(好資料)2005-2008北京大學自主招生保送生筆試考試試題

2008年北京大學自主招生 保送生筆試考試試題一，數學：1 求證：邊長為1的正五邊形對角線長為（5+1）/ 2。2 已知六邊形AC1BA1CB1中AC1 = AB1，BC1 = BA1，CA1 = CB1，A+B+C=A1+B1+C1， 求證：ABC 面積是六邊形AC1BA1CB1的一半。3 已知：4 舉行排球單循壞賽，南方球隊比北方球隊多9支，南方球隊總得白銀谷一書的讀后感分是北方球隊的9倍。 求證：冠軍是一支南方球隊。（勝得1分 敗得0分）5 （僅理科同學做）在O-xyz空間坐標系中：xoy平面中 0y2-x2 繞 y 軸旋轉一周構成一個不透光立體。在點(1,0,1)設置一光源，xoy 平面內有一以原點為圓心的圓C，被光照到的長度為2，求C上未被照到的長度。二，語文：第一大題（本題共3小題，30分，閱讀下文，完成13題）然惠施之口談自以為最賢曰天地其壯乎施存雄而無數南方有倚人焉曰黃繚問天地所以不墜不陷風雨雷霆之故惠施不辭而應不慮而對遍為萬物說說而不休多而無已猶以為寡益之以怪以反人為實而欲以勝人為名是以與眾不適也弱于德強于物其涂隩矣由天地之道觀惠施之能其由一蚊一虻之勞者也其于物也何夫充一尚可曰愈貴道幾矣惠施不能以此自寧散于萬物而不厭卒以善辯為名惜乎惠施之才駘蕩而不得逐萬物而不反是窮響以聲形與影競走悲夫（莊子雜篇天下）一、上文加標點。（9分）二、解釋文中加點的字詞（6分）：倚人：隩：庸充一：充一：駘蕩：窮：三、根據你對這段文字的理解，回答下列問題（15分）：惠施口辯之學具有哪些特點？莊子是如何評價惠施口辯之學的？你是否同意莊子的看法？為什么？第二大題（本題公四小題，30分。閱讀下面的作品，完成14題）讀山趙園，我不大愛山；或不如說，較之山，更喜歡水。這無關“仁”“智”，不過個人趣味而已。我總覺得，山較之水遠于“人境”。水像是天然的“屬人”的，有水源處即有人煙；而山，則意味著對于人的挑戰(zhàn)。也因如此，山民比起水民，其生存更有悲壯的顏色。據說南方的山，多為徙自中原的客家據有。給他們留下山地，不消說決非出于土著的好意。在我看來，山民之于山與其說是倚托，不如說是對抗。山民是在與山的對抗中延續(xù)其歷史的。古代皇帝的陵墓稱“山陵”。你去看看南方的淺山，有不少處儼若鬼國。即使如香港新界那樣繁華的所在，沙田周圍的山，也有被死人密密麻麻地占了去的。這是否也在提示著山的更宜于死人而非生人？還有被人抱怨占盡名山的僧伽，也像是證明著山的“出世間”，至少證明了山的適于營造禪境。八九年的乘客輪過三峽，為刀劈斧削般的山石所震撼，只覺得造物的嚴酷：這樣的山石更像是神造天設的有關生存絕境的象征。更令人驚嘆的，是那山腰間的一線，有看起來極小的孩子背了書包在走。你竟看不出他從哪里走出來的，又能走到哪里去，他的身前身后，只是一色的石壁，尋不出一點人的痕跡。你由那些山的巨大體量，和堅硬的線條，讀出的是對于人的渺小與其無力的嘲弄移動在山腰間的，是那樣小小的一個人。九O年初冬在湘西的猛洞河“漂流”時，我也這樣耐心地搜尋過人跡。那倒是一片蔥蓉的山，正如國畫山水，卻也如國畫山水似的遠于活的人生你徒然地想在那些山壁上找一處能安置一椽的所在，同樣發(fā)現了那山是天然地不宜于人的。它只是人的觀賞對象，它不屬于活的人生。我也看過夜的山。在那龐大的陰影上，吸引我的，永遠是似虛懸空際的一兩星燈火。我會久久地揣想著那燈下的一份生活，似親身領受了淪肌浹膚的凄清。有水源處即有人聚；而山，提示的從來更是人的宿命的孤獨與寂寞。差不多因為同樣的原因，我對國畫，總缺乏鑒賞的熱情。我也如讀真的山，禁不住要在其上搜尋世俗生活的跡象。國畫山水間也有人，高士隱逸：對于山與人的關系，這到是個恰切的詮釋。我也知道，我說這些，等于自成了既乏藝術素質又乏哲學領悟能力，自承了對于“抽象性”的拒斥，經驗與趣味的不可救藥的平庸以至于“俗”。因此在寫了山之后，我并不自信能讀山，讀懂了山。我由“山”上讀出的，或許只是我本人頑強的世俗性格。我最后得承認，我是在一片極大的平原上、且在一條極大的河邊長大的。如果我申請寫在這里的只是一個平原人對山的“讀解”，或許不至于使愛山者感到冒犯？一九九四年六月一下列對文章內容的理解，正確的兩項是（4分）A本文標題中的“讀”字透露著把“山”當成一本大書進行領悟的含義。B文章開頭所揭示的人與山的對抗性構成了本文的一個貫穿性行文線索。C結尾道出作者不愛山的真正原因在于作者是在平原與大河邊長大的。D作者之所以對國畫缺乏鑒賞的熱情，是因為其中缺乏對人的描畫。E本文擇取了自己觀山的幾個經驗斷片，表達了對山與人的關系的懸想。二文章開頭“無關仁智”的典故來自論語中的“_,_.”（2分）文章倒數第二段稱三回答下面問題（14分）：1文章倒數第二段稱題：“山，提示的從來更是人的宿命的孤獨與寂寞?！蹦闶欠裢膺@一判斷？請簡單給出你的理由。（4分）答_。2最后一段，作者說：“我也知道，我說這些，等于自承了既乏藝術氣質又乏哲學領悟能力，自承了對于抽象性的拒斥，經驗與趣味的不可救藥的平庸以至于俗?！逼纷x全文，你覺得作者的自我評價是否準確？為什么？（6分）答_。3文章的第二段和結尾一段中各有一個問句，請談談問句的運用在本篇文章中所產生的效果。（4分）答_。四你本人愛山還是愛水？試用散文文體寫出你自己“愛”的理由。（不超過100字，14分）答_。第三大題 作文（40分）閱讀下面的材料，自選角度，自擬題目，寫一偏議論文。文章不少于800字。有人認為：中華文化光輝燦爛，但其中也有嚴重的缺陷。權利文化、人才文化、財富文化，都有嚴重缺陷。比如人才文化的缺陷是，對實干的人求全責備，對不干事的人委曲求全。財富文化的主流就有問題不患寡而患不均，這個思想本身就是違背財富增長規(guī)律的。傳統(tǒng)文化的缺陷，使中國人形成了普遍的文化理念，可以稱之為“兩恨文化”恨能人，恨富人。富人是有形資產的代表者，能人是無形資產的代表者，有形資產和無形資產是經濟發(fā)展的兩個翅膀。但是，我們傳統(tǒng)文化中的“兩恨文化”如同兩把剪刀，總是不失時機地把這兩個翅膀不斷地剪掉，“兩恨文化”2006年北京大學自主招生 保送生筆試考試試題一，數學：1、設OABC是棱長為1的正四面體。OB中點為M，ON：NC=1：2，如圖，求過A，M，N三點平面與O點距離d。2、設，g（k）是k的多項式。（1）、設f（a）與 k無關，求常數a。（2）、求一次多項式g（k），使得f（g(k)）與k無關。（3）、設g（k）是二次以上多項式，證明f（g(k)）必與k有關。（4）、設,為f（x）=0的解。試求,滿足的議程，并用圖形表示出來，其中取作橫坐標軸，取作為縱坐標軸。（5）、如果,是整數，求出與這樣,對應的所有k值。3、F1，F2是橢圓 （ab0）的焦點。（1）、設l是該橢圓的一條切線，H1，H2分別是F1，F2在l上的垂足。證明：F1H1 F2H2=b2。（2）、設l1，l2是該橢圓過橢圓外一點P的兩條切線，切點分別為T1，T2。證明：F1PT1=F2PT2。5、函數f（x）的導函數f(x)連續(xù)，且f（0）=0，f(0)=a。記曲線y=f（x）與p（t,0）最近的點為Q(s,f(s)，求極限值二、語文：1、請寫出一個由四個不同的漢字組長的短語，要求每個字的偏旁部首相同并且意思清楚。（8分）2、請寫一句由十個不同的漢字組成的話，要求意思清楚并且每個字的聲母都是卷舌音，zh、ch、sh、r。（10分）3、用文言擬寫一段意思完整的話，不超過50字。要求其中至少出現三個次“之”字，并且每次的用法不同。（12分）4、先默寫一首古人的五言絕句，然后每句在適當處增加兩個字，改寫成七言絕句。要求基本合乎格律，意思連貫完整。思想意境可以與原詩不同。（30分：默寫10分，改寫20分）默寫：改寫：5、作文：貪官檢討某官員貪污腐敗被揭發(fā)查處，在單位全體大會上做檢討。請模擬該貪官的心理和口氣寫一篇檢討發(fā)言，要求該檢討表面上深刻嚴肅，實際上避重就輕，言辭華而不實，堆砌雕琢，企圖敷衍了事。字數600700。（40分）2007年北京大學自主招生 保送生筆試考試試題一，數學：1：設f(x)=x2-53x+196+| x2-53x+196|.求f(1)+f(2)+f(50)的值。（25分）2：證明：對任何實數k方程x2+y2-2kx-(6+2k)y-2k-31=0過兩個定點。（25分）3：解方程組（25分）4：（僅理科同學做）設長方體的三邊長為a,b,c 。且a b c.設P和Q為此長方形最遠的兩個頂點。 求從P沿長方形表面至Q最短路程的長度。（25分）二，英語：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 (來福槍), 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(心理學)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（含義）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（過量）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