“北约”自主招生入学考试模拟试卷一
2012北约自主招生试题
2012北约自主招生试题：语文模拟试题来源：高分网文章作者：timeivy 发布日期：2012-01-29 二维码2012北约自主招生试题 2012自主招生试题 2012自主招生模拟试题 2012自主招生语文模拟试题2012北约自主招生试题：语文模拟试题2012 自主招生水平模拟测试（北约）科目：语文考试时间：2011 年1 月12 日注意事项：1. 答卷前，考生务必将自己的姓名，学校填写在答题卡上2. 将答案写在答题卡上，写在本试卷上无效3. 考试结束后，只需将答题卡交回本试卷满分100 分。
请将答案和必要的解答过程写在答题纸上。
另有5 分奖励分，如个别题目表现特别出色，可酌情在满分基础上额外加分。
一、语言基础知识（10 分）1、中国人民代表大会常务委员会通过立法的形式来“反独止独”，是天经地义、________的（）A. 不容置喙B. 无可非议C. 无可厚非2、下面句子中，与其它艺术手法不一样的一组是（）A．燕山雪花大如席B．半江瑟瑟半江红C．飞流直下三千尺，疑是银河落九天3、契诃夫这篇小说所表现的思想是相当复杂的：既嘲笑了当时的所谓“上流社会”，也_________了一些虚无思想。
（）A. 寄予B. 寄寓C. 寄于4、美国态度比较强硬地反对解除对华武器禁售令，其中重要原因之一是____大陆与台湾统一。
（）A. 阻挡B. 阻止C. 阻挠5、表示同样意思的词语，词性可能不同。
比如：“突然”是形容词，“忽然”就是副词。
以下各组，词义相近且词性相同的一组是（）A．“红”和“火红” B. “激动”和“冲动”C. “刚才”和“刚刚”6、为了弄清这起偷渡人员被蛇头推入大海造成六死二伤的惨案的真相，福建警方决定成立专案组，立案________ （）A. 侦察B. 侦查C. 侦破7、棋摊摊主卖个破绽，引路人______，骗取钱财。
（）A. 入网B. 入瓮C. 入彀8、现代汉语中，“好热闹”和“好不热闹”表达的意思是一样的。
2022“北约”13校联考自主招生试卷-语文
2022“北约”13校联考自主招生试卷-语文一、选择正确的或者最好的表达形式（10分）1、为爱护语言的纯洁，禁止在广告中用谐音字______成语。
A篡改 B窜改 C纂改2、大伙儿推举在学界______的朱德熙先生担任学会主席。
A深负众望B不负众望 C深孚众望3、只要有诚心，再厚的冰也会______。
A融解 B熔化 C溶化4、棋摊摊主卖个破绽，引路人______，骗取钱财。
A入网 B入瓮 C入彀5、所有机票代售点，一律不得向旅客收取或______收取手续费。
A变向 B变相 C 变项6、当时正值三年自然灾难，______尚有困难，有谁操心可有可无的戏班子的存亡。
A 裹腹 B裹肤 C果腹7、政府领导作为人们的公仆，要______都关怀群众的疾苦。
A不时不刻 B时时刻刻 C无时无刻8、我国的农业生产取得了举世______的伟大成就，第一应归功于改革开放的政策。
A瞩目 B侧目 C注目9、中国队20号前锋一脚远射，令对方门将______，皮球正入网中。
A措不及防 B猝手及防 C猝不及防10、把这些数据放在一起，就能看出______来。
A端倪 B端睨 C端眤二、文言文阅读（10分）州郡遇圣节锡宴，率命猥妓数十群舞于庭，作“天下太平”字，殊为不经。
而唐《乐府杂录》云：“舞有字，以舞人亚身于地，布成字也。
”王建《宫词》云：“罗衫叶叶绣重重，金凤银鹅各一丛。
每遇舞头分两向，太平万岁字当中。
”则此事由来久矣。
（周密《齐东野语》）1、文中所叙是一种什么景象？周密对此有何看法？2、结合现实生活中所见，谈谈你对类似现象的看法。
三、将下段古文翻译为现代汉语（20分）古者先王尽力于亲民加事于明法彼法明则忠臣劝罚必则邪臣止忠劝邪止而地广主尊者秦是也群臣朋党比周以隐正道、行私曲而地削主卑者山东是也乱弱者亡，人之性也治强者王古之道也越王勾践恃大朋之龟与吴战而不胜身臣入宦于吴反国弃龟明法亲民以报吴则夫差为擒故恃鬼神者慢于法恃诸侯者危其国（《韩非子·饰邪》）四、现代文阅读（20分）不久前我在鄯善迪坎儿村，见一大棵梭梭树长在路旁。
2012北约自主招生水平模拟试题(一)
2012北约自主招生模拟试题（一）一．基础知识1.依次填入下列各句横线处的词语，最恰当的一组是（）①逐步推广使用清洁的可再生能源，减少使用污染环境的能源，是环境恶化的正确选择。
②随着人们自律程度的不断提高，过去有些需要用铁栏杆来维持的地方，现在只要拉绳或画线就行了。
③具有世界影响的中国画大师张干千，人物、花、鸟、鱼虫、走兽无一不精，尤其画山水。
A.遏制次序善于B.遏制秩序擅长C.遏止秩序擅长D.遏止次序善于2.依次填入下列各句横线处的词语，最恰当的一组（）①每年三月，全国人大代表和政协委员都聚集北京，共商_______。
②连学好母语都需要花大力气，下苦功夫，_______学习外语呢?③这种偷梁换柱的行为对国人的诚信造成了负面影响，国人也因此觉得_______受损。
A．国是况且荣誉 B. 国事何况名誉C．国是何况名誉 D. 国事况且荣誉3.依次填入下列格局中横线处的词，最恰当的一组是（）①谈起抗震救灾，温总理______很深。
他动情地说：“这次抗震救灾，更加深了我对人民的爱。
②在破解开发型资源城市转型难题的过程中，该市______原有资源，以钒钛资源开发为重点，努力打造世界级的产业集群。
③作者科尔曼年轻气盛，观点鲜明，但常常论据不足或论证不周，_______显得犀利有余，老练不够。
A．感受依托未免B．感触依附未免C．感触依托不免D．感受依附不免4.下列各句横线处应填入的词语，最恰当的一组是（）①对严复提出的“信.雅.达”的翻译标准，有学者为：“信”是忠于原作，“达”是忠于读者，“雅”是对于文学语言的忠诚。
②走在大街上，天色微暗，行人稀少，几片雪花飘落，更平添了几分寒意。
③“天生我材必有用”，这不是诗人，而是在怀才不遇的情况下，仍希望终有一日能大展宏图。
A.解释偶然妄自尊大B.解读偶然夜郎自大C.解释偶尔妄自尊大D.解读偶尔夜郎自大5、退居二线，摆脱了繁忙的事务，可没过几天日子，他又闲不住了。
( )A.安静B.清静C．清净6、下列文学流派及文人并称中说法中不正确的一项是( )A、三曹:曹操、曹丕、曹植B 、元曲四大家：关汉卿、马致远、郑光祖、王实甫C 、桐城派：方苞、姚鼐D 、初唐四杰：王勃、杨炯、卢照邻、骆宾王7、说法有误的项是（）Ａ、上元就是元宵节，至日就是冬至日，仲秋就是重阳节。
清北学长精心打造——北约华约卓越自主招生物理力学部分模拟训练题及参考答案
清北学长精⼼打造——北约华约卓越⾃主招⽣物理⼒学部分模拟训练题及参考答案“北约”“华约”“卓越”⾃主招⽣⼒学部分模拟试题⼀．选择题（以下每题中有⼀个或⼀个以上选项符合题意，每⼩题3分，共30分）1．如图所⽰，⼀质量为m 的质点在半径为R 的半球形容器中，由静⽌开始⾃边缘上的⼀点滑下，到达最低点B 时，它对容器的正压⼒N 。
则质点⾃A 滑到B 的过程中，摩擦⼒对其所做的功为（A ）1(3)2R N mg - （B ）1(3)2R mg N - （C ）1()2R N mg -（D ）1(2)2R N mg -2．有⼀“不倒翁”，由半径为R 的半球体与顶⾓为60o的圆锥体组成（如图），它的重⼼在对称轴上。
为（A ）34R。
（B ）2R 。
（C ）R 3 。
（D ）条件不⾜，⽆法确定。
3. θ⾓的光滑斜⾯上的物块相对于斜⾯向下的加速度a′=13 gsinθ，由此可以推断车厢在⽔平⾯上的加速度为 (A)a0=23gtgθ； (B) a0=23gctgθ (C) a0=23gsinθ：(D) a0=23gcosθ4．将质量为2m 的⽊板静⽌地放在光滑⽔平⾯上，⼀质量为m 的⽊块以⽔平初速v 0由⽊板左端恰能滑⾄⽊板的右端与⽊板相对静⽌。
⽊块运动过程中所受摩擦⼒始终保持不变。
现将⽊板分成长度与质量相等的两段（a 、b ）后紧挨着仍放在光滑⽔平⾯上，让⽊块仍以相同的初速度v 0由⽊板a 的左端开始滑动，则（A ）⽊块仍能滑到⽊板b 的右端并与⽊板保持相对静⽌。
（B ）⽊块滑到⽊板b 的右端后飞离⽊板。
（C ）⽊块滑到⽊板b 的右端前就与⽊板保持相对静⽌。
（D ）后⼀过程产⽣的热量⼩于原来过程产⽣的热量。
5．如图所⽰，⼀半径为R 、质量为M 的1/4光滑圆弧槽D ，放在光滑的⽔平⾯上，有⼀质量为m 的⼩球由A 点静⽌释放，在下滑到B 点的过程中，下述说法正确的是（A ）以地⾯为参考系，⼩球到达B 处时相对于地的速度v 满⾜12mv2＝mgR（B ）以槽为参考系，⼩球到达B 处时相对于槽的速度v ’满⾜12mv ’2＝mgR（C ）以地⾯为参考系，以⼩球、槽和地球为系统，机械能守恒（D ）不论以槽或地⾯为参考系，以⼩球、槽和地球为系统的机械能均不守恒6.空中有⼀⽓球，下⽅连⼀绳梯，它们的总质量为M ，在梯上站⼀质量为m 的⼈。
北约自主招生英语全真模拟试题(含解析)新人教版
Part 1.cloze (20%)and I spent all my spare time (10) the countryside in search of fresh specimens to (11) to my collection of pets. (12) on I went for a year to the City Zoo, as a student (13) , to get experience of the large animals, such as lions, bears, bison and ostriches, (14) were not easy to keep at home. When I left, I (15) had enough money of my own to be able to (16) my first trip and I have been going (17) ever since then. Though a collector's job is not an easy one and is full of (18) , it is certainly a job which will appeal (19) all those who love animals and (20) .1. A. how B. where C. when D. whether2. A. region B. field C. place D. case3. A. clarity B. emotion C. sentiment D. affection4. A. except B. but C. except for D. but for5. A. recite B. recognize C. read D. repeat6. A. volume B. noise C. voice D. pitch7. A. close B. shut C. stop D. comfort8. A. grew B. was growing C. grow D. grown9. A. many B. amount C. number D. supply10. A. living B. cultivating C. reclaiming D. exploring11. A. increase B. include C. add D. enrich12. A. later B. further C. then D. subsequently13. A. attendant B. keeper C. member D. aide14. A. who B. they C. of which D. which15. A. luckily B. gladly C. nearly D. successfully16. A. pay B. provide C. allow D. finance17. A. normally B. regularly C. usually D. often18. A. expectations B. sorrows C. excitement D. disappointments19. A. for B. with C. to D. from20. A. excursion B. travel C. journey D. TripPart 2 grammar (15%)21.______, I must do another experiment.A. Be it ever so lateB. It is ever so lateC. It be ever so lateD. So late it be ever22. America will never again have as a nation the spirit of adventure as it______before the West was settled.A. couldB. wasC. wouldD. did23. I______ this book in a secondhand bookstore on Nanjing Road.A. came intoB. came aboutC. came roundD. came across24. As teachers we should concern ourselves with what is said, not what we think______.A. ought to be saidB. must sayC. have to be saidD. need to say25. The people at the party were worried about Susan because no one was aware______ she had gone.A. where thatB. of whereC. the place whereD. the place26. The Managing Director said that improving relations with the association would not be easy, but that they ______to try.A. would have decidedB. decideC. have decidedD. had decided27. We must______ that the experiment is controlled as rigidly as possible.A. secureB. ensureC. assureD. issue28. At no time______ other countries.A. China will invadeB. will invade ChinaC. will China invadeD. invade will China29. This is an ideal site for a university______ it is far from the downtown area.A. provided thatB. now thatC. so thatD. in that30. Although Asian countries are generally more ______in social customs than Western countries, there have been several notable examples of women leaders in both China and India.A. conservativeB. confidentialC. comprehensiveD. consistent31. Statistics is a discipline ______all the other sciences.A. affectedB. affectingC. to be affectedD. being affected32. On turning the corner, we saw the road ______steeply.A. departingB. descendingC. decreasingD. depressing33. As a salesman, he works on a (an)______basis, taking 10% of everything he sells.A. incomeB. commissionC. salaryD. pension34. It is not so much the language ______the cultural background that makes the book difficult to understand.A. butB. norC. asD. like35. After______ seemed an endless night, it was time for them to open the boxes of presents.A. itB. thatC. whatD. there36. Because Edgar was convinced of the accuracy of this fact, he ______his opinion.A. struck atB. strove forC. stuck toD. stood for37.______it is you' re found, you must give it back to the person it belongs to.A. ThatB. BecauseC. WhateverD. However38. There are nations whose lack of contact with the outside world has______ poverty.A. fallen intoB. consisted inC. resulted inD. come up to39. Although he refused to act on my suggestion, he had to admit that______ whatI said.A. it was something inB. there was something inC. it was something as forD. there was something upon40. The pressure ______causes Americans to be energetic, but it also puts them undera constant emotional strain.A. to competeB. competingC. to be competedD. having competed41. Because of the unexpected changes, they postponed ______us an answer.A. givingB. have givenC. to giveD. to have given42. There ought to be less anxiety over the perceived risk of mountain climbing than______in the public mind today.A. existsB. existC. exitingD. to exist43. As a ______actor, he can perform, sing, dance and play several kinds of musical instruments.A. flexibleB. versatileC. sophisticatedD. productive44. He was ______to steal the money when he saw it lying on the table.A. draggedB. temptedC. elicitedD. attracted45. The new teacher was very nervous ______she was well prepared.A. despiteB. unlessC. evenD. even though46. The pollution question as well as several other issues is going to be discussed when the Congress is in ______again next spring.A. assemblyB. sessionC. conferenceD. convention47. Christmas is a Christian holy day usually celebrated on December 25th______the birth of Jesus Christ.A. in accordance withB. in terms ofC. in favor ofD. in honor of48. Since it is too late to change my mind now, I am______ to carrying out the plan.A. obligedB. committedC. engagedD. resolved49. It was a bold idea to build a power station in the deep valley, but it______ as well as we had hoped.A. came offB. went offC. brought outD. make out50. To survive in the intense trade competition between countries, we must______ the qualities and varieties of products we make to the world-market demand.A. improveB. enhanceC. guaranteeD. gearPart 3 reading comprehension (40%)Passage 1It is not often realized that women held a high place in southern European societies in the 10th and 11th centuries. As a wife, the woman was protected by the setting up of a dowry (嫁妆). Admittedly, the purpose of this was to protect her against the risk of desertion, but in reality its function in the social and family life of the time was much more important. The dowry was the wife’s right to receive a tenth of all her husband’s property. The wife had the right to with hold consent, in all transactions the husband would make, and more than just a right; the documents show that she enjoyed a real power of decision, equal to that of her husband. In no case do the documents indicate any degree of difference in the legal status of husband and wife.The wife shared in the management of her husband’s personal property, but the opposite was not always true. Women seemed perfectly prepared to defend their own inheritance against husbands who tried to exceed their rights, and on occasion they showed a fine fighting spirit. A case in point is that of Maria Vivas. Having agreed with her husband Miro to sell a field she had inherited, for the needs of the household, she insisted on compensation. None being offered, she succeeded in dragging her husband to the scribe to have a contract duly drawn up assigning her a piece of land from Miro’s personal inheritance. The unfortunate husband was obliged to agree, as the contract says, “for the sake of peace.” Either through the dowry or through being hot-tempered, the wife knew how to win herself, with the context of the family,a powerful economic position.51.Originally, the purpose of a dowry is to_________.A give a woman the right to receive all her husband’s propertyB help a woman to enjoy a higher position in the familyC protect a woman against the risk of desertionD both A and C52.According to the passage, the legal status of the wife in marriage was__________.A higher than that of a single womanB higher than that of her husbandC lower than that of her husbandD the same as that of her husband53. Why does the author give us the example of Maria Vivas?A To show that the wife shared in the management of her husband s personal property.B To show that the wife can defend her own inheritance.C To prove that women have powerful position.D To illustrate how women win her property.54.The compensation Maria Vivas got for the field is____________.A some of the land Miro had inheritedB a tenth of Miro’s landC money for household expensesD money form Miro’s inheritance55. The author’s attitude towards Maria Vivas is_____________.A sympatheticB disapprovalC indifferentD objectivePassage 2A few common misconceptions. Beauty is only skin-deep. One' s physical assets and liabilities don' t count all that much in a managerial career. A woman should always try to look her best.Over the last 30 years, social scientists have conducted more than 1,000 studies of how we react to beautiful and not- so-beautiful people. The virtually unanimous conclusion: Looks do matter, more than most of us realize. The data suggest, for example, the physically attractive individuals are more likely to be treated well by their parents, sought out as friends, and pursued romantically. With the possible exception of women seeking managerial jobs they are also more likely to be hired, paid well, and promoted.Un-American, you say, unfair and extremely unbelievable? Once again, the scientists have caught us mouthing pieties (虔诚) while acting just the contrary. Their typical experiment works something like this. They give each member of a group--college students, perhaps, or teachers or corporate personnel managers a piece of paper relating an individual' s accomplishments. Attached to the paper is a photograph. While the papers all say exactly the same thing the pictures are different. Some show a strikingly attractive person, some an average-looking character, and some an unusually unattractive human being. Group members are asked to rate the individual on certain attributes, anything from personal warmth to the likelihood that he or she will be promoted.Almost invariably, the better looking the person in the picture, the higher the person is rated. In the phrase, borrowed from Sappho, that the social scientists use to sum up the common perception, what is beautiful is good.In business, however, good looks cut both ways for women, and deeper than for men. A Utah State University professor, who is an authority on the subject, explains:In terms of their careers, the impact of physical attractiveness on males is only modest. But its potential impact on females can be tremendous, making it easier, for example, for the more attractive to get jobs where they are in the public eye. on another note, though, there is enough literature now for us to conclude that attractive women who aspire (追求) to managerial positions do not get on as well as who may be less attractive.56. In "Beauty is only skin-deep", "skin-deep" can be replaced by______.A. decoratingB. superficialC. expressiveD. demanding57. "One's physical assets and liabilities don' t count all that much in a managerial career."(paral) can be interpretated as______.A. whether or not one looks good or bad, it doesn' t affect much one' s managerial careerB. in one' s managerial career, he may deal with cases like assets and liabilitiesC. in one' s managerial career, he may rarely deal with cases like assets and liabilitiesD. whether or not one looks good or bad, it may affect much one' s managerial career58. The result of research carried out by social scientists show that______.A. people do not realize the importance of looking one' s bestB. women in pursuit of managerial jobs are not likely to be paid wellC. good -looking women aspire to managerial positionsD. attractive people generally have an advantage over those who are not59. "Good looks cut both ways for women" (Para.5) means that______.A. attractive women have tremendous potential impact on public jobB. good-looking women always get the best of everythingC. being attractive is not always an advantage for womenD. attractive women do not do as well as unattractive women in managerial positions60. It can be inferred from the passage that in the business world______.A. handsome men are not affected as much by their looks as attractive women areB. physically attractive women who are in the public eye usually do quite wellC. physically attractive men and women who are in the public eye usually get along quite wellD. good looks are important for women as they are for menPassage 3In 1935, the clarinetist and bandleader Benny Goodman, aged just twenty six, left New York with his fourteen piece “swing” band and, traveling in a ragtag group of cars, headed for the huge Palomar Ballroom in Los Angeles. It was not an easy trip. There were half a dozen dismal, sparsely attended one nighters and three weeks at a dance hall in Denver, where the band was forced to play waltzes, tangos, and novelty numbers. On the opening night at the Palomar, the band played ballad numbers in the first set, and there was little response from the dancers. Then oneof the musicians said, if they were going to bomb again they might well do it in style. So Goodman called for his hot, often uptempo arrangements, many of them by the ingenious black bandleader and arranger Fletcher Henderson, and the kids stopped dancing, clustered around the bandstand, and began roaring. Before the weeks at the Palomar were over, it was clear that Goodman had suddenly made jazz—still a suspect and largely subliminal American folk music, despite the brilliant inventions during the previous decade of Jelly Roll Morton and others—into a popular music. Goodman s surprising ways continued. In 1936, he shook up the white entertainment establishment by hiring two black musicians—the elegant pianist Teddy Wilson and the plunging vibraphonist Lione Hampton. (To be sure, Wilson and Hampton did not play in the band; instead, they appeared with Goodman and the drummer Gene Krupa during intermissions.) A year later, when the band went into the Paramount Theater in New York for three weeks, legions of kids appeared, and a screaming, dancing riot nearly took place. It was the first great American show frenzy, and it prepared the way for the Sinatra frenzy of 1947, and for all the Beatles frenzies, and for all the mindless rock borne frenzies of the Seventies and Eighties.Then, on the night of January 16, 1938, Goodman, challenging the long hairs, took his band into a sold out Carnegie Hall. The big band played a dozen numbers, the trio two numbers, and the quartet five numbers. Despite the immediate rumblings from Olin Downes, the Times s classical music critic (“The playing last night, if noise, speed and beat, all old devices, are heat, was “hot” as it could be, but nothing came of it all, and in the long run it was decidedly monotonous”), Goodman s concert moved jazz even further up the American popular register. ［412 words］61. This passage is mainlyA a general review of Jazz music.B a biography of Benny Goodman.C about the origin of American folk music.D about how jazz became popular in America.62. Which of the following statements is true according to the passage?A The band s first music show in Los Angles was an immediate success.B Goodman is considered the father of Jazz music.C Benny Goodman was unknown to public when he left New York.D The band scheduled to play waltzes, tangos and novelty numbers at a dance hall in Denver.63. It could be inferred from the passage thatA Jazz is a style of music native to America.B Classic music had become outdated at Goodman s time.C Morton and Goodman were contemporaries.D Goodman was the first bandleader who hired Black musicians in 1930s.64. The phrase “shake up” (Line 1,Paragraph 2) in the context probably meansA to give a very unpleasant shock.B to make changes to an organization.B to get rid of a problem.。
2019年北约自主招生报名入口
2019年北约自主招生报名入口
篇一：2019年自主招生模拟试卷(北约)数学及答案WORD
2019年自主招生模拟试卷（北约）
1．已知等腰直角△PQR的三个顶点分别在等腰直角△ABC的三条边上，记△PQR，△ABC的面积分别为S△PQR，S△ABC，则S?PQRS?ABC
的最小值为．
解答：如图5-1所示，
A
P H
B图5-1 图5-2
（1）当?PQR的直角顶点在?ABC的斜边上，则P,C,Q,R四点共圆，
?APR??CQR?180??BQR,所以sin?APR?sin?BQR.在?APR,?BQR中分别应
用正弦定理得
PRARQRBR
?,?.又?A??B?45,故PR?QR,故sinAsinAPRsinBsinBQR
AR?BR即R为AB的中点.
S?PQR1
BC,所以2S?ABC
1
(BC)2
PR1???,此22BCBC4
2
过R作RH?AC于H，则PR?RH?
时
S?PQRS?ABC
的最大值为
1
. 4
（2）当?PQR的直角顶点在?ABC的直角边上，如图5-2所示，设
BC?1,CR?x(0?x?1),?BRQ??(0???
在Rt?CPR中，PR?
?
2
),则?CPR?90??PRC??BRQ??.
CRx
?, sin?sin?
x3
,?RQB????QRB??B????, sin?4x
PQRB1?x。
“北约”自主招生数学试题及答案(2010-2014)
2014年北约自主招生数学试题1.圆心角为60的扇形面积为6π,求它围成的圆锥的表面积.1.【解】设扇形的半径为r ,则由21623r ππ=⨯,得6r =. 于是扇形的弧长为623l ππ=⨯=,其即为圆锥的底面周长,于是圆锥的底面半径为1, 所以底面面积为21ππ⨯=,也所以圆锥的表面积为67S πππ=+=.2.将10个人分成3组,一组4人,两组各3人,有多少种分法.2.【解】由题知所有分组方法有3341074222100C C C N A ==种.3.如果2()lg(2)f x x ax a =-+的值域为R ,求a 的取值范围.3.【解】由题意22u x ax a =-+的值域包含区间(0,)+∞,则22u x ax a =-+与x 有交点, 故2(2)40a a ∆=--≥,解得1a ≥或0a ≤.4.设2()2()()33a b f a f b f ++=,且(1)1,(4)7f f ==,求(2014)f .4.【解】由(1)1,(4)7f f ==得421(4)2(1)(2)()333f f f f +⨯+===; 124(1)2(4)(3)()533f f f f +⨯+===,由数学归纳法可推导得*()21,f n n n N =-∈, 所以(2014)4027f =.5.已知1x y +=-且,x y 都是负数,求1xy xy+的最值.5.【解】由0,0x y <<可知,1||1||||1x y x y x y +=-⇒+=⇒+=,所以2(||||)1||||||44x y xy x y +=⨯≤=,即1(0,]4xy ∈,令1(0,]4t xy =∈,则易知函数1y t t =+在(0,1]上递减,所以其在1(0,]4上递减,于是1xy xy +有最小值117444+=,无最大值.6.已知22()arctan14x f x c x +=+-在11(,)44-上是奇函数,求c .6.【解】奇函数(0)0f =,故arctan2c =-.7.证明tan3是无理数.7.【证明】由三角公式22tan tan tan tan 2,tan()1tan 1tan tan ααβααβααβ+=+=--⋅, 若tan3是有理数,则tan 6,tan12,tan 24为有理数,再由tan 6和tan 24可得tan 30为有理数,这与3tan 30=!因此,tan3是无理数.8.已知实系数二次函数()f x 与()g x 满足3()()0f x g x +=和()()0f x g x -=都有双重实根,如果已知()0f x =有两个不同的实根,求证()0g x =没有实根.8.【证】由题可设2211223()()(),()()()f x g x a x b f x g x a x b +=--=-,其中120,0a a ≠≠, 则22221222112211()[()()],()[()3()]44f x a x b a x bg x a x b a x b =-+-=---, 由()0f x =有两个不同的实根,则必有12,a a 异号,且120a a +≠, 此时22212112211221()[()2()]4f x a a x a b a b x a b a b =+-+++,即2222112212112212124()4()()4()0a b a b a a a b a b a a b b ∆=+-++=-->,所以12b b ≠, 故此时观察2211221()[()3()]4g x a x b a x b =---可知,12,3a a -同号,且1230a a -≠,12b b ≠,故()0g x >恒成立,即证明()0g x =没有实根.9.1213,,,a a a 是等差数列,{|113}i j k M a a a i j k =++≤<<≤,问:7160,,23是否可以同时在M 中,并证明你的结论.9.【解】不可以同时在M 中,下面给予证明.假设7160,,23同时在M 中,设*(113,)k a a kd k k N =+≤≤∈,其中d 为公差,则*{3()|113}{3|636,}M a i j k d i j k a md m m N =+++≤<<≤=+≤≤∈于是存在正整数6,,36x y z ≤≤,使得30,73,21633a xd a yd a zd ⎧⎪+=⎪⎪+=⎨⎪⎪+=⎪⎩从而7(),216()3y x d z x d ⎧-=⎪⎪⎨⎪-=⎪⎩也所以2132y x z x -=-,由于21,32互质,且,y x z x --为整数,则有||21,||32y x z x -≥-≥, 但||36630z x -≤-=,矛盾!假设错误,即证明7160,,23不可以同时在M 中.10.已知12,,,n x x x R +∈,且121n x x x =,求证:12)(2)1)n n x x x +≥.10.【证】(一法:数学归纳法)①当1n =时,111x =≥=右边,不等式成立; ②假设*(1,)n k kk N =≥∈时,不等式12)(2)1)k k x x x +≥成立.那么当1n k =+时,则1211k k x x x x +=,由于这1k +个正数不能同时都大于1,也不能同时都小于1,因此存在两个数,其中一个不大于1,另一个不小于1,不妨设11,01k k x x +≥<≤, 从而111(1)(1)01k k k k k k x x x x x x +++--≤⇒+≥+,所以1212)(2(2)k kx x x x ++ 12112)[22()]kk kk x x xx x x ++=+++11212)(2(2(1)1)(21)k k k k x x x x ++≥+≥= 其中推导上式时利用了1211()1k k k x x x x x -+=及n k =时的假设,故1n k =+时不等式也成综上①②知,不等式对任意正整数n 都成立. (二法)左边展开得12)(2)n x x x+12121212111()(2)()k k nnn n n k i i j i i i n i i j ni i i nx x x x x x x x x ---=≤<≤≤<<<≤=+++++∑∑∑由平均值不等式得1112121212111211()(())k k knn nk k k k C C C k k ki i i nii i n n n i i i ni i i nx x x C x x x C x x x C --≤<<<≤≤<<<≤≥==∑∏故12)(2)n x x x +1122))2)(2)(21)n n n n kknnn n nnC C C C ---≥++++=+,即证. (三法)由平均值不等式有111()n nnk k n ==≥……①;111(n nn k k n ==≥……②①+②得1()nk k n n x =≥,即12)(2)1)n n x x x +≥成立.2013年北约自主招生数学试题与答案（时间90分钟，满分120分）1．和1A. 2B. 3C. 5D. 6解析：显然，多项式23()(2)(1)2f x x x ⎡⎤=---⎣⎦的系数均为有理数，且有两根分别为和1.和1-于5.若存在一个次数不超过4的有理系数多项式432()g x ax bx cx dx e =++++，其两根分别为和1,,,,a b c d e 不全为0，则：420(42)(2020a c e ga c eb d b d ++=⎧=++++=⇒⎨+=⎩(1(7)(232(630g a b c d e a b c d a b c =-+----+++++=702320a b c d e a b c d +---=⎧⇒⎨+++=⎩ 即方程组：420(1)20(2)70(3)2320(4)630(5)a c eb d a bcde a b c d a b c ++=⎧⎪+=⎪⎪+---=⎨⎪+++=⎪++=⎪⎩，有非0有理数解. 由（1）+（3）得：110a b c d ++-= （6） 由（6）+（2）得：1130a b c ++= （7） 由（6）+（4）得：13430a b c ++= （8） 由（7）-（5）得：0a =，代入（7）、（8）得：0b c ==，代入（1）、（2）知：0d e ==.于是知0a b c d e =====，与,,,,a b c d e 不全为0矛盾.所以不存在一个次数不超过4的有理系数多项式()g x和1和1为两根的有理系数多项式的次数最小为5.2． 在66⨯的表中停放3辆完全相同的红色车和3辆完全相同的黑色车，每一行每一列只有一辆车，每辆车占一格，共有几种停放方法？ A. 720 B. 20 C. 518400 D. 14400解析：先从6行中选取3行停放红色车，有36C 种选择.最上面一行的红色车位置有6种选择；最上面一行的红色车位置选定后，中间一行的红色车位置有5种选择；上面两行的红色车位置选定后，最下面一行的红色车位置有4种选择。
北约自主招生语文试题(1)
2014综合性大学自主选拔录取联合考试（北约）人文科学基础——文科试卷语文部分一、选择题（每道题2分，共10分）1．与“常、胖、剑”不是一类的是（）A．吊B．畔C．到2．下列成语正确的是（）A．一脉相成B．按部就班C．带罪立功3．“六六三十六”最多可以有几种理解（）A．1B．3C．54．“红楼隔雨相望冷，珠箔飘灯独自归”，这句诗的作者是（）A．杜甫B．李白C．李商隐5．王国维描述的三种学术境界最初的一种是（）A．衣带渐宽终不悔，为伊消得人性悴。
B．昨使西风凋碧树、独上高楼、望尽天涯路。
C．众里寻他千百度，蓦然回首，那人却在灯火阑珊处。
二、填空题（每空1分，共10分）6．有一种江湖黑话，“布”用“摆故”表示，“普”用“排骨”表示，据此，“母”可以用两个字“”与“”来表示。
7．很多人的第一次骄傲是从戴上北大清华校徽开始的。
8．同是我这一个人，要写正经的文章就为了推敲出一个字出心肝，若写些所谓小品，我却是日试万言，可待。
9．研究学习调查分析保证10．高端大气上档次，低调奢华，时尚亮丽，可爱乡村非主流。
三、将下段古文翻译成现代汉语（20分）11．今王公夫人其所富其所贵皆王公大人骨肉之亲无故富贵面目美好者也今王公大人骨肉之亲无故富贵面目美好者焉故必知哉若不知使治其国家则其国家之乱可得而知也今天下之士君子皆欲富贵而恶贫贱然女何为而得富贵而辟贫贱哉曰莫若为王公大人骨肉之亲无故富贵面目美好者王公大人骨肉之亲无故富贵面目美好者此非可学能者也使不知辩德行之厚若禹汤文武不加得也王公大人骨肉之亲躄喑聋瞽①暴为桀纣不加失也是故以赏不当贤罚不当暴……若此则饥者不得食寒者不得衣乱者不得治——选自《墨子·尚贤下》【注】①躄（bì），跛足。
喑（yīn），哑巴。
瞽（gǔ），瞎子。
四、指出下面古文的标点断句错误，并加以纠正。
（每小题2分，共4分）12．楚子之为令尹也，杀大司马薳，掩而取其室。
在襄三十年。
○薳，于委反。
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25. The paper-covered book of quizzes was a________to the class's mathematics textbook.
A. improvementB. requirementC. supplementD. mission
3．C。suffice it to say表示it's enough to say。suffocate“窒息”。
4。A。句子的意思是：为了保护总统，特勤处的车在前面开道，华盛顿的摩托车在两边骑行。flank“在两边”；flash“一闪而过”；flap“拍打”；fleck“斑点，微粒”。
5．D。这句话的意思是：在会计账目中要显示：已投资金额，现金储备，剩余储备和未分配利润。surplus“剩余的”；surpass“超过”。
A. smuggleB. smudgeC. smugD. smother
10.Moreover, they also have a powerful and effective print, broadcasting and electronicmedia, which are________tools to help disseminate their culture.
1.The growing concerns about identity theft may give a________to fingerprint verification technology.
A. chaseB. boostC. intakeD. ignore
2.The power to legislate________with the people who may elect representatives to act ontheir behalf.
6．B。这句话的意思是：卖糖果的利润都已经平分给了男童子军们和女童子军们。allot“分配”；allure“吸引，引诱”；allege“声称，断言”。
7．A。这句话的意思是：我们看到这么多令人恐怖的数据：多少人在挨饿，多少人是文盲，多少人没有清洁的饮水和卫生。illiterate“文盲”；illicit"违法的”；illiberal“不开明的，不自由的”；illogical“没有逻辑的”。
A. concedeB. disapproveC. supersedeD. dodge
13.I regret getting involved with my daughter's________problems; what is done is to bringtrouble to my ears.
26.Although the national government has introduced some new laws on the subject, it is thestate government that are________responsible for pollution control.
15.No tree becomes rooted and sturdy unless many a wind________it.
A. assailsB. intriguesC. assertsD. flatters
16.In many countries, most radio stations________the air from midnight to four in themorning.
A. practiceB. intentionC. stateD. occasion
23.Mr. Anderson presided________the board meeting on behalf of the chairman.
A. atB. overC. onD. in
24.On the desert travellers often see________rivers and lakes.
7.We see so many statistics that horrify us: how many are hungry, how many are________,how many are denied access to clean water and sanitation.
A. illiterateB. illicitC. illiberalD. illogical
A. marvelousB. maritalC. marbleD. martial
14.I________imagining how my late life would be if I had not saved enough money now.
A. get toB. get away fromC. get inD. get by
A. involvesB. featuresC. characterizesD. protrudes
Keys：
1．B。这句话意为：人们对身份盗窃越来越关注，这可能让指纹验证技术兴盛起来。give a boost to是固定搭配，表示“使……兴盛，繁荣”。
2．B。这句话意为：立法权在于人们可以选举代表来为他们行使权利。resipond“反应”。
21.Susan found that her new job did not provide her with sufficient________for her ability.
A. capacityB. openingC. rangeD. scope
22.We'll accept your cheque, although it is not our normal________.
A. reserveB. residesC. resignsD. responds
3.I won't go into all the depressing details;________it to say that the whole affair was anutter disaster.
A. serviceB. sufferC. sufficeD. suffocate
A. go onB. go offC. go throughD. go along with
17.The fishermen usually use a crane to________fish trapped from the sea near Phuket,Thailand.
A. hoistB. holdC. hugD. host
4.To protect the president, a Secret Service car set the pace ahead and Washingtonmotorcycles rode________.
A. flankB. flashC. flapD. fleck
5.Invested capital, capital reserve,________reserve and undistributed profit shall beshown by items in accounting statement.
18.Any________of a character in this book to a living person is purely incidental.
A. referenceB. rehearsalC. reluctanceD. resemblance
19.Better have skill than property. Better keep your word than be________. Better writewell than plentifully.
A. temptationB. contentmentC. boundariesD. supplement
28.________the depressing situation, a strong leadership and efficient management arerequired for survival of the company.
A. absurdB. eloquentC. arrogantD. intimate
20.Their refusal to compromise is a major________that stands in the way of further peacetalks.
A. obstacleB. complicationC. entityD. hazard
A. stubbornB. chronicC. potentD. edible
11.It's a popular________to suppose that money always brings happiness.
A. factB. fallacyC. fantasyD. fancy
12.It's easy to________a spear in the daylight, but it is difficult to avoid an arrow in thedark.
A. ConcerningB. BesidesC. DespiteD. Given
ck of employment outside the home tends to make women________to depression.
A. vulnerableB. immuneC. indifferentD. sensitive
30.The Christmas dinner includes poultry for the main course, salad, bread and vegetablesand________a variety of desserts, for example, pies, puddings and ice-cream.