20100年01月试卷

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2000年高考数学(理科)真题及答案[全国卷I]

2000年普通高等学校招生全国统一考试数学(理工农医类)本试卷分第I 卷(选择题)和第II 卷(非选择题)两部分。

第I 卷1至2页。

第II 卷3至9页。

共150分。

考试时间120分钟。

第I 卷(选择题 60分)注意事项：1、答第I 卷前，考生务必将自己的姓名、准考证号、考试科目用铅笔涂写在答题卡上。

2、每小题选出答案后，用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，再选涂其它答案，不能答在试题卷上。

3、考试结束，监考人将本试卷和答题卡一并收回。

选择题：本大题共12小题；第每小题5分，共60分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

(1)设集合A 和B 都是自然数集合N ，映射f:A →B 把集合A 中的元素n映射到集合B 中的元素2n +n ，则在映射f 下，象20的原象是(A)2 (B)3 (C)4 (D)5i 3对应的向量按顺时针方向旋转3π，i 33+2，3， 6，(4)已知sin α>sin β，那么下列命题成立的是(A)若α、β是第一象限角，则cos α>cos β(B)若α、β是第二象限角，则tg α>tg β(C)若α、β是第三象限角，则cos α>cos β(D)若α、β是第四象限角，则tg α>tg β(5)函数y=-x cos x 的部分图象是(6)《中华人民共和国个人所得税法》规定，公民全月工资、薪金所得不超过 800元的部分不必纳税，超过800元的部分为全月应纳税所得额。

此项税款按下表分段累进计算：<div align="center"> 全月应纳税所得额税率不超过500元的部分 5%超过500元至2000元的部分 10%超过2000元至5000元的部分 15%… …</div>某人一月份应交纳此项税款26.78元，则他的当月工资、薪金所得介于800~900元 (B)900~1200元(C)1200~1500元 (D)1500~2800元(7)若a >b >1，)2lg(),lg (lg 21,lg lg ba R Q P +=+=⋅=βαβα,则(A)R<P<Q (B)P<Q< R(C)Q< P<R (D)P< R<Q(8)以极坐标系中的点(1,1)为圆心，1为半径的圆的方程是(A))4cos(2πθ-=p (B))4sin(2πθ-=p (C))1sin(2-=θp (D))1sin(2-=θp(9)一个圆柱的侧面展开图是一个正方形，这个圆柱的全面积与侧面积的比是(A) (B) (C) (D)(10)过原点的直线与圆相切，若切点在第三象限，则该直线的方程是(A) (B) (C) (D)(11)过抛物线的焦点F 作一条直线交抛物线于P 、Q 两点，若线段PF 与FQ 的长分别是p 、q ，则等于(A)2a(B)(C)4a(D)(12)如图，OA是圆锥底面中心O到母线的垂线，OA绕轴旋转一周所得曲面将圆锥分成体积相等的两部分，则母线与轴的夹角为2000年普通高等学校招生全国统一考试数学(理工农医类)第II卷(非选择题90分)注意事项：第II卷共7页，用钢笔或圆珠笔直接答在试题卷中。

2000全国高考真题试卷

2000全国高考真题试卷2000年的全国高考真题试卷，是当时中国教育部门为全国高中毕业生设计的统一考试试卷。

这份试卷涵盖了语文、数学、英语、物理、化学、生物、历史、地理、政治等多个学科，旨在全面考察学生的学科知识与综合能力。

以下是对2000年全国高考真题试卷的概述。

# 语文试卷2000年的语文试卷主要分为文言文阅读、现代文阅读、作文三个部分。

文言文阅读部分考查了学生对古代文献的理解和翻译能力；现代文阅读部分则侧重于现代汉语的阅读理解和分析能力；作文部分则要求学生根据给定的材料或题目，撰写一篇有逻辑、有深度的文章。

# 数学试卷数学试卷通常包括代数、几何、概率统计等部分。

代数部分考查了学生的代数运算能力和方程求解技巧；几何部分则测试了学生对图形性质的理解和空间想象能力；概率统计部分则涉及到数据的收集、处理和分析。

# 英语试卷英语试卷一般包含听力、阅读、写作和翻译四个部分。

听力部分考查学生的英语听力理解能力；阅读部分测试学生对英语文章的阅读和理解；写作部分要求学生根据给定的题目或情景，撰写英语文章；翻译部分则是对英汉互译能力的测试。

# 物理试卷物理试卷通常包含力学、热学、电磁学、光学和原子物理学等部分。

这些部分考查了学生对物理概念的理解和物理定律的应用能力，以及解决物理问题的能力。

# 化学试卷化学试卷涵盖了无机化学、有机化学、物理化学和分析化学等内容。

考查学生对化学原理的理解、化学反应的分析以及化学实验技能。

# 生物试卷生物试卷包括细胞生物学、遗传学、生态学、进化论等内容。

考查学生对生物学基本概念的理解，以及对生物学现象的分析和解释能力。

# 历史试卷历史试卷通常包括中国古代史、近现代史、世界史等部分。

考查学生对历史事件的了解、历史人物的评价以及历史发展的分析。

# 地理试卷地理试卷包括自然地理和人文地理两部分。

考查学生对地理环境、地理现象的理解，以及对地理问题的分析能力。

# 政治试卷政治试卷主要涉及政治理论、时事政治等内容。

2000年高考全国物理试题(含答案)

2000年普通高等学校招生全国统一考试物理本试卷分第I 卷（选择题）和第II 卷（非选择题），第I 卷1至3页，第II 卷4至11页，共150分，考试时间120分钟。

第I 卷注意事项：1．答第I 卷前，考生务必将自己的姓名、准考证号、考试科目用铅笔涂写在答题卡上。

2．每小题选出答案后，用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，再选涂其它答案，不能答在试题卷上。

3．考试结束，将本试卷和答题卡上并交回。

4．必要时可以使用下列物理量。

真空中光速s m c /1038⨯= 万有引力常量2211/1067.6kg m N G ⋅⨯=-普朗克常量s J h ⋅⨯=-34106.6电子的电量C e 19106.1-⨯= 地球半径m R 6104.6⨯= 电子的质量kg m e 31101.9-⨯=一．本题共10小题；每小题4分，共40分。

在每小题给出的四个选项中，有的小题只有一个选项正确，有的小题有多个选项正确。

全部选对的得4分，选不全的得2分，有选错或不答的得0分。

1．最近几年，原子核科学家在超重元素岛的探测方面取得重大进展。

1996年科学家们在研究某两个重离子结合成超重元素的反应时，发现生成的超重元素的核X AZ 经过6次a 衰变后的产物是Fm 254100。

由此，可在判定生成的超重元素的原子序数和质量数分别是（A ）124，259 （B ）124，265 （C ）112，265 （D ）112，2772．对于一定量的理想气体，下列四个论述中正确的是（A ）当分子热运动变剧烈时，压强必变大（B ）当分子热运动变剧烈时，压强可以不变（C ）当分子间的平均距离变大时，压强必变小（D ）当分子间的平均距离变大时，压强必变大3．某人造地球卫星因受高空稀薄空气的阻气作用，绕地球运转的轨道会慢慢改变，每次测量中卫星的运动可近似看作圆周运动。

某次测量卫星的轨道半径为1r ，后来变为2r ，12r r <。

2000年1月全国自考(公共关系)真题试卷(题后含答案及解析)

2000年1月全国自考（公共关系）真题试卷(题后含答案及解析) 题型有：1. 单项选择题 4. 简答题 5. 论述题7. 填空题8. 判断题单项选择题1．形成公众关系和影响公众舆论的前提是( )。

A．大众传播B．组织形象C．社会交往D．传播沟通正确答案：D2．现代公共关系发展史上的第一本公共关系专著是( )。

A．《公共关系学》B．《舆论》C．《有效公共关系》D．《公众舆论的形成》正确答案：D3．世界上第一个在企业内部设立公关部的是( )。

A．美国电话电报公司B．美国福特汽车公司C．日本本田公司D．日本松下电器公司正确答案：A4．民主政治取代专制政治，这是公共关系产生的( )。

A．文化条件B．历史条件C．政治条件D．经济条件正确答案：C5．发展有中国特色的公共关系学的前提是( )。

A．加强宣传B．扩大组织C．研究国情D．积极应用正确答案：C6．在部门隶属型公共关系机构中较好的一种形式是( )。

A．归属于销售部门B．归属于广告宣传部门C．归属于接待部门D．归属于办公室正确答案：D7．与组织自身相关性最强的一类公众对象是( )。

A．内部公众B．顾客公众C．媒介公众D．政府公众正确答案：A8．价值观念、职业道德是( )。

A．人员形象的内涵B．人员形象的外显C．文化形象的内涵D．文体形象的外显正确答案：C9．情调、风格、含义是( )。

A．文化形象的内涵B．文化形象的外显C．标识形象的内涵D．标识形象的外显正确答案：C10．当组织与环境发生某种冲突时，为了摆脱被动局面，应采取的公关活动方式是( )。

A．建设型公关B．防御型公关C．进攻型公关D．矫正型公关正确答案：C11．适用于规模不大的人口总体的抽样方法是( )。

A．间隔随机抽样B．分层随机抽样C．分区多级随机抽样D．整群抽样正确答案：A12．进行民意测验的主要工具是( )。

A．问卷法B．抽样C．资料分析D．实施调查正确答案：A13．在公关调查中，对于了解某些历史性问题的一种常用的行之有效的方法是( )。

2000年全国统一高考物理试卷【含答案;word版;可再编辑】

2000年全国统一高考物理试卷一．本题共10小题；每小题4分，共40分．在每小题给出的四个选项中，有的小题只有一个选项正确，有的小题有多个选项正确．全部选对的得4分，选不全的得2分，有选错或不答的得0分．1. 最近几年，科学家在超重元素的探测方面取得重大进展，1996年科学家们在研究某两个重原子结合成超重原子的反应时，发现生成的超重元素的原子核24X经过6次α衰变后的产物是100253Fm．由此可以判断生成的超重元素的原子序数和质量数分别是（）A.124、259B.124、265C.112、265D.112、2772. 对于一定质量的理想气体，下列四个论述中正确的是（）A.当分子热运动变剧烈时，压强必变大B.当分子热运动变剧烈时，压强可以不变C.当分子间的平均距离变大时，压强必变小D.当分子间的平均距离变大时，压强必变大3. 某绕地运行的航天探测器因受高空稀薄空气的阻力作用，绕地球运行的轨道会慢慢改变．每次测量中探测器的运动可近似看作是圆周运动．某次测量探测器的轨道半径为r1，后来变为r2，r2<r1．以E K1、E K2表示探测器在这两个轨道上的动能，T1、T2表示探测器在这两个轨道上绕地球运动的周期，则（）A.E K2<E K1，T2<T1B.E K2<E K1，T2>T1C.E K2>E K1，T2<T1D.E K2>E K1，T2>T14. 对于水平放置的平行板电容器，下列说法正确的是（）A.将两极板的间距加大，电容将增大B.将两极板平行错开，使正对面积减小，电容将减小C.在下板的内表面上放置一面积和极板相等、厚度小于极板间的陶瓷板，电容将增大D.在下板的内表面上放置一面积和极板相等、厚度小于极板间距的铝板，电容将增大5. 图中活塞将气缸分成甲、乙两气室，气缸、活塞（连同拉杆）是绝热的，且不漏气，以E甲、E乙分别表示甲、乙两气室中气体的内能，则在将拉杆缓慢向外拉的过程中（）A.E甲不变，E乙减小 B.E甲增大，E乙不变C.E甲增大，E乙减小 D.E甲不变，E乙不变6. 图中为X射线管的结构示意图，E为灯丝电源．要使射线管发出X射线，须在K、A两电极间加上几万伏的直流高压，则（）A.高压电源正极应接在P点，X射线从K极发出B.高压电源正极应接在P点，X射线从A极发出C.高压电源正极应接在Q点，X射线从K极发出D.高压电源正极应接在Q点，X射线从A极发出7. 一列横波在t=0时刻的波形如图中实线所示，在t=1s时刻的波形如图中虚线所示，由此可以判定此波的（）A.波长一定是4cmB.周期一定是4sC.振幅一定是2cmD.传播速度一定是1cm/s8. A与B是两束平行的单色光，它们从空气射入水中的折射角分别为r A、r B，若r A>r B；则（）A.在空气中A的波长大于B的波长B.在水中A的传播速度大于B的传播速度C.A的频率大于B的频率D.在水中A的波长小于B的波长1 / 7。

2000年1月大学英语四级(CET-4)真题试卷四级真题+答案详解+听力原文

2000年1月大学英语四级(CET-4)真题试卷Part I Listening Comprehension (20 minutes)Section ADirections: In this section, you will hear 10 short conversations. At the end of each conversation, a question will be asked about what was said. Both theconversation and the question will be spoken only once. After eachquestion there will be a pause. During the pause, you must read the fourchoices marked A), B), C) and D), and decide which is the best answer.Then mark the corresponding letter on the Answer Sheet with a single linethrough the center.Example:You will hear:You will read:A) At the office.B) In the waiting room.C) At the airport.D) In a restaurant.From the conversation we know that the two were talking about some work they will start at 9 o’clock in the morning and have to finish at 2 in the afternoon. Therefore, D) “5 hours” is the correct answer. You should choose [D] on the Answer Sheet and mark it with a single line through the center.Sample Answer [A] [B] [C] [D]1. A) The woman is a close friend of the man.B) The woman has been working too hard.C) The woman is seeing a doctor.D) The woman is tired of her work.2. A) This apple pie tastes very good.B) His mother likes the pie very much.C) This pie can’t match his mother’s.D) His mother can’t make apple pies.3. A) Take a walk.B) Give a performance.C) Listen to the music.D) Dance to the music.4. A) Read an article on political science.B) Present a different theory to the class.C) Read more than one article.D) Choose a better article to read.5. A) The woman would understand if she did Mary’s job.B) The woman should do the typing for Mary.C) The woman should work as hard as Mary.D) The woman isn’t a skillful typist.6. A) He wants to make an appointment with Mr. Smith.B) He wants to make sure that Mr. Smith will see him.C) He wants to change the time of the appointment.D) He wants the woman to meet him at three o’clock.7. A) He gets nervous very easily.B) He is an inexperienced speaker.C) He is an awful speaker.D) He hasn’t prepared his speech well.8. A) She didn’t like the books the man bought.B) There wasn’t a large selection at the bookstore.C) The man bought a lot of books.D) She wanted to see what the man bought.9. A) Buy a ticket for the tem o’clock flight.B) Ask the man to change the ticket for her.C) Go to the airport immediately.D) Switch to a different flight.10. A) Dr. Lemon is waiting for a patient.B) Dr. Lemon is busy at the moment.C) Dr. Lemon has lost his patience.D) Dr. Lemon has gone out to visit a patient.Section BDirections: In this section, you will hear 3 short passages. At the end of each passage,you will hear some questions. Both the passage and the questions will bespoken only once. After you hear a question, you must choose the bestanswer from the four choices marked A), B), C) and D). Then mark thecorresponding letter on the Answer Sheet with a single line through thecenter.Passage oneQuestions 11 to 14 are based on the passage you have just heard.11. A) A car outside the supermarket.B) A car at the bottom of the hill.C) Paul’s car.D) The sports car.12. A) Inside the car.B) At the foot of the hill.C) In the garage.D) In the supermarket.13. A) The driver of the sports car.B) The two girls inside the car.C) The man standing nearby.D) The salesman from London.14. A) Nobody.B) The two girls.C) The bus driver.D) Paul.Passage TwoQuestions 15 to 17 are based on the passage you have just heard.15. A) His friend gave him the wrong key.B) He didn’t know where the back door was.C) He couldn’t find the key to his mailbox.D) It was too dark to put the key in the lock.16. A) It was getting dark.B) He was afraid of being blamed by his friend.C) The birds might have flown away.D) His friend would arrive any time.17. A) He looked silly with only one leg inside the window.B) He knew the policeman wouldn’t believe him.C) The torch light made him look very foolish.D) He realized that he had made a mistake.Passage ThreeQuestions 18 to 20 are based on the passage you have just heard.18. A) The threat of poisonous desert animals and plants.B) The exhaustion of energy resources.C) The destruction of oil wells.D) The spread of the black powder from the fires.19. A) The underground oil resources have not been affected.B) Most of the desert animals and plants have managed to survive.C) The oil lakes soon dried up and stopped evaporating.D) The underground water resources have not been polluted.20. A) To restore the normal production of the oil wells.B) To estimate the losses caused by the fires.C) To remove the oil left in the desert.D) To use the oil left in the oil lakes.Part II Reading Comprehension (35 minutes)Directions: There are 4 passages in this part. Each passage is followed by some questions or unfinished statements. For each of them there are four choicesmarked A), B), C) and D). You should decide on the best choice and markthe corresponding letter on the Answer Sheet with a single line through thecenter.Passage OneQuestions 21 to 25 are based on the following passage.Unless we spend money to spot and prevent asteroids (小行星) now, one might crash into Earth and destroy life as we know it, say some scientists.Asteroids are bigger versions of the meteoroids (流星) that race across the night sky. Most orbit the sun far from Earth and don’t threaten us. But there are also thousands ofasteroids whose orbits put them on a collision course with Earth.Buy $50 million worth of new telescopes right now. Then spend $10 million a year for the next 25 years to locate most of the space rocks. By the time we spot a fatal one, the scientists say, we’ll have a way to change its course.Some scientists favor pushing asteroids off course with nuclear weapons. But the cost wouldn’t be cheap.Is it worth it? Two things experts consider when judging any risk re: 1) How likely the event is; and 2) How bad the consequences if the event occurs. Experts think an asteroid big enough to destroy lots of life might strike Earth once every 500,000 years. Sounds pretty rare—but if one did fall, it would be the end of the world. “If we don’t take care of these big asteroids, they’ll take care of us,” says one scientist. “It’s that simple.”The cure, though, might be worse than the disease. Do we really want fleets of nuclear weapons sitting around on Earth? “The world has less to fear from doomsday (毁灭性的) rocks than from a great nuclear fleet set against them,” said a New York Times article.21. What does the passage say about asteroids and meteoroids?A) They are heavenly bodies different in composition.B) They are heavenly bodies similar in nature.C) There are more asteroids than meteoroids.D) Asteroids are more mysterious than meteoroids.22. What do scientists say about the collision of an asteroid with Earth?A) It is very unlikely but the danger exists.B) Such a collision might occur once every 25 years.C) Collisions of smaller asteroids with Earth occur more often than expected.D) It’s still too early to say whether such a collision might occur.23. What do people think of the suggestion of using nuclear weapons to alter thecourses of asteroids?A) It sounds practical but it may not solve the problem.B) It may create more problems than it might solve.C) It is a waste of money because a collision of asteroids with Earth is very unlikely.D) Further research should be done before it is proved applicable.24. We can conclude from the passage that ________.A) while pushing asteroids off course nuclear weapons would destroy the worldB) asteroids racing across the night sky are likely to hit Earth in the near futureC) the worry about asteroids can be left to future generations since it is unlikely tohappen in our lifetimeD) workable solutions still have to be found to prevent a collision of asteroids withEarth25. Which of the following best describes the author’s tone in this passage?A) Optimistic.B) Critical.C) Objective.D) Arbitrary.Passage TwoQuestions 26 to 30 are based on the following passage.Believe it or not, optical illusion (错觉) can cut highway crashes.Japan is a case in point. It has reduced automobile crashes on some roads by nearly 75 percent using a simple optical illusion. Bent stripes, called chevrons (人字形), painted on the roads make drivers think that they are driving faster than they really are, and thus drivers slow down.Now the American Automobile Association Foundation for Traffic Safety in Washington D.C. is planning to repeat Japan’s success. Starting next year, the foundation will paint chevrons and other patterns of stripes on selected roads around the country to test how well the patterns reduce highway crashes.Excessive speed plays a major role in as much as one fifth of all fatal traffic accidents, according to the foundation. To help reduce those accidents, the foundation will conduct its tests in areas where speed-related hazards are the greatest—curves, exit slopes, traffic circles, and bridges.Some studies suggest that straight, horizontal bars painted across roads can initially cut the average speed of drivers in half. However, traffic often returns to full speed within months as drivers become used to seeing the painted bars.Chevrons, scientists say, not only give drivers the impression that they are driving faster than they really are but also make a lane appear to be narrower. The result is a longer lasting reduction in highway sped and the number of traffic accidents.26. The passage mainly discusses ________.A) a new way of highway speed controlB) a new pattern for painting highwaysC) a new approach to training driversD) a new type of optical illusion27. On roads painted with chevrons, drivers tend to feel that ________.A) they should avoid speed-related hazardsB) they are driving in the wrong laneC) they should slow down their speedD) they are approaching the speed limit28. The advantage of chevrons over straight, horizontal bars is that the former________.A) can keep drivers awakeB) can cut road accidents in halfC) will have a longer effect on driversD) will look more attractive29. The American Automobile Association Foundation for Traffic Safety plans to________.A) try out the Japanese method in certain areasB) change the road signs across the countryC) replace straight, horizontal bars with chevronsD) repeat the Japanese road patterns30. What does the author say about straight, horizontal bars painted across roads?A) They are falling out of use in the United States.B) They tend to be ignored by drivers in a short period of time.C) They are applicable only on broad roads.D) They cannot be applied successfully to traffic circles.Passage ThreeQuestions 31 to 35 are based on the following passage.Amtrak (美国铁路客运公司) was experiencing a downswing in ridership (客运量) along the lines comprising its rail system. Of major concern to Amtrak and its advertising agency DDB Needham, were the long-distance western routes where ridership had been declining significantly.] At one time, trains were the only practical way to cross the vast areas of the west. Trains were fast, very luxurious, and quite convenient compared to other forms of transportation existing at the time. However, times change and the automobile became America’s standard of convenience. Also, air travel had easily established itself as the fastest method of traveling great distances. Therefore, the task for DDB Needham was to encourage consumers to consider other aspects of train travel in order to change their attitudes and increase the likelihood that trains would be considered for travel in the west.Two portions of the total market were targeted: 1) anxious fliers—those concerned with safety, relaxation, and cleanliness and 2) travel-lovers—those viewing themselves as relaxed, casual, and interested in the travel experience as part of their vacation. The agency then developed a campaign that focused on travel experiences such as freedom,escape, relaxation, and enjoyment of the great western outdoors. It stressed experiences gained by using the trains and portrayed western train trips as wonderful adventures.Advertisements showed pictures of the beautiful scenery that could be enjoyed along some of the more famous western routes and emphasized the romantic names of some of these trains (Empire Builder, etc.). These ads were strategically placed among family-oriented TV shows and programs involving nature and America in order to most effectively reach target audiences. Results were impressive. The Empire Builder, which was focused on in one ad, enjoyed a 15 percent increase in profits on its Chicago to Seattle route.31. What’s the author’s purpose in writing this passage?A) To show the inability of trains to compete with planes with respect to speed andconvenience.B) To stress the influence of the automobile on America’s standard of convenience.C) To emphasize the function of travel agencies in market promotion.D) To illustrate the important role of persuasive communication in changingconsumer attitudes.32. It can be inferred from the passage that the drop in Amtrak ridership was due to thefact that ________.A) trains were not suitable for short distance passenger transportationB) trains were not the fastest and most convenient form of transportationC) trains were not as fast and convenient as they used to beD) trains could not compete with planes in terms of luxury and convenience33. To encourage consumers to travel by train, DDB Needham emphasized ________.A) the freedom and convenience provided on trainsB) the practical aspects of train travelC) the adventurous aspects of train tripsD) the safety and cleanliness of train trips34. The train ads were placed among family-oriented TV programs involving nature andAmerica because ________.A) they could focus on meaningful travel experiencesB) they could increase the effectiveness of the TV programsC) their profits could be increased by some 15 percentD) most travel-lovers and nervous fliers were believed to be among the audiences35. According to the passage, the Empire Builder enjoyed an increase in ridership andprofits because ________.A) the attractiveness of its name and route was effectively advertisedB) it provided an exciting travel experienceC) its passengers could enjoy the great western outdoorsD) it was widely advertised in newspapers and magazines in Chicago and SeattlePassage FourQuestions 36 to 40 are based on the following passage.Why does cram go bad faster than butter? Some researchers think they have the answer, and it comes down to the structure of the food, not its chemical composition—a finding that could help rid some processed foods of chemical preservatives.Cream and butter contain pretty much the same substances, so why cream should sour much faster has been a mystery. Both are emulsions—tiny globules (小球体) of one liquid evenly distributed throughout another. The difference lies in what’s in the globules and what’s in the surrounding liquid, says Brocklehurst, who led the investigation.In cream, fatty globules drift about in a sea of water. In butter, globules of a watery solution are locked away in a sea of fat. The bacteria which make the food go bad prefer to live in the watery regions of the mixture. “This means that in cream, the bacteria are free to grow throughout the mixture,” he says.When the situation is reversed, the bacteria are locked away in compartments (隔仓室) buried deep in the sea of fat. Trapped in this way, individual colonies cannot spread and rapidly run out of nutrients (养料). They also slowly poison themselves with their waste products. “In butter, you get a self-limiting system which stops the bacteria growing,” says Brocklehurst.The researchers are already working with food companies keen to see if their products can be made resistant to bacterial attack through alterations to the food’s structure. Brocklehurst believes it will be possible to make the emulsions used in salad cream, for instance, more like that in butter. The key will be to do this while keeping the salad cream liquid and not turning it into a solid lump.36. The significance of Brocklehurst’s research is that ________.A) it suggested a way to keep some foods fresh without preservativesB) it discovered tiny globules in both cream and butterC) it revealed the secret of how bacteria multiply in cream and butterD) it found that cream and butter share the same chemical composition37. According to the researchers, cream sours fast than butter because bacteria________.A) are more evenly distributed in creamB) multiply more easily in cream than in butterC) live on less fat in cream than in butterD) produce less waste in cream than in butter38. According to Brocklehurst, we can keep cream fresh by ________.A) removing its fatB) killing the bacteriaC) reducing its water contentD) altering its structure39. The word “colonies” (Line 2, Para. 4) refers to ________.A) tiny globulesB) watery regionsC) bacteria communitiesD) little compartments40. Commercial application of the research finding will be possible if salad cream canbe made resistant to bacterial attack ________.A) by varying its chemical compositionB) by turning it into a solid lumpC) while keeping its structure unchangedD) while retaining its liquid formPart III Vocabulary and Structure (20 minutes)Directions: There are 30 incomplete sentences in this part. For each sentence there are four choices marked A), B), C) and D). Choose the ONE that bestcompletes the sentence. Then mark the corresponding letter on the AnswerSheet with a single line through the center.41. She ought to stop work; she has a headache because she ________ too long.A) has been readingB) had readC) is readingD) read42. Niagara Falls is a great tourist ________, drawing millions of visitors every year.A) attentionB) attractionC) appointmentD) arrangement43. I don’t mind ________ the decision as long as it is not too late.A) you to delay makingB) your delaying makingC) your delaying to makeD) you delay to make44. The hopes, goals, fears and desires ________ widely between men and women,between the rich and the poor.A) alterB) shiftC) transferD) vary45. Corn originated in the New World and thus was not known in Europe untilColumbus found it ________ in Cuba.A) being cultivatedB) been cultivatedC) having cultivatedD) cultivating46. The sale usually takes place outside the house, with the audience ________ onbenches, chairs or boxes.A) having seatedB) seatingC) seatedD) having been seated47. This kind of glasses manufactured by experienced craftsmen ________ comfortably.A) is wornB) wearsC) wearingD) are worn48. Some diseases are ________ by certain water animals.A) transplantedB) transformedC) transportedD) transmitted49. Wouldn’t you rather your child ________ to bed early?A) goB) wentC) would goD) goes50. Although Anne is happy with her success she wonders ________ will happen to herprivate life.A) thatB) whatC) itD) this51. The words of his old teacher left a ________ impression on his mind. He is stillinfluenced by them.A) staying notB) not to stayC) that he would not stayD) that he not stay52. Mike’s uncle insists ________ in this hotel.A) whateverB) whomeverC) whicheverD) whoever53. We agreed to accept ________ they thought was the best tourist guide.A) whateverB) whomeverC) whicheverD) whoever54. It is our ________ policy that we will achieve unity through peaceful means.A) consistentB) continuousC) considerateD) continual55. Between 1974 and 1997, the number of overseas visitors expanded ________27%.A) byB) forC) toD) in56. Although many people view conflict as bad, conflict is sometimes useful ________it forces people to test the relative merits of their attitudes and behaviors.A) by whichB) to whichC) in thatD) so that57. He is ________ about his chances of winning a gold medal in the Olympics nextyear.A) optimisticB) optionalC) outstandingD) obvious58. Sometimes I wish I ________ in a different time and a different place.A) be livingB) were livingC) would liveD) would have lived59. The director was critical ________ the way we were doing the work.A) atB) inC) ofD) with60. In a sudden ________ of anger, the man tore up everything within reach.A) attackB) burstC) splitD) blast61. ________ she realized it was too late to go home.A) No sooner it grew dark thanB) Hardly did it grow dark thatC) Scarcely had it grown dark thanD) It was not until dark that62. In Britain people ________ four million tons of potatoes every year.A) swallowB) disposeC) consumeD) exhaust63. I’d ________ his reputation with other farmers and business people in thecommunity, and then make a decision about whether or not to approve a loan.A) take into accountB) account forC) make up forD) make out64. It is essential that these application forms ________ back as early as possible.A) must be sentB) will be sentC) are sentD) be sent65. She cooked the meat for a long time so as to make it ________ enough to eat.A) mildB) slightC) lightD) tender66. We take our skin for granted until it is burned ________ repair.A) beyondB) forC) withoutD) under67. The computer revolution may well change society as ________ as did the IndustrialRevolution.A) certainlyB) insignificantlyC) fundamentallyD) comparatively68. ________ in this way, the situation doesn’t seem so disappointing.A) To look atB) Looking atC) Looked atD) To be looked at69. A lot of ants are always invading my kitchen. They are a thorough ________.A) nuisanceB) troubleC) worryD) anxiety70. Some women ________ a good salary in a job instead of staying home, but theydecided not to work for the sake of the family.A) must makeB) should have madeC) would makeD) could have madePart IV Cloze (15 minutes)Directions: There are 20 blanks in the following passage. For each blank there are four choices marked A), B), C) and D) on the right side of the paper. You shouldchoose the ONE that best fits into the passage. Then mark thecorresponding letter on the Answer Sheet with a single line through thecentre.In a telephone survey of more than 2,000 adults, 21% said they believed the sun revolved (旋转) around the earth. An __71__ 7% did not know which revolved around __72__ I have no doubt that __73__ all of these people were __74__ in school that the earth revolves around the sun; __75__ may even have written it __76__ a test. But they never __77__ their incorrect mental models of planetary (行星的) __78__ because their everyday observations didn’t support __79__ their teachers told them: People see the sun “moving” __80__ the sky as morning turns to night, and the earth seems stationary (静止的) __81__ that is happening.Students can learn the right answers __82__ heart in class, and yet never combined them __83__ their working models of the world. The objectively correct answer the professor accepts and the __84__ personal understanding of the world can __85__ side by side, each unaffected by the other.Outside of class, the student continues to sue the __86__ model because it has always worked well __87__ that circumstance. Unless professors address __88__ errors in students’ personal models of the world, students are not __89__ to replace them with the __90__ one.71. A) excessiveB) extraC) additionalD) added72. A) whatB) whichC) thatD) other73. A) virtuallyB) remarkablyC) ideallyD) preferably74. A) learnedB) suggestedC) taughtD) advised75. A) thoseB) theseC) whoD) they76. A) onB) withC) underD) for77. A) formedB) alteredC) believedD) thought78. A) operationB) positionC) motionD) location79. A) howB) whichC) thatD) what80. A) aroundB) acrossC) onD) above81. A) sinceB) soC) whileD) for82. A) toB) byC) inD) with83. A) withB) intoC) toD) along84. A) adult’sB) teacher’sC) scientist’sD) student’s85. A) existB) occurC) surviveD) maintain86. A) privateB) individualC) personalD) own87. A) inB) withC) onD) for88. A) generalB) naturalC) similarD) specific89. A) obligedB) likelyC) probableD) partial90. A) perfectB) betterC) reasonableD) correctPart V Writing (30 minutes)Directions: For this part, you are allowed thirty minutes to write a composition on the topic How I Finance My College Education. You should write at least 120words, and base your composition on the outline (given in Chinese) below:1. 上大学的费用(tuition and fees)可以通过多种途径解决2. 哪种途径适合于我(说明理由)How I Finance My College Education2000年1月四级参考答案19 / 40 2000年1月四级参考答案Part IPart IIPart IIIPart IV2000年1月四级听力原文20 / 402000年1月四级听力原文1. M: Hi, Jane, do you have some changes? I have to make a call on the payphone.W: Payphone? Why not use my mobile phone? Here you are.Q: What will the man most probably do?2. M: Can you tell me the title of this oil painting?W: Sorry, I don’t know for sure, but I guess it is an early 18 century work. Let me look it up in the catalog.Q: Where does this conversation most probably take place?3. M: I am worried about those classes I missed when I was sick.W: I will try to bring you up today on what we’ve done.Q: What does the woman mean?4. W: Hey Dan. I hear you’re meeting Susan’s parents for the first time.M: Yeah, next weekend. Fortunately, her father loves to fish, so we will have so many things to talk about.Q: What can be inferred about Dan?5. W: Professor White’s presentation seemed to go on forever. I was barely able to stayawake.M: How could you sleep through it? It is one of the best that I have ever heard on this topic.Q: What does the man think of Professor White’s presentation?6. W: I am looking for quality paper to type my essay. I don’t see any on the shelf.M: I saw some in the stockroom this morning. I will go and check.Q: What does the woman want to buy?7. M: It seems that we’ll have another fine day tomorrow. Let’s go to the seaside.W: OK. But we’ll have to leave very early, or else we’ll get caught in the traffic.Q: What does the woman suggest?8. M: Do you know James? He is in your class.W: Certainly. In fact he was the first person I got to know in my class. I still remember the look on his face when he showed up late on the first day of school.Q: Why did the woman remember James so well?9. W: The man at the garage thinks that I take good care of my car.。

2000年真题试卷(word版)

2000年全真试题Part ⅠClose TestDirections：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 glowingperiod after the end of the Second World War, it had a market eight times larger than any competitor, 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 Yoko 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. 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 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 orproblems 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］Section ⅣWriting(15 points)36.Directions:A. Study the following two pictures carefully and write an essay of at least 150 words.B. Your essay must be written neatly on ANSWER SHEET 2.C. Your 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 Test1. 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。

2000年全国统一高考数学试卷(理科)

2000年全国统一高考数学试卷（理科）一、选择题（共12小题，每小题5分，满分60分）1．（5分）（2000•全国）设集合A和B都是自然数集合N，映射f：A→B把集合A中的元素n映射到集合B中的元素2n+n，则在映射f下，象20的原象是（）A．2 B．3 C．4 D．52．（5分）（2000•新课程）在复平面内，把复数对应的向量按顺时钟方向旋转，所得向量对应的复数是（）A．2 B．C．﹣3i D．3+3．（5分）（2000•新课程）一个长方体共一顶点的三个面的面积分别是，，，这个长方体对角线的长是（）A．2 B．3 C．6 D．4．（5分）（2000•全国）已知sinα＞sinβ，那么下列命题成立的是（）A．若α、β是第一象限角，则cosα＞cosβB．若α、β是第二象限角，则tanα＞tanβC．若α、β是第三象限角，则cosα＞cosβD．若α、β是第四象限角，则tanα＞tanβ5．（5分）（2000•新课程）函数y=﹣xcosx的部分图象是（）A． B．C．D．6．（5分）（2000•新课程）《中华人民共和国个人所得税法》规定，公民全月工资、薪金所得不超过800元的部分不必纳税，超过800元的部分为全月应纳税所得额，此项税款按下表分段累进计算：全月应纳税所得额税率不超过500元的部分5%超过500元至2000元的部分10%超过2000元至5000元的部分15%……某人一月份应交纳此项税款26.78元，则他的当月工资、薪金所得介于（）A．800～900元 B．900～1200元C．1200～1500元D．1500～2800元7．（5分）（2000•新课程）若a＞b＞1，P=，Q=（lga+lgb），R=lg，则（）A．R＜P＜Q B．P＜Q＜R C．Q＜P＜R D．P＜R＜Q8．（5分）（2000•全国）以极坐标系中的点（1，1）为圆心，1为半径的圆的方程是（）A．B．C．ρ=2cos（θ﹣1） D．ρ=2sin （θ﹣1）9．（5分）（2000•新课程）一个圆柱的侧面展开图是一个正方形，这个圆柱的全面积与侧面积的比是（）A．B．C．D．10．（5分）（2000•新课程）过原点的直线与圆x2+y2+4x+3=0相切，若切点在第三象限，则该直线的方程是（）A．y=B．y=﹣C．D．11．（5分）（2000•新课程）过抛物线y=ax2（a＞0）的焦点F作一直线交抛物线于P、Q两点，若线段PF与FQ的长分别是p、q，则+等于（）A．2a B．C．4a D．12．（5分）（2000•全国）如图，OA是圆锥底面中心O到母线的垂线，OA绕轴旋转一周所得曲面将圆锥分成体积相等的两部分，则母线与轴的夹角为（）A．B．C．D．二、填空题（共4小题，每小题4分，满分16分）13．（4分）（2000•全国）乒乓球队的10名队员中有3名主力队员，派5名参加比赛，3名主力队员要安排在第一、三、五位置，其余7名队员选2名安排在第二、四位置，那么不同的出场安排共有种（用数字作答）．14．（4分）（2000•新课程）椭圆的焦点F1、F2，点P为其上的动点，当∠F1PF2为钝角时，点P横坐标的取值范围是．15．（4分）（2000•新课程）设{a n}是首项为1的正项数列，且（n+1）a n+12﹣na n2+a n+1a n=0（n=1，2，3，…），则它的通项公式是a n=．16．（4分）（2000•新课程）如图，E、F分别是正方体的面ADD1A1、面BCC1B1的中心，则四边形BFD1E在该正方体的面上的射影可能是．（要求：把可能的图的序号都填上）三、解答题（共6小题，满分74分）17．（12分）（2000•全国）已知函数，x∈R．（1）当函数y取得最大值时，求自变量x的集合；（2）该函数的图象可由y=sinx（x∈R）的图象经过怎样的平移和伸缩变换得到？18．（12分）（2000•新课程）如图，已知平行六面体ABCD﹣A1B1C1D1的底面ABCD 是菱形，且∠C1CB=∠C1CD=∠BCD=60°．（1）证明：C1C⊥BD；（2）假定CD=2，CC1=，记面C1BD为α，面CBD为β，求二面角α﹣BD﹣β的平面角的余弦值；（3）当的值为多少时，能使A1C⊥平面C1BD？请给出证明．19．（12分）（2000•新课程）设函数，其中a＞0，（1）解不等式f（x）≤1；（2）证明：当a≥1时，函数f（x）在区间[0，+∞）上是单调函数．20．（12分）（2000•新课程）（1）已知数列{c n}，其中c n=2n+3n，且数列{c n+1﹣pc n}为等比数列，求常数p；（2）设{a n}、{b n}是公比不相等的两个等比数列，c n=a n+b n，证明数列{c n}不是等比数列．21．（12分）（2000•全国）某蔬菜基地种植西红柿，由历年市场行情得知，从二月一日起的300天内，西红柿场售价与上市时间的关系如图一的一条折线表示；西红柿的种植成本与上市时间的关系如图二的抛物线段表示．（1）写出图一表示的市场售价与时间的函数关系式p=f（t）；写出图二表示的种植成本与时间的函数关系式Q=g（t）；（2）认定市场售价减去种植成本为纯收益，问何时上市的西红柿纯收益最大？（注：市场售价各种植成本的单位：元/102㎏，时间单位：天）22．（14分）（2000•新课程）如图，已知梯形ABCD中|AB|=2|CD|，点E分有向线段所成的比为λ，双曲线过C、D、E三点，且以A、B为焦点，当时，求双曲线离心率e的取值范围．2000年全国统一高考数学试卷（理科）参考答案与试题解析一、选择题（共12小题，每小题5分，满分60分）1．（5分）（2000•全国）设集合A和B都是自然数集合N，映射f：A→B把集合A中的元素n映射到集合B中的元素2n+n，则在映射f下，象20的原象是（）A．2 B．3 C．4 D．5【考点】3C：映射．【分析】A中的元素为原象，B中的元素为象，令2n+n=20即可解出结果．【解答】解：由2n+n=20求n，用代入法可知选C．故选：C．【点评】解决象与原象的互化问题要注意以下两点：（1）分清象和原象的概念（2）确定对应关系2．（5分）（2000•新课程）在复平面内，把复数对应的向量按顺时钟方向旋转，所得向量对应的复数是（）A．2 B．C．﹣3i D．3+【考点】A5：复数的运算．【专题】11 ：计算题．【分析】由题意知复数对应的向量按顺时钟方向旋转，需要把已知向量对应的复数乘以复数的沿顺时针旋转后的复数，相乘得到结果．【解答】解：∵由题意知复数对应的向量按顺时钟方向旋转，∴旋转后的向量为．故选：B．【点评】本题考查复数的运算，考查复数与向量的对应，是一个基础题，复数的代数形式和三角形式是复数运算中常用的两种形式，注意两种形式的标准形式，不要在简单问题上犯错误．3．（5分）（2000•新课程）一个长方体共一顶点的三个面的面积分别是，，，这个长方体对角线的长是（）A．2 B．3 C．6 D．【考点】L2：棱柱的结构特征．【专题】11 ：计算题．【分析】设出长方体的三度，利用面积公式求出三度，然后求出对角线的长．【解答】解：设长方体三度为x，y，z，则．三式相乘得．故选：D．【点评】本题考查棱柱的结构特征，考查计算能力，空间想象能力，是基础题．4．（5分）（2000•全国）已知sinα＞sinβ，那么下列命题成立的是（）A．若α、β是第一象限角，则cosα＞cosβB．若α、β是第二象限角，则tanα＞tanβC．若α、β是第三象限角，则cosα＞cosβD．若α、β是第四象限角，则tanα＞tanβ【考点】G3：象限角、轴线角．【专题】11 ：计算题．【分析】由于题中条件没有给出角度的范围，不妨均假定0≤α，β≤2π，结合三角函数的单调性加以解决．【解答】解：若α、β同属于第一象限，则，cosα＜cosβ；故A 错．第二象限，则，tanα＜tanβ；故B错．第三象限，则，cosα＜cosβ；故C错．第四象限，则，tanα＞tanβ．（均假定0≤α，β≤2π．）故D正确．答选为D．【点评】本题考查三角函数的性质，三角函数的性质是三角部分的核心，主要指：函数的定义域、值域，函数的单调性、对称性、奇偶性和周期性．5．（5分）（2000•新课程）函数y=﹣xcosx的部分图象是（）A． B．C．D．【考点】3A：函数的图象与图象的变换；3M：奇偶函数图象的对称性；H7：余弦函数的图象．【专题】31 ：数形结合．【分析】由函数的表达式可以看出，函数是一个奇函数，因只用这一个特征不能确定那一个选项，故可以再引入特殊值来进行鉴别．【解答】解：设y=f（x），则f（﹣x）=xcosx=﹣f（x），f（x）为奇函数；又时f（x）＜0，此时图象应在x轴的下方故选：D．【点评】本题考查函数的图象，选择图象的依据是根据函数的性质与函数本身的局部特征．6．（5分）（2000•新课程）《中华人民共和国个人所得税法》规定，公民全月工资、薪金所得不超过800元的部分不必纳税，超过800元的部分为全月应纳税所得额，此项税款按下表分段累进计算：全月应纳税所得额税率不超过500元的部分5%超过500元至2000元的部分10%超过2000元至5000元的部分15%……某人一月份应交纳此项税款26.78元，则他的当月工资、薪金所得介于（）A．800～900元 B．900～1200元C．1200～1500元D．1500～2800元【考点】3B：分段函数的解析式求法及其图象的作法．【专题】16 ：压轴题；33 ：函数思想．【分析】首先理解所得税的征收方式，分别算得个人当月工资S≤800，S∈[800，1300]，S∈（1300，2800]时应缴的税额的最大值，然后再根据税款26.78元，确定工资额．【解答】解：设收入为S元，税款为M元，则当S≤800时，M=0；当S∈[800，1300]时，M≤500•5%=25；当S∈（1300，2800]时，M≤25+1500•10%=175．题设M=26.78，故S=1300+（26.78﹣25）÷10%=1317.8．故选：C．【点评】本题考查分段函数的应用问题．7．（5分）（2000•新课程）若a＞b＞1，P=，Q=（lga+lgb），R=lg，则（）A．R＜P＜Q B．P＜Q＜R C．Q＜P＜R D．P＜R＜Q【考点】7F：基本不等式及其应用．【专题】11 ：计算题．【分析】由平均不等式知．．【解答】解：由平均不等式知．同理．故选：B．【点评】本题考查均值不等式的性质和应用，解题时要注意公式的灵活运用．8．（5分）（2000•全国）以极坐标系中的点（1，1）为圆心，1为半径的圆的方程是（）A．B．C．ρ=2cos（θ﹣1） D．ρ=2sin （θ﹣1）【考点】Q4：简单曲线的极坐标方程．【专题】11 ：计算题．【分析】设圆上任意一点的极坐标为（ρ，θ），直接利用极径的长为1得到关于极角与极径的关系，化简即得圆的极坐标方程．【解答】解：设圆上任意一点的极坐标为（ρ，θ），则由半径为1得，，化简得，所求方程是ρ=2cos（θ﹣1）．故选：C．【点评】本题考查点的极坐标方程的求法，能在极坐标系中用极坐标刻画点的位置，体会在极坐标系和平面直角坐标系中刻画点的位置的区别．9．（5分）（2000•新课程）一个圆柱的侧面展开图是一个正方形，这个圆柱的全面积与侧面积的比是（）A．B．C．D．【考点】LE：棱柱、棱锥、棱台的侧面积和表面积；L5：旋转体（圆柱、圆锥、圆台）．【专题】11 ：计算题．【分析】设圆柱底面积半径为r，求出圆柱的高，然后求圆柱的全面积与侧面积的比．【解答】解：设圆柱底面积半径为r，则高为2πr，全面积：侧面积=[（2πr）2+2πr2]：（2πr）2=．故选：A．【点评】本题考查圆柱的侧面积、表面积，考查计算能力，是基础题．10．（5分）（2000•新课程）过原点的直线与圆x2+y2+4x+3=0相切，若切点在第三象限，则该直线的方程是（）A．y=B．y=﹣C．D．【考点】JE：直线和圆的方程的应用．【分析】画出图形，利用三角函数可以求直线的斜率，求出直线方程．【解答】解：如图，圆方程为（x+2）2+y2=12，圆心为A（﹣2，0），半径为1，．故选：C．【点评】本题考查直线和方程的应用，数形结合的数学思想，是基础题．11．（5分）（2000•新课程）过抛物线y=ax2（a＞0）的焦点F作一直线交抛物线于P、Q两点，若线段PF与FQ的长分别是p、q，则+等于（）A．2a B．C．4a D．【考点】KH：直线与圆锥曲线的综合问题．【专题】11 ：计算题；16 ：压轴题．【分析】设PQ直线方程是，则x1，x2是方程的两根，，同理q=x2r．由此可知+的值．【解答】解：如图：设PQ直线方程是，则x1，x2是方程的两根，，其中．同理q=x2r．从而===4a．故选：C．【点评】本题考查抛物线的性质，解题时要认真审题，仔细解答．12．（5分）（2000•全国）如图，OA是圆锥底面中心O到母线的垂线，OA绕轴旋转一周所得曲面将圆锥分成体积相等的两部分，则母线与轴的夹角为（）A．B．C．D．【考点】L3：棱锥的结构特征．【专题】11 ：计算题；13 ：作图题；15 ：综合题；16 ：压轴题．【分析】设过A点的一条母线为BC，其中B为顶点，过A点作OB的垂线交OB 于D，令圆锥体的体积为V，OC=R，DA=r，母线与轴夹角为∠OBA=∠β，求出上部两个圆锥的体积的和，再求出大圆锥的体积，两个之比为，然后求出β的值．【解答】解；设过A点的一条母线为BC，其中B为顶点，过A点作OB的垂线交OB于D，令圆锥的体积为V，OC=R，DA=r，母线与轴夹角为∠OBC=∠β将OBA看作是底面积相等的两个锥形，r2π•BD+r2π•0D=V r2π•OB=V…①V=R2π•OB…②由①、②得R2=2•r2（R=r），r=OA•COSβOA=R•COSβ，r=R•COS2β，COS2β==β=故选：D．【点评】本题考查圆锥的结构特征，考查分析问题解决问题的能力，是基础题．二、填空题（共4小题，每小题4分，满分16分）13．（4分）（2000•全国）乒乓球队的10名队员中有3名主力队员，派5名参加比赛，3名主力队员要安排在第一、三、五位置，其余7名队员选2名安排在第二、四位置，那么不同的出场安排共有252种（用数字作答）．【考点】D9：排列、组合及简单计数问题．【专题】11 ：计算题．【分析】由题意知3名主力队员要安排在第一、三、五位置，其余7名队员选2名安排在第二、四位置，根据分步计数原理知共有A33A72，实际上是选出两个，再在两个位置上排列．【解答】解：∵3名主力队员要安排在第一、三、五位置，其余7名队员选2名安排在第二、四位置，∴根据分步计数原理共有A33A72=3•2•1•7•6=252．故答案为：252．【点评】排列与组合问题要区分开，若题目要求元素的顺序则是排列问题，排列问题要做到不重不漏，有些题目带有一定的约束条件，解题时要先考虑有限制条件的元素．14．（4分）（2000•新课程）椭圆的焦点F1、F2，点P为其上的动点，当∠F1PF2为钝角时，点P横坐标的取值范围是为：．【考点】K4：椭圆的性质．【专题】11 ：计算题．【分析】设p（x，y），根据椭圆方程求得两焦点坐标，根据∠F1PF2是钝角推断出PF12+PF22＜F1F22代入p坐标求得x和y的不等式关系，求得x的范围．【解答】解：如图，设p（x，y），则，且∠F1PF2是钝角⇔x2+5+y2＜10．故答案为：．【点评】本题主要考查了椭圆的简单性质和解不等式．属基础题．15．（4分）（2000•新课程）设{a n}是首项为1的正项数列，且（n+1）a n+12﹣na n2+a n+1a n=0（n=1，2，3，…），则它的通项公式是a n=．【考点】8H：数列递推式．【专题】11 ：计算题；16 ：压轴题．【分析】先对（n+1）a n+12﹣na n2+a n+1a n=0进行化简得到，再由累乘法可得到数列的通项公式是a n．【解答】解：∵（n+1）a n+12﹣na n2+a n+1a n=0∴（另解﹣a n不合题意舍去），∴•…•=，即，故答案为：．【点评】本题主要考查数列递推关系式的应用和累乘法．求数列通项公式的一般方法﹣﹣公式法、累加法、累乘法、构造法等要熟练掌握．16．（4分）（2000•新课程）如图，E、F分别是正方体的面ADD1A1、面BCC1B1的中心，则四边形BFD1E在该正方体的面上的射影可能是②③．（要求：把可能的图的序号都填上）【考点】L7：简单空间图形的三视图．【专题】13 ：作图题；16 ：压轴题．【分析】由三视图的定义研究四边形BFD1E在该正方体的面上的射影可分为：上下、左右、前后三个方向的射影，由于线是由点确定的，故研究四边形的四个顶点在三个投影面上的射影，再将其连接即可得到三个视图的形状，按此规则对题设中所给的四图形进行判断即可．【解答】解：因为正方体是对称的几何体，所以四边形BFD1E在该正方体的面上的射影可分为：上下、左右、前后三个方向的射影，也就是在面ABCD、面ABB1A1、面ADD1A1上的射影．四边形BFD1E在面ABCD和面ABB1A1上的射影相同，如图②所示；四边形BFD1E在该正方体对角面的ABC1D1内，它在面ADD1A1上的射影显然是一条线段，如图③所示．故②③正确故答案为②③【点评】本题考点是简单空间图形的三视图，考查根据作三视图的规则来作出三个视图的能力，三视图的投影规则是：“主视、俯视长对正；主视、左视高平齐，左视、俯视宽相等”．本题是根据三视图投影规则来选择正确的视图，三视图是高考的新增考点，不时出现在高考试题中，应予以重视三、解答题（共6小题，满分74分）17．（12分）（2000•全国）已知函数，x∈R．（1）当函数y取得最大值时，求自变量x的集合；（2）该函数的图象可由y=sinx（x∈R）的图象经过怎样的平移和伸缩变换得到？【考点】HJ：函数y=Asin（ωx+φ）的图象变换；H5：正弦函数的单调性．【专题】11 ：计算题．【分析】（1）利用二倍角公式和两角和的正弦函数化简函数为y=sin（2x+）+，借助正弦函数的最大值，求出函数y取得最大值时，自变量x的集合；（2）由y=sinx（x∈R）的图象，按照先φ，向左平移，把得到的图象上各点横坐标缩短到原来的倍（纵坐标不变），图象上各点纵坐标缩短到原来的倍（纵坐标不变），最后把得到的图象向上平移个单位长度，得到函数y=sin （2x+）+的图象；【解答】解：（1）y=cos2x+sinxcosx+1=（2cos2x﹣1）++（2sinxcosx）+1=cos2x+sin2x+=（cos2x•sin+sin2x•cos）+=sin（2x+）+（6分）y取得最大值必须且只需2x+=+2kπ，k∈Z，即x=+kπ，k∈Z．所以当函数y取得最大值时，自变量x的集合为{x|x=+kπ，k∈Z}（8分）（2）将函数y=sinx依次进行如下变换：①把函数y=sinx的图象向左平移，得到函数y=sin（x+）的图象；②把得到的图象上各点横坐标缩短到原来的倍（纵坐标不变），得到函数y=sin（2x+）的图象；③把得到的图象上各点纵坐标缩短到原来的倍（横坐标不变），得到函数y=sin （2x+）的图象；④把得到的图象向上平移个单位长度，得到函数y=sin（2x+）+的图象；综上得到函数y=cos2x+sinxcosx+1的图象．（12分）【点评】本小题主要考查三角函数的图象和性质，考查利用三角公式进行恒等变形的技能以及运算能力．注意函数图象的变换的顺序：→φ→ω→A→b的过程．18．（12分）（2000•新课程）如图，已知平行六面体ABCD﹣A1B1C1D1的底面ABCD 是菱形，且∠C1CB=∠C1CD=∠BCD=60°．（1）证明：C1C⊥BD；（2）假定CD=2，CC1=，记面C1BD为α，面CBD为β，求二面角α﹣BD﹣β的平面角的余弦值；（3）当的值为多少时，能使A1C⊥平面C1BD？请给出证明．【考点】LO：空间中直线与直线之间的位置关系；LW：直线与平面垂直；MJ：二面角的平面角及求法．【专题】11 ：计算题；14 ：证明题．【分析】（1）要证线线垂直，只要证线面垂直，由线面垂直的判定定理，只要找到一条直线垂直于两条相交直线即可，由题意易得，∴△C1BD为等腰三角形，故AC和BD交于O，则C1O⊥BD，又AC⊥BD，命题可证．（2）由（1）知∠C1OC是二面角α﹣BD﹣β的平面角，由余弦定理解△C1OC即可．（3）可先猜测的值，然后证明A1C⊥平面C1BD．只要证A1C⊥平面C1BD内的两条相交直线即可，易得BD⊥平面AC1，BD⊥A1C．同理再证BC1⊥A1C即可．【解答】解：（1）证明：如图连接AC、设AC和BD交于O，连接C1O∵四边形ABCD是菱形，∴AC⊥BD，BD=CD．又∵∠BCC1=∠DCC1，C1C=C1C，∴△C1BC≌△C1DC∴C1B=C1D，∵DO=OB∴C1O⊥BD，但AC⊥BD，AC∩C1O=O，∴BD⊥平面AC1C，又C1C⊂平面AC1C∴C1C⊥BD．（2）解：由（1）知AC⊥BD，C1O⊥BD，∴∠C1OC是二面角α﹣BD﹣β的平面角．在△C1BC中，BC=2，C1C=，∠BCC1=60°，∴C1B2=22+（）2﹣2×2××cos60°=∵∠OCB=30°，∴OB=BC=1∴C1O2=C1B2﹣OB2=，∴C1O=即C1O=C1C．作C1H⊥OC，垂足为H．∴点H是OC的中点，且OH=，所以cos∠C1OC==．（3）如图：当=1时，能使A1C⊥平面C1BD由（1）知，BD⊥平面AC1C，∵A1C⊂平面AC1C，∴BD⊥A1当=1时，平行六面体的六个面是全等的菱形，同BD⊥A1C的证法可得BC1⊥A1C，又BD∩BC1=B，∴A1C⊥平面C1BD．【点评】本小题主要考查直线与直线、直线与平面的关系，逻辑推理能力．19．（12分）（2000•新课程）设函数，其中a＞0，（1）解不等式f（x）≤1；（2）证明：当a≥1时，函数f（x）在区间[0，+∞）上是单调函数．【考点】7E：其他不等式的解法；3E：函数单调性的性质与判断．【专题】11 ：计算题；15 ：综合题；32 ：分类讨论．【分析】（1）不等式f（x）≤1，转化为一元二次不等式组，根据a的范围求解不等式即可．（2）当a≥1时，利用函数单调性的定义，即：在区间[0，+∞）上任取x1，x2，使得x1＜x2，证明f（x1）﹣f（x2）＞0，从而证明函数f（x）在区间[0，+∞）上是单调减函数．【解答】（1）解：不等式f（x）≤1即，由此得1≤1+ax，即ax≥0，其中常数a＞0．所以，原不等式等价于即（3分）所以，当0＜a＜1时，所给不等式的解集为；当a≥1时，所给不等式的解集为{x|x≥0}．（6分）（2）证明：在区间[0，+∞）上任取x1，x2使得x1＜x2==∵，∴，又x1﹣x2＜0，∴f（x1）﹣f（x2）＞0，即f（x1）＞f（x2）．所以，当a≥1时，函数f（x）在区间[0，+∞）上是单调递减函数．（12分）【点评】本小题主要考查不等式的解法、函数的单调性等基本知识，分类讨论的数学思想方法和运算、推理能力．20．（12分）（2000•新课程）（1）已知数列{c n}，其中c n=2n+3n，且数列{c n+1﹣pc n}为等比数列，求常数p；（2）设{a n}、{b n}是公比不相等的两个等比数列，c n=a n+b n，证明数列{c n}不是等比数列．【考点】87：等比数列的性质．【专题】11 ：计算题；14 ：证明题；16 ：压轴题．﹣pc n）2=（c n+2﹣pc n+1）（c n﹣pc n 【分析】（1）利用等比中项的性质可推断出（c n+1），整理后求得p的值．﹣1（2）设{a n}、{b n}的公比分别为p、q，为证{c n}不是等比数列只需证c22≠c1•c3．利用等比数列的通项公式分别表示出a n和b n，表示出c22的表达式，整理由于p≠q，推断出p2+q2＞2pq，进而推断出c22≠c1•c3，进而可知{c n}不是等比数列．【解答】解：（1）因为{c n﹣pc n}是等比数列，故有+1（c n﹣pc n）2=（c n+2﹣pc n+1）（c n﹣pc n﹣1），+1将c n=2n+3n代入上式，得[2n+1+3n+1﹣p（2n+3n）]2=[2n+2+3n+2﹣p（2n+1+3n+1）]•[2n+3n﹣p（2n﹣1+3n﹣1）]，即[（2﹣p）2n+（3﹣p）3n]2=[（2﹣p）2n+1+（3﹣p）3n+1][（2﹣p）2n﹣1+（3﹣p）3n﹣1]，整理得（2﹣p）（3﹣p）•2n•3n=0，解得p=2或p=3．（2）设{a n}、{b n}的公比分别为p、q，p≠q，c n=a n+b n．为证{c n}不是等比数列只需证c22≠c1•c3．事实上，c22=（a1p+b1q）2=a12p2+b12q2+2a1b1pq，c1•c3=（a1+b1）（a1p2+b1q2）=a12p2+b12q2+a1b1（p2+q2）．由于p≠q，p2+q2＞2pq，又a1、b1不为零，因此c22≠c1•c3，故{c n}不是等比数列．【点评】本小题主要考查等比数列的概念和基本性质，推理和运算能力．21．（12分）（2000•全国）某蔬菜基地种植西红柿，由历年市场行情得知，从二月一日起的300天内，西红柿场售价与上市时间的关系如图一的一条折线表示；西红柿的种植成本与上市时间的关系如图二的抛物线段表示．（1）写出图一表示的市场售价与时间的函数关系式p=f（t）；写出图二表示的种植成本与时间的函数关系式Q=g（t）；（2）认定市场售价减去种植成本为纯收益，问何时上市的西红柿纯收益最大？（注：市场售价各种植成本的单位：元/102㎏，时间单位：天）【考点】3H：函数的最值及其几何意义；5C：根据实际问题选择函数类型．【专题】12 ：应用题；16 ：压轴题；33 ：函数思想．【分析】（1）观察图一可知此函数是分段函数（0，200）和（200，300）的解析式不同，分别求出各段解析式即可；第二问观察函数图象可知此图象是二次函数的图象根据图象中点的坐标求出即可．（2）要求何时上市的西红柿纯收益最大，先用市场售价减去种植成本为纯收益得到t时刻的纯收益h（t）也是分段函数，分别求出各段函数的最大值并比较出最大即可．【解答】解：（1）由图一可得市场售价与时间的函数关系为（2分）由图二可得种植成本与时间的函数关系为．（4分）（2）设t时刻的纯收益为h（t），则由题意得h（t）=f（t）﹣g（t），即h（t）=（6分）当0≤t≤200时，配方整理得h（t）=．所以，当t=50时，h（t）取得区间[0，200]上的最大值100；当200＜t≤300时，配方整理得h（t）=，所以，当t=300时，h（t）取得区间（200，300）上的最大值87.5（10分）、综上，由100＞87.5可知，h（t）在区间[0，300]上可以取得最大值100，此时t=50，即从二月一日开始的第50天时，上市的西红柿纯收益最大．（12分）【点评】本小题主要考查由函数图象建立函数关系式和求函数最大值的问题，考查运用所学知识解决实际问题的能力．22．（14分）（2000•新课程）如图，已知梯形ABCD中|AB|=2|CD|，点E分有向线段所成的比为λ，双曲线过C、D、E三点，且以A、B为焦点，当时，求双曲线离心率e的取值范围．【考点】KC：双曲线的性质．【专题】11 ：计算题；16 ：压轴题．【分析】首先以AB的垂直平分线为γ轴，直线AB为x轴，建立直角坐标系，记，其中为双曲线的半焦距，h是梯形的高，用定比分点坐标公式可求得x0和y0的表达式．设双曲线方程，将点C、E坐标和e分别代入双曲线方程联立后求得e和h的关系式，根据λ的范围求得e的范围．【解答】解：如图，以AB的垂直平分线为γ轴，直线AB为x轴，建立直角坐标系xOγ，则CD⊥γ轴．因为双曲线经过点C、D，且以A、B为焦点，由双曲线的对称性知C、D关于γ轴对称，依题意，记，其中为双曲线的半焦距，h是梯形的高，由定比分点坐标公式得，．设双曲线的方程为，则离心率，由点C、E在双曲线上，将点C、E坐标和代入双曲线的方程，得，①．②由①式得，③将③式代入②式，整理得，故由题设得，，解得，所以，双曲线的离心率的取值范围为[]．【点评】本小题主要考查坐标法、定比分点坐标公式、双曲线的概念和性质，推理、运算能力和综合应用数学知识解决问题的能力．考点卡片1．函数的图象与图象的变换【函数图象的作法】函数图象的作法：通过如下3个步骤（1）列表；（2）描点；（3）连线．解题方法点拨：一般情况下，函数需要同解变形后，结合函数的定义域，通过函数的对应法则，列出表格，然后在直角坐标系中，准确描点，然后连线（平滑曲线）．命题方向：一般考试是以小题形式出现，或大题中的一问，常见考题是，常见函数的图象，有时结合函数的奇偶性、对称性、单调性知识结合命题．【图象的变换】1．利用描点法作函数图象其基本步骤是列表、描点、连线．首先：①确定函数的定义域；②化简函数解析式；③讨论函数的性质（奇偶性、单调性、周期性、对称性等）．其次：列表（尤其注意特殊点、零点、最大值点、最小值点、与坐标轴的交点等），描点，连线．2．利用图象变换法作函数的图象（1）平移变换：y=f（x）a＞0，右移a个单位（a＜0，左移|a|个单位）⇒y=f（x﹣a）；y=f（x）b＞0，上移b个单位（b＜0，下移|b|个单位）⇒y=f（x）+b．（2）伸缩变换：y=f（x）y=f（ωx）；y=f（x）A＞1，伸为原来的A倍（0＜A＜1，缩为原来的A倍）⇒y=Af（x）．（3）对称变换：y=f（x）关于x轴对称⇒y=﹣f（x）；y=f（x）关于y轴对称⇒y=f（﹣x）；y=f（x）关于原点对称⇒y=﹣f（﹣x）．（4）翻折变换：y=f（x）去掉y轴左边图，保留y轴右边图，将y轴右边的图象翻折到左边⇒y=f （|x|）；y=f（x）留下x轴上方图将x轴下方图翻折上去y=|f（x）|．解题方法点拨1、画函数图象的一般方法（1）直接法：当函数表达式（或变形后的表达式）是熟悉的基本函数或解析几何中熟悉的曲线时，可根据这些函数或曲线的特征直接作出．（2）图象变换法：若函数图象可由某个基本函数的图象经过平移、翻折、对称得到，可利用图象变换作出，但要注意变换顺序，对不能直接找到熟悉函数的要先变形，并应注意平移变换与伸缩变换的顺序对变换单位及解析式的影响．（3）描点法：当上面两种方法都失效时，则可采用描点法．为了通过描少量点，就能得到比较准确的图象，常常需要结合函数的单调性、奇偶性等性质讨论．2、寻找图象与函数解析式之间的对应关系的方法（1）知图选式：①从图象的左右、上下分布，观察函数的定义域、值域；②从图象的变化趋势，观察函数的单调性；③从图象的对称性方面，观察函数的奇偶性；④从图象的循环往复，观察函数的周期性．利用上述方法，排除错误选项，筛选正确的选项．（2）知式选图：①从函数的定义域，判断图象的左右位置；从函数的值域，判断图象的上下位置；②从函数的单调性，判断图象的变化趋势；③从函数的奇偶性，判断图象的对称性．④从函数的周期性，判断图象的循环往复．利用上述方法，排除错误选项，筛选正确选项．。

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2010年1月高等教育自学考试英语语法试题课程代码：10056请将答案填在答题纸相应位置上Ⅰ、单项选择题（本大题共19小题，每题1分，共19分）Multiple choices: for each of the following sentences, there are four choices marked A, B, C and D, choose the one that best completes the sentence (19 points, 1 point for each):1. In the past men generally preferred that their wives ____________ in the home.A. workedB. would workC. workD. were working2. ____________ of the burden of ice, the balloon climbed up and drifted to the South.A. To be freeB. FreeingC. To freeD. Freed3. Those part-time students expect____________ some jobs on campus during the coming summer vacation.A. to offerB. be offeredC. to be offeredD. been offered4. Some bosses dislike____________ people to share their responsibilities; they keep all important matters tightly in their own hands.A. to allowB. allowingC. been allowedD. be allowed5. From the tears in Tom’s eyes we can deduce that something sad____________.A. must have occurredB. might be occurringC. would have occurredD. should occur6. Do they have____________ air-conditioners for cooling the rooms in summer?A. many aB. enoughC. a great deal ofD. a bit of7. There is____________ iron in this mine than in that mine.A. muchB. a great deal of10056# 英语语法试题第1 页共4 页C. lessD. a lot of8. ____________ work has to be done before the plant goes into operation.A. MuchB. DoubleC. A numberD. Neither9. Don’t worry about the seats. There are____________ chairs in the room.A. plenty ofB. anyC. bothD. most10. The students spent____________ their time working in the fields.A. bothB. mostC. moreD. half11. His ill-health may well be____________ malnutrition.A. due toB. next toC. thanks toD. up to12. ____________ the many delays, we shall get to our destination in time.A. In the way ofB. In case ofC. In spite ofD. In the event of13. Expenditure is twenty pounds____________ income.A. in point ofB. in the pay ofC. in the wake ofD. in excess of14. I consulted the lawyer____________ my claim.A. in view ofB. with reference toC. with a view toD. with an eye to15. Agriculture is the country’s chief source of wealth, wheat____________ by far the biggest cereal crop.A. isB. areC. to beD. being16. He____________ to escape but his conscience prevented him from doing that.A. had intendedB. has intendedC. had been intendingD. has been intending10056# 英语语法试题第2 页共4 页17. The policy____________ made, the next problem was how to carry it out.A. having beenB. beingC. had beenD. was18. All flights____________ because of the storm, they decided to take the train.A. having canceledB. were canceledC. having been canceledD. have been canceled19. ____________ no cause for alarm, the old man went back to his bedroom.A. There wasB. SinceC. BeingD. There beingⅡ、填空题（本大题共10小题，每题1分，共10分）：请用所给动词的虚拟形式填空Fill in the blanks with the proper subjunctive form of the verbs in brackets (10 points, 1 point for each):1. I recommend that favorable consideration ____________ (be) given to his application for admission.2. If he ____________ (be) here now, I don’t know you’d have the guts to flirt with his secretary.3. My father suggested that I ____________ (enter) Harvard rather than to start a business now.4. When I entered his big office that afternoon, he didn’t say a word, nor did he raise his head, as if I ____________ (be) invisible.5. Far ____________ (be) it from me to turn my back to her when she is in need of my help.6. He ran away lest they ____________ (catch) him.7. I wish I ____________ (be) taller and stronger so that they wouldn’t dare to treat me by rough handling.8. It is desirable that everybody ____________ (mind) his or her own business.9. I propose that a woman member of the committee ____________ (be) appointed for the chair.10. It is very important that the textbooks ____________ (be) available before school starts.Ⅲ、名词解释（本大题共5小题，每题3分，共15分）Define the following terms with examples (15 points, 3 points for each):1. bound morpheme2. collective nouns3. foreign plurals10056# 英语语法试题第3 页共4 页4. conversion5. simple sentenceⅣ.句子改写题（本大题共10小题，每题2分，共20分）Rewrite the following sentences as required (20 points, 2 points for each):A. Rewrite the following sentences using passive voice:1. All the students who are applying for the government loan must observe this rule.2. A group of children built the sand castle.3. The removal men damaged our grandfather’s clock.4. This studio will probably blow up your photograph well.5. The government must put an end to the political crisis as soon as possible.B. Combining sentences using the relative clause:6. My special gratitude goes to Professor Weir. Without his help this project would have been impossible.7. She was afraid people would consider her ambitious and aggressive. She was actually not ambitious or aggressive.8. He is a psychiatrist. I know him. He can give you advice.9. He is a Jack of all trades. He has done thousands of things. He has accomplished nothing.10. When I was in Stratford, I visited the house. Shakespeare is said to have lived there for several years before he left for London.Ⅴ.问答题（本大题共6小题，共36分）Answer the following questions with the help of examples (36 points):1. What are determiners? (5 points)2. What are the two major semantic categories of modal auxiliaries? (6 points)3. When adjectives are used in the dynamic sense, what are their syntactic and semantic features?(5 points)4. What is the difference between coordination and subordination? (6 points)5. Discuss various grammatical forms that disjuncts may take. (10 points)6. As a future time expression, what special meaning does the simple present impart? (4 points)10056# 英语语法试题第4 页共4 页。