2007复旦附中自主招生试题

上海四大名校高中自主招生往年试题大全[复旦附中]考智慧、测文理知识综合运用能力自主招生题：■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。

■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。

推优题：■学生、家长对于学校的选择热情高涨。

小学生要进名气大的中学往往是几十个人争一个位子;在今年的自主招生和推优生招生工作中也可以看到人们对名校趋之若鹜。

针对这种现状，请你谈谈进“名校”的利弊。

题目背后：该题主要通过学生对进“名校”利弊的辨析，了解学生对于“名校”的定义以及对于自己未来的设计。

■总是觉得别人自私的人，通常对待他人也不免有些自私之嫌;总是觉得别人对不起自己的人，自己对别人也未必厚道;总是觉得别人没有趣味的人，自己也通常是令人烦闷的。

读了这段话，你有什么感想与启发?题目背后：现代学生大多是独生子女，遇到问题往往只考虑自己的利益，极少考虑他人的感受。

该题主要检测学生的自省态度，让学生懂得“你对别人的观感和态度其实很大程度上取决于别人对你的观感和态度”。

2007年复旦大学自主招生考试数学试题选择题（每题5分，共150分，答对得5分，答错扣2分，不答得0分） 1．三边均为整数，且最大边长为11的三角形，共有 个． A ．20B ．26C ．30D ．362．若a>1，b>1且lg （a+b ）=lga+lgb ，则lg （a −1）+lg （b −1）= ． A ．lg2B ．1C ．不是与a 、b 无关的常数D ．03．已知z ∈C ，若∣z ∣＝2－4i ，则z1的值是 ． A ．3＋4i B ．i 5453+ C ．i 154153+ D ．i 254253- 4．已知函数f （x ）=cos （x k 2316++π）+cos （x k 2316--）=23sin （x 23+π），其中x 为实数且k 为整数．则f （x ）的最小正周期为 ．A ．3πB ．2π C ．πD ．2π5．已知A ＝｛（x ，y ）∣y ≥x 2｝，B={（x ，y ）∣x 2+（y −a ）2≤1}．则使A∩B＝B 成立的充分必要条件为 ．A ．a=45B ．a≥45 C ．0<a<1 D ．a≥16．已知平面上三角形ABC 为等边三角形且每边边长为a ，在AB 和BC 上分别取D ，E 两点使得AD ＝BE ＝3a，连接A ，E 两点以及C ，D 两点．则AE 和CD 之间的最小夹角为 ． A ．9πa B ．3πa C ．3π D ．以上均不对7．已知数列｛a n ｝满足3a n+1+a n =4，（n≥1），且a 1=9， 其前n 项之和为S n ，则满足不等式∣S n −n −6∣<1251的最小整数是45． A ．6B ．7C ．8D ．98．将一个四棱锥的每个顶点染上一种颜色，并使用一条棱的两端点异色，若只有五种颜色可供使用，则不同的染色方法的总数为 ．A ．120B ．260C ．340D ．4209．设甲乙两个袋子中装有若干个均匀白球和红球，且甲乙两个袋子中的球数比为1∶3．已知从甲袋中摸到红球的概率为31，而将甲乙两个袋子中的球装在一起后，从中摸到红球的概率为32．则从乙袋中摸到红球率为 ． A ．97 B ． 4519C ．3013D ．4522 10．方程f （x ）=543423322212321---------x x x x x x x x x =0 的实根的个数是 ．A ．1个B ． 2个C ．3个D ．无实根11．已知a ，b 为实数，满足（a+b ）59=−1，（a −b ）60=1，则∑=-601)(n n nb a＝ ．A ．0121B ．−49C ．0D ．2312．a=21是“直线（a+2）x +3a y +1=0与直线（a −2）x +（a+2）y −3=0相互垂直”的 ． A ．充分必要条件B ．充分而不必要条件C ．必要而不充分条件D ．既不充分也不必要条件13．设函数y =f （x ）对一切实数x 均满足f （2+x ）=f （2−x ），且方程f （x ）=0恰好有7个不同的实根，则这7个不同实根的和为 ．A ．0B ．10C ．12D ．1414．已知α，β，γ分别为某三角形中的三个内角且满足tan 2βα+=sin γ，则下列四个表达式:（1）tan αtan β=1 （2）0<sin α+sin β≤2 （3）sin 2α+sin 2β=1 （4）cos 2α+cos 2β=sin 2γ中，恒成立的是 ．A ．（1）（3）B ．（10（4）C ．（2）（3）D ．（2）（4）15．设S n =1+2+…+n，n ∈N ．则∞→n lim1)32(2++n nS n nS ＝ ．A ．2B ．321C ．161 D ．6416．复数z =iia 212+-（a ∈R ，i=1-）在复平面上对应的点不可能位于 ． A ．第一象限B ．第二象限C ．第三象限D ．第四象限17．已知f （x ）=asin x +b 3x ＋4（a ，b 为实数）且f [lg （lg 310）]=5，则f [lg （lg3）]= ．A ．−5B ．−3C ．3D ．随a ，b 取不同值而取不同值18．已知四棱锥P －ABCD ，底面ABCD 是菱形，∠DAB ＝3π，PD ⊥平面ABCD ，线段PD ＝AD ，点E 是AB 的中点，点F 是PD 的中点，则二面角P －AB －F 的平面角的余弦值＝ ．A ．21 B ．552 C ．1475D ．1473 19．在（32-）50的展开式中有 项为有理数． A ．10B ．11C ．12D ．1320．棱长为a 的正方体内有两球互相外切，且两球各与正方体的三个面相切．则两球半径之和为为 ．A ．无法确定B ．aC ．a 233-D ．a 255- 21．在集合{1，2，…11}中任选两个作为椭圆方程12222=+by a x 中的a 和b ，则能组成落在矩形区域{（x ，y ）||x |<11，|y |<9}内的椭圆个数是 ．A ．70B ．72C ．80D ．8822．设a ，b ，c 为非负实数，且满足方程02562684495495=+⨯-++++cb a cb a ，则a+b+c的最大值和最小值 ．A ．互为倒数B ．其和为13C ．其乘积为4D ．均不存在23．给定正整数n 和正常数a ，对于满足不等式a 12+a n+12≤a 的所有等差数列a 1，a 2，a 3，…，和式∑++=1211n n i a的最大值＝ ．A ．)1(210+n aB ．n a210 C ．)1(25+n aD ．n a 2524．设z 0（z 0≠0）为复平面上一定点，z 1为复平面上的动点，其轨迹方程为|z 1−z 0|=|z 1|，z 为复平面上另一个动点满足z 1z =−1．则z 在复平面上的轨迹形状是 ．A ．一条直线B ．以01z -为圆心，01z 为半径的圆 C ．焦距为012z 的双曲线 D ．以上均不对25．一个球与正四面体的六条棱都相切，若正四面体的棱长为a ，则这个球的体积为 ．A ．3123a π B ．343a π C ．3242a π D ．3243a π 26．已知函数f （x ）的定义域为（0，2），则函数g （x ）=f （x +c ）+f （x −c ） 在 0＜21时的定义域为 ．A ．（1−c ，2+c ）B ．（c ，2−c ）C ．（1−c ，2−c ）D ．（c ，2+c ） 27．设函数f （x ）=sin （2x +ϕ），（−π<ϕ<0），y =f （x ）图象的一条直线x =8π．则ϕ的值为 ．A ．4πB ．43πC ．－43πD ．2π28．设f （x ）是定义在实数集上的周期为2的周期函数，且是偶函数．已知当x ∈[2，3]时，f （x ）=−x ，则当x ∈[－2，0］时，f （x ）的表达式为 ．A ．−3+|x +1|B ．2−|x +1|C ．3−|x +1|D ．2+|x +1|29．当a 和b 取遍所有实数时，则函数f （a ，b ）=（a+5−3|cosb|）2+（a −2）|sinb|）2所能达到的最小值为 ．A ．1B ．2C ．3D ．430．对任意实数x ，y ，定义运算x ºy 为x ºy ＝a x +b y +c xy ，其中a ，b ，c 为常数，且等式右端中的运算为通常的实数加法、乘法运算．已知1º2＝3，2º3＝4且有一个非零实数d ，使得对于任意实数x 均有x ºd=x ，则d= ．A ．－4B ．－2C ．1D ．4历年自主招生考试数学试题大全专题下载链接：/a760682.html链接打开方法：1、按住ctrl键单击链接即可打开专题链接2、复制链接到网页。

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。

上海四大名校高中自主招生往年试题大全上海四大名校高中自主招生往年试题大全[复旦附中]考智慧、测文理知识综合运用能力自主招生题：■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。

■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?试题精选：1、请归纳总结一下你在初中阶段学习过的数学方法。

2、以一道题目为例，阐述一下其中蕴含的数学方法。

3、请你谈谈某著名数学家对数学界和数学文化的贡献。

4、运用你所学过的物理知识，设计一个符合要求的电路实验(要求多解)题目背后：华师大二附中副校长袁军告诉记者，仅以“数学方法”一题，就难倒了不少学生。

不少学生在老师告诉其数学方法的定义之后，依然无法顺利作答，有的学生则在明白之后侃侃而谈。

暂且不论对错，这两种表现就将学生的不同特点跃然纸上。

他说，理科的学习并不是做题、做实验，在两者的基础上，懂得归纳理科的理论、方法，才是真正对这门学科感兴趣的学生。

而学生不仅要做题、做实验，更应主动关注学科的文化内涵，这样才能在学科道路上走得更远。

[格致中学]创新题目考查学生多方面素养“老鼠为什么吱吱叫?”参加完格致中学的自主招生面试，不少考生都对这道试题念念不忘。

今年的自主招生和推优，格致中学另辟蹊径，研究出了一种“人机对话”的测试办法，包括语数外在内的多门学科老师每人精心炮制出了一组试题，以期对学生的综合素质进行考量。

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。

哈佛北大精英创立7年上海复翱蜒匚语试题及答案解析1. You should pay attention to the way ____ you stand and sit. A. of B. that C. which D. 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 con tact can ___ n ervous ness. A. sig nal B. mark C. sigh D. desig n【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 assista nt because she greets every customer cheerfully. A. looked upon B. regarded C. viewed D. con sidered【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。

上海复旦附中自主招生英语试题31.They are fed up_______the old routine.A.withB.ofC.atD.on32.He is such a(n)_______teacher that has devoted all his and energy to his students.A.conscientiousB.consciousC.academicD.scientific33.We are looking for someone with a real sense of_______to the job.mitteemitmentmunitymission34.There are fewer working hours in the executive jobs,_______the job stress is comparatively higher.A.thatB.whereC.whichD.what35.Since you are_______to the seafood,you’d better avoid eating it.A.sensibleB.sentimentalC.sensitiveD.sensory36.During the celebration,fireworks have been_______at the bay.A.set outB.set aboutC.set upD.set off37.They declared the war,for they believed that country had_______the weapons of mass destruction.A.liberatedB.counteredC.approvedD.proliferated38.The journalist reported the_______of children labors who had worked many days on end.A.expansionB.expeditionC.exploitationD.explorationWhat is the thing called happiness?For centuries,people were too busy pursuing it39much time analyzing it.Now a pioneering band of researchers has finally bagged the elusive quarry or at least taken its ing such sophisticated new tools 40the five-item Life Satisfaction Scale and the seven-point Delighted-terrible Scale(On a scale of one to seven,how do you feel about your life?),social psychologists have plumbed the heart of happiness.And their answer to the age-old 41is that it all depends.Happiness,that is,42what makes.you feel happy,which is why psyc1hologists often call it“subjective well-being.”But from studies of various age and population groups in the United States and abroad,they have reached some44at the top of the charts is not,as many might expect,success,youth,good looks or any of those45assets.The clear winner is relationship,close ones, followed by happy marriage.Supportive,intimate connections with other people seem ing simple survey questions,psychologist David Myers found that the47happy people are those in unhappy marriages.Happiest are those who married 48their“best friend.”39.A.to spend B.spending C.has spent D.have spent40.Alike B.alike C.as D.for instance41.A.psychology B.mystery C.solution D.trick42.A.results in B.leans against C.dependes on D.arrives at43.A.realistic B.idealistic C.objective D.individualistic44.A.endlessly B.contradictorily C.harmoniously D.consistrntly45.Aenviable B.reliabele C.inevitable D.endurable46.A.vastly B.tremendously C.swiftly D.basically47.A.most B.best C.least D.worst48.A.to B.with C.for D.off上海复旦附中自主招生英语试题(2)Sarah Alexander celebrated the start of her last year at Wells College the way many other seniors before her have.She ran across the picturesque to the shores of Cayuga Lake,where she jumped into the water.So did many of her fellow seniors.But dozens of students decided to stay away, especially the relatively few newly arrived male students.Wells College,which since1868had educated only women,began accepting men this year in hopes of bolstering its dwindling enrollment.For many students and alumnae,it was a crushing decision.After the college announced last October that it would go coeducational,about half of the students protested and two filed a lawsuit,which they later dropped.The students—33men and383women–campus late month Both sexes are now trying to navigate new social landscape.Mr.Phillips said“You can’t do guy stuff.Every time you want to sit and watch sports or a game,it turns into a movie.”The women were“some what nasty.”I could see the dirty looks in their eyes,”he said.“But I was not going to let that stop me from coming.”Wells was a place where women did not have to fuss over their appearance or fight to be taken seriously by their professors.They could enjoy the camaraderie of their campus sisters and their playful traditions.Besides jumping into the lake,the women dance around the maypole each May and kiss the feet of the statue of Minerva,the Roman goddess of wisdom,before exams.Ms.Alexander said,“People told us we wouldn’t notice a difference,but from the moment men arrived on campus not could notice a difference.Waking up early to put on makeup,and that’s odd,”she said.Henry Wells,a founder of Wells Fargo and a friend of Cornell’s benefactor, Ezra Cornell established this college,when women were not considered capable of higher learning.“Give her the opportunity,”he wrote.Henry Wells,a founder of Wells Fargo and a friend of Cornell’s benefactor, Ezra Cornell established this college,when were not considered capable of higher learning.“Give her the opportunity,”he wrote.The great-great-great-great granddaughter of Henry Wells,Stephanie Redmond, 18,of Washington State,said that earlier this year a Wells student had tracked her down and asked her to support the protest.But Ms.Redmond said the move the move to admit men had encouraged her to enroll at Wells this year as a freshman.She plans on a career in engineering,a male-dominated field,and said attending an all-women’s college might have put her at a disadvantage.49.The primary reason for the Wells College to accept men is that.A.its enrollment rate is declineB.the campus is lack of vigor and vitalityC.it will face the destiny of being closed downD.all-women’s college might put a woman at a disadvantage50.A typical behavior for seniors to do that.A.they jog along the picturesque campusB.they switch sports programs to a movieC.they celebrate their year by jumping into a lakeD.they swim in Cayuga Lake accompanied by friends51.The change after turning into a coed college is that.A.dirty looks in women’s eyes have disappearedB.women get up early to make upC.women are waking up early to studyD.women dance with men around the maypole52.The attitude of the author is that.A.she hares a tradition of all-women schoolsB.she calls on women in support the protestC.she dislikes the change and hopes to file a lawsuitD.she objectively describes the new and uneasy coeducation53.Which of the following statements is Not true?A.The enrollment of male students caused controversy,B.The grandchildren of the college founder benefited most.C.The current president of the college was also its graduate.D.The founder hoped to give women opportunities of higher education.But what is teacher quality?How can one measure it reliably?An analysis is issued a sample of data a Texas school district.Experts argue convincingly that teacher effectiveness should be measured by students’gains on standardized tests:Mr.Smith is presumably a better teacher than Ms.Brown if his students consistently improve their test scores more than hers do.Though this approach is appealing,there are tricky issues.For example,what if Ms.Brown teaches in a school where students score so high there is little room for improvement?The authors try to correct for this problem,as well as other sorts of measurement issues,to generate a measurement of teacher effectiveness.The paper is primarily concerned with how this measure is related to other observable teacher characteristics.The first finding is that is a large variation in teacher effectiveness:some teachers consistently have a larger impact on their students’achievement than others.Second,easily observable characteristics like having a master’s degree or a passing score on the teacher certification exam are not correlated with teacher effectiveness.Then what does matter?The most important single influence is experience: first-year teachers are much less effective than others.The second year is significantly better,and by the fourth year,most teachers hit their stride.It is not entirely clear whether this experience effect is learning by doing (the more you teach,the more effective you become)or survival of the fittest(those who are not good at teaching tend to drop out early).From my reading of the paper,both effects appear important and there is no simple answer.The data do suggest,however,that teacher effectiveness is pretty clear by the end of the second year,so the information to make an informed decision is available at that time.The authors also investigate the contentious issue of racial matching of students and teachers.Here they find strong evidence that minority teachers tend to be more effective with minority students.Again,it is unclear whether this is because of a role model effect(students respond better of their own race)or anempathy effect(teachers empathize better with students of their own race)or something else entirely.The authors also look at teacher mobility.There is some evidence that teachers who quit teaching or switch schools tend to be below average in effectiveness.This is consistent with the survival-of-the-fittest model.54.The schoolmaster could decide wisely whether to further employ the teacher by the end of the.A.the first yearB.the second yearC.the third yearD.the fourth year55.The phrase“hit their stride”most probably means“”.A.reach their normal levelB.become confidentC.walk with long stepsD.get bored56.The author of this passage the view that.A.teachers will perform better with time passingB.ineffective teachers should leave earlier rather than laterC.teacher’s effectiveness is apparent after a couple of yearsD.a master’s degree will improve teacher’s effectiveness57.Why do black teachers tend to be more effective with black students?A.Students feel secure,so they respond better.B.Teachers sympathize with students of their own race.C.There are entirely some other identified reasons.D.The reasons are far from clear and definite.58.Which of the following may serve as the best title?A.Tenure,Turnover and the Quality of TeachingB.Impact of Teacher Quality on Student LearningC.Different Sorts of Measurement IssuesD.Survival-of-the-fittest Model vs.Learning-by-doing Model。

语文：1．[唐]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.对于解析：整句翻译：学业由于勤奋而专精，由于玩乐而荒废；德行由于独立思考而有所成就，由于因循随俗而败坏。

所以，于翻译为“由于，在于”。

“在于”和“在”的意思不同。

【C】2．［当］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.把象牙加工成器物解析：题目中的问句为“准确含义”，所以解释这个字的含义即可。

【D】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.那样解析：翻译为我不欺骗你，你不欺骗我。

演变到后来变成成语“尔虞我诈”。

【C】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、反复恳切地说解析：首先排除选项B，其次“苦口”容易想到成语“苦口婆心”，与老师这个人物相匹配。

【D】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.面目全非解析：涂脂抹粉：为了掩盖丑恶本质而粉饰打扮。

改头换面：只更改外表形式，容实质不变。

庐山面目：事物真相或者本来面目。

面目全非：改变得不像样子。

乔装打扮：进行伪装，隐藏身份。

【C】6．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.山穷水尽解析：寸草不生：土地贫瘠，一点草都不生长。

复旦附中数学考试试卷一、选择题（每题4分，共20分）1. 下列哪个选项是正确的？A. 2x + 3 = 5x - 1B. 2x + 3 = 5x + 1C. 2x + 3 = 5x - 2D. 2x + 3 = 5x + 22. 已知函数f(x) = x^2 - 4x + 4，求f(2)的值。

A. 0B. 4C. 8D. 123. 计算以下表达式的值：(3x - 2)(2x + 1)。

A. 6x^2 + x - 4B. 6x^2 + 5x - 2C. 6x^2 - x - 4D. 6x^2 + x + 24. 以下哪个图形是中心对称图形？A. 正方形B. 等边三角形C. 圆D. 以上都不是5. 已知a = 3，b = 2，求a^2 - b^2的值。

A. 5B. 7C. 9D. 11二、填空题（每题3分，共15分）6. 计算表达式2x^2 - 3x + 1在x = 1时的值：_________。

7. 一个圆的半径为5，求其面积：_________。

8. 已知等差数列的首项为3，公差为2，求第5项的值：_________。

9. 计算以下三角函数值：sin(30°) = _________。

10. 将分数3/4化简为最简分数：_________。

三、解答题（每题10分，共40分）11. 解方程：3x - 7 = 2x + 8。

12. 证明：对于任意实数a和b，(a + b)^2 = a^2 + 2ab + b^2。

13. 已知函数f(x) = 2x - 3，求f(-1)的值，并画出函数的图像。

14. 一个长方体的长为4，宽为3，高为2，求其体积。

四、附加题（10分）15. 证明勾股定理：在一个直角三角形中，直角边的平方和等于斜边的平方。

注：请在答题纸上清晰、工整地书写答案，保持卷面整洁。

89.“世界从何而来？”这一西方哲学的热门话题，由一中国圣贤作了简明扼要的回答：“无，名天地之始；有，名万物之母”；“天下万物生于有，有生于无”。

问：依据义判断，该圣人当是。

A.孔子B.孟子C.老子D.墨子90.《资治通鉴》卷必有如下一段文字：“十一月，沛公悉召诸县父老、豪杰，谓曰：”父老苦秦苛法久矣！吾与诸侯约，先人关者王之；吾当王关中。

”问：文中“沛公”当指以下哪个帝王？A.汉武帝B.汉高祖C.楚霸王D.楚怀王91.湖南岳麓书院有一对联，上联为“惟楚有材于斯为盛”；下联为“沅生芷草澧育兰花”，为冯友兰所书。

问：上联中所谓“惟楚有材”，是因为。

A.古时湖南为楚地B.芷兰盛产于楚地C.岳麓书院多人才D.冯氏出生在楚地92.在儒家思想逐渐成为中华民族传统精神主干的过程中，有三位思想家的作用举世公认：孔子、董仲舒、朱熹。

董仲舒提出：“罢黜百家，独尊儒术”，使孔子创立的儒学从诸子百家中跃居独尊地位。

问：董仲舒提出上述主张，中国出于时期。

A.西周B.东周C.西汉D.东汉93.“单于最初为中国古代北方游牧民族首领的称号，唐朝诗人卢纶亦作有《塞下曲》，提及“单于”：“月黑雁飞高，单于夜遁逃。

欲将轻骑逐，大雪满弓刀。

”问：诗中的“单于”当指民族的首领。

A.匈奴B.女真C.突厥D.回纥94.美籍华裔史学家黄仁宇在《中国大历史》中写道：“北宋之东北是××所成立的朝代――辽，××属蒙古语系，他们活跃于中国东北地区已逾300年，即使仿效中国朝代所成立的辽，也比宋早出现53年。

”A.回纥B.吐蕃C.契丹D.女真95.江苏无锡东林书院遗址(今东林小学)内有一楹联：“风声雨声读书声，声声入耳；家事国事天下事，事事关心。

”某史籍曾对当年东林书院情景作如是评论：“讲习之余，往往讽议朝政，裁量人物。

朝士慕其风者，多遥相应和。

”问：该点评当年东林书院情景的史籍当为。

A.《唐史》B.《宋史》C.《元史》D.《明史》96.在中国与某西方列强签署的不平等条约中，有下列条款：“合众国贸易船只进中国港口湾泊，仍旧各领事等官督同船主人等经管，中国无从统辖。

复旦附中2007学年上学期高三期中考试物理试卷2007－11－15一、选择题（14×4）1．中子内有—个电量为＋2e/3的上夸克和两个电量为－e/3凼小夸克。

—个简单的模型是三夸克都在一个半径为r 的圆周上的三个等分点上，如图所示，能正确表示各夸克受静电力作用的是2．可以发射这样一颗人造地球卫星，使其圆轨道 A 与地球表面上某一纬度线（非赤道）是共面同心圆 B 与地球表面上某—经度线所决定的圆是共面同心圆C 与地球表面上赤道线是共面同心圆，且卫星相对地球表面是静止的D 与地球表面上赤道线是共面同心圆，且卫星相对地球表面是运动的3．太阳从东边升起西边落下，这是自然现象。

在某些条件下，在纬度较高的地区上空飞行的飞机上，旅客可以看到太阳从西边升起的奇妙现象，这些条件是A 时间必须是在清晨，飞机正在由东向西飞行，飞机的速度必须较大B 时间必须是在清晨，飞机正在由西向东飞行，飞机的速度必须较大C 时间必须是在傍晚，飞机正在由东向西飞行，飞机的速度必须较大D 时间必须是在傍晚，飞机正在由西向东飞行，飞机的速度不能太大⒋．在光滑水平桌面上一质量为m 的小球，以速度v 沿位于水平面内的任意方向，由小孔O 射入一特殊区域，该区域位于图中MN 的上方。

在该区域小球始终受到一垂直于小球运动方向且与小球速度在同一水平面内的外力F 的作用，力F 大小恒定不变。

下列图中阴影部分表示小球所有可能经过的区域，其中R ＝mv 2/F ，哪个图是正确的？5．将一个电动传感器接到计箅机上，就可以测量快速变化的力，用这种方法测得某单摆摆动时悬线上拉力的大小随肘间变化的曲线如图所示，根据此图提供的信息作出以下判断 A 摆球的摆动周期T ＝0.6s B t ＝0.2s 摆球正好经过最低点 C t ＝1.1s 摆球正好经过最低点 D 摆球摆动过程中机械能守恒6．右图甲，波源s 从平衡位置y ＝0开始振动，运动方向竖直向上（y 轴的正方向）、振动周期T ＝0.01s ，产生的简谐波向左、右传播，波速均为v ＝80m/s 。