(好資料)2005-2008北京大學(xué)自主招生保送生筆試考試試題

2008年北京大學(xué)自主招生 保送生筆試考試試題一，數(shù)學(xué)：1 求證：邊長(zhǎng)為1的正五邊形對(duì)角線長(zhǎng)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(duì)比北方球隊(duì)多9支，南方球隊(duì)總得白銀谷一書(shū)的讀后感分是北方球隊(duì)的9倍。 求證：冠軍是一支南方球隊(duì)。（勝得1分 敗得0分）5 （僅理科同學(xué)做）在O-xyz空間坐標(biāo)系中：xoy平面中 0y2-x2 繞 y 軸旋轉(zhuǎn)一周構(gòu)成一個(gè)不透光立體。在點(diǎn)(1,0,1)設(shè)置一光源，xoy 平面內(nèi)有一以原點(diǎn)為圓心的圓C，被光照到的長(zhǎng)度為2，求C上未被照到的長(zhǎng)度。二，語(yǔ)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(wú)數(shù)南方有倚人焉曰黃繚問(wèn)天地所以不墜不陷風(fēng)雨雷霆之故惠施不辭而應(yīng)不慮而對(duì)遍為萬(wàn)物說(shuō)說(shuō)而不休多而無(wú)已猶以為寡益之以怪以反人為實(shí)而欲以勝人為名是以與眾不適也弱于德強(qiáng)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(wàn)物而不厭卒以善辯為名惜乎惠施之才駘蕩而不得逐萬(wàn)物而不反是窮響以聲形與影競(jìng)走悲夫（莊子雜篇天下）一、上文加標(biāo)點(diǎn)。（9分）二、解釋文中加點(diǎn)的字詞（6分）：倚人：隩：庸充一：充一：駘蕩：窮：三、根據(jù)你對(duì)這段文字的理解，回答下列問(wèn)題（15分）：惠施口辯之學(xué)具有哪些特點(diǎn)？莊子是如何評(píng)價(jià)惠施口辯之學(xué)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(ài)山；或不如說(shuō)，較之山，更喜歡水。這無(wú)關(guān)“仁”“智”，不過(guò)個(gè)人趣味而已。我總覺(jué)得，山較之水遠(yuǎn)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(duì)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(jù)說(shuō)南方的山，多為徙自中原的客家據(jù)有。給他們留下山地，不消說(shuō)決非出于土著的好意。在我看來(lái)，山民之于山與其說(shuō)是倚托，不如說(shuō)是對(duì)抗。山民是在與山的對(duì)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(guó)。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(yíng)造禪境。八九年的乘客輪過(guò)三峽，為刀劈斧削般的山石所震撼，只覺(jué)得造物的嚴(yán)酷：這樣的山石更像是神造天設(shè)的有關(guān)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(lái)極小的孩子背了書(shū)包在走。你竟看不出他從哪里走出來(lái)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(diǎn)人的痕跡。你由那些山的巨大體量，和堅(jiān)硬的線條，讀出的是對(duì)于人的渺小與其無(wú)力的嘲弄移動(dòng)在山腰間的，是那樣小小的一個(gè)人。九O年初冬在湘西的猛洞河“漂流”時(shí)，我也這樣耐心地搜尋過(guò)人跡。那倒是一片蔥蓉的山，正如國(guó)畫(huà)山水，卻也如國(guó)畫(huà)山水似的遠(yuǎn)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(xiàn)了那山是天然地不宜于人的。它只是人的觀賞對(duì)象，它不屬于活的人生。我也看過(guò)夜的山。在那龐大的陰影上，吸引我的，永遠(yuǎn)是似虛懸空際的一兩星燈火。我會(huì)久久地揣想著那燈下的一份生活，似親身領(lǐng)受了淪肌浹膚的凄清。有水源處即有人聚；而山，提示的從來(lái)更是人的宿命的孤獨(dú)與寂寞。差不多因?yàn)橥瑯拥脑?，我?duì)國(guó)畫(huà)，總?cè)狈﹁b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(guó)畫(huà)山水間也有人，高士隱逸：對(duì)于山與人的關(guān)系，這到是個(gè)恰切的詮釋。我也知道，我說(shuō)這些，等于自成了既乏藝術(shù)素質(zhì)又乏哲學(xué)領(lǐng)悟能力，自承了對(duì)于“抽象性”的拒斥，經(jīng)驗(yàn)與趣味的不可救藥的平庸以至于“俗”。因此在寫(xiě)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(qiáng)的世俗性格。我最后得承認(rèn)，我是在一片極大的平原上、且在一條極大的河邊長(zhǎng)大的。如果我申請(qǐng)寫(xiě)在這里的只是一個(gè)平原人對(duì)山的“讀解”，或許不至于使愛(ài)山者感到冒犯？一九九四年六月一下列對(duì)文章內(nèi)容的理解，正確的兩項(xiàng)是（4分）A本文標(biāo)題中的“讀”字透露著把“山”當(dāng)成一本大書(shū)進(jìn)行領(lǐng)悟的含義。B文章開(kāi)頭所揭示的人與山的對(duì)抗性構(gòu)成了本文的一個(gè)貫穿性行文線索。C結(jié)尾道出作者不愛(ài)山的真正原因在于作者是在平原與大河邊長(zhǎng)大的。D作者之所以對(duì)國(guó)畫(huà)缺乏鑒賞的熱情，是因?yàn)槠渲腥狈?duì)人的描畫(huà)。E本文擇取了自己觀山的幾個(gè)經(jīng)驗(yàn)斷片，表達(dá)了對(duì)山與人的關(guān)系的懸想。二文章開(kāi)頭“無(wú)關(guān)仁智”的典故來(lái)自論語(yǔ)中的“_,_.”（2分）文章倒數(shù)第二段稱三回答下面問(wèn)題（14分）：1文章倒數(shù)第二段稱題：“山，提示的從來(lái)更是人的宿命的孤獨(dú)與寂寞?！蹦闶欠裢膺@一判斷？請(qǐng)簡(jiǎn)單給出你的理由。（4分）答_。2最后一段，作者說(shuō)：“我也知道，我說(shuō)這些，等于自承了既乏藝術(shù)氣質(zhì)又乏哲學(xué)領(lǐng)悟能力，自承了對(duì)于抽象性的拒斥，經(jīng)驗(yàn)與趣味的不可救藥的平庸以至于俗?！逼纷x全文，你覺(jué)得作者的自我評(píng)價(jià)是否準(zhǔn)確？為什么？（6分）答_。3文章的第二段和結(jié)尾一段中各有一個(gè)問(wèn)句，請(qǐng)談?wù)剢?wèn)句的運(yùn)用在本篇文章中所產(chǎn)生的效果。（4分）答_。四你本人愛(ài)山還是愛(ài)水？試用散文文體寫(xiě)出你自己“愛(ài)”的理由。（不超過(guò)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(xiě)一偏議論文。文章不少于800字。有人認(rèn)為：中華文化光輝燦爛，但其中也有嚴(yán)重的缺陷。權(quán)利文化、人才文化、財(cái)富文化，都有嚴(yán)重缺陷。比如人才文化的缺陷是，對(duì)實(shí)干的人求全責(zé)備，對(duì)不干事的人委曲求全。財(cái)富文化的主流就有問(wèn)題不患寡而患不均，這個(gè)思想本身就是違背財(cái)富增長(zhǎng)規(guī)律的。傳統(tǒng)文化的缺陷，使中國(guó)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(chǎn)的代表者，能人是無(wú)形資產(chǎn)的代表者，有形資產(chǎn)和無(wú)形資產(chǎn)是經(jīng)濟(jì)發(fā)展的兩個(gè)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(shí)機(jī)地把這兩個(gè)翅膀不斷地剪掉，“兩恨文化”2006年北京大學(xué)自主招生 保送生筆試考試試題一，數(shù)學(xué)：1、設(shè)OABC是棱長(zhǎng)為1的正四面體。OB中點(diǎn)為M，ON：NC=1：2，如圖，求過(guò)A，M，N三點(diǎn)平面與O點(diǎn)距離d。2、設(shè)，g（k）是k的多項(xiàng)式。（1）、設(shè)f（a）與 k無(wú)關(guān)，求常數(shù)a。（2）、求一次多項(xiàng)式g（k），使得f（g(k)）與k無(wú)關(guān)。（3）、設(shè)g（k）是二次以上多項(xiàng)式，證明f（g(k)）必與k有關(guān)。（4）、設(shè),為f（x）=0的解。試求,滿足的議程，并用圖形表示出來(lái)，其中取作橫坐標(biāo)軸，取作為縱坐標(biāo)軸。（5）、如果,是整數(shù)，求出與這樣,對(duì)應(yīng)的所有k值。3、F1，F(xiàn)2是橢圓 （ab0）的焦點(diǎn)。（1）、設(shè)l是該橢圓的一條切線，H1，H2分別是F1，F(xiàn)2在l上的垂足。證明：F1H1 F2H2=b2。（2）、設(shè)l1，l2是該橢圓過(guò)橢圓外一點(diǎn)P的兩條切線，切點(diǎn)分別為T1，T2。證明：F1PT1=F2PT2。5、函數(shù)f（x）的導(dǎo)函數(shù)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(diǎn)為Q(s,f(s)，求極限值二、語(yǔ)文：1、請(qǐng)寫(xiě)出一個(gè)由四個(gè)不同的漢字組長(zhǎng)的短語(yǔ)，要求每個(gè)字的偏旁部首相同并且意思清楚。（8分）2、請(qǐng)寫(xiě)一句由十個(gè)不同的漢字組成的話，要求意思清楚并且每個(gè)字的聲母都是卷舌音，zh、ch、sh、r。（10分）3、用文言擬寫(xiě)一段意思完整的話，不超過(guò)50字。要求其中至少出現(xiàn)三個(gè)次“之”字，并且每次的用法不同。（12分）4、先默寫(xiě)一首古人的五言絕句，然后每句在適當(dāng)處增加兩個(gè)字，改寫(xiě)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(shī)不同。（30分：默寫(xiě)10分，改寫(xiě)20分）默寫(xiě)：改寫(xiě)：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(huì)上做檢討。請(qǐng)模擬該貪官的心理和口氣寫(xiě)一篇檢討發(fā)言，要求該檢討表面上深刻嚴(yán)肅，實(shí)際上避重就輕，言辭華而不實(shí)，堆砌雕琢，企圖敷衍了事。字?jǐn)?shù)600700。（40分）2007年北京大學(xué)自主招生 保送生筆試考試試題一，數(shù)學(xué)：1：設(shè)f(x)=x2-53x+196+| x2-53x+196|.求f(1)+f(2)+f(50)的值。（25分）2：證明：對(duì)任何實(shí)數(shù)k方程x2+y2-2kx-(6+2k)y-2k-31=0過(guò)兩個(gè)定點(diǎn)。（25分）3：解方程組（25分）4：（僅理科同學(xué)做）設(shè)長(zhǎng)方體的三邊長(zhǎng)為a,b,c 。且a b c.設(shè)P和Q為此長(zhǎng)方形最遠(yuǎn)的兩個(gè)頂點(diǎn)。 求從P沿長(zhǎng)方形表面至Q最短路程的長(zhǎng)度。（25分）二，英語(yǔ)：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(lái)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(xué))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(guò)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