复旦附中自招真题解析
复旦附中自招语文真题(含答案与解析)
复旦大学附中自招语文真题1．[唐]韩愈《进学解》：“业精于勤，荒于嬉；行成于思，毁于随。
”这一句子中“于”的意思是。
A．在 B.从 C.由于 D.对于2．［唐］王充《论衡·量知篇》：“人之学问，知能成就，犹骨象玉石，切磋琢磨。
”其中“磋”字的准确含义是。
A.搓弄B.商量讨论C.摘取D.把象牙加工成器物3．《左传·宣公十五年》：“我无尔诈，尔无我虞。
”句中前一个“尔”的意思是。
A．如此 B.而已 C.你 D.那样4．“苦口老师归寂日，知恩弟子庆生辰。
”（［宋］惠洪《石门文字禅·云庵生辰》）其中“苦口”一词的含义是。
A.佛口B.说话太多口变苦C.口气沉重D.不辞烦劳、反复恳切地说5．当代小说家毕淑敏在《提醒幸福》中写道：“幸福有时会同我们开一个玩笑，乔装打扮而来。
机遇、友情、成功、团圆……它们都酷似幸福，但它们并不等同于幸福。
”与这里的“乔装打扮”一语的意思最远的一顶是。
A.涂脂沫粉B.改头换面C.庐山面目D.面目全非6．韩小蕙在《悠悠心会》中写道：“有的夫妻一个屋檐下厮守一辈子，有的同事一个办公室对坐几十年，就是没话，心灵始终隔膜着一片寸草不生的荒漠。
”与这里的“寸草不生”一语的意思最近的一项是。
A. 赤地千里B.天府之国C.鱼米之乡D.山穷水尽7.2004年的印度洋地震海啸令当地人民不及防，造成了巨大的人员伤亡和财产损失，但海啸无情人有情，通过中国国际救援队队员等多方救助后情况就得到了改善。
句中方框应填入的字是。
A.防B.措C.猝D.促8．［清］刘熙载《艺论》：“是其苦心孤诣，且不欲徇非常人意，况肯徇非常人之意乎？”句中“苦心孤诣”一语的结构属于。
A.并列式B.偏正式C.补充式D.主谓式9．蒋子龙在《乔厂长上任记》中写道：“但是，他相信生活不是命运，也不是赶机会，而是需要智慧和斗争的无情逻辑！因此他要采取大会战孤注一掷。
”这里的“孤注一掷”在句中作。
A.补语B.状语C.宾语D.谓语10．纯洁的爱情体现着优美的。
【考试必备】2018-2019年最新复旦大学附属中学初升高自主招生语文模拟精品试卷【含解析】【4套试卷】
2018-2019年最新复旦大学附属中学自主招生语文模拟精品试卷（第一套）（满分：100分考试时间：90分钟）一、语文基础知识（18分，每小题3分）1．下列词语中加点的字，读音全都正确的一组是（）A．连累(lěi) 角(juã)色河间相(xiàng) 冠冕(miǎn)堂皇B专横(hâng) 忖(cǔn)度涮(shuàn) 羊肉妄加揣(chuāi)测C．笑靥(yâ) 顷(qīng)刻汗涔(cãn)涔休戚(qì)相关D慨叹(kǎi) 俨(yǎn)然刽子手(kuàì) 刎(wěn)颈之交2、下列各项中字形全对的是（）A、橘子州偌大急躁光阴荏苒B、蒙敝犄角慰籍书生意气C、敷衍磕绊笔竿艰难跋涉D、翱翔斑斓屏蔽自怨自艾3、依次填入下列各句横线上的词语，最恰当．．的一项是（）⑴虽然他尽了最大的努力，还是没能住对方凌厉的攻势，痛失奖杯。
⑵那些见利忘义，损人利己的人，不仅为正人君子所，还很可能滑向犯罪的深渊。
⑶我认为，真正的阅读有灵魂的参与，它是一种个人化的精神行为。
A.遏制不耻必需B.遏止不耻必需C.遏制不齿必须D.遏止不齿必须4、下列句中加点的成语，使用恰当的一句是（）A、故宫博物院的珍宝馆里，陈列着各种奇珍异宝、古玩文物，令人应接不暇。
B、任何研究工作都必须从积累资料做起，如果不掌握第一手资料，研究工作只能是空中楼阁．．．．。
C、电影中几处看来是闲笔，实际上却是独树一帜之处。
D、这部精彩的电视剧播出时，几乎万人空巷，人们在家里守着荧屏，街上显得静悄悄的。
5、下列句子中，没有语病的一项是（）A 大学毕业选择工作那年，我瞒着父母和姑姑毅然去了西藏支援边疆教育。
B北京奥运会火炬接力的主题是‚和谐之旅‛，它向世界表达了中国人民对内致力于构建和谐社会，对外努力建设和平繁荣的美好世界。
C他不仅是社会的一员，同时还是宇宙的一员。
他是社会组织的公民，同时还是孟子所说的‚天民‛。
上海复旦附中自主招生英语试题(3)含答案
上海复旦附中自主招生英语试题(3)1.A.increasinglyB.loweringmonD.solutionsE.individuallyF. callingG.dependent H.shortcomings I.consumption J.introduced K.sensesA United Nations panel on climate change says global warming is causing extreme weather all over the world and is__41__on governments to come up with new ideas to curb gas emissions. Since much of the air pollution comes from coal-fired power plants,scientists in Denmark are trying to lower their nation’s energy needs with new types of smart streetlights.Our__42__industrialized world needs huge amounts of electrical energy,but our power plants still rely mostly on technology__43__as early as the19th century—coal—powered plants, hydroelectric dams or somewhat never nuclear energy,all of which have their own__44__.But scientists say we can slow down global warming by__45__energy demands for street lights.These__46__features of the world’s urban areas require a lot of electricity.The U.S.Energy Information Administration estimates that in2012,lighting for buildings, streets and highways in the ed about274billion kilowatt hours.In a bid to make Copenhagen the world’s first carbon-neutral city by2025,scientists in the Danish capital are testing a variety of new street lighting technologies.Kim Brostrom is the chief technical officer at the Danish Outdoor Lighting Lab.“We have installed nine kilometers of streets,we have280masts placed here,we have50 different__47__,we have10different management systems,and we have a lot of different sensors and things out in the open area,”said Brostrom.Chief science officer Jakob Andersen says the lights can be managed__48__from a tablet computer or a smart phone.The main goal is to lower energy__49__when the light is not needed.So the lamp brightens up only when it__50__an approaching pedestrian,cyclist or vehicle.Some of them even have a backup wind generator or a solar cell.2.Diet Coke,diet Pepsi,diet pills,on-fat diet,vegetable diet…We are__51__by the word “diet”everywhere we look and listen.We have so easily been attracted by the promise and__52__ of diet products that we have stopped thinking about what diet products are doing to us.We are paying for products that__53__us psychologically and physically(身体上).Diet products significantly weaken us psychologically.On one level,we are not allowing our brain to__54__that our weight problems lie not in actually losing the weight,but in controlling the__55__of fatty,high-calorie,unhealthy foods.Diet products allow us to jump over the thinking stage and go straight for the scale(秤)instead.All we have to do is to swallow or__56__ the word“diet”in food labels.On another level,diet products have greater psychological effects.Every time we have azero-calorie drink,we are telling ourselves without our__57__that we don’t have to work to get results.Diet products make people believe that gain comes without pain,and that life can be without resistance a(n)__58__.The danger of diet products lies not only in the psychological effects they have on us,but also in the physical harm that they cause.Diet foods can__59__harm our bodies because consuming them instead of healthy foods means we are preventing our bodies from having__60__ nutrients(营养成分).Diet foods and diet pills__61__zero calorie only because the diet industry has created chemicals to produce these wonder products.Diet products may not be__62__,and the chemical that go into diet products are potentially dangerous.Now that we are aware of the effects that diet products have on us,it is time to__63__think about buying them.Losing weight lies in the power of minds,not in the power of chemicals. __64__we realize this,we will be much better able to resist diet products,and__65__prevent the psychological harm that comes from using them.51. A.confused B.surrounded C.mixed D.fascinated52. A.potential B.affection C.obligation D.calculation53. A.weaken B.harm C.enforce D.inspire54. A.admire B.argue C.deny D.admit55. A.assumption B.digestion C.dissolution D.consumption56. A.recognize B.foresee C.overlook D.research57. A.frustration B.ignorance C.awareness D.emphasis58. A.maintenance B.efficiency C.struggle D.setback59. A.indirectly B.inevitably C.incredibly D.innocently60. A.extra B.basic anic D.delicate61. A.contain B.persist C.exclude D.melt62. A.nutritional B.poisonous C.ridiculous D.sensitive63. A.strongly B.enthusiastically C.eagerly D.seriously64. A.Unless B.While C.Though D.Once65. A.therefore B.otherwise C.meanwhile D.furthermore 3.It was a bitter cold evening in northern Virginia many years ago.The old man’s beard was glazed by winter’s frost while he waited for a ride across the river.The wait seemed endless.His body became numb and stiff from the frigid north wind.It was long before he heard the faint,steady rhythm of hooves(马蹄)along the frozen path. Anxiously watching several horsemen coming up,he let the first one pass by without any effort to get his attention,then another passed by,and another.Finally,the last rider drew near where the old man sat like a snow statue when old man caught his eyes and said,“Sir,would you mind giving an old man a ride to the other side?”Stopping his horse,the rider replied,“Sure!Jump aboard.”Seeing the old man unable to lift his half-frozen body from the ground,the horseman got down to help him.The horseman took him not just across the river,but to his destination just a few miles away.As they approached the tiny but cozy cottage,the horseman’s curiosity caused him to inquire,“Sir,I noticed you let several other riders pass by without making an effort to secure a ride.Then I came up and you immediately asked me for a ride.I am curious why,on such a bitter night,you would wait and ask the last rider.What if I had refused and left you here?”The old man looked the rider straight in the eyes and replied,“I reckon I know people pretty good.I looked into the eyes of the other riders and immediately found no concern for my situation. It would have been useless even to ask them for a ride.But when I looked into your eyes,your gentle spirit would welcome the opportunity to give me assistance in my time of need.”Those heart-warming comments touched the horseman deeply.“I’m so grateful for what you have said,”he told the old man.“May I never get too busy in my own affairs that I fail to respond to the needs of others with kindness and compassion.”With that,Thomas Jefferson turned his horse around and made his way back to the White House.66.Why didn’t the old man ask the previous riders for a ride?A.Because he was waiting for the last rider.B.Because his efforts failed to get their attention.C.Because he assumed they had no concern for him.D.Because he was too numb to lift his half-frozen body.67.What caused the last rider to stop and help the old man?A.The old man’s poor situation.B.The old man’s warm comments.C.His own affairs.D.Kindness and sympathy.68.What do you know about the old man?A.He judged people by looking into their eyes.B.He lived in a cozy cottage a few miles away.C.He gave the last rider an opportunity to help.D.He recognized the president at first.69.Which can be the best title of this text?A.Look into your eyes.passion of a great man.C.The last rider to help.D.Return to the White House.4.International Book ClubHave you ever thought of joining a book club and buying new books through the post?Here at the International Book Club,we already have many members buying books from us by mail. Immediate benefits：●As a special offer,you may choose any reduced price books from our new members’book list,to the value of$6in total(plus postage and packing).By doing this,you will save pounds on the publishers’prices.●Tick the box on your form to order a free watch.●If you reply within seven days,we will send you another free gift carefully chosen from ourbook list by our staff.●Order a DVD from the many on offer in our list,at half the recommended retail price.When you’ve joined：As a member,you’ll enjoy savings of between30%and50%off the publisher’s price onevery book you buy,and what’s more,they’ll come straight to your door.Your free club magazine arrives once a month,to keep you up to date with the latest bestsellers.This means that every year we offer over1,000books to choose from.On the Internet,you can find all our titles for the year on our exclusive members’website.Being a member：All we are asking you to do while you are a member is to choose four books during your first year.After that,you can decide on the number of books you wish to take.In each of our monthly club magazines,our experienced staff choose a Club Choice book—a work of fiction or a reference title which they feel is particularly worth buying,and which is offered at an extra special price.However,if you do not want this book,just say so in the space provided on the form.We will always send the book if we do not receive this.So,return your application form today,but hurry—it’s not every day we can make you an offer like this.To apply to become a member,all you need to do is simply fill in the enclosed form and return it in the postage paid envelope supplied.Before you know it,your books will be with you.Please don’t send any money now,as we will send you your bill with the books.And remember,you have up to a fortnight to decide if you wish to keep the books you have ordered.You should then either return the books or send your payment.70.Which of the following doesn’t belong to the benefits of being a club member?A.Get four books for free in the first year.B.Order a free watch.C.Get a gift for nothing.D.Order a DVD at a low price.71.Every month the club provides a free club magazine in order to_______.A.let readers know the number of books to be soldB.keep readers well informed of recent bestselling booksC.make readers know the club’s developmentD.attract more and more readers to join the club72.If a book is worth$100,how much will a member probably save if he buys one?A.$20B.$40C.$60D.$7073.What should you do if you want to join the book club?A.Just fill in a form with personal information and send the club an email.B.Ask other club members to recommend you to the club.C.Fill in an application form with needed information and return it to the club.D.Apply for a membership card.5.In1789the ernment passed a law which said that the land of the American Indians could never be taken from them without their agreement.One hundred years later,however,the Indians only had a very small part of the land that originally belonged to them.How did this great injustice occur?After1812white settlers began to move west across North America.At first,the settlers and the Indians lived in peace.However,the number of settlers increased greatly every year,and slowly the Indians began to see the white settlers as a danger to their survival.To feed themselves,the settlers killed more and more wild animals.The Indians,who depended on these animals for food,had to struggle against starvation.The settlers also brought with them many diseases which were common in white society,but which were new for the Indians.Great numbers of Indians became sick and died.Between1843and1854the Indian population in one area of the country went down from100,000to30,000.More land was needed for the increasing number of white settlers.In Washington,the old respect for the rights of the Indians disappeared.The old promises to the Indians were broken;the government began to move groups of Indians from their original homelands to other poorer parts of the country.Some Indians reacted angrily and violently to this treatment.They began to attack white settlers,and the Indian war began.For30years,until the late1880s,different groups of Indians fought against the injustices of the white man.They had a few famous successes,but the result of the struggle was never in doubt.There were too many white soldiers,and they were too powerful.Many Indians were killed;the survivors were moved from their homelands to different area of the country.It was a terrible chapter in the history of a country that promised freedom and equality to everyone.74.It can be inferred from the passage that______.A.in the U.S.there were many laws that provided the rights of American IndiansB.the law which was passed in1789by the ernment was not successfully carried outC.in the19th century no injustices were done against the Indians by the ernmentD.the majority of white settlers were openly opposed to the law passed in178975.According to the passage which of the following is TRUE?A.The Indians believed that killing too many wild animals had disturbed the balance of nature.B.The government began to have a better understanding of the Indians in the fifties of the 19th century.C.Between1843and1854about70,000Indians were killed in the battle.D.The whites carried serious diseases into where the Indians lived.76.It is implied in the passage that______.A.the Indians had many great successes in the Indians warsB.the Indians had no doubt that they would win the warsC.after the war the Indians stayed where they were beforeD.the Indians were too weak to win the struggle77.What is the writer’s opinion about the treatment that the Indians received from the U.S. government?A.He believed that the government always respected the rights of the Indians.B.He believed that the government can’t be criticized for its treatment to the Indians.C.He believed that the government treated the Indians unjustly.D.He believed that the government’s unfair treatment against the Indians was not on purpose.6.The question of whether our government should promote science and technology or the liberal arts in higher education isn’t an either/or proposition(命题),although the current emphasis on preparing young Americans for STEM(science,technology,engineering,maths)-related fields can make it seem that way.The latest congressional report acknowledges the critical importance of technical training,but also asserts that the study of the humanities(人文学科)and social sciences must remain central components of America’s educational system at all levels.Both are critical to producing citizens who can participate effectively in our democratic society,become innovative(创新的)leaders,and benefit from the spiritual enrichment that the reflection on the great ideas of mankind over time provides.Parents and students who have invested heavily in higher education worry about graduates’job prospects as technological advances and changes in domestic and global markets transform professions in ways that reduce wages and cut jobs.Under these circumstances,it’s natural to look for what may appear to be the most“practical”way out of the problem“Major in a subject designed to get you a job”seems the obvious answer to some,though this ignores the fact that many disciplines in the humanities characterized as“soft”often,in fact,lead to employment and success in the long run.Indeed,according to surveys,employers have expressed a preference for students who have received a broadly-based education that has taught them to write well,think critically,research creatively,and communicate easily.Moreover,students should be prepared not just for their first job,but for their4th and5th jobs, as there’s little reason to doubt that people entering the workforce today will be called upon to play many different roles over the course of their careers.The ones who will do the best in this new environment will be those whose educations have prepared them to be flexible.The ability to draw upon every available tool and insight—picked up from science,arts,and technology—to solve the problems of the future,and take advantage of the opportunities that present themselves, will be helpful to them and the United States.(Note:Answer the questions or complete the statements in NO MORE THAN TWELVE WORDS.)78.The latest congressional report suggests that________________________________.79.What is the main concern of students when they choose a major?80.What kind of job applicants do employers look for?81.What suggestions does the author give to college students?7.In order to study enzymes(酶),a small piece of potato is cut into very thin pieces.These thin pieces are placed in a little glass container and covered with water.Then a little of the proper chemical is added.Immediately,because of the enzyme present in the potato,the chemical starts joining with the oxygen in the air above the water.If the container is entirely closed,a partial vacuum(真空)is framed inside.If the container is now connected with a fine tube which is dipped in water,the water is sucked part way up the tube because of the vacuum.The scientists doing the experiment carefully notice how far up the tube is when water is sucked in a certain time.The higher it is sucked,the more of that particular enzyme and evenabout the way in which it operates.And all the time we are working with amounts far too small to see or weigh.1.What do the scientists want to find out in the experiment?a.Whether enzyme is present in the potato.b.What particular enzyme there is in the potato.c.How much enzyme there is in the potato.d.How enzyme works in the potato.A.a and bB.c and dC.b and dD.a and c2.The proper title for the passage is______.A.How a Vacuum Is FormedB.How Enzyme Is StudiedC.How Enzyme Works in a PotatoD.How Much Enzyme There Is in the Potato3.Which of the following correctly shows how the experiment is done?A.Put very thin pieces or potato in a vacuum container.B.Connect the glass container with a tube through which oxygen is sent in.C.Add some chemical to the water before thin pieces of potato are put in.D.Place thin pieces of potato in a glass container,cover them with water and then close it.4.The result of the study shows that______.A.the higher water is sucked,the less of enzyme in the potato isB.the more water is put into,the more of enzyme in the potato isC.the higher water is sucked,the more of enzyme in the potato isD.the lower water is sucked,the more of enzyme in the potato is上海复旦附中自主招生英语试题(3)1.FAJHB CDEIK2.BABDD ACCAB AADDA3.CDAB4.ABBC5.BDDC6.78.The humanities and STEM subjects should be given equal importance.79.Their chances of getting a good job.80.Those who have received a well-rounded education.81.Preparing themselves to be flexible;achieving every available tool and insight.7.BBDC。
最新历年上海复旦附中自招英语试题及答案解析
1. You should pay attention to the way _____ you stand and sit.A. ofB. thatC. whichD. how【正确选项】B【考查内容】定语从句【试题分析】本题考察the way 后接定语从句的用法。
the way 后接定语从句有三种形式：1.不用引导词；2.用that 做引导词；3.用in which 做引导词。
本题的考察点是第2 种。
同学们根据汉语思维可能误选D。
总而言之，同学们对这三种形式一定要牢记！2. Lack of eye contact can _____ nervousness.A. signalB. markC. sighD. design【正确选项】A【考查内容】词语辨析【试题分析】本题考察高中英语词汇的辨析。
根据句子意思：缺少眼神交流可以说明一个人很紧张。
A 选项signal 有“表示；表明；预示”的意思，符合题意。
B 选项mark 是“做记号，做标记”的意思；C 选项sigh 是“叹气”的意思，单词拼写与signal 类似，同学们可能误选。
D 选项design 是“设计”的意思。
总而言之，只有A 选项符合题意！3. Miss Yang is _____ a good shop assistant because she greets every customer cheerfully.A. looked uponB. regardedC. viewedD. considered【正确选项】D【考查内容】词语辨析【试题分析】本题考察高中英语词汇及词组的辨析。
本题难度较大，根据句意：杨小姐被认为是一名优秀的商店售货员因为她会愉快地与每一位顾客打招呼。
题目的四个选项都有“被视为，被看成是”的意思，所以本题的难点在于这些词语的搭配的辨析！A, B, C 三个选项的错误之处在于应在单词后加上as 才正确。
例如：Miss Yang is lookedupon/regarded/viewed as a good shop assistant because she greets every customer cheerfully. 本题只有considered 才可以直接用在题干中。
上海市复旦附中英语自招真题试卷共3份及答案
上海复旦附中自主招生英语试题（1）选择题：31.They are fed up_______the old routine.A.withB.ofC.atD.on固定搭配：厌倦，厌烦be fed up with32.He is such a(n)_______teacher that has devoted all his and energy to his students.A.conscientiousB.consciousC.academicD.scientific形容词辨析：conscientious认真负责的，本着良心的；conscious有意识的；academic学术的；scientific科技的。
根据题意：他是如此有良知的老师以至于将所有精力花在学生身上。
33.We are looking for someone with a real sense of_______to the job.mitteemitmentmunitymission名词辨析：committee委员会；commitment承诺；community社区，commission委员会。
根据题意：我们在寻找一个对工作有责任感的人。
34.Since you are_______to the seafood,you’d better avoid eating it.A.sensibleB.sentimentalC.sensitiveD.sensory形容词辨析：sensible明智的；sentimental多愁善感的；sensitive敏感的；sensory感官的。
根据题意：由于你对海鲜过敏，你最好不要吃。
35.During the celebration,fireworks have been_______at the bay.A.set outB.set aboutC.set upD.set off动词词组辨析：set out出发，着手于；set about着手于；set up建立；set off出发，（烟花爆竹的）点燃36.There are fewer working hours in the executive jobs,_______the job stress is comparatively higher.A.thatB.whereC.whichD.what定语从句，the job stress is comparatively higher in the executive jobs37.They declared the war,for they believed that country had_______the weapons of mass destruction.A.liberatedB.counteredC.approvedD.proliferated动词辨析：liberate解放；counter反击；approve批准，proliferate激增，根据题意，由于认为那个国家扩散了大规模杀伤性武器，他们宣战了。
复旦附中自主招生物理真题整理
复旦附中自主招生物理真题整理【例1】一斜面长10米，高1米，一重100牛的物块恰好能沿此斜面匀速向下滑动，若以平行于斜面的力F将此物块匀速推上斜面，则F= ________ N 。
【例2】如图所示，试管A漂浮在水面上，试管B悬浮在水中，试管A与试管B都封闭有一定量的空气，以下说法正确的是（）A. 将试管A上提一微小距离，放手后试管A不会回到原来位置B. 将试管A下压一微小距离，放手后试管A会回到原来位置C. 将试管B上提一微小距离，放手后试管B会回到原来位置D. 将试管B下压一微小距离，放手后试管B会回到原来位置【例3】下雨了。
如果忘了带伞又必须在雨中行走，是走还是跑才能被雨少淋？美国Discovery探索频道的节目《流言终结者》中，两位实验专家通过控制变量法得到的结论是跑步比走路淋雨多。
但节目中也提及美国北卡罗来州的两名气象学家曾做过这个实验，得到结果却是跑步比走路淋的雨少40%。
同样的问题的出了两个截然相反的结论。
让我们建立如下物理模型，讨论这个问题。
淋雨量问题涉及的主要因素有：单位体积降雨量 ，竖直雨速v雨，水平风速v风，人的行走速度v人(当跑步时，v人比较大)，行走的直线距离L1和人的淋浴面积。
人可简化为一个长方体模型，如图所示，可能被淋到的面为：S顶，S 正(代表人的正面)，S背。
若以上条件均已知，则(1) 在无风的情况下，即v风=0，人在雨中行走或跑步，S顶，S 正，S背三个面中，哪个面的淋雨为0？(2) 请写出无风时，淋雨量不为0的各面的淋雨量的表达式。
由此，在无风的情况，是走还是跑才能被雨少淋？(3) 若有风，且背面有风，求雨滴相对于地面的速度大小，并写出总淋雨量的表达式，说明是走还是跑才能被雨少淋。
【例4】一、正文：圆周运动大家学习了有关物体运动的知识，但研究的基本都是直线运动，而直线运动是物体运动的最简单形式，实际生活中，绝大部分物体的运动都不是直线运动，所以我们有必要对物体运动的研究进行拓展，而今天我们要研究的是最简单曲线运动之一的圆周运动。
复旦附中自招试题答案
2011复旦附中自主招生英语试卷答案解析I. Grammar：1.【D】考查主谓一致，as well as为就远原则，另外句子是陈述现在存在的一种现象，因此用一般现在时。
2.【B】在昨天之前我不知道他会来，应该为过去将来时。
要注意的是come等表示来的词可以使用进行时表示将来时，这里就是用过去进行时表示过去将来时的例子。
3．【D】考查情态动词。
解释为应该4.【A】in addition解释为除此之外5.【D】本题考查形容词比较级前的修饰词，要注意more不能再修饰比较级。
但time翻译为“时光”时，为可数名词。
6．【B】考查介词，句子意为计划花费3000万到5000万之间的费用，因此选between7.【C】本题考查代词，我不喜欢这个表演，事实上大家都不喜欢，选none8.【C】本题考查分词做状语。
首先患病与主语Professor Lee一致，并且是主动发出的动作，因此使用现在分词，时间词for years，因此要使用完成时态Having suffered。
9.【A】本题考查分词作状语。
使用方向盘与one主语一致，并且动作由one主动发出，因此选择现在分词，句子是在陈述事实，因此用一般现在时。
10.【C】题目中hear about，about是介词，后接动名词。
Robert和失业直接是主动关系，不需要使用被动。
11.【A】本题为陷阱题，can’t help doing解释为情不自禁做某事，但是根据句子的意思，因为他在做蛋糕，所以不能帮助，因此帮助做某事为help sb.(to) do.12.【B】固定搭配。
admit doing sth. 表示承认做过某事。
13.【C】固定搭配，be used to doing sth. 习惯做某事。
14.【A】考查非限制性定语从句，由which引导。
15.【D】考查连词，根据前后句关系，东京是全世界物价最高的国家，东京仍然是世界上最拥挤的城市之一，因此是表示虽然，是让步状语从句。
上海复旦附中自主招生英语试题(3)含答案(20200802193610).pdf
上海复旦附中自主招生英语试题(3)1.A.increasinglyB.loweringmonD.solutionsE.individuallyF. callingG.dependent H.shortcomings I.consumption J.introduced K.sensesA United Nations panel on climate change says global warming is causing extreme weather all over the world and is__41__on governments to come up with new ideas to curb gas emissions. Since much of the air pollution comes from coal-fired power plants,scientists in Denmark areenergy needs with new types of smart streetlights.trying to lower their nation’ｓOur__42__industrialized world needs huge amounts of electrical energy,but our powerplants, plants still rely mostly on technology__43__as early as the19th century—coal—powered hydroelectric dams or somewhat never nuclear energy,all of which have their own__44__.But scientists say we can slow down global warming by__45__energy demands for street lights.urban areasrequire a lot of electricity.These__46__features of the world’ｓThe U.S.Energy Information Administration estimates that in2012,lighting for buildings, streets and highways in the ed about274billion kilowatt hours.first carbon-neutral city by2025,scientists in the In a bid to make Copenhagen the world’ｓDanish capital are testing a variety of new street lighting technologies.Kim Brostrom is the chief technical officer at the Danish Outdoor Lighting Lab.“We h ave installed nine kilometers of streets,we have280masts placed here,we have50 different__47__,we have10different management systems,and we have a lot of differentsaid Brostrom.sensorsand things out in the open area,”Chief science officer Jakob Andersen says the lights can be managed__48__from a tablet computer or a smart phone.The main goal is to lower energy__49__when the light is not needed.So the lamp brightens up only when it__50__an approaching pedestrian,cyclist or vehicle.Some of them even have a backup wind generator or a solar cell.2.Diet Coke,diet Pepsi,diet pills,on-fat diet,vegetable diet…We are__51__by the word everywhere we look and listen.We have so easily been attracted by the promise and__52__“diet”of diet products that we have stopped thinking about what diet products are doing to us.We are paying for products that__53__us psychologically and physically(身体上).Diet products significantly weaken us psychologically.On one level,we are not allowing our brain to__54__that our weight problems lie not in actually losing the weight,but in controlling the__55__of fatty,high-calorie,unhealthy foods.Diet products allow us to jump over the thinking stage and go straight for the scale(秤)instead.All we have to do is to swallow or__56__ in food labels.the word“diet”On another level,diet products have greater psychological effects.Every time we have azero-calorie drink,we are telling ourselves without our__57__that we don’ｔhave to work to get results.Diet products make people believe that gain comes without pain,and that life can be without resistance a(n)__58__.The danger of diet products lies not only in the psychological effects they have on us,but also in the physical harm that they cause.Diet foods can__59__harm our bodies because consuming them instead of healthy foods means we are preventing our bodies from having__60__ nutrients(营养成分).Diet foods and diet pills__61__zero calorie only becausethe diet industry has created chemicals to produce these wonder products.Diet products may not be__62__,and the chemical that go into diet products are potentially dangerous.Now that we are aware of the effects that diet products have on us,it is time to__63__think about buying them.Losing weight lies in the power of minds,not in the power of chemicals. __64__we realize this,we will be much better able to resist diet products,and__65__prevent the psychological harm that comes from using them.51. A.confused B.surrounded C.mixed D.fascinated52. A.potential B.affection C.obligation D.calculation53. A.weaken B.harm C.enforce D.inspire54. A.admire B.argue C.deny D.admit55. A.assumption B.digestion C.dissolution D.consumption56. A.recognize B.foresee C.overlook D.research57. A.frustration B.ignorance C.awareness D.emphasis58. A.maintenance B.efficiency C.struggle D.setback59. A.indirectly B.inevitably C.incredibly D.innocently60. A.extra B.basic anic D.delicate61. A.contain B.persist C.exclude D.melt62. A.nutritional B.poisonous C.ridiculous D.sensitive63. A.strongly B.enthusiastically C.eagerly D.seriously64. A.Unless B.While C.Though D.Once65. A.therefore B.otherwise C.meanwhile D.furthermore3.beard was It was a bitter cold evening in northern Virginia many years ago.The old man’ｓfrost while he waited for a ride across the river.The wait seemed endless.His glazed by winter’ｓbody became numb and stiff from the frigid north wind.It was long before he heard the faint,steady rhythm of hooves(马蹄)along the frozen path. Anxiously watching several horsemen coming up,he let the first one passby without any effort to get his attention,then another passed by,and another.Finally,the last rider drew near where the old man sat like a snow statue when old man caught his eyes and said,“Sir,would you mind giving an old man a ride to the other side?”Seeing the old man unable to lift Stopping his horse,the rider replied,“Sure!Jump aboard.”his half-frozen body from the ground,the horseman got down to help him.The horseman took him not just across the river,but to his destination just a few miles away.curiosity causedhim to inquire, As they approached the tiny but cozy cottage,the horseman’ｓ“Sir,I noticed you let several other riders passby without making an effort to secure a ride.Then I came up and you immediately asked me for a ride.I am curious why,on such a bitter night,you would wait and ask the last rider.What if I had refused and left you here?”The old man looked the rider straight in the eyes and replied,“Ｉreckon I know people pretty good.I looked into the eyes of the other riders and immediately found no concern for my situation. It would have been useless even to ask them for a ride.But when I looked into your eyes,your gentle spirit would welcome the opportunity to give me assistancein my time of need.”so grateful for what you Those heart-warming comments touched the horseman deeply.“I’ｍhe told the old man.“May I never get too busy in my own affairs that I fail to respond have said,”to the needs of others with kindness and compassion.”With that,Thomas Jefferson turned his horse around and made his way back to the White House.the old man ask the previous riders for a ride?66.Why didn’ｔA.Because he was waiting for the last rider.B.Because his efforts failed to get their attention.C.Because he assumed they had no concern for him.D.Because he was too numb to lift his half-frozen body.67.What caused the last rider to stop and help the old man?warm comments.poor situation. B.The old man’ｓA.The old man’ｓC.His own affairs.D.Kindness and sympathy.68.What do you know about the old man?A.He judged people by looking into their eyes.B.He lived in a cozy cottage a few miles away.C.He gave the last rider an opportunity to help.D.He recognized the president at first.69.Which can be the best title of this text?A.Look into your eyes.passion of a great man.C.The last rider to help.D.Return to the White House.4.International Book ClubHave you ever thought of joining a book club and buying new books through the post?Here at the International Book Club,we already have many members buying books from us by mail. Immediate benefits：As a special offer,you may choose any reduced price books from our new members’book list, to the value of$6in total(plus postage and packing).By doing this,you will save pounds on prices.the publishers’Tick the box on your form to order a free watch.If you reply within seven days,we will send you another free gift carefully chosen from our book list by our staff.Order aDVD from the many on offer in our list,at half the recommended retail price.joined：When you’veprice on As a member,you’ll enjoy savings of between30%and50%off the publisher’ｓevery book you buy,and what’ｓcome straight to your door.Your free club magazinemore,they’llarrives once a month,to keep you up to date with the latest bestsellers.This means that every year we offer over1,000books to choose from.On the Internet,you can find all our titles for the yearwebsite.on our exclusive members’Being a member：All we are asking you to do while you are a member is to choose four books during your first year.After that,you can decide on the number of books you wish to take.In each of our monthly club magazines,our experienced staff choose a Club Choice book—a work of fiction or a reference title which they feel is particularly worth buying,and which is offered at an extra special price.However,if you do not want this book,just say so in the space provided on the form.We will always send the book if we do not receive this.not every day we can make you an So,return your application form today,but hurry—it’ｓoffer like this.To apply to become a member,all you need to do is simply fill in the enclosed form and return it in the postage paid envelope supplied.send any money now,as we Before you know it,your books will be with you.Please don’ｔwill send you your bill with the books.And remember,you have up to a fortnight to decide if you wish to keep the books you have ordered.You should then either return the books or send your payment.belong to the benefits of being a club member?70.Which of the following doesn’ｔA.Get four books for free in the first year.B.Order a free watch.C.Get a gift for nothing.D.Order a DVD at a low price.71.Every month the club provides a free club magazine in order to_______.A.let readers know the number of books to be soldB.keep readers well informed of recent bestselling booksdevelopmentC.make readers know the club’ｓD.attract more and more readers to join the club72.If a book is worth$100,how much will a member probably save if he buys one?A.$20B.$40C.$60D.$7073.What should you do if you want to join the book club?A.Just fill in a form with personal information and send the club an email.B.Ask other club members to recommend you to the club.C.Fill in an application form with neededinformation and return it to the club.D.Apply for a membership card.5.In1789the ernment passeda law which said that the land of the American Indians could never be taken from them without their agreement.One hundred years later,however,the Indians only had a very small part of the land that originally belonged to them.How did this great injustice occur?After1812white settlers began to move west across North America.At first,the settlers and the Indians lived in peace.However,the number of settlers increased greatly every year,and slowly the Indians began to see the white settlers as a danger to their survival.To feed themselves,the settlers killed more and more wild animals.The Indians,who depended on these animals for food,had to struggle against starvation.The settlers also brought with them many diseaseswhich were common in white society,but which were new for the Indians.Great numbers of Indians became sick and died.Between1843and1854the Indian population in one area of the country went down from100,000to30,000.More land was needed for the increasing number of white settlers.In Washington,the old respect for the rights of the Indians disappeared.The old promises to the Indians were broken;the government began to move groups of Indians from their original homelands to other poorer parts of the country.Some Indians reacted angrily and violently to this treatment.They began to attack white settlers,and the Indian war began.For30years,until the late1880s,different groups of Indians fought against the injustices of the white man.They had a few famous successes,but the result of the struggle was never in doubt.There were too many white soldiers,and they were too powerful.Many Indians were killed;the survivors were moved from their homelands to different area of the country.It was a terrible chapter in the history of a country that promised freedom and equality to everyone.74.It can be inferred from the passagethat______.A.in the U.S.there were many laws that provided the rights of American IndiansB.the law which was passed in1789by the ernment was not successfully carried outC.in the19th century no injustices were done against the Indians by the ernmentD.the majority of white settlers were openly opposed to the law passedin178975.According to the passagewhich of the following is TRUE?A.The Indians believed that killing too many wild animals had disturbed the balance of nature.B.The government began to have a better understanding of the Indians in the fifties of the 19th century.C.Between1843and1854about70,000Indians were killed in the battle.D.The whites carried serious diseasesinto where the Indians lived.76.It is implied in the passagethat______.A.the Indians had many great successes in the Indians warsB.the Indians had no doubt that they would win the warsC.after the war the Indians stayed where they were beforeD.the Indians were too weak to win the struggle77.What is the writer’ｓopinion about the treatment that the Indians received from the U.S. government?A.He believed that the government always respected the rights of the Indians.be criticized for its treatment to the Indians.B.He believed that the government can’ｔC.He believed that the government treated the Indians unjustly.unfair treatment against the Indians was not onD.He believed that the government’ｓpurpose.6.The question of whether our government should promote science and technology or thean either/or proposition(命题),although the current emphasis liberal arts in higher education isn’ｔon preparing young Americans for STEM(science,technology,engineering,maths)-related fieldscan make it seemthat way.The latest congressional report acknowledges the critical importance of technical training,butalso asserts that the study of the humanities(人文学科)and social sciences must remain centraleducational system at all levels.Both are critical to producing citizens components of America’ｓwho can participate effectively in our democratic society,become innovative(创新的)leaders,and benefit from the spiritual enrichment that the reflection on the great ideas of mankind over time provides.Parents and students who have invested heavily in higher education worry about graduates’job prospects as technological advances and changes in domestic and global markets transformnatural to look professions in ways that reduce wages and cut jobs.Under these circumstances,it’ｓway out of the problem“Major in a subjectfor what may appear to be the most“practical”designed to get you a job”seems the obvious answer to some,though this ignores the fact thatoften,in fact,lead to employment andmany disciplines in the humanities characterized as“soft”success in the long run.Indeed,according to surveys,employers have expressed a preference for students who have received a broadly-based education that has taught them to write well,think critically,research creatively,and communicate easily.Moreover,students should be prepared not just for their first job,but for their4th and5th jobs, little reason to doubt that people entering the workforce today will be called upon toas there’ｓplay many different roles over the course of their careers.The ones who will do the best in thisnew environment will be those whose educations have prepared them to be flexible.The ability toup from science,arts,and technology—to draw upon every available tool and insight—pickedsolve the problems of the future,and take advantage of the opportunities that present themselves,will be helpful to them and the United States.(Note:Answer the questions or complete the statements in NO MORE THAN TWELVE WORDS.)78.The latest congressional report suggeststhat________________________________.79.What is the main concern of students when they choosea major?80.What kind of job applicants do employers look for?81.What suggestions does the author give to college students?7.In order to study enzymes(酶),a small piece of potato is cut into very thin pieces.These thin pieces are placed in a little glass container and covered with water.Then a little of the proper chemical is added.Immediately,because of the enzyme present in the potato,the chemical starts joining with the oxygen in the air above the water.If the container is entirely closed,a partial vacuum(真空)is framed inside.If the container is now connected with a fine tube which is dippedin water,the water is sucked part way up the tube becauseof the vacuum.The scientists doing the experiment carefully notice how far up the tube is when water is sucked in a certain time.The higher it is sucked,the more of that particular enzyme and evenabout the way in which it operates.And all the time we are working with amounts far too small to see or weigh.1.What do the scientists want to find out in the experiment?a.Whether enzyme is present in the potato.b.What particular enzyme there is in the potato.c.How much enzyme there is in the potato.d.How enzyme works in the potato.A.a and bB.c and dC.b and dD.a and c2.The proper title for the passageis______.A.How a Vacuum Is FormedB.How Enzyme Is StudiedC.How Enzyme Works in a PotatoD.How Much Enzyme There Is in the Potato3.Which of the following correctly shows how the experiment is done?A.Put very thin pieces or potato in a vacuum container.B.Connect the glass container with a tube through which oxygen is sent in.C.Add some chemical to the water before thin pieces of potato are put in.D.Place thin pieces of potato in a glass container,cover them with water and then close it.4.The result of the study shows that______.A.the higher water is sucked,the less of enzyme in the potato isB.the more water is put into,the more of enzyme in the potato isC.the higher water is sucked,the more of enzyme in the potato isD.the lower water is sucked,the more of enzyme in the potato is上海复旦附中自主招生英语试题(3)1.FAJHB CDEIK2.BABDD ACCAB AADDA3.CDAB4.ABBC5.BDDC6.78.The humanities and STEM subjects should be given equal importance.79.Their chances of getting a good job.80.Those who have received a well-rounded education.81.Preparing themselves to be flexible;achieving every available tool and insight.7.BBDC。
2018年上海市复旦附中自主招生物理真题及答案解析
正因为万有引力的存在，十九世纪四十年代 奥本 勒维耶 通过经典力学分析天王星轨
道的摄影后预测勒海王星的位置。十九世纪末天文学家根据对海王星的观察推测有其他行星 摄动天王星轨道。
我们相信，通过以上内容的阅读，你已经对匀速圆周运动有了一个初步的了解，接下来， 请回答以下问题：
二、问题：
1、判断以下说法是否正确：正确打“√”，错误打“ ” 1 360 2 ， 45 /4 ( )
2 匀速圆周运动的物体，周期越小，转的越快( ) 3 不同的匀速圆周运动中，相同时间内线速度大的物体一定比线速度小的物体转的圈 数多。( ) 4 对匀速圆周运动的物体进行受力分析的时候，向心力一定要画，因为它是客观存在 的。( ) 5 万有引力定律可以解释人造卫星绕地球做匀速圆周运动的原因，万有引力提供向心 力。( )
淋雨量问题涉及的主要因素有：单位体积降雨量 ，竖直雨速 v 雨，水平风速 v 风，人
的行走速度 v 人(当跑步时，v 人比较大)，行走的直线距离 L1 和人的淋浴面积。人可简化 为一个长方体模型，如图所示，可能被淋到的面为：S 顶，S 正(代表人的正面)，S 背 。若以 上条件均已知，则
(1) 在无风的情况下，即 v =0，人在雨中行走或跑步，S 顶，S 正，S 背三个面中，哪个面的 风
淋雨为 0？ (2) 请写出无风时，淋雨量不为 0 的各面的淋雨量的表达式。由此，在无风的情况，是 走还是跑才能被雨少淋？ (3) 若有风，且背面有风，求雨滴相对于地面的速度大小，并写出总淋雨量的表达式， 说明是走还是跑才能被雨少淋。
【例 4】
一、正文：
圆周运动
大家学习了有关物体运动的知识，但研究的基本都是直线运动，而直线运动是物体运动 的最简单形式，实际生活中，绝大部分物体的运动都不是直线运动，所以我们有必要对物体 运动的研究进行拓展，而今天我们要研究的是最简单曲线运动之一的圆周运动。 物体在以某点为圆心半径为 R 的圆周上运动，即物体运动时其轨迹是圆周的运动叫“圆周运 动”，它是一种最常见的曲线运动。例如吊扇、车轮、皮带轮等都做圆周运动。圆周运动分 为匀速圆周运动和变速圆周运动（如：竖直平面内绳/杆转动小球、竖直平面内的单摆运动）。 在圆周运动中，最常见和最简单的是匀速圆周运动（匀速圆周运动实际上是指速度大小始终 保持不变的圆周运动）
复旦附中自主招生题
复旦附中自主招生题，主要考智慧、测文理知识综合运用能力。
1、说游戏，每个人都玩过游戏，从纵向的角度来看，游戏有时代特征，有年龄特点；从横向的角度来看，游戏有益智类、竞技类、休闲类等等。
当然，在游戏中，也有一些趣味低下、恶作剧的内容。
请谈谈你对“游戏”的思考。
题目背后：初三学生特别喜欢这道题目，他们谈杀人游戏、弄堂游戏、CS等电脑游戏、魔兽世界等网络游戏，甚至有人说出“传承网络游戏”等另类观点。
复旦附中副校长吴坚说，出这道贴近生活的题目，就是让学生有话可说，充分发挥出学生各自的个性。
2、说外语，随着全球化时代的到来，作为最古老而又最基本的交流工具，语言的重要性显得日益突出。
“英语热”在当前上海中学生中持续升温。
你是如何看待“母语”学习与“外语”学习之间的关系的？可不可以借用数学名词或符号来回答这一题目？
题目背后：题目出得有点刁难学生，可学生们的回答却充满了智慧。
有学生用“正比例函数”指出母语、外语学习的相辅相成，有同学用“2条平行线”表达母语、外语学习同样重要，还有同学用“母语学习在底层、外语学习在上层，共同构成圆柱体”，来强调学好母语是学好外语的基础。
吴坚说，该题主要考查学生文理知识综合运用的能力。
【考试必备】2018-2019年最新复旦附中初升高自主招生语文模拟精品试卷【含解析】【4套试卷】
2018-2019年最新复旦附中自主招生语文模拟精品试卷（第一套）（满分：100分考试时间：90分钟）一、语文基础知识（18分，每小题3分）1．下列词语中加点的字，读音全都正确的一组是（）A．连累(lěi) 角(jué)色河间相(xiàng) 冠冕(miǎn)堂皇B专横(hèng) 忖(cǔn)度涮(shuàn) 羊肉妄加揣(chuāi)测C．笑靥(yè) 顷(qīng)刻汗涔(cén)涔休戚(qì)相关D慨叹(kǎi) 俨(yǎn)然刽子手(kuàì) 刎(wěn)颈之交2、下列各项中字形全对的是（）A、橘子州偌大急躁光阴荏苒B、蒙敝犄角慰籍书生意气C、敷衍磕绊笔竿艰难跋涉D、翱翔斑斓屏蔽自怨自艾3、依次填入下列各句横线上的词语，最恰当．．的一项是（）⑴虽然他尽了最大的努力，还是没能住对方凌厉的攻势，痛失奖杯。
⑵那些见利忘义，损人利己的人，不仅为正人君子所，还很可能滑向犯罪的深渊。
⑶我认为，真正的阅读有灵魂的参与，它是一种个人化的精神行为。
A.遏制不耻必需B.遏止不耻必需C.遏制不齿必须D.遏止不齿必须4、下列句中加点的成语，使用恰当的一句是（）A、故宫博物院的珍宝馆里，陈列着各种奇珍异宝、古玩文物，令人应接不暇。
B、任何研究工作都必须从积累资料做起，如果不掌握第一手资料，研究工作只能是空中楼阁．．．．。
C、电影中几处看来是闲笔，实际上却是独树一帜之处。
D、这部精彩的电视剧播出时，几乎万人空巷，人们在家里守着荧屏，街上显得静悄悄的。
5、下列句子中，没有语病的一项是（）A 大学毕业选择工作那年，我瞒着父母和姑姑毅然去了西藏支援边疆教育。
B北京奥运会火炬接力的主题是“和谐之旅”，它向世界表达了中国人民对内致力于构建和谐社会，对外努力建设和平繁荣的美好世界。
C他不仅是社会的一员，同时还是宇宙的一员。
他是社会组织的公民，同时还是孟子所说的“天民”。
2023年复旦附中自招英语真题(含答案)上海自主招生
2023年复旦附中自招英语真题(含答案)上海自主招生第一部分：听力理解 (20分)题目1短对话1题目： What is the man's main problem? What is the man's main problem?- A. He forgot to bring his passport.- B. He missed his flight.- C. His luggage got lost.答案： B. He missed his flight. B. He missed his flight.短对话2题目： What did the man think of the movie? What did the man think of the movie?- A. He found it boring.- B. He thought it was amazing.- C. He didn't watch it.答案： B. He thought it was amazing. B. He thought it was amazing.题目2长对话题目： What is the woman worried about? What is the woman worried about?- B. The recent increase in homework.- C. Her lack of sleep.答案： C. Her lack of sleep. C. Her lack of sleep.题目3短文题目： What is the topic of the talk? What is the topic of the talk?- A. Time management tips.- B. The importance of exercise.- C. Ways to stay organized.答案： A. Time management tips. A. Time management tips.第二部分：阅读理解 (40分)题目1短文1题目： What is the main subject of the passage? What is the main subject of the passage?- A. The benefits of traveling.- B. The history of ancient cities.- C. The impact of tourism.答案： A. The benefits of traveling. A. The benefits of traveling.题目2短文2题目： What is the purpose of this advertisement? What is the purpose of this advertisement?- A. To promote a new restaurant.- B. To sell discount tickets.- C. To invite people to a concert.答案： B. To sell discount tickets. B. To sell discount tickets.题目3短文3题目： What does the word "sustainability" mean? What does the word "sustainability" mean?- A. The ability to continue without causing damage.- B. Using resources in a wasteful manner.- C. The state of being easily replaced.答案： A. The ability to continue without causing damage. A. The ability to continue without causing damage.题目4长文题目： What kind of people was the author talking about in the passage? What kind of people was the author talking about in the passage?- A. People who enjoy adventure sports.- B. People who struggle with anxiety.- C. People who work in stressful jobs.答案： B. People who struggle with anxiety. B. People who struggle with anxiety.第三部分：写作 (40分)请根据以下提纲写一篇英语短文，题目自拟。
复旦附中自招真题解析
D
sin DAQ
立
APO OEB BOE AOP AO AP x ，
智
24 ， 25
立 方
【解析】 （1） cos DAB cos B
52 52 62 7 2 52 25
上
y
sin DAQ AQ AO AP 2
k 2 k 2 2 2 k 1 4 2 k 1 2k 2 2k 5 k 2 为完全平方数， 2 2
k 4 、 3 、 1 ，验证成立，于是 m 2 、
两机场之间的距离都不相等，则任意一个机场降落的飞机架数的最大值为____________．
部 资
A
料
， 严
13. 设 n n 10 个机场，每一机场起飞一架飞机，飞到离起飞机场最近的机场降落，且任何
1
2
O 60
3
立 方
内
1
5
O B 【答】5 【解析】首先有五架飞机在 O 降落是可以构造的，只需 O 为正五边形 ABCDE 的中心， 其他飞机场在较远处即可． 其次证明不可能有六架飞机在 O 降落， 如图，对于任意一个飞机场 O 考虑它 60 夹角方向，若区域内有 A 、 B 两飞机场， 则 AOB 60 ，若 A 、 B 同时飞往 O ，则 AO AB ， BO AB ， AB 为 AOB 最大边， AOB 为最大角矛盾； 于是对飞机场 O ，在夹角为 60 的区域内最多有一架飞机． 若存在六架 A 、 B 、 C 、 D 、 E 、 F 飞机飞到点 O ，以 OA 为边界将点 O 的圆周角 6 等分，则形成如图五块区域，每块区域内最多一架飞机，与六架飞机飞到点 O 矛盾．
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【解析】设直角三角形三边分别为
a
b
c
，
a2 ab
b2
2
a
c2 b
c
有 c2 a2 b2 2b2 c 2b ab 2 b b 2b 2 2 2 b 7b a 7 ，
而 ab 2a b c 20 b b a 5 ，
若 a 5 ，25 c bc b c b 25 ，c b 1 c 13 ，b 12 代入两式验证成立；
两机场之间的距离都不相等，则任意一个机场降落的飞机架数的最大值为____________．
A
1
A
2
1
60
【答】5
O
3
5
4
60
O
B
【解析】首先有五架飞机在 O 降落是可以构造的，只需 O 为正五边形 ABCDE 的中心，
其他飞机场在较远处即可．
其次证明不可能有六架飞机在 O 降落， 如图，对于任意一个飞机场 O 考虑它 60 夹角方向，若区域内有 A 、 B 两飞机场， 则 AOB 60 ，若 A 、 B 同时飞往 O ，则 AO AB ， BO AB ， AB 为 AOB 最大边， AOB 为最大角矛盾； 于是对飞机场 O ，在夹角为 60 的区域内最多有一架飞机． 若存在六架 A 、 B 、 C 、 D 、 E 、 F 飞机飞到点 O ，以 OA 为边界将点 O 的圆周角 6 等分，则形成如图五块区域，每块区域内最多一架飞机，与六架飞机飞到点 O 矛盾．
综上 x 1 或 1． 2
2. 已知函数 y 2x2 a 5 x 32b x b 3 图像关于 y 轴对称，
则 a b ______________． 【答】4． 【解析】由题意二次函数对称轴 x 0 ，定义域关于原点对称 a 5 0 ， 2b b 3 0 a b 51 4．
2015
1
2018
1 3
1 9
1 12
1 10
1 13
1 2015
1 2018
1 3
1 9
1 10
1 11
1 2016
1 2017
1 2018
90S 30 3 30 30 30 30 9+ 6 30 30 30
9
11 2016 2017 2018 99 2016 2017 2018
x2 32
x2 32
4
BH
18x x2 9
2x2
9x
18
0
无解
（3） EBC 90 ，则 C 、 B 、 A 共线， AE 为 BAC 角平分线，
x 3 x 3 ，综上 BE 3 或 3 ．
4x 5
2
2
11. 如图，OA、OD 是 O 的半径，延长 OA 至 B，使 OA AB ，C 是 OA 的中点，AOD 为
综上 k 2 ．
2x 8, x 3
4. 在同一个直角坐标系中，已知直线 y kx 与函数 y 2, 3 x 3 图象恰好有三个公共
2x 4, x 3
y
点，则 k 的取值范围是______________．
6
【答】 2 k 2 ． 3
3
【解析】原函数图象大致如图， 当 k 0 ， y kx 过二四象限不满足题意，
复旦附中自招试题
一、填空题
1. 已知 x a b c ，则 x ______________． bc ac ab
【答】 1 或 1． 2
a b c x
【解析】由题意
b
a
c
x
a
b
c
2
a
b
c
x
c a b x
若 a b c 0 ，则 x a a 1 ， b c a
若 a b c 0 ，则 x 1 ． 2
S 3 1 2 33 x 31 2 y 1 1 2 x y 2
33 x34 x y 1 y x y 1 x y 2
3
3
2
2
2
2x2 xy 2 y2 102x 3y 1684
2
x
y 4
102 4
2
15 8
y
62
316
于是当 x 27 ， y 6 时， S 取最小值 316．
若 a 6 ， 36 c bc b c b 18 ， c b 2 c 10 ， b 8 代入两式验证成立；
综上 a,b,c 6,8,10 或 5,12,13 ，满足条件的三角形有 2 个．
13. 设 nn 10 个机场，每一机场起飞一架飞机，飞到离起飞机场最近的机场降落，且任何
17. 设 x 是实数，不大于 x 的最大整数叫做 x 的整数部分，记作x ，如1.2 1， 3 3 ，
1.3 2 ，
（1） S
1
1
10 11 12 1112 12
10 11 1112
1
，求90S ；
2016 2017 12
2016 2017
（2）解关于
x
的方程：
x2
【答】4．
A
【解析】设 AB 、 BC 、 CA 分别为 n 1 、 n 、 n 1，则
BD2 DC2 AB2 AC2 n 12 n 12
BD DC
4
BD DC
BC
n
B
DC
8. 已知实数 m，n（其中 m n 1 ）分别满足：19m2 99m 1 0 ， n2 99n 19 0 ， 则 mn 4m 1 ______________． n 【答】 5 ．
二、解答题
14. 关于 x 的方程 x2 2m 1 x 2m2 m 0 的两个根分别为 x1 ， x2 ．
（1）若 x1 x2 5 ，求 m 的值； （2）若 x1 ， x2 均为整数，求 m 的值．
【答】（1） m 1，（2） m 2 ， 3 ， 1 ， 0 ． 22
【解析】（1） 5 2m 12 4 2m2 m 4m2 8m 1 m 1 ；
（1）求 y 关于 x 的函数关系式，并写出 x 的取值范围； （2）联结 QE，若 PQE 与 POQ 相似，求 AP 的长．
【答】（1） y 24 x2 12 x ， 0 x 5 ；
25 5
2
D
（2）5．
【解析】（1） cos DAB
cos B
52
52 62 2 52
7 25
PA O
锐角 ，连接 CD、BD，且 CD a ，则 BD ______________．
【答】 2a ．
【解析】设 OC 1 ，则 OB 4 ，
D
OD OA 2 ， OC OB OD2 ，
OCD ∽ ODB ，相似比1: 2
BD 2CD 2a ．
O
C
A
B
12. 已知直角三角形的三边长都是整数，且其面积与周长在数值上相等，若将全等的三角形 都作为同一个，那么这样的直角三角形的个数是______________个． 【答】2．
【解析】由 19m2 99 19m 19 0 19m 、 n 均为 x2 99x 19 0 的解，
若它们为不同解，则19m n 19 矛盾 19m n
原式 m 19m 4m 1 19m2 99m 1 95m 5 ．
19m
19m
9. 若关于 x 的方程 x 2 x2 4x m 0 有三个根，且这三个根恰好可以作为一个三角形
（2）由 x1 x2 2m 1 2m 为整数设为 k ，
k
12
4
2
k 2
2
k 2
k
12
2k 2 2k
5 k 22 为完全平方数，
k 4 、 3 、 1，验证成立，于是 m 2 、 3 、 1 、 0 ． 22
15. 如图，ABC 中，AB BC 5 ，AC 6 ，过点 A 作 AD / /BC ，点 P、Q 分别是射线 AD、 线段 BA 上的动点，且 AP BQ ，过点 P 作 PE / / AC 交线段 AQ 于点 O．联结 PQ，记 AP x ， POQ 面积为 y．
36x
显然 k 0 ，当 y kx 过 3, 2 则 k 2 ，恰有两交点，
3
当 k 2 ，三条直线平行，于是 2 k 2 ． 3
5. 如图，在梯形 ABCD 中， AB / /CD ， CD AB ，设 E、F 分别是 AC、BD 的中点，AC 与 BD 交于点 O，已知 OEF 是边长为 1 的正三角形， BOC 的面积为 15 3 ，则梯形 4 ABCD 的面积为______________．
A
D
A
D
B
B
B
E
C
B
EH
C
【答】 3 或 3 ． 2
【解析】设 BE x ，过 B 作 BH BC 于 H ，
（1） BEC 90 ， AEB 45 ， x AB 3 ，
（2） BCE 90 ， B 在 CD 上， H 与 C 重合，
由 BB AE ， BB 2 x 3 ， BH BB 3
sin DAQ 24 ，
25
Q
APO OEB BOE AOP AO AP x ，
AQ 5 x ， AO AQ x 5
B
2
y sin DAQ AQ AO AP 12 5 2x x
2
25
EC
y 24 x2 12 x ， 0 x 5
25 5
2
（2）若 PQO ∽ PEQ ，
的取值范围是______________．
【答】 a 2 ．
A
D
【解析】以 AD 中点为圆心 a 为半径作圆应与 BC 有交点， 2
a 1 a 2． 2
B
C
7. 已知锐角 ABC 的三边长恰为三个连续正整数，AB BC CA ，若 BC 边上的高为 AD，