“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。
历年北约自主招生真题试题汇总
⾃主招⽣“北约”挑战⼤考对联还要讲笑话 ⾼校⾃主招⽣三⼤联盟昨⽇笔试⼴东6000考⽣在华⼯赴考试题鲜活“南⽅供暖”“雾霾”皆⼊题 “北约”、“华约”、“卓越”⾼校⾃主招⽣三⼤联盟昨⽇举⾏笔试，⼴东省内考点设在华南理⼯⼤学，6000考⽣赴考，校园内车满为患。
不少试题别出⼼裁，让⼈眼前⼀亮。
“北约”题⽬“吐槽”雾霾天⽓要求考⽣给“北京雾锁车迷路”对下联，还拿“⾼考状元”开涮要求写⼀则笑话。
2011年，北⼤等13校联合⾃主招⽣考试，7科⼀天考完，从早8时30分到晚8点20分，持续近12个⼩时，考智⼒更考体⼒。
今年，三⼤联盟考试携⼿瘦⾝，三个⼩时就考完了。
“华约”语⽂题的特点是没有作⽂，仅有三篇短⽂阅读，两篇现代⽂，⼀篇古⽂。
其中⼀篇给出⼀段涉及喜剧的材料，请考⽣根据滑稽⼈格进⾏性格倾向分析。
另外⼀篇与现实紧密相关，要求考⽣针对南⽅冬季是否应该供暖谈谈⾃⼰的看法。
“卓越”要求考⽣写400到500字的⼩作⽂，涉及很多⼈听都没听过的“煎饼⼈”。
煎饼⼈是指掌握多个领域的技能和知识的⼈，有⼈说煎饼⼈“⾯⾯会，⾯⾯松”，有⼈说煎饼⼈是复合型⼈才，考⽣要谈谈对此的观点。
记者采访多位学⽣获悉，三⼤联盟的数学题⽬虽不能说简单，但都不是很难。
的变化是“华约”从之前的“10+5”(10道选择题+5道答题)变成了仅有7道⼤题。
2013年⾃主招⽣：北约华约惨兮兮卓越考⽣笑嘻嘻 3⽉16⽇上午，“北约”、“华约”和卓越联盟⾃主招⽣“三国杀”正式开幕。
不少考⽣⾛出考场后直呼理科难，尤其是“北约”和“华约”的数学题。
据了解，“北约”数学题有6道选择题和4道⼤题，物理是4道选择、4道填空和4道⼤题。
考⽣普遍认为物理考试难度⼀般，没有超出⾼考范畴，数学却让考⽣犯难。
省实验中学成绩排名前三⼗的⼀个男同学也表⽰，“北约”数学题与往年风格⾮常不同，更加重视推理能⼒⽽⾮解题能⼒。
说起“华约”理科试题，考⽣⼤都愁云惨雾。
“考题与⾼考很有区别，很多题⽬都不在⾼考考纲范围内”来⾃茂名⾼州的⼀名刘姓考⽣卷⼦只做了⼀半，她说题量虽然不⼤，但⽐较难，和⾃⼰之前复习准备的内容完全“搭不上边⼉”。
北约华约自主招生试题
“华约”7校联考部分试题：上午科目：“阅读与写作”阅读部分（50分）一、现代文阅读：杨福家的《哥本哈根精神》二、现代文阅读：老舍的《五九》三、古代诗文阅读1.辛弃疾《清平乐校检山园，书所见》2.《南齐书良政》断句3.翻译《论语泰伯》《韩非子外储说右下》写作部分（50分）你对忧患意识是怎样认识的？请写一篇文章，谈谈你的思想和认识，角度自选，立意自定，标题自拟；不要编造虚假事实论据，不要套作，不得抄袭。
二、英文和中英文综合：试卷总分100分，包括的题型有完形填空、英语(论坛)翻译与写作。
完形填空：一篇。
选词填空：6选5，在6个短句中选择5个，完成整篇文章。
英语翻译与写作：先将一篇中文材料，内容与理想的受教育者有关，先将中文翻译成英文，再一篇150字左右的短文。
下午清华7校自主招生进行了数学和“自然科学”或“人文与社会”的考试，高考(微博)网赴现场了解到了考生考试的一些情况。
下午科目：数学数学总分100分，包括选择题和解答题，其中选择题10个，每个3分，解答题5个，涉及到的知识点包括概率、函数、三角函数、数列、解析几何等。
考生普遍反映题量大，时间紧，来不及做完。
题很难，相当于竞赛难度，前五道选择题和后五道选择题难度相差很大，前五道在课本内都可以找到，后五道来自课本之外。
自然科学理综总分100分，物理题量较大，比化学占的分值要多，物理题包括10个选择题，每个3分，有不定向选择题，解答题；化学题包括选择题10个，填空题、解答题。
物理题比较有深度，与课本结合紧密，但只要参加过竞赛，这些题基本都能解答出来。
大题中，有一道机械能的题。
部分物理题：物体x在平面上做简谐运动，AB两点相距16厘米，物体x由A运动到B用时一秒，并在AB两点有相同的速率，物体x在1秒后再次通过B，求周期与振幅。
（单选）一个氢原子外电子吸收一个光子后，______化学题有部分竞赛题，特别难，很多题都没见过，题量大，没做完，考到一个关于石墨烯、分子结构、轨道理论的题。
“北约”“华约”自主招生数学模拟试题带答案.doc
2014年“北约”“华约”自主招生模拟试题数学（满分150分）第一部分：填空题（共5小题 每题10分）1. 若tan 2α=,则224sin 3sin cos 5cos αααα--= 1 .2. 在复数集C 内,方程22(5)60x i x --+=的解为 .3. 设8219)22015()22015(+++=x ，求数x 的个位数字.4. 设{|100600,}A n n n N =≤≤∈，则集合A 中被7除余2且不能被57整除的数的个数为______70_______.5. 设P 是抛物线2440y y x --=上的动点,点A 的坐标为(0,1)-,点M 在直线PA 上, 且分PA 所成的比为2:1,则点M 的轨迹方程是 9y ²-12x-4=0 . 第二部分：解答题（共5小题 每题20分）1设集合()12log 32A x x ⎧⎫⎪⎪=-≥-⎨⎬⎪⎪⎩⎭，21a B x x a ⎧⎫=>⎨⎬-⎩⎭．若A B ≠∅，求实数a 的取值范围-1≤a ＜0或0＜a ≤32. 为了搞好学校的工作，全校各班级一共提了P )(+∈N P 条建议.已知有些班级提出了相同的建议，且任何两个班级都至少有一条建议相同，但没有两个班提出全部相同的建议.求证该校的班级数不多于12-P 个3. 设平面向量(3,1)a =-,13(,2b =.若存在实数(0)m m ≠和角((,))22ππθθ∈-, 使向量2(tan 3)c a b =+-,tan d ma b θ=-+,且c d ⊥.(I)求函数()m f θ=的关系式; (II)令tan t θ=,求函数()m g t =的极值.4. 已知双曲线的两个焦点分别为1F ,2F ,其中1F 又是抛物线24y x =的焦点,点A (1,2)-, B (3,2)在双曲线上.(I)求点2F 的轨迹方程; (II)是否存在直线y x m =+与点2F 的轨迹有且只 有两个公共点?若存在,求实数m 的值,若不存在,请说明理由.5. 已知a ，b 均为正整数，且,sin )(),20(2sin ,2222θπθθn b a A b a ab b a n n ⋅+=<<+=>其中求证：对一切*N ∈n ，n A 均为整数参考答案一、 选择题1. 由tan 2α=,得sin 2cos αα=,有22sin 4cos αα=,即221cos 4cos αα-=. 则21cos 5α=,原式=222216cos 6cos 5cos 5cos 1αααα--==. 2. 设x a bi =+,,a b R ∈,代入原方程整理得22(2256)(45)0a b a b ab a b i --+-++-=有2222560450a b a b ab a b ⎧--+-=⎨+-=⎩,解得11a b =⎧⎨=⎩或3232a b ⎧=⎪⎪⎨⎪=-⎪⎩,所以1x i =+或3322x i =-. 3. 直接求x 的个位数字很困难，需将与x 相关数联系，转化成研究其相关数. 【解】令])22015()22015[(,)22015()22015(82198219+++=+-+-=y x y 则 ])22015()22015[(8219-+-+，由二项式定理知，对任意正整数n.)2201515(2)22015()22015(22 +⋅⋅+=-++-n n n n n C 为整数，且个位数字为零.因此，x y +是个位数字为零的整数.再对y 估值， 因为2.0255220155220150=<+=-<， 且1988)22015()22015(-<-， 所以.4.02.02)22015(201919<⨯<-<<y 故x 的个位数字为9.【评述】转化的思想很重要，当研究的问题遇到困难时，将其转化为可研究的问题.4. 解：被7除余2的数可写为72k +. 由100≤72k +≤600.知14≤k ≤85.又若某个k 使72k +能被57整除，则可设72k +=57n . 即5722877n n k n --==+. 即2n -应为7的倍数. 设72n m =+代入，得5716k m =+. ∴14571685m ≤+≤. ∴m =0,1.于是所求的个数为70．5. 设点P 00(,)x y ,M (,)x y ,有0203x x +⨯=,02(1)3y y +⨯-=,得03x x =,032y y =+ 而2000440y y x --=,于是得点M 的轨迹方程是291240y x --=.二、 解答题1. 解：{}13A x x =-≤<，()(){}30B x x a x a =--<． 当0a >时，{}03B x a x a =<<<，由AB ≠∅得03a <<； 当0a <时，{}30B x a x a =<<<，由A B ≠∅得1a >-； 当0a =时，{}20B x x =<=∅，与AB ≠∅不符． 综上所述，()()1,00,3a ∈-2. 证明：假设该校共有m 个班级，他们的建议分别组成集合m A A A ,,,21 。
北约自主招生能力测试数学试题(含参考答案
综合性大学自主选拔录取联合考试自然科学基础——理科试卷数学部分（北约）一、选择题（每小题8分，合计48分）1．圆心角为3π的扇形的面积为6π，则它围成的圆锥的表面积为（ B ）．A ．B ．7πC ．D ．解：由2166S R ππ==扇形得6R =，由263r ππ=⨯得1r =，故它围成的圆锥的表面积为267r πππ+=．2．将10个人分为3组，一组4人，另两组各3人，共有（ C ）种分法．A ．1070B ．2014C ．2100D ．4200解：433106321002C C C N ==． 3．已知2()2()()33a b f a f b f ++=，(1)1f =，(4)7f =，则(2014)f =（ A ）． A ．4027 B ．4028 C ．4029 D ．4030 解：421(4)2(1)(2)()333f f f f +⨯+===，124(1)2(4)(3)()533f f f f +⨯+===，猜想*()21()f n n n N =-∈，假设()21f n n =-对3(1)n k k ≤≥都成立，则(31)3(1)2(1)2(31)1f k f k f k +=+-=+-，(32)3(2)2(2)2(32)1f k f k f k +=+-=+-，(33)3(3)2(3)2(33)1f k f k f k +=+-=+-，所以*()21()f n n n N =-∈．4．若2()lg(2)f x x ax a =-+的值域为R ，则a 的取值范围是（ D ）．A ．01a ≤≤B ．C ．D ．0a ≤或1a ≥解：由题知，{}2(0,)2y y x ax a +∞⊆=-+，故2(2)40a a ∆=--≥，解得：0a ≤或1a ≥．5．已知1x y +=-，且x 、y 均为负实数，则1xy xy+有（ B ）． A ．最大值174 B ．最小值174 C ．最大值174- D ．最小值174-解：1()()x y =-+-≥104xy <≤，而函数1()f t t t=+在(0,1)上单调递减，在(1,)+∞单调递增，故1()()4f xy f ≥，即1174xy xy +≥，当且仅当12x y ==-时取等号． 6．已知22()arctan14x f x C x +=+-在(,)44ππ-上为奇函数，则C =（ B ）． A ．0 B ．arctan 2- C ．arctan 2 D ．不存有解：由()0f x =得arctan(2)arctan 2C =-=-，此时()()f x f x +-22arctan14x x +=-22arctan 214x C x -+++4arctan()2arctan 203=--=，故arctan 2C =-符合题意．二、解答题（每题18分，共72分）7．证明：0tan3R ∉．证明：设0tan 3Q ∈，则0tan 6tan12tan 24tan 30tan(624)Q Q Q Q ∈⇔∈⇔∈⇔=+∈，这与0tan 303Q =矛盾． 8．已知实系数二次函数()f x 和()g x ，若方程()()f x g x =和3()()0f x g x +=都只有一个偶重根，方程()0f x =有两个不等的实根，求证：方程()0g x =没有实根． 解：设2()f x ax bx c =++，2()g x dx ex f =++，0ad ≠，所以2()4()()b e a d c f -=--，2(3)4(3)(3)b e a d c f +=++，所以223124b e ac df +=+，又240b ac ->，所以22()44(4)0g x e df b ac ∆=-=--<，所以方程()0g x =没有实根．9．已知1a ，2a ，…，13a 成等差数列，{}113i j k M a a a i j k =++≤<<≤，问：0，72，163是否能够同时在M 中？并证明你的结论．解：设该数列的公差为d ，∴p ∃，q ，*r N ∈，130a pd +=，173()2a p q d ++=，1163()3a p q r d +++=，∴2111q r =，∴21q ≥，11p ≥，又0123p ≥++=，∴35p q r ++≥， 又12111033p q r ++≤++=，与上式矛盾，故0，72，163不能够同时在M 中．10．i x （1i =，2，…，n ）为正实数，且11nii x==∏，求证：1)1)nn i i x =≥∏．解：由AM GM -不等式得：11(n i n =≥，11(ni n =≥两式相加得：1≥，故1)1)nn i i x =≥∏．。
名校自主招生北约物理模拟试卷
2013年高水平大学自主选拔学业能力测试北约物理模拟试卷（一）一、选择题（每题有一个或几个符合要求 （4′×8T=32′）1.真空中有一平行板电容器，两极板分别由铂和钾（其极限波长分别为λ1和λ2）制成，板面积为S ，间距为d 。
现用波长为λ（λ1＜λ＜λ2）的单色光持续照射两板内表面，则电容器的最终带电量Q 正比于（ ） 2.由两个完全相同的波源S 1与S 2发出的两列机械波在同种介质中传播，某时刻的情况如图所示，其中实线表示波峰，虚线表示波谷，下列说法正确的是（ ）A ．处于波峰与波峰相遇处的质点振动一定最强B ．处于波谷与波谷相遇处的质点振动一定最弱C ．振动最强的质点的位移始终最大,大小为每一列波振幅的2倍D ．振动最弱的质点就是该时刻处于波峰与波谷的交点,除此之外没有其它质点3.如图所示，均匀细杆AB 质量为M ，A 端装有转轴，B 端连接细线通过滑轮和质量为m 的重物C 相连，若杆AB 呈水平，细线与水平方向夹角为? 时恰能保持平衡，则杆对轴A 的作用力大小，下面表达式中不正确的有（ ）B. Mg2 sin ?C. M 2－2Mm sin ?＋m 2g D. Mg －mg sin ?4.如图所示，一块折射率为n 1=的平行玻璃板浸在水中，一束自然光入射到水面上时，反射光是完全偏振光，现要使玻璃表面的反射光也是完全偏振光，已知水的折射率n 2=34。
θ是玻璃表面和水平面的夹角。
则下面有关图中θ、r 、i 、i ′的大小正确的是（ ）A. i=53° r=37°B. i=53° θ=arctan 89 C. θ=arctan89 -37° r=53° D. i ′= arctan 89r=30° 5.如图所示的电路中，三个电容器完全相同，电源电动势ε1 = ，ε2 = ，开关K 1和K 2接通前电容器均未带电，则K 1和K 2接通后，有关三个电容器的电压U ao 、U bo 和U co 下列正确的是（ ）A ．Uao= Ubo= —B ．Uao= Uco=C ．Ubo= Uco= —D ．Uao=— Ubo=6.潮汐现象主要是由于月球对地球的不同部分施加不同的万有引力而产生的，可以近似认为地球表面均有水覆盖，如果地球与月球的相对位置如图所示，则在图中a 、b 、c 、d 四点中（ ） A ．a 点处于高潮，c 点处于低潮。
2019年“北约”、“华约”自主招生语文模拟试题
1 2019年“北约”自主招生语文模拟试题 一、选择最好的表达形式。
（10分）1．第一次庭审时，原告律师向法庭所作的 ，揭露了三年来原告在这起家庭暴力案件中遭受虐待的真相。
A ．申诉B ．申述C ．表白D ．陈述2．微生物“偷渡”到太空并在空间繁殖，目前已成为载人航天领域中一个 解决的严重问题。
A ．亟待B ．急需C ．有待D ．必须3．这些反映20世纪二三十年代广泛风貌的老照片，是他用了近十年的时间千辛万苦 的。
最近，他决定举办一个小型展览。
A ．收集B ．整理C ．搜集D ．寻觅4．税务部门出售的发票是严格按照国家的政策法规执行的，价格由国家物价部门统一 。
A ．规定B ．商定C ．认定D ．核定5．下列对联，最适合祝贺老师70岁寿辰的一联是A ．碧桃献岁宜家受福 花甲逢春获寿延年B ．为学有宗古稀成庆 诲人无倦恩重及门C ．乐道安贫音容宛在 因材施教手泽犹存D ．执掌教坛垂七十载 栽培桃李满三千株6．清人张潮在其《幽梦影》中曾说：“对渊博友如读异书，对风雅友如读名人诗文，对谨饬友如读圣贤经传，对滑稽友如阅传奇小说。
”这话确有见地，人生一世，除了亲情、爱情外，友情更是不可缺的。
因为 。
A ．友情是一种广度，亲情是一种深度，而爱情则是一种纯度B ．友情是一种纯度，爱情是一种深度，而亲情则是一种广度C ．爱情是一种纯度，亲情是一种深度，而友情则是一种广度D ．亲情是一种深度，爱情是一种纯度，而友情则是一种广度7．几十年来，霍金的身体禁锢在轮椅中， ， ， ， 。
他以极度残疾之身，取得极其辉煌的科学成就，成为自爱因斯坦以来引力物理学领域最大的权威。
A ．他执著地寻求着“我们从何处来，我们往何处去”的答案B ．震动了整个理论物理学界C ．发现了一个又一个宇宙运行的重大奥秘D ．思维却遨游于广袤的太空8．西北风呜呜地叫着， 。
就是骄傲的大鹰，也不敢在这样的天气里试试它的翅膀。
风里还夹着潮湿的气息，这是大雪的前兆。
高考专题自主招生模拟试卷(北约).docx
2015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PQR ABCS S ∆∆的最小值为 ．解答：如图5-1所示，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，180,APR CQR BQR ∠=∠=-∠o 所以sin sin .APR BQR ∠=∠在,APR BQR ∆∆中分别应用正弦定理得,sin sin sin sin PR AR QR BR A APR B BQR==.又45,A B ∠=∠=o故PR QR =,故AR BR =即R 为AB 的中点.过R 作RH AC ⊥于H ，则12PR RH BC ≥=,所以22221()124PQR ABC BC S PR S BC BC ∆∆=≥=,此时PQR ABCS S ∆∆的最大值为14. （2）当PQR ∆的直角顶点在ABC ∆的直角边上，如图5-2所示，设1,(01),(0)2BC CR x x BRQ παα==≤≤∠=<<,则90.CPR PRC BRQ α∠=-∠=∠=o在Rt CPR ∆中，,sin sin CR xPR αα== 在BRQ ∆中，31,,sin 4x BR x RQ PR RQB QRB B ππαα=-==∠=-∠-∠=+, AB P H由正弦定理, 1sin 3sin sin sin sin()44xPQ RB xB PQB αππα-=⇔=⇔∠+1sin cos 2sin x ααα=+，因此2221111()()22sin 2cos 2sin PQR x S PR ααα∆===+.这样，PQR ABCS S ∆∆2222111()cos 2sin (12)(cos sin )5αααα=≥=+++，当且仅当arctan 2α=取等号，此时PQR ABCS S ∆∆的最小值为15.2. 若集合{}2015*(,)(1)(2)()10,,A m n m m m n m Z n N =++++++=∈∈L ，则集合A中的元素个数为 ． 解答：由已知得20162015(21)25n n m ++=，因为,21n n m ++一奇一偶，所以,21n n m ++两者之一为偶数，即为2016201620162201620152,25,25,,25L 共有2016种情况，交换顺序又得到2016种情形，所以集合A 共有4032个元素. 3．若数列{}n a 的前n 项和nS =32n n -，*n N ∈，则20151182i i a i =+-∑= ．答案：20156048. 解答：1211352,n n n i i i i a a a n n -===-=-+∑∑又10a =，故2*352()n a n n n N =-+∈, 20152015201511111111()823(1)31i i i i a i i i i i =====-=+-++∑∑∑20156048. 4．若22sin cos 161610xx +=，则cos4x = .答案：12-. 解答:设2sin 16,116xt t =≤≤，则22cos 1sin 161616x x t-==，代入方程得16102,t t t +=⇒=或8t =，即21sin 4x =或34，所以cos4x =12-。
北约自主招生试题
北约自主招生试题一、文化历史类题目：1. 请简述欧洲文艺复兴对当时社会的影响及其对现代社会的意义。
2. 罗马帝国的崩溃对欧洲历史产生了怎样的影响？请详细阐述。
二、政治经济类题目：1. 北约成立的背景和目的是什么？请分析北约对国际政治经济格局的影响。
2. 英国脱欧对北约的影响是什么？请谈谈你的观点。
三、科技发展类题目：1. 人工智能技术对军事领域的应用有哪些？请从优势和挑战两个方面进行分析。
2. 无人机技术对现代战争起到了怎样的作用？请详细说明。
四、国际安全类题目：1. 请简述北约在维护欧洲安全方面的作用，并提出你认为的北约应该在未来加强的方面。
2. 战略武器对国际安全有何影响？请以导弹和核武器为例进行阐述。
五、环境问题类题目：1. 军事活动对环境造成的影响是什么？请列举具体案例并提出相应解决方案。
2. 如何平衡军事安全与环境保护之间的关系？请谈谈你的看法。
六、国际合作类题目：1. 北约与联合国在维护国际安全方面的合作关系是怎样的？请从历史和现实两个层面进行解析。
2. 北约与俄罗斯之间的紧张关系对国际合作产生了怎样的影响？请谈谈你的观点。
七、人权问题类题目：1. 军事冲突对人权的影响是怎样的？请从平民保护、逃难和战俘待遇等方面进行阐述。
2. 军队的职责与人权的保护有何冲突？请谈谈你的理解。
八、未来发展类题目：1. 非传统安全威胁对北约的影响是什么？请以网络安全和恐怖主义为例进行讨论。
2. 请设想未来战争的形态，并分析相应应对策略。
以上是北约自主招生试题的一部分，希望你能根据自己的知识和理解进行回答，展示出你对相关问题的见解和思考能力。
祝你成功！。
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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.