay should meet the requirements below:1）Describe the pictures.2）Deduce the purpose of the painter of the pictures.3）Suggest counter-measures.2000年英语试题答案Part ⅠCloze T est1. C2. A3. B4. A5. C6. D7. B8.D9. C 10. DPart ⅡReading ComprehensionPassage 111. C 12. D 13.B 14. APassage 215.C 16.B 17.A 18.DPassage 319.B 20.A 21.C 22.DPassage 423.B 24.D 25.C 26.APassage 527.A 28.C 29.D 30.BPart ⅢEnglish-Chinese Translation31.在现代条件下，这需要程度不同的集中控制措施，从而就需要获得诸如经济学和运筹学等领域的专家的协助。

2004年全国硕士研究生入学统一考试数学一真题及答案

2004年全国硕士研究生入学统一考试数学一试题答案一、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ln y x =上与直线1x y +=垂直的切线方程为．【答案】1y x =- 【考点】导数的几何意义【难易度】★ 【详解】解析：由11)(ln =='='xx y ，得1x =, 可见切点为)0,1(，于是所求的切线方程为 )1(10-⋅=-x y ，即 1-=x y .（2）已知()x x f e xe -'=，且(1)0f =，则()f x = ．【答案】21ln 2x 【考点】不定积分的换元法【难易度】★★ 【详解】解析：令t e x=，则t x ln =，于是有t t t f ln )(='，即 .ln )(xxx f =' 积分得2ln 1()ln (ln )ln 2x f x dx xd x x C x ===+⎰⎰. 利用初始条件(1)0f =, 得0C =，故所求函数为()f x = 21ln 2x .（3）设L 为正向圆周222x y +=在第一象限中的部分，则曲线积分x y y x Ld 2d -⎰的值为．【答案】π23 【考点】第二类曲线积分的计算；格林公式【难易度】★★★ 【详解】解析：正向圆周222=+y x 在第一象限中的部分，可表示为.20:,sin 2,cos 2πθθθ→⎩⎨⎧==y x于是θθθθθπd ydx xdy L]sin 2sin 22cos 2cos 2[220⋅+⋅=-⎰⎰=.23sin 2202πθθππ=+⎰d （4）欧拉方程)0(02d d 4d d 222>=++x y xyx x y x 的通解为．【答案】221x C x C y+=，其中12,C C 为任意常数【考点】欧拉方程【难易度】★★ 【详解】解析：令te x =，则dtdy x dt dy e dx dt dt dy dx dy t 1==⋅=-，][11122222222dtdy dt y d x dx dt dt y d x dt dy x dx y d -=⋅+-=，代入原方程，整理得02322=++y dt dydty d ，解此方程，得通解为 .221221xc x c e c ec y t t+=+=-- （5）设矩阵210120001A ⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦，矩阵B 满足**2ABA BA E ＝＋，其中*A 为A 的伴随矩阵，E 是单位矩阵，则B = ．【答案】19【考点】抽象型行列式的计算；伴随矩阵【难易度】★★ 【详解】解析：方法1：已知等式两边同时右乘A ，得A A BA A ABA +=**2，而3=A ，于是有A B AB +=63，即 A B E A =-)63(，再两边取行列式，有363==-A B E A ，而 2763=-E A ，故所求行列式为.91=B 方法2：由题设条件**2ABA BA E =+ 得 *(2)A E B A E-=两边取行列式，得*21A E B A E -==其中 2101203001A ==， 312A A A -*===9 0102100001A E -==1故1192B A E A*==- （6）设随机变量X 服从参数为λ的指数分布，则{}P X DX >= ．【答案】e1【考点】指数分布【难易度】★★ 【详解】解析：由题设，知21λ=DX ，于是}{DX X P >=dx e X P x ⎰+∞-=>λλλλ1}1{=.11ee x=-∞+-λλ 二、选择题（本题共8小题，每小题4分，满分32分．在每小题给出的四个选项中，只有一项是符合题目要求的，把所选项前的字母填在题后的括号内．）（7）把0x +→时的无穷小量t t t t t t xxx d sin ,d tan ,d cos 3022⎰⎰⎰===γβα排列起来，使排在后面的是前一个的高阶无穷小，则正确的排列次序是（）（A ）,,αβγ （B ）,,αγβ （C ）,,βαγ （D ）,,βγα 【答案】（B ）【考点】无穷小量的比较【难易度】★★ 【详解】解析：方法1：0cos 2tan lim cos tan limlim 22002=⋅==+++→→→⎰⎰xxx dtt dt t x xx x x αβ，可排除(C),(D)选项，又 xx x x dtt dtt x xxx x tan 221sin lim tan sin limlim 2300302⋅==+++→→→⎰⎰βγ=∞=+→20lim 41x x x ，可见γ是比β低阶的无穷小量，故应选(B). 方法2：221000cos cos lim limlim ,x kkk x x x t dt t x x kxα+++-→→→=⎰洛欲使上式极限存在但不为0，应取1k =，0lim 1x xα+→=，所以（当+→0x 时）α与x 同阶.2120000tan tan 22tan lim limlim lim ,x kkk k x x x x tdt x x xx x kx kx β++++--→→→→⋅==⎰洛欲使上式极限存在但不为0，应取3k =,有302lim 3x x β+→=，所以（当+→0x 时）β与3x 同阶. 31322120000sin sin lim lim lim lim ,22xk k k k x x x x t dtx x xx x kx kx γ++++---→→→→==⎰洛欲使上式极限存在但不为0，应取2k =,有201lim 4x x γ+→=，所以（当+→0x 时）γ与2x 同阶.因此，后面一个是前面一个的高阶小的次序是,,αγβ，选（B ）.（8）设函数()f x 连续，且(0)0f '>，则存在0δ>，使得（）（A ）()f x 在(0,)δ内单调增加．（B ）()f x 在(,0)δ-内单调减少．（C ）对任意的(0,)x δ∈有()(0)f x f >．（D ）对任意的(,0)x δ∈-有()(0)f x f >．【答案】（C ）【考点】函数极限的局部保号性；导数的概念【难易度】★★ 【详解】解析：由导数的定义，知,0)0()(lim)0(0>-='→xf x f f x根据极限的保号性，知存在0>δ，当),0()0,(δδ -∈x 时，有0)0()(>-xf x f即当)0,(δ-∈x 时，()(0)f x f <; 而当),0(δ∈x 时，有()(0)f x f >. 故应选(C).（9）设n n a∑∞=1为正项级数，下列结论中正确的是（）（A ）若0lim =∞→n n na ，则级数n n a∑∞=1收敛．（B ）若存在非零常数λ ，使得λna nn =∞→lim ，则级数n n a ∑∞=1发散．（C ）若级数n n a∑∞=1收敛，则0lim 2=∞→n n a n ．（D ）若级数n n a∑∞=1发散，则存在非零常数λ ，使得λna n n =∞→lim ．【答案】（B ）【考点】比较审敛法的极限形式【难易度】★★ 【详解】解析：方法1：排斥法：取n n a n ln 1=，则n n na ∞→lim =0，但∑∑∞=∞==11ln 1n n n nn a 发散，排除(A)，(D)；又取nn a n 1=，则级数∑∞=1n na收敛，但∞=∞→n n a n 2lim ，排除(C), 故应选(B).方法2：证明(B)正确. lim n n na λ→∞=,即lim 1n n a nλ→∞=.因为11n n∞=∑发散，由比较判别法的极限形式知，1nn a∞=∑发散.（10）设()f x 为连续函数，1()d ()d t tyF t yf x x =⎰⎰,则(2)F '=（）（A ）2(2)f （B ）(2)f （C ）(2)f - （D ）0 【答案】（B ）【考点】积分上限的函数及其导数【难易度】★★★ 【详解】解析：方法1：交换积分次序，得⎰⎰=tt ydx x f dy t F 1)()(=⎰⎰⎰-=t x tdx x x f dx dy x f 111)1)((])([于是，)1)(()(-='t t f t F ，从而有 )2()2(f F ='，故应选(B). 方法2：设()()x f x Φ=111()()[()()]()(1)()t t t tyF t dy f x dx t y dy t t y dy ==Φ-Φ=Φ--Φ⎰⎰⎰⎰()()(1)()()()(1),F t t t t t f t t ''=Φ-+Φ-Φ=- (2)(2)F f '=，选(B).（11）设A 是3阶方阵，将A 的第1列与第2列交换得B ，再把B 的第2列加到第3列得C ，则满足AQ C =的可逆矩阵Q 为（）（A ）010100101⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦．（B ）⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡100101010．（C ）⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡110001010．（D ）⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡100001110．【答案】（D ）【考点】矩阵的初等变换【难易度】★★ 【详解】解析：由题设，有B A =⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡100001010， 100010100011011100011100.001001001001B A A AQ ⎡⎤⎡⎤⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥===⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎣⎦⎣⎦故011100001Q ⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦，应选(D). （12）设A ，B 为满足0AB =的任意两个非零矩阵，则必有（）（A ） A 的列向量组线性相关，B 的行向量组线性相关．（B ） A 的列向量组线性相关，B 的列向量组线性相关．（C ） A 的行向量组线性相关，B 的行向量组线性相关．（D ） A 的行向量组线性相关，B 的列向量组线性相关．【答案】（A ）【考点】向量组线性相关的判别法【难易度】★★ 【详解】解析：方法1：设A 为n m ⨯矩阵，B 为s n ⨯矩阵，则由0AB =知，n B r A r <+)()(，其中n 是矩阵A 的列数，也是B 的行数又,A B 为非零矩阵，必有()0,()0r A r B >>. 可见(),()r A n r B n <<, 即A 的列向量组线性相关，B 的行向量组线性相关，故应选(A).方法2：由0AB =知，B 的每一列均为0Ax =的解，而B 为非零矩阵，即0Ax =存在非零解，可见A 的列向量组线性相关.同理，由0AB =知，O A B TT =，于是有T B 的列向量组线性相关，从而B 的行向量组线性相关，故应选(A).方法3：设 (),i j l m A a ⨯=()i j m n B b ⨯=, 记 ()12m A A A A =0AB =⇒()11121212221212n n m m m mn b b b b b b A A A bb b ⎛⎫⎪⎪⎪⋅⋅⋅ ⎪⎪⎝⎭()1111110mmn m n m b A b A b A b A =++++=（1）由于0B ≠, 所以至少有一 0i j b ≠(1,1i m j n ≤≤≤≤), 从而由（1）知, 112210j j i j i m m b A b A b A b A +++++= , 于是 12,,,m A A A 线性相关.又记 12m B B B B ⎛⎫⎪ ⎪= ⎪ ⎪ ⎪⎝⎭ ,则0AB =⇒11121121222212m m l l l m m a a a B a a a B a a a B ⎛⎫⎛⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⋅⋅⋅ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭ 1111221211222211220m m m m l l l m m a B a B a B a B a B a B a B a B a B +++⎛⎫⎪+++ ⎪== ⎪ ⎪ ⎪+++⎝⎭ 由于0A ≠,则至少存在一 0i j a ≠(1,1i l j m ≤≤≤≤),使 11220i i i j j im m a B a B a B a B ++++= , 从而 12,,,m B B B 线性相关,故应选（A ）.（13）设随机变量X 服从正态分布(0,1)N ，对给定的(01)αα<<，数u α满足{}P X u αα>=．若{}P X x α<= ，则x 等于（）（A ）2u α．（B ）21α-u．（C ）21αu -．（D ）u 1-α ．【答案】（C ）【考点】标准正态分布；分位数的概念【难易度】★★★ 【详解】解析：由标准正态分布概率密度函数的对称性知，αα=-<}{u X P ，于是}{2}{}{}{}{11x X P x X P x X P x X P x X P ≥=-≤+≥=≥=<-=-α即有21}{α-=≥x X P ，可见根据定义有21α-=u x ，故应选（C ）. （14）设随机变量12,,,(1)n X X X n > 独立同分布，且其方差为20σ>．令i ni X n Y ∑==11，则（）（A ）n Y X 21),(Cov σ=．（B ）21),(Cov σ=Y X ．（C ）212)(σn n Y X D +=+．（D ）211)(σnn Y X D +=-．【答案】（A ）【考点】随机变量的方差的性质；协方差的性质【难易度】★★ 【详解】解析：先计算1(,)Cov X Y ，因为11ni i Y X n ==∑，故1111112111(,)(,)(,)(,)n ni i i i Cov X Y Cov X X Cov X X Cov X X n n n ====+∑∑=.1121σnDX n = 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12分）设2e a b e <<<，证明 )(e 4ln ln 222a b a b ->-．【考点】拉格朗日中值定理；函数单调性的判别【难易度】★★★ 【详解】解析：方法1：对函数x 2ln 在[,]a b 上应用拉格朗日中值定理，得.),(ln 2ln ln 22b a a b a b <<-=-ξξξ设t t t ln )(=ϕ，则2ln 1)(t tt -='ϕ，当t e >时， ,0)(<'t ϕ 所以)(t ϕ单调减少，从而)()(2e ϕξϕ>，即2222ln ln ee e =>ξξ，故 )(4ln ln 222a b e a b ->-. 方法2：设x e x x 224ln )(-=ϕ，则 24ln 2)(e x x x -='ϕ， 2ln 12)(xx x -=''ϕ, 所以当x e >时，,0)(<''x ϕ 故)(x ϕ'单调减少，从而当2e x e <<时， 044)()(222=-='>'e e e x ϕϕ，即当2e x e <<时，)(x ϕ单调增加.因此当2e x e <<时，)()(a b ϕϕ>，即 a ea b e b 22224ln 4ln ->-，故 )(4ln ln 222a b e a b ->-. 方法3：设2224()ln ln ()x x a x a e ϕ=---, 则 2ln 4()2x x x e ϕ'=-21l n ()2xx xϕ-''=,∴x e >时, ()0x ϕ''<()x ϕ'⇒ , 从而当2e x e <<时,22244()()0x e e eϕϕ''>=-=, 2e x e ⇒<<时, ()x ϕ单调增加.2e a b e ⇒<<<时, ()()0x a ϕϕ>=。

2000年研究生入学考试中医综合科目试题及标准答案(CX型题)

103、肺肾阴虚证，可见
104、肝肾阴虚证，可见
A、胁胀痛 B、太息 C、两者均有 D、两者均无
105、肝气郁结证，可见
106、肝胆湿热证，可见
A、涩肠止泻 B、化湿行气 C、两者均可 D、两者均非
107、白豆莞的功效是
108、肉豆莞的功效是
A、补肝肾、强筋骨、安胎 B、祛风湿
A、复元活血汤 B、桃核承气汤 C、血府逐瘀汤 D、生化汤
147、复元活血汤的功用是
A、活血祛瘀 B、温经止痛 C、疏肝通络 D、软坚散结
148、下列方剂中具有温阳健脾作用的是
A、温脾汤 B、健脾丸 C、实脾散 D、归脾汤
149、济川煎主治证的主要临床表现是
A、大便秘结 B、头目眩晕 C、腰膝酸软 D、小便清长
A、运化无权，纳食不化 B、升清减弱，升降失司
C、健运失权，气血生化无源 D、统摄失司，血溢脉外
127、胃气虚的病理表现为
A、饮食无味，胃纳不佳 B、脘腹胀满，隐痛
C、恶心呕吐，呃逆嗳气 D、升举无力，内脏下垂
128、望舌形的内容，包括
A、胖大 B、点刺 C、歪斜 D、裂纹
129、肝火上炎证与肝阳上亢证的相同症状有
A、心主血脉 B、肾主蒸化 C、肝主疏泄 D、肾主封藏
122、对肺通调水道具有调节作用的生理功能是
A、肝主疏泄 B、肾主气化 C、脾主运化 D、腠理开合
123、胆为六腑之一，又属奇恒之腑，是由于
A、胆为“中精之府”，内藏精汁 B、胆无传化饮食物作用
C、胆附于肝，为空腔器官 D、胆为“中正之官”，脏腑皆取决于胆
A、眩晕头痛 B、急躁易怒 C、失眠多梦 D、口咽干燥

2004年全国硕士研究生入学统一考试数学（三）试卷答案和评分参考

2004年全国硕士研究生入学统一考试数学（三）试卷答案和评分参考2004年全国硕士研究生入学统一考试数学（三）试卷答案和评分参考一、填空题（本题共6小题，每小题4分，满分24分.把答案填写在题中横线上.）（1）若0sin lim(cos )5xx x x b e a→-=-，则a = 1 ，b = -4 .（2）函数(,)f u v 由关系式[(),]()f xg y y x g y =+确定，其中函数()g y 可微，且()0g y ≠，则2f u v=??2()[()]g v g v '-.（3）设21,2,()21,2,x xe x f x x ?-≤-≥?则212(1)f x dx -=?12-.（4）二次型222123122313(,,)()()()f x x x x x x x x x =++-++的秩为 2 . （5）设随机变量X 服从参数为λ的指数分布，则{P X >=1e.（6）设总体X 服从正态分布21(,)N μσ，总体Y 从正态分布2 2(,)N μσ，112,,,n X X X 和212,,,n Y Y Y 分别是来自总体X 和Y 的简单随机样本，则12221112()()2n n i j i j X X Y Y E n n ==??-+-??+-∑∑= 2σ . 二、选择题（本题共8小题，每小题4分，满分32分，在每小题给出的四个选项中，只有一个是符合题目要求的，把所选项前的字母填在题后面的括号内.）（7）函数2sin(2)()(1)(2)x x f x x x x -=--在下列哪个区间内有界.(A)(1,0)-. (B)(0,1). (C)(1,2). (D)(2,3). 【 A 】（8）设()f x 在(,)-∞+∞内有定义，且lim ()x f x a →+∞=，1(),0,()0,0,f xg x xx ?≠?=??=?则(A)0x =必是()g x 的第一类间断点. （B ）0x =必是()g x 的第二类间断点. （C ）0x =必是()g x 的连续点.（D ）()g x 在点0x =处的连续性与a 的取值有关. 【 D 】（9）设()(1),f x x x =-则(A)0x =是()f x 的极值点，但(0,0)不是曲线()y f x =的拐点. (B)0x =不是()f x 的极值点，但(0,0)是曲线()y f x =的拐点. (C)0x =是()f x 的极值点，且(0,0)是曲线()y f x =的拐点.(D)0x =不是()f x 的极值点，(0,0)也不是曲线()y f x =的拐点. 【 C 】（10）设有以下命题：①若()2121n n n u u ∞-=+∑收敛，则1n n u ∞=∑收敛.②若1n n u ∞=∑收敛，则10001n n u ∞+=∑收敛.③若1lim1n n nu u +→+∞>收敛，则1n n u ∞=∑发散.④若()1n n n u v ∞=+∑收敛，则11,n n n n u v ∞∞==∑∑都收敛. 【 B 】（11）设()f x '在[,]a b 上连续，且()0,()0f a f b ''><，则下列结论中错误．．的是 (A)至少存在一点0(,)x a b ∈，使得0()()f x f a >. (B)至少存在一点0(,)x a b ∈，使得0()()f x f b >. (C)至少存在一点0(,)x a b ∈，使得0()0f x '=.(D)至少存在一点0(,)x a b ∈，使得0()0f x = 【 D 】（12）设n 阶矩阵A 与B 等价，则必有(A)当(0)A a a =≠时，B a =.(B)当(0)A a a =≠时，B a =-. (C)当0A ≠时，0B =.(D)当0A =时，0B =. 【 D 】 (13)设n 阶矩阵A 的伴随矩阵*0A ≠，若1234,,,ξξξξ是非齐次线性方程组Ax b =的互不相等的解，则对应的齐次线性方程0Ax =的基础解系(A)不存在. (B)仅含一个非零解向量.(C)含有两个线性无关的解向量. (D)含有三个线性无关的解向量. 【 B 】 (14)设随机变量X 服从正态分布(0,1)N ,对给定的(01)αα<<,数a u 满足{}a P X u α>=.若{}P X x α<=,则x 等于（A ）2a u . （B ）12-. （C ）12a u -. （D ）1a u - 【 C 】三、解答题（本题共9小题，满分94分，解答题应写出文字说明、证明过程或演算步骤.）(15)(本题满分8分)求 22201cos lim sin x x x x →??-解 22201cos lim sin x x x x →??-22222sin cos limsin x x x xx x→-=22401sin 24limx x xx→-= ……2分01sin 44lim2x x xx→-= ……4分 201cos 4lim 6x x x→-= ……6分0sin 4lim 3x x x →= 4 3= ……8分 (16)(本题满分8分) 求)Dy d σ??，其中D 是由圆224x y +=和22 (1)1x y ++=所围成的平面区域（如图）.解法1)))DD D y d y d y d σσσ=-大圆小圆……2分)D y d σ+??大圆D D yd σσ=+大大（根据对称性）2220d r dr πθ=+?=163π ……4分)D y d σ+??小圆D D yd σσ=+小小32cos 2220d r dr πθπθ-=+??329=，……7分所以)16(32)9Dy d σπ=-??……8分解法 2 由积分区域对称性和被积函数的奇偶性0Dyd σ=?? ……1分原式0Dσ=+??12D D σσ??=+上上2……2分22222002cos 22d r dr d r dr πππθθθ-??=+……5分4462()339ππ??=+- 16(32)9π=- ……8分[注]：1D σ??上定限1分，计算1分.D σ??上2定限1分，计算1分.（17）（本题满分8分）设(),()f x g x 在[,]a b 上连续，且满足()(),[,)x x a a f t dt g t dt x a b ≥∈??, ()(),b b a af t dtg t dt =证明：()().bb a axf x dx xg x dx ≤证令()()(),()(),x aF x f x g xG x F t dt =-=?由题设知()0,[,]G x x a b ≥∈()()0,()(),G a G b G x F x '=== ……2分从而()(),b b aaxF x dx xdG x =()(),b baaxG x G x dx =-(),baG x dx =-? ……4分由于()0,[,]G x x a b ≥∈，故有()0,ba G x dx -≤? ……6分即 ()0baxF x dx ≤?.因此 ()()bb aaxf x dx xg x dx ≤……8分（18）（本题满分9分）设某商品的需求函数为1005Q P =-，其中价格(0,20)P ∈，Q 为需求量. （I ）求需求量对价格的弹性(0);d d E E > （II ）推导(1)d dR Q E dP=-（其中R 为收益），并用弹性d E 说明价格在何范围内变化时，降低价格反而使收益增加.解 (I) 20d P P E Q Q P'==-. ……2分（II ）由,R PQ =得dR Q P Q dP'=+(1)P Q Q Q'=+(1)d Q E =-. ……4分又由 120d P E P==-，得10P =. ……5分当1020P <<时，1d E >，于是0dR dP<. ……7分故当1020P <<时，降低价格反而使收益增加. ……9分（19）（本题满分9分）设级数468()242462468xxxx +++-∞<<+∞的和函数为()S x .求：（I ）()S x 所满足的一阶微分方程；（II ）()S x 的表达式. 解（I ） 468(),242462468xxxS x =+++易见(0)0.S = ……1分357()224246xxS x '=+++246224246x x xx ??=+++……2分 2().2x x S x ??=+……4分因此()S x 是初值问题3,(0)02xy xy y '=+=的解. ……4分（II ）方程32xy xy '=+的通解为32xdx xdx x y e e dx c -=+222xxC e=--+, ……7分由初始条件(0)0y =，求的1C =. ……8分故22212xxy e=-+-，因此和函数222()12xxS x e=-+- ……9分（20）（本题满分13分）设123(1,2,0),(1,2,3),(1,2,2),(1,3,3)TTTTa ab a b αααβ==+-=---+=-. 试讨论当,a b 为何值时，（I ）β不能够由123,,ααα线性表示；（II ）β可由123,,ααα惟一线性表示，并求出表示式；（III ）β可由123,,ααα惟一线性表示，但表示式不惟一，并求出表达式. 解设有数123,,k k k ，使得112233k k k αααβ++= （*）……1分记123(,,)A ααα=.对矩阵()A β施以初等行变换，有111122230323A a b aa b β?-?+-- ? ?-+-?（）=010001a b ?→- ? ?-?……3分（I ）当0a b =，为任意常数时，有111101000A a b a b β?-?→- ? ?-?（）可知()()r A r A β≠，故方程组（*）无解，β不能由123,,ααα线性表示.……5分（II ）当0,a ≠且a b ≠时，()()3r A r A β==，故方程组（*）有惟一解123111,,0k k k a a=-==，则β可由123,,ααα惟一地线性表示，其表示式为12111a aβαα?=-+ ……7分（III ）当0a b =≠时，对A β（）施以初等行变换，有110011011000a A a β??-→- ?（）. ……9分可知()()2r A r A β==，故方程组（*）有无穷多解，其全部解为123111,,k k c k c a a ??=-=+=，其中c 为任意常数. β可由123,,ααα线性表示，但表示式不惟一，其表示式为……11分123111c c a a βααα?=-+++ ? ??. ……13分（21）（本题满分13分）设n 阶矩阵11b b A b b= ? ? ??（I ）求A 的特征值和特征向量；（II ）求可逆矩阵P ，使得1P AP -为对角矩阵. 解（I ）1? 当0b ≠时，111bb b b E A bbλλλλ-------=---1[1(1)][(1)]n n b b λλ-=----- ……3分故A 的特征值为121(1),1.n n b b λλλ=+-===-对于11(1)n b λ=+-，设A 的属于特征值1λ的一个特征向量为1ξ，则1111[1(1)]1b b b bn b b bξξ?? ? ?=+- ? ? ??解得 1(1,1,,1)Tξ= ，所以全部特征向量为1(1,1,,1)Tk k ξ= （k 为任意非零常数）……5分对于21n b λλ===- ，解齐次线性方程组[(1)]0b E A x --=，由111000(1)000b b b b b b b E A b bb ----- ?--=→ ? ? ? ? ? ?---?，解得基础解系2(1,1,0,,0)Tξ=-3(1,0,1,,0)Tξ=-2(1,0,0,,1)Tξ=-故全部特征向量为2233n n k k k ξξξ+++ （2,,n k k 是不全为零的常数）. ......7分2?当0b =时，特征11n λλ=== ，任意非零列向量均为特征向量. (9)分（II ）1?当0b ≠时，A 有n 个线性无关的特征向量，令12(,,,)n P ξξξ= ，则{}11(1),1,,1.P AP diag n b b b -=+--- ……11分2?当0b =时，A E =，对任意可逆矩阵P ，均有1P AP E -= ……13分[注]: 1(1,1,,1)Tξ= 也可由求解齐次线性方程组1()0E A x λ-=得出.（22）（本题满分13分）设A B 、为两个随机事件，且111432PP P （A）=，（B A）=，（A B）=，令1,0,A X A ?=?发生，不发生； 1,0,B Y B ?=??，发生不发生. 求：（I ）二维随机变量(,)X Y 的概率分布；（II ）X 与Y 的相关系数X Y ρ；（III ）22Z X Y =+的概率分布.解（I ）()()()1,12P A B P A P B A ==()()()1,6P A B P B P B A == ……2分则{}(){}()()(){}()()(){}()11,1,1211,0,610,1,120,0P X Y P A B P X Y P A B P A P A B P X Y P AB P B P A B P X Y P A B========-=====-====()()()()211[]3P A B P A P B P AB =-=-+-= ，（或{}11120,01126123P X Y ===---=），……6分即 (,)X Y 的概率分布为（II ）方法 1111(),(),(),4612EX P A EY P B E XY =====则1(,)()24C ov X Y E X Y E X E Y =-= 22222211(),4635(),(),1636E X P A E YP B D X E X E X D Y E Y E Y == ===-==-=(,)1XY C ov X Y ρ==……9分方法 2 ,X Y 的概率分布分别为X 01，Y 01.P3414P 5616则 111,,(),4612E X E Y E X Y ==而故 1(,)(),24C ov X Y E XY EX EY =-= 22222211,,4635(),(),1636E XE YD XE X E X D Y E Y E Y ===-==-=XY ρ==……9分（III ）Z 的可能取值为012，，，{}{}{}{}{}200,0,3110,11,04P Z P X Y P Z P X Y P X Y =========+===，{}{}121,1,12P Z P X Y =====……13分即Z 的概率分布为Z 012.P2314112（23）（本题满分13分）设总体X 的分布函数为1,(;;)0,x F x x x βαααβα->? ?=≤?其中参数0,1,αβ>>设12,,,n X X X 为来自总体X 的简单随机样本.（I ）当1α=时，求未知参数β的矩估计量；（II ）当1α=时，求未知参数β的最大似然估计量；（III ）当2β=时，求未知参数α的最大似然估计量. 解当1α=时，X 的概率密度为111,1,(;)0,1,x F x xx ββ+?->?=??≤?……1分（I ）由于11(;),1EX xf x dx x dx xβββββ+∞+∞+-∞===-?……2分令1X ββ=-，解得1X X β=-，所以参数β的矩估计量为1X X β=- ……4分（II ）对于总体X 的样本值12,,,n x x x ，似然函数为1121,1(1,2,,)()(;)()0,nni n i x i n L f x x x x βββα+=?>=?==??∏其他……6分当1(1,2,,)i x i n >= 时，()L β>0，取对数得1ln ()ln (1)ln ,ni i L n x βββ==-+∑两边对β求导，得1ln ()ln ,nii d L nx d βββ==-∑1ln ()0,ln nid xβββ===∑令，解得故β的最大似然估计量为1.ln nii nXβ==∑ ……9分（III ）当2β=时，X 的概率密度为232,(;)0,x f x x x αααα>?=??≤?对于总体X 的样本值12,,,n x x x ，似然函数为31212,(1,2,,)()(;)()0,n nni n i x i n L f x x x x αααα=?>=?==??∏，……11分当(1,2,,)i x i n α>= 时，α越大，()L α越大，因而的最大似然估计值为{}12m in ,,,n x x x α= 则的最大似然估计量为{}12m in ,,,n X X X α= ……13分。

2004年全国硕士研究生入学统一考试数学一试题及答案

2004年全国硕士研究生入学统一考试数学(一)试题及答案一、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y=lnx 上与直线1=+y x 垂直的切线方程为 1-=x y .【分析】本题为基础题型，相当于已知切线的斜率为1，由曲线y=lnx 的导数为1可确定切点的坐标。

【详解】由11)(ln =='='xx y ，得x=1, 可见切点为)0,1(，于是所求的切线方程为 )1(10-⋅=-x y ，即 1-=x y .【评注】本题也可先设切点为)ln ,(00x x ，曲线y=lnx 过此切点的导数为11=='=x y x x ，得10=x ，由此可知所求切线方程为)1(10-⋅=-x y ，即 1-=x y . （2）已知xxxe e f -=')(，且f(1)=0, 则f(x)=2)(ln 21x . 【分析】先求出)(x f '的表达式，再积分即可。

【详解】令t e x=，则t x ln =，于是有t t t f ln )(='，即 .ln )(x xx f =' 积分得 C x dx x x x f +==⎰2)(ln 21ln )(. 利用初始条件f(1)=0, 得C=0，故所求函数为f(x)= 2)(ln 21x .（3）设L 为正向圆周222=+y x 在第一象限中的部分，则曲线积分⎰-Lydx xdy 2的值为π23 . 【分析】利用极坐标将曲线用参数方程表示，相应曲线积分可化为定积分。

【详解】正向圆周222=+y x 在第一象限中的部分，可表示为.20:,sin 2,cos 2πθθθ→⎩⎨⎧==y x于是θθθθθπd y d x x d y L]s i n 2s i n 22c o s 2c o s 2[220⋅+⋅=-⎰⎰=.23sin 2202πθθππ=+⎰d（4）欧拉方程)0(024222>=++x y dx dyx dxy d x 的通解为 221x c x c y +=. 【分析】欧拉方程的求解有固定方法，作变量代换te x =化为常系数线性齐次微分方程即可。

2000年全国硕士研究生入学统一考试数学一二试题(word版)

2000年全国硕士研究生入学统一考试理工数学一试题详解及评析一、填空题(1)0=⎰ . （2）曲面2222321x y z ++=在点()1,2,2-的法线方程为 .（3）微分方程'''30xy y +=的通解为 . （4）已知方程组12312112323120x a x a x ⎡⎤⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥+=⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥-⎣⎦⎣⎦⎣⎦无解，则a = . (5)设两个相互独立的事件A 和B 都不发生的概率为1,9A 发生B 不发生的概率与B 发生A 不发生的概率相等，则()P A = .二、选择题（1）设()(),f x g x 是恒大于零得可导函数，且()()()()''0f x g x f x g x -<，则当a xb <<时，有（A ）()()()()f x g b f b g x > （B ）()()()()f x g a f a g x >（C ）()()()()f x g x f b g b > （D ）()()()()f x g x f a g a >（2）设()22221:0,S x y z az S ++=≥为S 在第一卦限中的部分，则有（A ）14S S xdS xdS =⎰⎰⎰⎰ （B ）14S S ydS xdS =⎰⎰⎰⎰ （C ）14SS zdS xdS =⎰⎰⎰⎰ （D ）14S S xyzdS xyzdS =⎰⎰⎰⎰ （3）设级数1n n u∞=∑收敛，则必收敛的级数为（A ）()11.n n n u n ∞=-∑ （B ）21n n u ∞=∑（C ）()2121.n n n uu ∞-=-∑ (D) ()11.n n n u u ∞+=+∑（4）设n 维列向量组()1,,m m n αα<线性无关，则n 维列向量组1,,m ββ线性无关的充分必要条件为（A ）向量组1,,m αα可由向量组1,,m ββ线性表示. （B ）向量组1,,m ββ可由向量组1,,m αα线性表示. （C ）向量组1,,m αα与向量组1,,m ββ等价. （D ）矩阵()1,,m A αα=与矩阵()1,,m B ββ=等价.（5）设二维随机变量(),X Y 服从二维正态分布，则随机变量X Y ξ=+与X Y η=-不相关的充分必要条件为(A)()().E X E Y =(B)()()()()2222.E X E X E Y E Y -=-⎡⎤⎡⎤⎣⎦⎣⎦ (C)()()22.E X E Y =(D)()()()()2222.E X E X E Y E Y +=+⎡⎤⎡⎤⎣⎦⎣⎦ 四、设,,x x z f xy g y y ⎛⎫⎛⎫=+ ⎪ ⎪⎝⎭⎝⎭其中f 具有二阶连续偏导数，g 具有二阶连续导数，求2.z x y ∂∂∂ 五、计算曲线积分22,4L xdy ydx I x y -=+⎰其中L 是以点()1,0为中心，R 为半径的圆周()1R >，取逆时针方向.六、设对于半空间0x >内任意的光滑有向封闭曲面,S 都有()()20,x S xf x dydz xyf x dzdx ezdxdy --=⎰⎰其中函数()f x 在()0,+∞内具有连续的一阶导数，且()0lim 1,x f x +→=求()f x . 七、求幂级数()1132n n n n x n∞=+-∑的收敛区域，并讨论该区间断电处的收敛性. 八、设有一半径为R 的球体，0P 是此球的表面上的一个定点，球体上任一点的密度与该点到0P 距离的平方成正比（比例常数0k >），求球体的重心位置.九、设函数()f x 在[]0,π上连续，且()()000,cos 0,f x dx f x xdx ππ==⎰⎰试证：在()0,π内至少存在两个不同的点12,ξξ，使()()120f f ξξ==.十、（本题满分6分）设矩阵A 的伴随矩阵*10000100,10100308A ⎡⎤⎢⎥⎢⎥=⎢⎥⎢⎥-⎣⎦且113,ABA BA E --=+其中E 为4阶单位矩阵，求矩阵.B十一、某试验性生产线每年一月份进行熟练工与非熟练工得人数统计，然后将16熟练工支援其他生产部门，其缺额由招收新的非熟练工补齐，新、老非熟练工经过培训及之间实践至年终考核有25成为熟练工.设第n 年一月份统计的熟练工和非熟练工所占百分比分别为n x 和n y ，记为向量n n x y ⎛⎫ ⎪⎝⎭. （1）求11n n x y ++⎛⎫ ⎪⎝⎭与n n x y ⎛⎫ ⎪⎝⎭的关系式并写成矩阵形式：1111;n n n n x x A y y ++++⎛⎫⎛⎫= ⎪ ⎪⎝⎭⎝⎭（2）验证1241,11ηη-⎛⎫⎛⎫== ⎪ ⎪⎝⎭⎝⎭是A 的两个线性无关的特征向量，并求出相应的特征值；（3）当111212x y ⎡⎤⎢⎥⎛⎫=⎢⎥ ⎪⎝⎭⎢⎥⎢⎥⎣⎦时，求11n n x y ++⎛⎫ ⎪⎝⎭. 十二、某流水生产线上每一个产品不合格的概率为()01p p <<,各产品合格与否相互独立，当出现一个不合格产品时即停机检修.设开机后第一次停机时已生产了产品的个数为,X 求X 的数学期望()E X 和方差()D X .十三、设某种元件的使用寿命X 的概率密度为()()22,,0, x e x f x x θθθθ--⎧>⎪=⎨≤⎪⎩其中0θ>为未知参数，又设12,,,n x x x 是X 的一组样本观测值，求参数θ的最大似然估计值.2000年全国硕士研究生入学统一考试理工数学二试题一．填空题（1）()30arctan lim ln 12x x x x →-=+ . （2）设函数()y y x =由方程2xy x y =+所确定，则0|x dy == . （3）2+∞=⎰ . （4）曲线()121x y x e =-的斜渐近线方程为 .（5）设10002300,04500067A E ⎡⎤⎢⎥-⎢⎥=⎢⎥-⎢⎥-⎣⎦为4阶单位矩阵，且()()1B E A E A -=+-,则()1B E -+＝ .二、选择题（1）设函数()bxx f x a e =+在(),-∞+∞内连续，且()lim 0x f x →-∞=，则常数,a b 满足（A ） 0,0a b << （B ）0,0a b >>（C ）0,0a b ≤> （D ）0,0a b ≥<（2）设函数()f x 满足关系式()()2''',f x f x x ⎡⎤+=⎣⎦且()'00f =，则（A ）()0f 是()f x 的极大值（B ）()0f 是()f x 的极小值（C ）点()()0,0f 是曲线()y f x =的拐点（D ）()0f 不是()f x 的极值，点()()0,0f 不是曲线()y f x =的拐点（3）设函数()(),f x g x 是大于零的可导函数，且()()()()''0,f x g x f x g x -<则当a x b <<时，有（A ）()()()()f x g b f b g x > （B ）()()()()f x g a f a g x >（C ）()()()()f x g x f b g b > （C ）()()()()f x g x f a g a >（4）若()30sin 6lim 0,x x xf x x →+=则()206lim x f x x→+为（A ）0 （B ）6 （C ）36 （D ）∞（5）具有特解123,2,3x x x y e y xe y e --===的3阶常系数齐次微分方程是（A ）''''''0y y y y --+= （B ）''''''0y y y y +--=（C ）''''''61160y y y y -+-= （D ）''''''220y y y y --+=三、设()()ln 1ln ,x f x x+=计算().f x dx ⎰四、设xOy 平面上有正方形(){},|01,01D x y x y =≤≤≤≤及直线():0l x y t t +=≥若()S t 表示正方形D 位于直线l 的左下方部分的面积，试求()()00.x S t dt x ≥⎰五、求函数()()2ln 1f x x x =+在0x =处的n 阶导数()()()03n f n ≥六、设函数()0cos ,xS x t dt =⎰ （1）当n 为正整数，且()1n x n ππ≤<+时，证明()()221;n S x n ≤<+（2）求()lim x S x x→+∞ 七、某湖泊的水量为,V 每年排入湖泊内含污染物A 的污水量为6V ，流入湖泊内不含A 的污水量为6V ，流出湖泊的水量为3V ，已知1999年底湖中A 的含量为05m ，超过国家规定指标，为了治理污染，从2000年初起，限制排入湖泊中含A 污水的浓度不超过0.m V 问至多需要经过多少年，湖泊中污染物A 的含量才可降至0m 以内？（注：设湖水中A 的浓度时均匀的）八、设函数()f x 在[]0,π上连续，且()()000,cos 0,f x dx f x xdx ππ==⎰⎰试证明：在()0,π内至少存在两个不同的点12,ξξ，使()()120.f f ξξ==九、已知()f x 是周期为5的连续函数，它在0x =的某个邻域内满足关系式()()()1sin 31sin 8f x f x x a x +--=+其中()a x 是当0x →时比x 高阶的无穷小，且()f x 在1x =处可导，求曲线()y f x =在点()()6,6f 处的切线方程.十、设曲线()20,0y ax a x =>≥与21y x =-交于点,A 过坐标原点O 和点A 的直线与曲线2y ax =围成一平面图形，问a 为何值时，该图形绕x 轴旋转一周所得的旋转体的体积最大？十一、函数()f x 在[]0,+∞上可导，()01f =，且满足等式()()()'010.1x f x f x f t dt x +-=+⎰ （1）求导数()'f x ；（2）证明：当0x ≥时，不等式()1x e f x -≤≤成立.十二、设11012,,0,,2180T T A B B αβγαβα⎡⎤⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥=====⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎢⎥⎣⎦,其中T β是β的转置，求解方程 22442.B A x A x B x γ=++十三、已知向量组12301,2,1110a b βββ⎡⎤⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥===⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥-⎣⎦⎣⎦⎣⎦与向量组1231392,0,6317ααα⎡⎤⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥===⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥--⎣⎦⎣⎦⎣⎦具有相同的秩，且3β可由123,,ααα线性表示，求,a b 的值.。