(好资料)2005-2008北京大学自主招生保送生笔试考试试题

2008年北京大学自主招生 保送生笔试考试试题一，数学：1 求证：边长为1的正五边形对角线长为（5+1）/ 2。2 已知六边形AC1BA1CB1中AC1 = AB1，BC1 = BA1，CA1 = CB1，A+B+C=A1+B1+C1， 求证：ABC 面积是六边形AC1BA1CB1的一半。3 已知：4 举行排球单循坏赛，南方球队比北方球队多9支，南方球队总得白银谷一书的读后感分是北方球队的9倍。 求证：冠军是一支南方球队。（胜得1分 败得0分）5 （仅理科同学做）在O-xyz空间坐标系中：xoy平面中 0y2-x2 绕 y 轴旋转一周构成一个不透光立体。在点(1,0,1)设置一光源，xoy 平面内有一以原点为圆心的圆C，被光照到的长度为2，求C上未被照到的长度。二，语文：第一大题（本题共3小题，30分，阅读下文，完成13题）然惠施之口谈自以为最贤曰天地其壮乎施存雄而无数南方有倚人焉曰黄缭问天地所以不坠不陷风雨雷霆之故惠施不辞而应不虑而对遍为万物说说而不休多而无已犹以为寡益之以怪以反人为实而欲以胜人为名是以与众不适也弱于德强于物其涂隩矣由天地之道观惠施之能其由一蚊一虻之劳者也其于物也何夫充一尚可曰愈贵道几矣惠施不能以此自宁散于万物而不厌卒以善辩为名惜乎惠施之才骀荡而不得逐万物而不反是穷响以声形与影竞走悲夫（庄子杂篇天下）一、上文加标点。（9分）二、解释文中加点的字词（6分）：倚人：隩：庸充一：充一：骀荡：穷：三、根据你对这段文字的理解，回答下列问题（15分）：惠施口辩之学具有哪些特点？庄子是如何评价惠施口辩之学的？你是否同意庄子的看法？为什么？第二大题（本题公四小题，30分。阅读下面的作品，完成14题）读山赵园，我不大爱山；或不如说，较之山，更喜欢水。这无关“仁”“智”，不过个人趣味而已。我总觉得，山较之水远于“人境”。水像是天然的“属人”的，有水源处即有人烟；而山，则意味着对于人的挑战。也因如此，山民比起水民，其生存更有悲壮的颜色。据说南方的山，多为徙自中原的客家据有。给他们留下山地，不消说决非出于土著的好意。在我看来，山民之于山与其说是倚托，不如说是对抗。山民是在与山的对抗中延续其历史的。古代皇帝的陵墓称“山陵”。你去看看南方的浅山，有不少处俨若鬼国。即使如香港新界那样繁华的所在，沙田周围的山，也有被死人密密麻麻地占了去的。这是否也在提示着山的更宜于死人而非生人？还有被人抱怨占尽名山的僧伽，也像是证明着山的“出世间”，至少证明了山的适于营造禅境。八九年的乘客轮过三峡，为刀劈斧削般的山石所震撼，只觉得造物的严酷：这样的山石更像是神造天设的有关生存绝境的象征。更令人惊叹的，是那山腰间的一线，有看起来极小的孩子背了书包在走。你竟看不出他从哪里走出来的，又能走到哪里去，他的身前身后，只是一色的石壁，寻不出一点人的痕迹。你由那些山的巨大体量，和坚硬的线条，读出的是对于人的渺小与其无力的嘲弄移动在山腰间的，是那样小小的一个人。九O年初冬在湘西的猛洞河“漂流”时，我也这样耐心地搜寻过人迹。那倒是一片葱蓉的山，正如国画山水，却也如国画山水似的远于活的人生你徒然地想在那些山壁上找一处能安置一椽的所在，同样发现了那山是天然地不宜于人的。它只是人的观赏对象，它不属于活的人生。我也看过夜的山。在那庞大的阴影上，吸引我的，永远是似虚悬空际的一两星灯火。我会久久地揣想着那灯下的一份生活，似亲身领受了沦肌浃肤的凄清。有水源处即有人聚；而山，提示的从来更是人的宿命的孤独与寂寞。差不多因为同样的原因，我对国画，总缺乏鉴赏的热情。我也如读真的山，禁不住要在其上搜寻世俗生活的迹象。国画山水间也有人，高士隐逸：对于山与人的关系，这到是个恰切的诠释。我也知道，我说这些，等于自成了既乏艺术素质又乏哲学领悟能力，自承了对于“抽象性”的拒斥，经验与趣味的不可救药的平庸以至于“俗”。因此在写了山之后，我并不自信能读山，读懂了山。我由“山”上读出的，或许只是我本人顽强的世俗性格。我最后得承认，我是在一片极大的平原上、且在一条极大的河边长大的。如果我申请写在这里的只是一个平原人对山的“读解”，或许不至于使爱山者感到冒犯？一九九四年六月一下列对文章内容的理解，正确的两项是（4分）A本文标题中的“读”字透露着把“山”当成一本大书进行领悟的含义。B文章开头所揭示的人与山的对抗性构成了本文的一个贯穿性行文线索。C结尾道出作者不爱山的真正原因在于作者是在平原与大河边长大的。D作者之所以对国画缺乏鉴赏的热情，是因为其中缺乏对人的描画。E本文择取了自己观山的几个经验断片，表达了对山与人的关系的悬想。二文章开头“无关仁智”的典故来自论语中的“_,_.”（2分）文章倒数第二段称三回答下面问题（14分）：1文章倒数第二段称题：“山，提示的从来更是人的宿命的孤独与寂寞。”你是否同意这一判断？请简单给出你的理由。（4分）答_。2最后一段，作者说：“我也知道，我说这些，等于自承了既乏艺术气质又乏哲学领悟能力，自承了对于抽象性的拒斥，经验与趣味的不可救药的平庸以至于俗。”品读全文，你觉得作者的自我评价是否准确？为什么？（6分）答_。3文章的第二段和结尾一段中各有一个问句，请谈谈问句的运用在本篇文章中所产生的效果。（4分）答_。四你本人爱山还是爱水？试用散文文体写出你自己“爱”的理由。（不超过100字，14分）答_。第三大题 作文（40分）阅读下面的材料，自选角度，自拟题目，写一偏议论文。文章不少于800字。有人认为：中华文化光辉灿烂，但其中也有严重的缺陷。权利文化、人才文化、财富文化，都有严重缺陷。比如人才文化的缺陷是，对实干的人求全责备，对不干事的人委曲求全。财富文化的主流就有问题不患寡而患不均，这个思想本身就是违背财富增长规律的。传统文化的缺陷，使中国人形成了普遍的文化理念，可以称之为“两恨文化”恨能人，恨富人。富人是有形资产的代表者，能人是无形资产的代表者，有形资产和无形资产是经济发展的两个翅膀。但是，我们传统文化中的“两恨文化”如同两把剪刀，总是不失时机地把这两个翅膀不断地剪掉，“两恨文化”2006年北京大学自主招生 保送生笔试考试试题一，数学：1、设OABC是棱长为1的正四面体。OB中点为M，ON：NC=1：2，如图，求过A，M，N三点平面与O点距离d。2、设，g（k）是k的多项式。（1）、设f（a）与 k无关，求常数a。（2）、求一次多项式g（k），使得f（g(k)）与k无关。（3）、设g（k）是二次以上多项式，证明f（g(k)）必与k有关。（4）、设,为f（x）=0的解。试求,满足的议程，并用图形表示出来，其中取作横坐标轴，取作为纵坐标轴。（5）、如果,是整数，求出与这样,对应的所有k值。3、F1，F2是椭圆 （ab0）的焦点。（1）、设l是该椭圆的一条切线，H1，H2分别是F1，F2在l上的垂足。证明：F1H1 F2H2=b2。（2）、设l1，l2是该椭圆过椭圆外一点P的两条切线，切点分别为T1，T2。证明：F1PT1=F2PT2。5、函数f（x）的导函数f(x)连续，且f（0）=0，f(0)=a。记曲线y=f（x）与p（t,0）最近的点为Q(s,f(s)，求极限值二、语文：1、请写出一个由四个不同的汉字组长的短语，要求每个字的偏旁部首相同并且意思清楚。（8分）2、请写一句由十个不同的汉字组成的话，要求意思清楚并且每个字的声母都是卷舌音，zh、ch、sh、r。（10分）3、用文言拟写一段意思完整的话，不超过50字。要求其中至少出现三个次“之”字，并且每次的用法不同。（12分）4、先默写一首古人的五言绝句，然后每句在适当处增加两个字，改写成七言绝句。要求基本合乎格律，意思连贯完整。思想意境可以与原诗不同。（30分：默写10分，改写20分）默写：改写：5、作文：贪官检讨某官员贪污腐败被揭发查处，在单位全体大会上做检讨。请模拟该贪官的心理和口气写一篇检讨发言，要求该检讨表面上深刻严肃，实际上避重就轻，言辞华而不实，堆砌雕琢，企图敷衍了事。字数600700。（40分）2007年北京大学自主招生 保送生笔试考试试题一，数学：1：设f(x)=x2-53x+196+| x2-53x+196|.求f(1)+f(2)+f(50)的值。（25分）2：证明：对任何实数k方程x2+y2-2kx-(6+2k)y-2k-31=0过两个定点。（25分）3：解方程组（25分）4：（仅理科同学做）设长方体的三边长为a,b,c 。且a b c.设P和Q为此长方形最远的两个顶点。 求从P沿长方形表面至Q最短路程的长度。（25分）二，英语：Part I Vocabulary and Structure(20%)Directions:There are 20 incomplete sentences in this part. For each sentence there are 4 choices marked A), B), C) and D). Choose the ONE answer that best completes the sentence. Then write the corresponding letter onAnswer Sheet I.1. Because he was seriously ill， hein bed waiting for the doctor to come.A. layB. laidC. liedD. lain2.“Perhaps you should go home now.”“No, I insisthere a while longer.”A. to stayB. for stayingC. on stayingD. to be staying3. As you know, the workersa fair wage for their hard work.A. askedB. declaredC. appliedD. demanded4. In my opinion, if you fail, dont lose your heart, just.A. dont stop to tryB. keep on tryingC. not give up tryingD. continue your tries5. The factthat a lat of factories were faced with a very difficult situation.A. informedB. intendedC. introducedD. indicated6. It would bea risk to let the child go to school by himself.A. followingB. passingC. runningD. carrying7. Take, for example, thesituations that doctors met with almost every night.A. emergenceB. emergencyC. encourageD. entertainment8. It is recorded that much of London wasby a big fire in the seventeenth century.A. destroyedB. damagedC. declinedD. decreased9. Teachers have been awarethe need for the newer methods used in schools.A. aboutB. forC. ofD. with10. In this way, the school and the home join forces in bringingthe fullest development of youngsters abilities.A. backB. downC. overD. about11. By the time you got to Greenwich youthe most historic parts of London.A. will be seeingB. will seeC. are going to seeD. will have seen12.“I have forgotten to buy sandwiches.”“It doesnt matter. You can have.”A. some of usB. our someC. some of oursD. some of our13. If not for these armed forces, the situation therewhat it is today.A. is neverB. would never have beenC. will never beD. was never14. Not onlyany harm, it helps digestion and is good for health.A. does the germ not do youB. that the germ will not do youC. the germ does not do youD. that the germ will do you15. It is clear that a great deal of energythis way.A. are wastedB. were wastedC. has wastedD. is wasted16. Both the buses will stop at the Peace Hotel, and you can takeof them to get there.A. eachB. eitherC. anyD. both17. She asked almost everyone she knew what kind of clothesfor the party.A. wearingB. wearC. to wearD. wears18. Spring, we may perhaps look forward to better weather.A. having comeB. has comeC. having teen comeD. is coming19. They were expecting the doctor to finish the operationdawn.A. onB. tillC. inD. before20.your daughter is well again, you no longer have anything to worry about.A. WhenB. SinceC. ThoughD. AfterPart II Reading Comprehension (40%)Directions:There are 2 passages in this part. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A), B), C) and D). You should decide on the best choice and mark the corresponding letter onAnswer Sheet I.Passage IMr. Richards was quite good at shooting with a rifle (来福枪), and he had taken part in several competitions in his small town. He had never actually won a prize, but each time he had done well and once he had come in fourth.Then he had to go to a big city on business for a month, and as he had noting much to do in the evenings, he joined the local rifle club, and spent several pleasant evenings shooting there.The rifle club had a very good first team, which used to take part in a lot of important shooting competitions. One of these took place while Mr. Richards was with them, and of course he went to see it. But one of the members of the clubs team suddenly fell ill just before the match, and the captain had to choose somebody else to take his place in a hurry. He had heard that Mr. Richards had taken part in several competitions already, and he had seen for himself at the club that, although he was not up to the standard of the clubs first team, he was quite a good shot. He therefore invited him to take the sick mans place.Mr. Richards felt greatly honored to be asked to shoot for such a good team, but he also felt very nervous, because he was afraid of making a fool of himself and letting down his team.In fact, he was so nervous that he could not keep his hand from trembling while he was shooting, with the result that he did very badlyin the competition .When he took his score card to his captain , he said ,“After seeing my score , I feel like going outside and shooting myself.”The captain looked at the card for a few minutes and then said ,“Well, you had better take two bullets with you if you do that.”21、How did it happen that Mr. Richards took part in the competition for the clubs first team?A) He was a member of the clubs first team.B )He was a first-rate shot in competitions.C) He wanted to take the sick mans place.D) He took part in the competition at the invitation of the captain.22、How did Mr. Richards feel after the competition?A) He felt uncomfortable.B) He was very much shocked.C) He felt very much ashamed.D) He was very angry with himself23、According to the passage, which of the following was true of Mr. Richards?A) Hejoinedthe local club to compete with other members.B) He was a man who had a strong sense of self-respect.C) He always came in first in all the competitions he took part in.D) He was full of confidence before the competition.24、What does the last sentence“You had better take two bullets with you if you do that.”mean?A) You are such a dad shot that youmightmiss the target while trying to kill yourself.B) The quality of the bullets is very dad. You had better take an extra one.C) One bullet is not powerful enough to kill a person.D) There are two bullets left in your rifle. You had better use them up.25、The tone of the last sentence is.A) humorousB) ironicalC) sadD) impolitePassage 2But enough of the joys of childhood. What about its pains? How many of us suffered during thosehappiest days of our lifeour schooldays? School is two things. It is the childs first taste of independence, the place where he must stand on hisown two feet, and stand up for himself. And it is the place where he gains the knowledge that is to prepare him for life in the outside, grown-up world of jobs and running a house and what to do in ones spare time.Nobody can govern childrensrelationshipswith each other. There must be worked out by each child individually. But the question of what children learn, and how they should learn it, is continually being debated and re-debated. Nobody dares any longer to defend the old system, which was good enough for our grandparents. The theorists of modern psychology(心理学)have stepped in to argue that we must understand the needs of children. Children are not just small adults; they are childrenwho must be respected as such.Well, you may say ,this is as it should be,anda good idea. But think further. What happens?Educationbecomes the responsibility not of teachers, but of psychologists. What happens then? Teaches worry too much about thepsychologicalimplications（含义）of their lessons, and forget about the subjects themselves. If a child dislikes a lesson, the teacher feels that it is his fault, not the childs. So teachers worry whether history isrelevantto modern young children. And do they dare to tell stories about violent battles? Or will this make the children themselves violent? Can they tell their classes about children of different races, or will this encourage racial hatred?You see, you can go too far. Influenced by education theorists, who have nothing better to do than write books about their ideas, teachers leave their teacher-training colleges filled with psychological ideas about children and their needs. Since onemodern methodrapidly replaces another, the poor kids will have had a good bellyful（过量）by the time they leave school.The result is that the children become bored and restless, and the teachers feel hopeless. The educational theorists invents new the theories; the parents are dissatisfied with their bad-tempered, ill-educated, undisciplined children, and blame the teachers. The children become violent: they get angry at both lessons and teachers, learn nothing, and play with knives in the classrooms. The teachers become frightened of the pupils, who areunableto keep control, and often leave the profession altogether.26、“The happiest days of our life”refer to the days when.A) we enjoyed childhoodB) many of us sufferedC) we enjoy independenceD) we were schoolchildren27、What the modern theoretical psychologists argue is that.A) nobody should defend the old systemB) children are adults though they are smallC) teachers should understand childrens needsD) children are better if they know what they learn28、What happens wheneducationbecomes the responsibility of psychologists?A) Teachers worry more about the subjects they usually teach.B) Teachers think more of the influence their lessons give onchildren.C) Teachers think of it more important to teach children history.D) Teachers dare to present lessons about violent battles.29、How do newly-qualified teachers go about their jobs?A) They use new methods and change them one after another.B) They make the children suffer over a long period.C) They make good preparations for their subjects.D) They fail to use their psychological training in their jobs.30、What is the result of this state of affairs?A) The teachers educate the children into a state of boredom.B) The parents are angry about their childrens knives.C) The children become restless and disappoint their parents.D) Neither teachers nor parents or children feel satisfied with the situation.PartTranslation(40%).Translate the underlinedsentencesin the following passage from English into Chinese. Write your translation on Answer Sheet :(20%)Thanks to the work of many scientists, we are now clear that many of the important earthquake（地震）regions are places where the movements of plates are happening and therefore, it becomes much easier to look for signs that an earthquake is coming soon. (1)In the past few years, there has been great excitement about the possibility of finding out when earthquakes are going to happen by measuring changes in the rocks, but we are still not sure whether this can be the basis for an efficient means of predicting earthquakes.But further research on this subject may suggest ways in which earthquakes can be predicted and prevented. (2)One idea is that itmightbe possible to reduce the pressures that have built up in rocks b