上交2018年自主招生试题
2018上海中学自招真题及答案
所以△ABE 和△ACD 是黄金三角形
在△ABE 中 AE 5 1 其中 AE 1 解得 BE 5 1
BE 2
2
（2）在△ACD 中过 A 作 AF 垂直CD 于点 F
易得FAD 18
所以 sin18 FD
AD
1 2= 5 1
【答案】（1） 6 c≤9 （2） 8104
【解析】（1）令 f 1 f 2 f 3 k ， g x f x k ， 0 k≤3 则 g x x 1 x 2 x 3 所以 f x g x k x3 6x2 11x 6 k
【答案】 45
4
【解析】如右图所示
易得 AC 92 122 15
所以OC 15
2
△C△OF∽ ABC
所以 OF OC 解得OF 45 即 EF 45
AB BC
8
4
8、任给一个正整数n ，如果n 是偶数，就将它减半（即 n ），如果n 是奇
2
数，则将它乘以 3 再加1（即 3n 1），不断重复这样的运算，现在请你研究：如 果对于正整数 n （首项）按照上述规则实施变换（注：1可以多次出现）后的第 八项为1，则 n 所有可能取值为
得到△ACB ，则点 C 的坐标是
【答案】
3 (,
3)
22
【解析】如右图所示易得
CAD BAO 60
过C 作CD x 轴于点 D 在△ACD 中 AC 1 易解得
AD 1 ， CD 3
2
2
即 C( 3 , 3 )
22
7、一张矩形纸片 ABCD ， AD 9， AB 12 ，将纸片折叠，使 A 、 C 两点重 合，折痕的长是
2018年上海中学自主招数学试卷-含答案详解
2018年上海中学自主招数学试卷一、选择题（本大题共4小题，共12.0分。
在每小题列出的选项中，选出符合题目的一项）1. 已知x2+ax−12能分解成两个整数系数的一次因式的积，则整数a的个数有( )A. 0B. 2C. 4D. 62. 如图，D、E分别为△ABC的底边所在直线上的两点，BD=EC，过A作直线l，作DM//BA 交l于M，作EN//CA交l于N.设△ABM面积为S1，△ACN面积为S2，则( )A. S1>S2B. S1=S2C. S1<S2D. S1与S2的大小与过点A的直线位置有关3. 设p1、p2、q1、q2为实数，则p1p2=2(q1+q2)，若方程甲：x2+p1x+q1=0，乙：x2+ p2x+q2=0，则( )A. 甲必有实根，乙也必有实根B. 甲没有实根，乙也没有实根C. 甲、乙至少有一个有实根D. 甲、乙是否总有一个有实根不能确定4. 设a=121+223+325+⋯+100722013，b=123+225+327+⋯+100722015，则以下四个选项中最接近a−b的整数为( )A. 252B. 504C. 1007D. 2013二、填空题（本大题共8小题，共24.0分）5. 已知1a +1b=1a+b，则ba+ab的值等于______ ．6. 有______个实数x，可以使得√120−√x为整数．7. 如图，△ABC中，AB=AC，CD=BF，BD=CE，用含∠A的式子表示∠EDF，则∠EDF=______．8. 在直角坐标系中，抛物线y=x2+mx−34m2(m>0)与x轴交于A，B两点.若A，B两点到原点的距离分别为OA，OB，且满足1OB −1OA=23，则m的值等于_______．9. 定圆A的半径为72，动圆B的半径为r，r<72且r是一个整数，动圆B保持内切于圆A且沿着圆A的圆周滚动一圈，若动圆B开始滚动时的切点与结束时的切点是同一点，则r共有______个可能的值．10. 学生若干人租游船若干只，如果每船坐4人，就余下20人，如果每船坐8人，那么就有一船不空也不满，则学生共有______人．11. 对于各数互不相等的正整数组(a1,a2,…a n)(n是不小于2的正整数)，如果在i<j时有a i>a j，则称a i与a j是该数组的一个“逆序”，例如数组(2,4,3,1)中有逆序“2，1”、“4，3”、“4，1”、“3，1”，其逆序数为4，现若各数互不相同的正整数组(a1,a2,a3,a4,a5,a6)的逆序数为2，则(a6,a5,a4,a3,a2,a1)的逆序数为______．12. 若n为正整数，则使得关于x的不等式1121<nx+n<1019有唯一的整数解的n的最大值为______．三、解答题（本大题共2小题，共16.0分。
【考试必备】2018-2019年最新上海交通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年最新上海交通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）③小屋在山的怀抱中，犹如在花蕊中一般，慢慢地花蕊绽开了一些，好像山后退了一些。
④当花瓣微微收拢，那就是夜晚来临了。
⑤小屋的光线既富于科学的时间性，也富于浪漫的文学性。
A．①③②④⑤ B．①④③②⑤ C．⑤③②①④ D．⑤③②④①二、阅读下面古诗文，完成7—14题。
（24分，7—12每题2分）勾践自会稽归七年，拊循其士民，欲用以报吴。
大夫逄同谏曰：“今夫吴兵加齐、晋，怨深于楚﹑越，名高天下，实害周室，德少而功多，必淫自矜。
为越计，莫若结齐，亲楚，附晋，以厚吴。
吴之志广，必轻战。
是我连其权，三国伐之，越承其弊，可克也。
”勾践曰：“善。
”其后四年。
吴士民罢弊，轻锐尽死于齐﹑晋。
而越大破吴，因而留围之三年，吴师败，越遂复栖吴王于姑苏之山。
吴王使公孙雄肉袒膝行而前，请成越王曰：“孤臣夫差敢布腹心，异日尝得罪于会稽，夫差不敢逆命，得与君王成以归。
今君王举玉趾而诛孤臣，孤臣惟命是听，意者亦欲如会稽之赦孤臣之罪乎？”勾践不忍，欲许之。
范蠡曰：“会稽之事，天以越赐吴，吴不取。
今天以吴赐越，越其可逆天乎？且夫君王蚤朝晏罢，非为吴邪？谋之二十二年，一旦而弃之，可乎？且夫天与弗取，反受其咎。
君忘会稽之厄乎？”勾践曰：“吾欲听子言，吾不忍其使者。
”范蠡乃鼓进兵，曰：“王已属政于执事，使者去，不者且得罪。
”吴使者泣而去。
勾践怜之，乃使人谓吴王曰：“吾置王甬东，君百家。
”吴王谢曰：“吾老矣，不能事君王！”遂自杀。
选自《史记·越王勾践世家》7．下列加点词语解释不正确的一项是（ ）A．越承其弊，可克也。
克：战胜 B．越遂复栖吴王于姑苏之山 栖：占领C．越其可逆天乎 逆：违背 D．吾老矣，不能事君王 事：侍奉8．下列加点词语古今意义相同的是（ ）A．今天以吴赐越 B．使者去，不者且得罪 C．谋臣与爪牙之士，不可不养而择也 D．微夫人之力不及此三、现代文阅读（14分） 大度读人 一个人就是一本书。
2017-2018学年上海市交大附中英语自招练习(五)
交大附中自招练习（五）I.Choice（30%）1.Paper produced every year is_______ the world’s production of vehicles.A.the three times of weight ofB.three times the weight ofC.as three times heavy asD.three times as heavier as2.He is a student of______.A.Class FirstB.the Class OneC.Class OneD.First Class3.This morning I had my finger_______.A.cuttingB.to cutC.to be cuttingD.cut4.The house had one of the windows_______in the storm yesterday.A.breakingB.to be breakingC.brokenD.to be broken5.You’d better______some money for special use.A.pick upB.set asideC.put offD.give6.In order to______with the advanced countries,we must keep learning.A.catch upB.get alongC.put upD.go on7.Do you mind______alone at home?A.Jane leavingB.Jane having leftC.Jane’s being leftD.Jane to be left8.The two things______they felt very proud were Jim’s gold watch and Della’s hair.A.about whichB.of whichC.in whichD.for which9.Not only______drive the car,but also________repair it.A.he is able to...he canB.is he able to...can heC.he is able to...can heD.is he able to...he can10.Meet me at the same place______you did yesterday.A.whereB.in whichC.thatD.as11.The world_______is made up of water.A.in that we liveB.on which we liveC.where we live inD.we live in12.The eating habits in the north are very much different_______those in the south.A.thenB.withC.asD.from13.This is a secret.Keep it______the two of us.A.betweenB.inC.amongD.inside14.I don’t like_______you speak to her.A.the wayB.the way in thatC.the way whichD.the way of which15.Was it in 1969______the American astronaut succeeded______landing on the moon.A.when...onB.that...onC.when...inD.that..in16._______he said so really disappointed the people present at the meeting.A.HowB.WhatC.ThatD.Why17.The question was_______we are going to take the children to the theater or to leave them at home.A.howB.whatC.ifD.whether18.Smith_______be a policeman,for he is much too short.A.needn’tB.can’tC.shouldD.may19.Jane's pale face suggested that she______ill,and her parents suggested that she______a medical examination.A.be....should haveB.was...haveC.should be... hadD.was...has20. Take it_________.Everything will be fine in a day or two.A.easyB.quietC.calmD.light21.I bought a shirt because it was good in quality and______in price.A.reasonableB.valuablefortableD.enjoyable22.The pair of shoes_______worn out.A.wasB.wereC.have beenD.had been23.All but one _______ here just now.A.isB.wasC.are 'D.were24.One more week,_______we will accomplish the task.A.orB.so thatC.andD.if25.The suit fitted him well______the color was a little brighter.A.except forB.except thatC.except whenD.besides26.Ps and Qs in the English language______”Pleases”and”Thank you”.A.are short ofB.are lack ofC.are short forD.are lacking in27.It is______that the English,in day-to-day contact with each other,is more_____than French or GermanmonB.believing...ordinaryC.believed...normalD.believed...formal28.There is little or no money for the expansion of classroom.A.areaB.fieldC.placeD.space29.The virus scan on your computer can easily ________this new kind of virus.A.killB.destroyC.damageD.harm30.It is generally_______that the old should_______the young person.A. acceptable...give way toB. accepted...give way toC. acceptable...lead the way toD. accepted...lead the way toII. Cloze ( 40% )(A)A 31 man was reported to_32 _by a pig he was __33_,according to the daily news in a certain newspaper. The report said the _34___ man, surnamed San, lived ____35___in a village not far away from the town.Raising pigs and chicken was his___36___and he bought the man-eating porker four years___37___.One morning last week,San was seen______the pig pen as usual.It was the last time anybody saw him____39___.Afraid that something was wrong,San’s neighbors broke into his home and found the pig______away on the elderly man’s bones.( )31.A.71-years-old B.71-year old C.71-year-old D.71 years old( )32.A.to be eaten B.to have been eaten C.eat D.have eaten( )33.A.raised B.growing C.raising D.grown( )34.A.elder B.older C.junior D.elderly( )35.A.alone B.lonely C.simply D.easily( )36.A.major B.hobby C.life D.course( )37.A.since B.ago C.before ter( )38. A. clearing B. cleaning C. working D. doing( )39.A.dead B.alike . C. lively D. alive( )40.A.running B.staying C.chewing D.tasting(B)“Two out of six, who committed suicide, died," the Labor Daily has reported. What 41 local citizens even more was the fact 42 most pupils at the school have not shown much 43 or sorrow about the tragedy. They seem to feel that death is not 44 frightening. It is quite common that simply____45___poison and going to sleep,_______which they never give up, is the best way to end their lives when they don’t feel happy enough.Surely enough, a group suicide, _47_ children at such a young age are so unhappy_48___end their lives, is extremely rare. Experts believe it may have _49_ to do with excessive pressure being put on children.A Beijing report said that more than l,000 children had written to the State Youth Commission 50 that they had too much homework and were not receiving sufficient care from their4 parents. Child welfare experts have appealed to parents to give their children more free time.( )41.A.pleased B.satisfied C.shocked D.relieved( )42.A.that B.which C.what D.where( )43. A. pleasure B. enjoyment C. regret D. excitement( )44.A.that B.such C.still D.even( )45.A.eating B.taking C.swallowing D.chewing( )46.A.on B.in C.with D.from( )47.A.in which B.in that C.on which D.on that( )48. A. in order to B. as to C. to D. in order that( )49.A.anything B.nothing C..something D.little( )50.A.wishing B.expecting C.quarreling plainingII .Lading Comprehension ( 20% )(A)Dear Editor,My Chinese teacher, who I also consider to be my friend, is very young. My classmates often make fun of him in class. But he hides his unhappiness and has never showed his anger.In fact,he feels hurt by their actions.How can I help him?I am looking forward to your suggestions. Yours sincerely,MikeDear Mike,The letter you wrote reached us yesterday,from which we know you are mature enough to understand your Chinese teacher’s emotion when he is hurt by your classmates.Do what you should do for any classmate who is being picked on(捉弄).Stand up for your teacher.If you are strong enough, you will be able to deal with that.To stand apart from the crowd and to speak your mind is very brave and wonderful thing to do.Many kids don’t realize that teachers have the same feeling just as you do.The simply love to be part of a crowd.If you stand up for your teacher and tell your classmates how unhappy they make him feel, many kids will feel bad about upsetting him.They will stop making fun of him.Perhaps your teacher has chosen to deal with these kids by ignoring them. But, if he is still feeling upset, he might feel better teaching in a different way. Suggest to him that he discipline them. Because he is still so young, he will have to work hard enough to gain his students' respect. But he must at least try.Normally, it is students who turn to teachers for help. But in this case, you can help your teacher. You will grow from the experience. You'll get a lot of respect, and you'll make your teacher friend's life a lot happier. These are our suggestions just for your reference. Hopefully they will work in dealing with the problem you face up to. Best wishes to you, and keep in touch if you have any problem with your study and some other fields related.Yours friendly.Editor( )51.The letter by Mike had covered the problem that .A. the students had some difficulty in learning ChineseB. his Chinese teacher lacked experience in dealing with his tough studentsC. his Chinese teacher was unhappy, but never showed his anger.D. Mike himself was hurt when he was not respected by his classmates( )52.The underlined phrase stand up [or the teacher in the first paragraph most probably means that . .A. to stand up when you are asked to answer a question in class.B. to be more polite, you should stand closer to your teacher when you chat with him.C. to support your teacher when you find what he is doing is right.D, to punish any classmate who makes fun of your Chinese teacher.( )53. One of the reasons why so many kids liked to make fun of the teacher was that___________.A. they just wanted to be on the side of a big crowd without considering the bad feeling that the Chinese teacher had.B. it might be easy for them to stand apart from a big crowd.C. they knew that kidding was just fun, would could keep the smooth running ofclassroom performance.D.they just wanted to make the Chinese teacher angry by doing so( )54.The advice, as good as if not better than, from the editor was that________.A.the Chinese teacher should first of all respect his kids in order to be well respectedB.the students should turn to the teacher for the exchange of their viewpoints on teaching and learningC.the Chinese teacher should make friends with his kidsD.Young as he was, the Chinese teacher should well discipline his students and at the same time he should worked hard to gain the students’ respect( )55.The Chinese teacher who teaches Mike is_________.A.middle-agedB.youngC.oldD.elderly(.B )There are many single parents because there are many divorces in the United States. A young woman who gets married must think carefully about having a child. There is 50 percent chance that she will have to take care of that child alone someday. Here is the story of one single parent who is happy with her life."My name is Sara. I am a secretary for a businessman in a small city. I have two daughters and a son. I was divorced three years ago. My ex-husband, Ron comes to see the children one or two times a month. He usually takes them to a movie or a restaurant."The life of a single parent is hard. I work all of the time. I work at my job all day.Then I gohome to work all evening. I am often tried when I get home at 5:30 in the evening. Tired or not, I make dinner for my children and listen to their problems. After dinner, I clean the house, wash clothes, shop for food, or help the children with their homework. My children are young, but they help me around the house.My biggest problem is money. When Ron and I divorced, he let me have the small house the children and I live in. I'm glad I have it because it is good for the children. Now I have to pay for it every month and pay the bills. That's difficult. I make about $ 18,000 a year at my job. Ron has to pay me$450 a month to help with the children. Everything is very expensive now. There isn't enough money for everything. I have to be very careful.Do I have to marry again? Maybe. I am going to be very careful. If I marry again, want to be sure it will be a good marriage this time. I don't want to marry. I am happier by myself than in a bad marriage”( )56.The word "ex-husband" (line 2 para.2) probably means .A. former husbandB. future husbandC. husbandD. Boyfriend( )57. What work does Sara NOT do in the evening?A. WashingB. ShoppingC. CleaningD. Going to a movie( )58.How much does Sarah Not do in the evening?A.WashingB.ShoppingC.CleaningD.Going to movie( )59.Sara’s biggest problem is that______.A.she is tired all of the timeB.she lacks moneyC.she has to do a lot of houseworkD.she has to look after her children alone( )60.The life of single parents is hard for Sara has to_______.A.get back at 5:30 in the eveningB. make dinner for her childrenC. work hard all dayD. clean the houseIV. Fill in the blanks with the words in their proper forms ( 10% )1. The new suspension bridge ______ ( design ) by the end of last month.2. ---Hi, Mary, you look tired.---I am tired. I_______( paint ) the living room all day.3. Robert is said to _______( study ) abroad, but I don't know what country he studied in.4. The reporter said that the UFO_______( travel) east to west when he saw it.5.The new secretary is supposed to report to the manager as soon as she _____( arrive).6. In some parts of the world, tea _______( serve ) with milk and sugar.7.The pen I thought I - ( lose ) is on my desk, right under my nose.8. As she was reading the newspaper, Granny ______( fall ) asleep.9. You don't have to describe her. I_______( meet ) her several times.10. I don't think Jim saw me; he_______( just stare ) into space.Key:I.BCDCB ACBDD DDAAD CDBBA AADCB CCDABII.CBCDA BBBDC CACAB DABCDIII.略IV.had been designed have been painting to have been studying was traveling arrives is served had lost fellHave met was just staring。
2018上海交通大学自主招生试题
上海交通大学化学注意事项：本试卷共有19道试题，总分100分。
一、填空题（共11小题） 1．【真题】将等物质的量的A 和B ，混合于2L 的密闭容器中，发生如下反应：()()()()3A g B g C g 2D g x ++═，经过5min 后测得D 的浓度为0.5mol /L ，()()A :B 3:5c c =，C 的反应速率是()0.1mol /L min ⋅，A 在5min 末的浓度是___________，B 的平均反应速率是___________，D 的平均反应速率是___________．x 的值是___________ 3．【真题】一定温度下，在2L 的密闭容器中，X 、Y 、Z 三种气体的物质的量随时间变化的曲线如图所示：（1）从反应开始到10s 时，用Y 表示的反应速率为______________________________。
（2）该反应的化学方程式为______________________________。
（3）若上述反应分别在甲、乙、丙三个相同的密闭容器中进行，经同一段时间后，测得三个容器中的反应速率分别为甲：()11X 0.3mol L s v --=⋅⋅；乙：()11Y 0.12mol L s v --=⋅⋅ 丙：()11Z 9.6mol L min v --=⋅⋅；则甲、乙、丙三个容器中反应速率由慢到快的顺序为______________________________。
5．【真题】叶绿素在光的作用下可将2CO 和2H O 转化为葡萄糖()6126C H O 和2O 。
????22612626CO 6H O C H O 6O −+−→+，葡萄糖可进一步合成淀粉()6105C H O n ⎡⎤⎣⎦。
科学家预言，在不久的将来，人类将模拟生物体内的这一变化过程，从工厂中由2CO 和2H O 直接生产出淀粉。
这样，合成优质叶绿素将十分重要。
叶绿素有a 、b 两种，已知某种叶绿素中仅含有C 、H 、O 、N 、Mg 五种元素，且知该叶绿素中各元素的质量分数分别是()C 73.99%w =，()H 8.072%w =，()O 8.969%w = ()N 6.278%w =，()Mg 2.691%w =经测定该叶绿素的相对分子质量小于1000，试确定该叶绿素的分子式。
【考试必备】2018-2019年最新交通大学附属中学初升高自主招生考试英语模拟精品试卷【含解析】【4套试卷】
2018-2019年最新交通大学附属中学自主招生考试英语模拟精品试卷（第一套）考试时间：120分钟总分：150分第I卷（选择题，共100分）第一节：单项填空（共25小题，每小题1分，满分25分）1. —When did the terrible earthquake in YaNan happen?—It happened ________ the morning of April 20, 2013.A. onB. atC. inD. /2. Our teacher told us ________ too much noise in class.A. to makeB. makeC. not to makeD. not make3. Here is your hat. Don’t forget______ when you __________.A. to put it on, leaveB. to wear it, leaveC. to wear it, will leaveD. putting it on, will leave4. The baby is sleeping. You _____ make so much noise.A. won’tB. mustn’tC. may notD. needn’t5. Since you are _____ trouble, why not ask _________ help?A. in, forB. in, toC. with, forD. with, to6. It’s about___________kilometers from Nanchong to Chengdu.A. two hundredsB. two hundreds ofC. two hundredD. two hundred of7. It is six years since my dear uncle ________China.A. leftB. has leftC. is leftD. had left8. —How long _______ you _______ the bicycle?—About two weeks.A. have, hadB. have, boughtC. did, buyD. have, have9. The Yellow River is not so ________ as the Yangtze River.A. longerB. longC. longestD. a long10. Mrs.Green usually goes shopping with ________ umbrella in ________ summer.A. a；theB. an； /C. the； aD. /；/11. At first, I was not too sure if he could answer the question. However, ____,he worked it out at last with the help of his friend.A. to my angerB. to my surpriseC. in other wordsD. ina word12. —Must I stay here with you?—No, you ______.You may go home, but you _____ go to the net bar (网吧).A. mustn't; needn'tB. needn't; mustn'tC. must; needD. need; must13. I ______ the newspaper while my mother _____TV plays yesterday evening.A. was reading; was watchingB. was reading; watchedC. read; was watchingD. read; would watch14. It's a rule in my class that our classroom ________ before 6：00 p. m.every day.A. be able to cleanB. should be cleaningC. must cleanD. must be cleaned15. —Tom wants to know if you ________ a picnic next Sunday.—Yes. But if it ________， we'll visit the museum instead.A. will have; will rainB. have; rainsC. have; will rainD. will have; rains16.—Would you mind looking after my dog while I'm on holiday?—________.A. Of course notB. Yes. I'd be happy toC. Not at all. I've no timeD. Yes, please17. Many students didn’t realize the importance of study _______they left school.A. whenB. untilC. afterD. unless18. My father _______ to Shanghai. He _______ for over 2 months.A. has been, has leftB. has gone, has goneC. has gone, has been awayD. has been, has gone19. They are your skirts. Please __________.A. put it awayB. put out itC. put them awayD. put them out20. —Please read every sentence carefully. you are,mistakes you’llmake.—Thank you for your advice.A. The more carefully; the fewerB. The more careful; the lessC. The more carefully; the lessD. The more careful; the fewer21. My friend is coming today but he didn’t tell me _______.A. when did the train arriveB. how did the train arriveC. when the train arrivedD. how the train arrived22. I felt it hard to keep up with my classmate s. But whenever I wantto _______, my teacher always encourages me to work harder.A. go onB. give upC. run awayD. give back23. —________ fine weather it is today!—Let's go for a picnic.A. WhatB. HowC. What aD. How a24.— Mary, you’re going to buy an apartment here, aren’t you?—Yes, but I can’t_______an expensive one.A. spendB. costC. payD. afford25. —Would you like to drink coffee or milk?—_________. Please give me some tea.A. NeitherB. BothC. EitherD. None第二节：完形填空（共20小题，每小题1分，满分20分）(A)Big schoolbags have been a serious problem for students for a long time.Maybe your schoolbag is too __26__ to carry, and it troubles you a lot __27__ you want to find a book out to read. Now an etextbook will __28__ you.It is said that etextbooks are going to be __29__ in Chinese middle schools.An etextbook, in fact, is a small __30__ for students.It is much __31__ than a usual schoolbag and easy to carry. Though it is as small as a book, it can __32__ all the materials (材料) for study.The students can read the text page by page on the __33__， take notes with the pointer (屏写笔). Or even “__34__” their homework to their teachers by sending emails. All they have to do is to press a button.Some people say etextbooks are good, but some say they may be __35__ for the students' eyes. What do you think of it?26.A.light B. heavy C. useful D. comfortable27.A.till B. after C. before D. when28.A.trouble B. prevent C. help D. understanded B. kept C. invented D. lent B. radio C. pen D. computer31.A.heavier B. lighter C. cheaper D. brighter32.A.hold B. build C. discover D. practice33.A.blackboard B. desk C. screen D. card34.A.find out B. hand in C. get back D. give back35.A.helpful B. famous C. good D. bad(B)Food is very important. Everyone needs to _36_ _well if he/she wants to have a strong body. Our minds also need a kind of food. This kind of food is__ 37 __.We begin to get a knowledge even when we are very young. Small children are __38__ in everything around them. They learn __39 __while they are watching and listening. When they are getting older, they begin to ___ 40__ story books, science books…anything they like. When they find something new, they have to ask questions and__41___ to find out the answers.What is the best ___42___to get knowledge? If we learn___43___ourselves, we will get the most knowledge, If we are__44___getting answers from others and don’t ask why, we will never learn more and understand___45_.36. A. sleep B. read C. drink D. eat37. A. sport B. exercise C. knowledge D. meat38. A. interested B. interesting C. weak D. meat39. A. everybody B. something C. nothing D. anything40. A. lend B. write C. think D. read41. A. try B. wait C. think D. need42. A. place B. school C. way D. road43. A. in B. always C. to D. by44. A. seldom B. always C. certainly D. sometimes45.A.harder B. much C. well D. better第三节：阅读理解（共25小题，每小题2分，满分50分）AFamous Museums_______ .A. BeijingB. LondonC. New YorkD. The USA47. New York Museum is America’s largest museum on American__________.A. areaB. historyC. collectionsD. buildings48. The Palace Museum. Which is in the center of Beijing, is also called“Forbidden City(紫禁城)” in China. It lies in __________.A.Chang’an StreetB. New Oxford StreetC. BerlingD. Chestnut Street49. According to the form, if you want to see ancient Chinese collections,you can visit ____ at most.A. one museumB. two museumsC. three museumsD. four museums50. Which of the following is TRUE according to the information above?A. Each ticket for the Palace Museum costs the same in the whole year.B. You don’t have to pay for tickets if you visit New York Museum on Monday.C. British Museum lies in Chestnut street, London.D. New York Museum is the largest in the world.BIn recent years, more and more people like to keep pets such as a dog, a cat, a monkey and other animals. But usually people would accept tame(温顺的) and loyal(忠诚的) animals as pets rather than dangerous ones such as a lion，a tiger or a snake.People love pets and take good care of them. The owners usually regard pets as good friends and some even consider them as members of the family. Although they are not human beings(人类), their behavior sometimes is better than human beings, for they are always loyal to their owners. There are always many stories about brave and smart pets. We often hear that a pet dog saved the owner's life or traveled thousands of miles to return home. Such stories often make pets more lovely.Some pets can also be trained to help people with some special work. For example, trained dogs can help the blind to walk and trained dogs and pigs can even help police to find where drugs are easily.But pets are sometimes trouble-makers. Some pets like dogs or snakes may hurt people without any warning. Some people may become ill after being hurt because of the virus carried by the pets. If they are not taken good care of, they will become very dirty and easily get ill. So pets are helpful to us but keeping pets is not an easy job.51. What animals are thought to be dangerous as pets?A. Cats.B. Dogs.C. Snakes.D. Monkeys52. Which of the following statements is TRUE about pets?A. All the pets are considered as family members.B. Pets always behave better than human beings.C. Sometimes some pets can protect their owners.D. Pets like traveling far away from home.53. Why do people train pets according to the passage?A. To make them more clever.B. To make them more lovely.C. To find drugs for the blind.D. To do some special work.54. What can we learn from the last paragraph?A. Pets often hurt strange people.B. Pets can live well with the virus.C. Pets are dirty and dangerous.D. Pets should be looked after well.55. What is the best title for the passage?A. Training Pets.B. Keeping Pets.C. Cleaning Pets.D.Loving Pets.CFrom Feb. 8 to Mar. 1 is our winter holiday. I think everybody did a lot in the holiday. But it seems that I did nothing and it was my most unlucky holiday.I spent a lot of time on my homework. Every morning my mother woke me up early and I had breakfast in a hurry. Then I had to do my homework almost the whole day! I’m not a very slow person but the homework was too heavy!I was also unlucky when playing. During the Spring Festival, I played fireworks but my finger was hurt because I was careless to light the fireworks. I began to fear playing with fireworks from then.I was still unlucky on my friend’s party. On my friend’s birthday, unusually I woke up at 10:50 because my parents went to visit my grandmother early in the morning. The party would start in 10 minutes! So I hurried to my friend’s home without breakfast. I returned very late that day and when I got home, my parents were very angry with me.Another worrying thing was my weight. Last term, I was 46 kg but nowI am 51 kg! I have to consider losing weight!56. How long did the winter holiday last?A. two monthsB. one monthC. 4 weeksD. 22 days57. The writer got up early every day during the holiday because ______.A. he had to finish homeworkB. he had to have breakfastC. he was a very slow personD. his mother was in a hurry58. He hurt his finger because of ________.A. the Spring FestivalB. his carelessnessC. the light of fireworksD. his fear of playing59. Why were the writer’s parents angry with him?A. Because he got up too late.B. Because he missed breakfast.C. Because he was late for the party.D. Because he came back home too late.60. What did the writer want to tell us in the passage?A. He had an unlucky holiday.B. He had too much homework.C. His parents were very strict.D. He planned to lose weight.DSteven Jobs, the designer of Apple Computer, was not clever when he was in school.At that time, he was not a good student and he always made troubles with his schoolmates.When he went into college, he didn't change a lot.Then he dropped out.But he was full of new ideas.After he left college, Steven Jobs worked as a video game designer.He worked there for only several months and then he went to India.He hoped that the trip would give him some new ideas and give him a change in life.Steven Jobs lived on a farm in California for a year after he returned from India.In 1975, he began to make a new type of computer.He designed the Apple Computer with his friend in his garage.He chose the name “Apple” just because it could help him to remember a happy summer he once spent in an apple tree garden.His Apple Computer was such a great success that Steven Jobs soon became famous all over the world.61.Steven Jobs was not a good student in school because he ________.A. never did his lessonsB. was full of new ideasC. always made troubles with his schoolmatesD. dropped out62.Did Steven Jobs finish college?A. Yes, he did.B. No, he didn't.C. No, he didn't go into college.D. We don't know.63.Steven Jobs designed his new computer ______.A. in IndiaB. with his friendC. in a pear tree gardenD. by himself64.Steven Jobs is famous for his ________ all over the world.A. new ideasB. appleC. Apple ComputerD. video games65.From this passage we know ________.A. Steven Jobs didn't finish his studies in the college because he hatedhis schoolmatesB. Steven Jobs liked traveling in India and CaliforniaC. Steven Jobs liked trying new things and making new ideas become trueD. Steven Jobs could only design video gamesEIf you go into the forest with friends, stay with them. If you don't, you may get lost. If you get lost, this is what you should do. Sit down and stay where you are. Don't try to find your friends. Let them find you. You can help them find you by staying in one place. There is another way to help your friends or other people to find you. You can shout or whistle (吹口哨) three times. Stop. Then shout or whistle three times again. Any signal given three times is a call for help.Keep up shouting or whistling. Always three times together. When people hear you, they will know that you are not just making a noise for fun. They will let you know that they have heard your signal. They will give you two shouts or two whistles. When a signal is given twice, it is an answer to a call for help.If you don't think that you will get help before night comes, try to make a little house with branches .Make yourself a bed with leaves and grass.When you need some water, you have to leave your little branch house to look for it. Don't just walk away .Pick off small branches and drop them as you walk in order to go back again easily.66.If you get lost in the forest, you should ________.A. walk around the forest to find your friendsB. stay in one place and give signalsC. climb up a tree and wait for your friends quietlyD. shout as loudly as possible67.Which signal is a call for help?A. Shouting one time as loudly as you can.B. Crying twice.C. Shouting or whistling three times together.D. Whistling everywhere in the forest.68.When you hear two shouts or two whistles, you know that ________.A. someone finds something interestingB. people will come and help youC. someone needs helpD. something terrible will happen69.Before night comes, you should try to make a little house with ________.A. stoneB. earthC. leaves and grassD. branches70.Which of the following is the best title?A. Getting Water in the ForestB. Spending the Night in the ForestC. Surviving (生存) in the ForestD. Calling for Help in the Forest 第四节：补全对话，从方框内7个选项中选择恰当的5个句子完成此对话(共5分)John: Hi, Karl. You were not here, in your class yesterday afternoon. What was wrong?Karl: 71________John: Sorry to hear that.72Karl: Much better. The fever is gone. But I still cough and I feel weak. John: 73Karl: Yes, I have. I went to the doctor’s yesterday afternoon. The doctor gave me some medicine and asked me to stay in bed for a few days. John: 74Karl: Because I’m afraid I’ll miss more lessons and I’ll be left behind. John: Don’t worry. Take care of yourself. 75第Ⅱ卷（非选择题,共50分）一、根据句意及所给提示，补全单词或用单词、固定短语、固定搭配的正确形式填空(10分)76. Many athletes won gold medals in the Olympics, they are our national h_____.77. Tom didn’t finish _____________( write) his test because he ran out of the time.78. The girl is making a model doll ___________ (care).79. The boy felt __________(困倦的) in class because he stayed up late last night.80. So Terrible! The airplane ______________(起飞) five minutes ago.81.I don't think students should be（允许）to bring mobile phones to school.82.I find it useless to spend much time（解释）it to him.83. She prefers keeping silent to（争吵）with others.84. It is important for us to be（有信心的）of doing everything.85. The doctor operated on the patient（成功）yesterday.二、汉译英, 一空一词（共5小题，每小题2分，计10分）86. 他默默地在雨中行走，浑身上下都被淋湿。
上海交通大学自主招生笔试面试真题
上海交通大学自主招生笔试面试真题
自主招生考试中,笔试和面试是考生和家长最为关注的,而每年都有关于自主招生脑洞大开的题目,大家很好奇自主招生考试都考什么?下面是上海交通大学往年自主招生部分笔试面试真题，仅供参考。
上海交通大学笔试题目中，数学和物理各45道题，两个科目的试卷足有13页，定成一本。
所有题目都是选择题，选错会倒扣分。
语文也是选择题，共有50道，主要根据四五篇文章做阅读，文章为学术类文章、文言文等。
题目涉及理解文章内容，也涉及到课外知识，需要广泛涉猎。
1、数学：几何，十个小题六个大题两个小时。
2、物理：力学，三个小题五个大题两个小时。
物理热力学有一个分析题。
3、语文：考到了“八仙过海”中的八仙，要求选择不是八仙的选项。
1、面试中，先是自我介绍，水平好的话可以申请用英语说，用中文版的话之后可能会让你用英语随便说点什么。
2、之后便是根据你的自我介绍和自荐信提问。
如果遇到一些比较刁钻的老师，便会故意为难你，比如问你的专业和他教的专业哪个难，无论你说哪个，他便会说另一个怎么怎么难来反驳，你再次反驳后，他依然会挑刺来反驳你，个人觉得只要说的有理有据，阐明自己的见解和理由就行了。
问问题也会涉及到个人经历，比如问你为什么会担任xx课代表，或者有没有参加过和专业相关的活动，以及竞赛经历，高考状况。
还有，对于本专业名人的了解不能拘泥于交大的，有的老师会特地要求不允许举例交大的名人，要求比较苛刻。
另外，竞赛证书是可以带进面试考场的，允许你展示获奖证书。
感谢您的阅读，祝您生活愉快。
【考试必备】2018-2019年最新交大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年最新交大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”。
2018上海市上海交通大学附属中学自招真题及答案
3． AB∥CD ， AB = 15 ， CD = 10 ， AD = 3 ， CB = 4 ，求 SABCD __________． 【答案】 【解析】解：设 AE = x ， BC∥FD ， 则：： AF = AB − CD = 5 ， GF =AF − AE =5 − x ，
A= D2 A= E2 FD2 − EF 2 即： 9 − x2 = 16 − (5 − x)2 ，
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10． G 为重心， DE 过重心，求 S△ADE max 以及 S△ADE min ，并证明结论．
A
D
E
B
C
【答案】 【解析】假设△ABC 面积为 S1 ，△ADE 面积为 S2 ， 设 AD = mAB ， AE = nAC ，由于 G 为△ABC 重心，易知： 1 + 1 =3 ，
A
D
G
D
E
B
C
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7．在直角坐标系中，正 △ABC
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y A
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17 【答案】
8 【解析】作 MH∥AC ， MG ⊥ BH ， 设 BH = x ，
OH = HC ⇒ 2 + x = 5 − x ， 2
2018年___自主招生数学试卷(含答案解析)
2018年___自主招生数学试卷(含答案解析)2018年___自主招生数学试卷一、选择题（本大题共6小题，共24.0分）1.√16的平方根是()A.4B.±4C.22.若√(1−x)2=x−1成立，则x满足()A.x≥1B.x≥C.x≤1D.±23.已知x=√5−1，则x2+2x的值是()A.2B.3C.4D.54.如图所示的四条直线a、b、c、d，直线a、b与水平线平行，以其中一条为x轴，d与水平线垂直，取向右为正方向；直线c、以其中一条为y轴，取向上为正方向．某同学在此坐标平面上画了二次函数x=xx2+2xx+2(x≠0)的图象如图，则下面结论正确的是()A.a为x轴，c为y轴B.a为x轴，d为y轴C.b为x轴，c 为y轴D.b为x轴，d为y轴5.如图，已知AB为圆的直径，C为半圆上一点，D为半圆的中点，xx⊥xx，垂足为H，HM平分∠xxx，HM交AB于x.若xx=3，xx=1，则MH长为()A.1B.1.5C.0.5D.0.76.如图，△xxx中，∠x=90°，D是BC边上一点，∠xxx=3∠xxx，xx=8，xx=7.则AB的值为()A.15B.20C.2√2+7D.2√2+√7二、填空题（本大题共10小题，共40.0分）7.已知实数x、y满足x+2x=5，则x−x=3.8.分解因式：x2+4xx+4x2+x+2x−2=(x+2x+1)2−3.9.在平面直角坐标系中，点A，B的坐标分别为(x,3)，(3x−1,3)，若线段AB与直线x=2x+1相交，则m的取值范围为(0,1)。
10.若一个圆锥的侧面展开图是半径为18cm，圆心角为240°的扇形，则这个圆锥的底面半径长是9cm。
11.如图，已知在矩形ABCD中，点E在边BC上，BE=2CE，将矩形沿着过点E的直线翻折后，点C、D、N处，B在同一直线上，分别落在M、F与BE交于点G.设AB=√3，那么△xxx的周长为4+4√3.12.如图，已知点x1，x2，…，xx均在直线x=x−1上，点x1，x2，…，xx均在双曲线x=−x上，x1x1⊥x并且满足：x1x2⊥x轴，x2x2⊥x轴，…，xx−1xx⊥x轴，xxxx⊥x轴，且x1x2=x2x3=…=xx−1xx，则n的最小值为2.1.由题意可知，点B在x轴负半轴，点A在x轴正半轴，且AB垂直于x轴，因此AB的斜率为0，即AB为x轴，所以B的纵坐标为0.又因为B在x轴负半轴，所以其横坐标为负数，设为-a。
【考试必备】2018-2019年最新上海交通大学附属中学初升高自主招生考试英语模拟精品试卷【含解析】【4套】
2018-2019年最新上海交通大学附属中学自主招生考试英语模拟精品试卷（第一套）考试时间：120分钟总分：150分第I卷（选择题，共100分）第一节：单项填空（共25小题，每小题1分，满分25分）1. —When did the terrible earthquake in YaNan happen?—It happened ________ the morning of April 20, 2013.A. onB. atC. inD. /2. Our teacher told us ________ too much noise in class.A. to makeB. makeC. not to makeD. not make3. Here is your hat. Don’t forget______ when you __________.A. to put it on, leaveB. to wear it, leaveC. to wear it, will leaveD. putting it on, will leave4. The baby is sleeping. You _____ make so much noise.A. won’tB. mustn’tC. may notD. needn’t5. Since you are _____ trouble, why not ask _________ help?A. in, forB. in, toC. with, forD. with, to6. It’s about___________kilometers from Nanchong to Chengdu.A. two hundredsB. two hundreds ofC. two hundredD. two hundred of7. It is six years since my dear uncle ________China.A. leftB. has leftC. is leftD. had left8. —How long _______ you _______ the bicycle?—About two weeks.A. have, hadB. have, boughtC. did, buyD. have, have9. The Yellow River is not so ________ as the Yangtze River.A. longerB. longC. longestD. a long10. Mrs.Green usually goes shopping with ________ umbrella in ________ summer. A. a；theB. an； /C. the； aD. /；/11. At first, I was not too sure if he could answer the question. However, ____,he worked it out at last with the help of his friend.A. to my angerB. to my surpriseC. in other wordsD. in a word12. —Must I stay here with you?—No, you ______.You may go home, but you _____ go to the net bar (网吧).A. mustn't; needn'tB. needn't; mustn'tC. must; needD. need; must13. I ______ the newspaper while my mother _____TV plays yesterday evening.A. was reading; was watchingB. was reading; watchedC. read; was watchingD. read; would watch14. It's a rule in my class that our classroom ________ before 6：00 p. m.every day.A. be able to cleanB. should be cleaningC. must cleanD. must be cleaned15. —Tom wants to know if you ________ a picnic next Sunday.—Yes. But if it ________， we'll visit the museum instead.A. will have; will rainB. have; rainsC. have; will rainD. will have; rains16.—Would you mind looking after my dog while I'm on holiday?—________.A. Of course notB. Yes. I'd be happy toC. Not at all. I've no timeD. Yes, please17. Many students didn’t realize the importance of study _______they left school.A. whenB. untilC. afterD. unless18. My father _______ to Shanghai. He _______ for over 2 months.A. has been, has leftB. has gone, has goneC. has gone, has been awayD. has been, has gone19. They are your skirts. Please __________.A. put it awayB. put out itC. put them awayD. put them out20. —Please read every sentence carefully. you are, mistakes you’ll make.—Thank you for your advice.A. The more carefully; the fewerB. The more careful; the lessC. The more carefully; the lessD. The more careful; the fewer21. My friend is coming today but he didn’t tell me _______.A. when did the train arriveB. how did the train arriveC. when the train arrivedD. how the train arrived22. I felt it hard to keep up with my classmate s. But whenever Iwant to _______, my teacher always encourages me to work harder.A. go onB. give upC. run awayD. give back23. —________ fine weather it is today!—Let's go for a picnic.A. WhatB. HowC. What aD. How a24. — Mary, you’re going to buy an apartment here, aren’t you?—Yes, but I can’t_______an expensive one.A. spendB. costC. payD. afford25. —Would you like to drink coffee or milk?—_________. Please give me some tea.A. NeitherB. BothC. EitherD. None第二节：完形填空（共20小题，每小题1分，满分20分）(A)Big schoolbags have been a serious problem for students for a long time.Maybe your schoolbag is too __26__ to carry, and it troubles you a lot __27__ you want to find a book out to read. Now an etextbook will __28__ you.It is said that etextbooks are going to be __29__ in Chinese middle schools.An etextbook, in fact, is a small __30__ for students.It is much __31__ than a usual schoolbag and easy to carry. Though it is as small as a book, it can __32__ all the materials (材料) for study.The students can read the text page by page on the __33__， take notes with the pointer (屏写笔). Or even “__34__” their homework to their teachers by sending emails. All they have to do is to press a button.Some people say etextbooks are good, but some say they may be __35__ for the students' eyes. What do you think of it?26.A.light B. heavy C. useful D. comfortable27.A.till B. after C. before D. when28.A.trouble B. prevent C. help D. understanded B. kept C. invented D. lent B. radio C. pen D. computer31.A.heavier B. lighter C. cheaper D. brighter32.A.hold B. build C. discover D. practice33.A.blackboard B. desk C. screen D. card34.A.find out B. hand in C. get back D. give back35.A.helpful B. famous C. good D. bad(B)。
2018-2020年上海四校自招数学试卷汇编版(含答案)--共9套
2018-2020年上海四校自招数学试卷汇编版（含答案）--共9套目录2018交附自招数学答案2018上中自招数学2018上中自招数学答案2019复附自招数学答案2019交附自招数学2020上中、交附、七宝自招上海中学自招试题上海中学自招真题解析2018上海市上海中学自招部分真题1、因式分解：6x3-11x2+x+4=【答案】(x-1)(3x-4)(2x+1)【解析】试根法易得x=1时，上式值为0.利用长除法可得原式=(x-1)(6x2-5x-4)=(x-1)(3x-4)(2x+1)2、设a>b>0，a2+b2=4ab，则a+b=a-b【答案】3【解析】令a+b=x，a-b=y则x>y>0a2+b2=4aba2+b2-2ab=2aby2=1(x2-y2)2x2=3y2xa+b=3=3即y a-b3、若x2+x-1=0，则x3+2x2+3=【答案】4【解析】降次法x2=1-x所以原式=x(1-x)+2(1-x)+3=x-x2+2-2x+3=-x-(1-x)+5=4(,34、已知1(b -c )2=(a -b )(c -a )，且a ≠0，则b +c =4a【答案】2【解析】1(b -c )2=(a -b )(c -a )4(c -b )2=4(a -b )(c -a )⎡⎣(c -a )+(a -b )⎤⎦2=4(c -a )(a -b )⎡⎣(c -a )-(a -b )⎤⎦2=0所以c -a =a -bb +c =2a 即b +c=2a5、一个袋子里装有两个红球和一个白球（仅颜色不同），第一次从中取出一个球，记下颜色后放回，摇匀，第二次从中取出一个球，则两次都是红球的概率是【答案】49【解析】P =2⨯2=43396,、直线l ：y =-3x +与x 、y 轴交于点A 、B ，△AOB 关于直线AB 对称得到△ACB ，则点C 的坐标是【答案】33)22【解析】如右图所示易得∠CAD =∠BAO =60︒过C 作CD ⊥x 轴于点D 在△ACD 中AC =1易解得AD =1，CD =3223C (,)223即7、一张矩形纸片ABCD，AD=9，AB=12，将纸片折叠，使A、C两点重合，折痕的长是【答案】45 4【解析】如右图所示易得AC=所以OC=152=15△C△OF∽ABC所以OF=OC解得OF=45即EF=45 AB BC848、任给一个正整数n，如果n是偶数，就将它减半（即n），如果n是奇2数，则将它乘以3再加1（即3n+1），不断重复这样的运算，现在请你研究：如果对于正整数n（首项）按照上述规则实施变换（注：1可以多次出现）后的第八项为1，则n所有可能取值为【答案】128/2/16/20/3/21【解析】92+12212418 12451081632642 163 20 21 1289、正六边形ABCDEF 的面积是6平方厘米，联结AC 、CE 、EA 、BD 、DF 、FB ，求阴影部分小正六边形的面积【答案】2【解析】将小六边形的相对顶点联结后易得：小正六边形的面积是大正六边形面积的13即面积为210、已知y 1=2x 2+(4-m )x +(4-m )与y =mx 在x 取任意实数时，至少有一个是正数，则m 的取值范围为【答案】m <4【解析】（1）当0<m 时，0<x ，y 2=mx >0，且x ≤0时，y 2≤0∴x ≤0时y 1>0∴y 1x =0>0故4-m >0∴m -4<04则∆<0解得-4<m <4∴0<m <4（2）当m <0时，同理解得m <0（3）当m =0时，y 1>0恒成立综上所述，m <411、已知a 、b 、c 是互不相等的实数，x 是任意实数，(x -a )2(x -b )2(x -c )2化简：++=(a -b )(a -c )(c -b )(a -b )(c -a )(c -b )【答案】1-(x -a )2(b -c )-(x -b )2(c -a )-(x -c )2(a -b )=(a -b )(b -c )(c -a )【解析】原式=(a -b )(b -c )(c -a )(a -b )(b -c )(c -a )=1212、已知实数a 、b 满足a 2+ab +b 2=1，t =ab -a 2-b 2，-⎩1则t 的取值范围是【答案】-3≤t ≤-13【解析】由a 2+b 2≥2ab ，a 2+b 2≥-2ab得⎧1-ab ≥2ab 解得-1≤ab ≤1⎨ab ≥-2ab 3t =ab -(1-ab )=2ab -1所以-3≤t ≤-1313、（1）求边长是1的正五边形的对角线长（2）求sin18︒【答案】（1）5+1（2）5-122【解析】（1）正五边形的一个内角大小为：(5-2)⨯180︒÷5=108︒所以△ABE 和△ACD 是黄金三角形在△ABE 中AE =BE 5-1其中AE =1解得BE =25+12（2）在△ACD 中过A 作AF 垂直CD 于点F易得∠FAD =18︒1所以sin18︒=FD =2=5-1AD5+122x y -1⎩14、（1）f (x )=x 3+ax 2+bx +c ，0<f (-1)=f (-2)=f (-3)<3，求c 的取值范围（2）f (x )=x 4+ax 3+bx 2+cx +d ，f (1)=10，f (2)=20，f (3)=30，求f (10)+f (-6)【答案】（1）6<c ≤9（2）8104【解析】（1）令f (-1)=f (-2)=f (-3)=k ，g (x )=f (x )=k ，0<k ≤3则g (x )=(x +1)(x +2)(x +3)所以f (x )=g (x )+k =x 3+6x 2+11x +6+k 故c =6+k ，又0<k <3所以6<c ≤9（2）f (1)=10，f (2)=20，f (3)=30令g (x )=f (x )-10x =x 4+ax 3+bx 2+(c -10)x +d则有g (1)=g (2)=g (3)=0令g (x )=0的第四个根是m 则g (x )=(x -1)(x -2)(x -3)(x -m )所以g (10)+g (-6)=9⨯8⨯7⨯(10-m )+(-7)⨯(-8)⨯(-9)(-6-m )=8064即f (10)+f (-6)=g (10)+g (-6)+40=810415、我们学过直线与圆的位置关系，根据材料完成问题（1）（2）背景知识：平面α：Ax +By +Cz +d =0；球：(x -a )2+(y -b )2+(z -c )2=R 2；点(a ,b ,c )到平面α的距离公式：d =球心到平面的距离为d ，当d <R 时，球与平面相交，当d =R 时，球与平面相切，当d >R 时，球与平面相离；问题（1）：若实数m 、n 、k 满足m +n +k =1，求m 2+n 2+k 2的最小值；问题（2）：解方程++=1(x +y +z )2⎧x =1【答案】（1）1（2）⎪y =2⎨3⎪z =3【解析】（1）设点(m ,n ,k )则该点在平面x +y +z =1上而所求m 2+n 2+k 2即为该点到原点距离的平方Aa +Bb +Cc +D A 2+B 2+C 2z -212+12+12y -1z -2x y -1x ⎨⎨原点到平面x +y +z =1的距离为：d =1=33⎛3⎫21所以(m 2+n 2+k 2)= ⎪=（2）配方法min⎝3⎭3++=1(x +y +z )2x +y +z -(2+2+2z -2)=0(-1)2+(⎧x =1-1)2+(⎧x =1-1)2=0⎪y -1=1解得⎪y =2⎪⎪z =3⎪z -2=1⎩x y -1z -2则交大附中自主招生试卷2018.03第一部分 1. 已知13x x +=-，求3311000x x++. 2. 11(1)x x x tx x x x +++=++有增根，求所有可能的t 之和.3. AB ∥CD ，15AB =，10CD =，3AD =，4CB =，求ABCD S .4. 346y x x =-+，若a x b ≤≤时，其中x 的最小值为a ，最大值为b ，求a b +.5. 22(2)y x m =-+，若抛物线与x 轴交点与顶点组成正三角形，求m 的值.6. DE 为»BC的切线，正方形ABCD 边长为200，»BC 以BC 为直径的半圆，求DE 的长.7. 在直角坐标系中，正ABC ∆，(2,0)B ，9(,0)2C 过点O 作直线DMN ，OM MN =， 求M 的横坐标.8. 四圆相切⊙B 与⊙C 半径相同，⊙A 过⊙D 圆心，⊙A 的半径为9，求⊙B 的半径.9. 横纵坐标均为整数的点为整点，（12m a <<），y mx a =+（1100x ≤≤），不经过整 点，求a 可取到的最大值.10. G 为重心，DE 过重心，1ABC S ∆=，求ADE S ∆的最值，并证明结论.第二部分（科学素养）1. 已知直角三角形三边长为整数，有一条边长为85，求另两边长（写出10组）.2. 阅读材料，根据凸函数的定义和性质解三道小题，其中第（3）小题为不等式证明 1212[(1)]()1()f bx b x bf x bf x ++<+-（1）14b =；（2）13b =.（注：选（1）做对得10分，选（2）做对得20分）3. 请用最优美的语言赞美仰晖班（80字左右）（17分）4. 附加题（25分） （2 points ） solve the following system of equations for 2122.2221w x y z w x y z w w x y z w x y z +++=⎧⎪+++=⎪⎨+++=⎪⎪+++=⎩（4 points ）Compute 98∞（6 points ）Solve the equation 1=.Express your answer as a reduced fraction with the numerator written in their prime factorization.The gauss function []x denotes the greatest less than or equal to xA ）（3 points ）Compute 2018!2015!2017!2016!+⎡⎤⎢⎥+⎣⎦B ）（4points ）Let real numbers 12,,,n x x x ⋅⋅⋅ be the solutions of the equation 23[]40x x --=，find the value of 22212n x x x ++⋅⋅⋅+ C ）（6 points ）Find all ordered triples (,,)a b c of positive real that satisfy ：[]3a bc =，[]4a b c =，and []5ab c =上海中学自主招生试卷2018.031.因式分解：326114x x x -++=2.设0a b >>，224a b ab +=，则a b a b+=-3.若210x x +-=，则3223x x ++=4.已知21()()()4b c a b c a -=--，且0a ≠，则b c a +=5.一个袋子里装有两个红球和一个白球（仅颜色不同），第一次从中取出一个球，记下颜色后放回，摇匀，第二次从中取出一个球，则两次都是红球的概率是6.直线:l y =+x 、y 轴交于点A 、B ，AOB ∆关于直线AB 对称得到ACB ∆，则点C 的坐标是7.一张矩形纸片ABCD ，9AD =，12AB =，将纸片折叠，使A 、C 两点重合，折痕长是8.任给一个正整数n ，如果n 是偶数，就将它减半（即2n ），如果n 是奇数，则将它乘以3加1（即31n +），不断重复这样的运算，现在请你研究：如果对正整数n （首项）按照上述规则施行变换（注：1可以多次出现）后的第八项为1，则n 所有可能取值为9.正六边形ABCDEF 的面积是6平方厘米，联结AC 、CE 、EA 、BD 、DF 、FB ，求阴影部分小正六边形的面积为10.已知212(4)(4)y x m x m =+-+-与2y mx =在x 取任意实数时，至少有一个是正数，则m 的取值范围为11.已知a 、b 、c 是互不相等的实数，x 是任意实数，化简：222()()()()()()()()()x a x b x c a b a c c b a b c a c b ---++=------12.已知实数a 、b 满足221a ab b ++=，22t ab a b =--，则t 的取值范围是13.（1）求边长为1的正五边形对角线长；（2）求sin18︒.14.（1）32()f x x ax bx c =+++，0(1)(2)(3)3f f f <-=-=-≤，求c 的取值范围；（2）432()f x x ax bx cx d =++++，(1)10f =，(2)20f =，(3)30f =，求(10)(6)f f +-.15.我们学过直线与圆的位置关系，根据材料完成问题（1）（2）类似给出背景知识：平面:0Ax By Cz d α+++=；球：2222()()()x a y b z c R -+-+-=；点(,,)a b c 到平面:0Ax By Cz d α+++=的距离公式：d =；球心到平面的距离为d ，当d R <时，球与平面相交，当d R =时，球与平面相切，当d R >时，球与平面相离；问题（1）：若实数m 、n 、k 满足1m n k ++=，求222m n k ++的最小值；问题（21()2x y z +=++.参考答案1.(1)(34)(21)x x x --+2. 3.4 4.2 5.49 6.33(,227.4548.128、2、16、20、3、219.22cm 10.4m <11.112.133t -≤≤-13.（112+；（2）14-14.（1）69c <≤；（2）810415.（1）13；（2）123x y z =⎧⎪=⎨⎪=⎩上海中学自主招生试题1、因式分解：326114x x x -++= ．【答案】()()()13421x x x --+．【解析】容易发现1x =是方程3261140x x x -++=的解，因此原式可以提出因式(1)x -，得到2(1)(654)x x x ---，对2(654)x x --用十字相乘可以得到原式等于(1)(34)(21)x x x --+．2、设0a b >>，224a b ab +=，则a b a b +=- ．【解析】由条件可得2()6a b ab +=，2()2a b ab -=．因此22()63()2a b ab a b ab +==-．由于0a b +>，0a b ->，所以a b a b+=- 3、若210x x +-=，则3223x x ++=． 【答案】4．【解析】对多项式用带余除法可得32223(1)(1)4x x x x x ++=+-++，而由条件2(1)(1)0x x x +-+=，因此原式的值等于4．4、已知()()()24b c a b c a -=--，且0a ≠，则b c a+=_________． 【答案】2．【解析】令a b m -=，c a n -=，则c b m n -=+，代入()()()24b c a b c a -=--中得()24m n mn +=，()20m n ∴-=，m n ∴=， 即a b c a -=-，即2a b c =+，2b c a+∴=． 5、一个袋子里装有两个红球和一个白球（仅颜色不同），第一次从中取出一个球，记下颜色后放回，摇匀，第二次从中取出一个球，则两次都是红球的概率是． 【答案】49．【解析】第一次取出红球的概率为23，且无论第一次取出什么球，第二次取出红球的概率仍为23，因此两次都是红球的概率是224339⨯=． 6、直线:l y =与x 、y 轴交于点A 、B ，AOB ∆关于直线AB 对称得到ACB ∆，则点C 的坐标是 ．【答案】32⎛ ⎝⎭．【解析】根据函数解析式可以算出A 、B 的坐标分别为(1,0)A，B ．由于ACB 是AOB 关于直线AB 对称得到的，所以AC AO =，BC BO =．设(,)C m n，则可列方程组2222(1)1(3m n m n ⎧-+=⎪⎨+=⎪⎩，解得32m n ⎧=⎪⎪⎨⎪=⎪⎩O重合，舍去．因此3(2C ．7、一张矩形纸片ABCD ，9AD =，12AB =，将纸片折叠，使A 、C 两点重合，折痕长是． 【答案】454． 【解析】由题意知折痕是线段AC 的中垂线，设它与AB ,CD 分别交于,M N ．设MB x =，则由MC MA =可列方程2229(12)x x +=-，解得218x =．同理有218DN =．作ME CD ⊥，垂足为E ，则四边形MECB 是矩形，因此9ME BC ==，218CE BM ==．可知274NE CD DN CE =--=．而454MN ==．因此折痕长为454． 8、任给一个正整数n ，如果n 是偶数，就将它减半——得到2n ，如果n 是奇数，则将它乘以3加1——得到31n +，不断重复这样的运算，如果对正整数n （视为首项）按照上述规则实施变换后（有些书可能多次出现）的第8项为1，则n 的所有可能取值为________．【答案】128，21，20，3，16，2．【解析】设某一项为k ，则它的前一项应该为2k 或者13k -． 其中13k -必为奇数，即()4mod 6k ≡， 按照上述方法从1开始反向操作7次即可．9、正六边形ABCDED 的面积是6平方厘米，联结AC 、CE 、EA 、BD 、DF 、FB ，求阴影部分小正六边形的面积为． 【答案】22cm ．【解析】右图中，阴影部分是正六边形，且与正六边形 ABCDEF的相似比为1:3．因为 ABCDEF 的面积是26cm ，所以阴影部分的面积为2632()cm ÷=．10、已知()()21244y x m x m =+-+-与2y mx =在x 取任意实数时，1y ，2y 至少有一个是正数，m 的取值范围是________．【答案】4m <．【解析】取0x =，则14y m =-，20y =，40m ∴->，4m <，此时函数1y 的对称轴404m x -=-<， 则对任意0x ≥总有10y >，只需考虑0x <；若04m ≤<，此时20y ≤，则对任意0x <，有10y >，()()24840m m ∴∆=---<，解得04m ≤<； 若0m <，此时20y >对0x <恒成立；综上，4m <．11、已知a ，b ，c 是互不相等的实数，x 是任意实数，化简：()()()()()()()()()222x a x b x c a b a c c b a b c a c b ---++=------________． 【答案】1．【解析】令()()()()()()()()()()2222x a x b x c f x mx nx k a b a c c b a b c a c b ---=++=++------， ()()()1f a f b f c ∴===，即222111ma na k mb nb k mc nc k ⎧++=⎪++=⎨⎪++=⎩，01m n k ==⎧∴⎨=⎩ ，即()1f x ≡．12、已知实数a ，b 满足221a ab b ++=，22t ab a b =--，则t 的取值范围是________． 【答案】133t -≤≤-． 【解析】方法一：考虑基本不等式222a b ab +≥． 则2212a b ab ab +=-≥，则113ab -≤≤， 又2221t ab a b ab =--=-，133t ∴-≤≤-，其中1a =，1b =-时，3t =-成立；a b ==时，13t =-成立． 方法二：逆用韦达定理．12t ab +=，()2302t a b ++=≥，3t ∴≥-，a b +=，故a ,b 是方程2102t x ++=的两个根， 314022t t ++∴∆=-⨯≥，解得13t ≤-， 133t ∴-≤≤-．13、（1）求边长为1的正五边形对角线长；（2）求sin18︒．【答案】（1（2． 【解析】（1）设正五边形ABCDE ，联结,AC BE ，且设它们交于点M ．可以计算得到36ABM ABC ∠=∠=︒，因此ABM ACB ，可得2AB AM AC =⋅．同时，72BMC CBM ∠=∠=︒，所以BC MC =．若正五边形边长为1，则1AB BC CM ===，设AC x =，则由2AB AM AC =⋅可列方程21(1)x x =-，解得x去）． （2）根据诱导公式，sin18cos72︒=︒．在（1）的五边形中，BM AM AC CM ==-=．作CH BM ⊥，垂足为H ，则等腰三角形BMC 中12BH HM BM ===72CBM ∠=︒，所以sin18cos72BH BC ︒=︒==．14、（1）()32f x x ax bx c =+++，()()()01233f f f <-=-=-≤，求c 的取值范围；（2）()432f x x ax bx cx d =++++，()110f =，()220f =，()330f =，求()()106f f +-．【答案】（1）69c <≤ ；（2）8104．【解析】（1）()()()01233f f f <-=-=-≤， ()0f x k ∴-=有三个实根1,2,3x =---，()()()()123f x k x x x ∴-=+++，展开得6c k =+，69c ∴<≤；（2）方程()100f x x -=有三个实根1,2,3x =，记第4个根为x p =，则()()()()()10123f x x x p x x x -=----，()()()()()12310f x x p x x x x ∴=----+，()()()()()()()106109871006789608104f f p p ∴+-=-⨯⨯⨯++--⨯-⨯-⨯--=．15、我们学过直线与圆的位置关系，根据材料完成问题（1）（2）类似给出背景知识：平面:0Ax By Cz D α+++=；球：()()()2222x a y b z c R -+-+-=；点(),,a b c 到平面:0Ax By Cz D α+++=的距离公式：d =；球心到平面的距离为d ，当d R <时，球与平面相交，当d R =时，球与平面相切，当d R>时，球与平面相离；问题（1）：若实数m 、n 、k 满足1m n k ++=，求222m n k ++的最小值；问题（2）()12x y z =++． 【答案】（1）13；（2）123x y z =⎧⎪=⎨⎪=⎩． 【解析】（1）条件可转化为点(,,)m n k 在平面10x y z ++-=上，而222m n k ++的最小值即该点到原点距离平方的最小值．这个距离最小为原点到平面10x y z ++-=的距离，而原点到平面的距离可由材料公式计算得到：3d ==，因此222m n k ++的最小值为213d =，等号在13m n k ===时取到．（2）移项后配方可以得到2221111)1)1)0222-+-+=，因此必有101010-==-=，于是解得123xyz=⎧⎪=⎨⎪=⎩．上海中学自招试题1、因式分解：326114x x x -++=．2、设0a b >>，224a b ab +=，则a b a b +=- ．3、若210x x +-=，则3223x x ++=．4、已知()()()24b c a b c a -=--，且0a ≠，则b c a +=_________．5、一个袋子里装有两个红球和一个白球（仅颜色不同），第一次从中取出一个球，记下颜色后放回，摇匀，第二次从中取出一个球，则两次都是红球的概率是．6、直线:l y =+与x 、y 轴交于点A 、B ，AOB ∆关于直线AB 对称得到ACB ∆，则点C 的坐标是．7、一张矩形纸片ABCD ，9AD =，12AB =，将纸片折叠，使A 、C 两点重合，折痕长是．8、任给一个正整数n ，如果n 是偶数，就将它减半——得到2n ，如果n 是奇数，则将它乘以3加1——得到31n +，不断重复这样的运算，如果对正整数n （视为首项）按照上述规则实施变换后（有些书可能多次出现）的第8项为1，则n 的所有可能取值为________．9、正六边形ABCDED 的面积是6平方厘米，联结AC 、CE 、EA 、BD 、DF 、FB ，求阴影部分小正六边形的面积为．10、已知()()21244y x m x m =+-+-与2y mx =在x 1y ，2y 至少有一个是正数，m 的取值范围是________．11、已知a ，b ，c 是互不相等的实数，x 是任意实数，化简：()()()()()()()()()222x a x b x c a b a c c b a b c a c b ---++=------________．12、已知实数a ，b 满足221a ab b ++=，22t ab a b =--，则t 的取值范围是________．13、（1）求边长为1的正五边形对角线长；（2）求sin18︒．14、（1）()32f x x ax bx c =+++，()()()01233f f f <-=-=-≤，求c 的取值范围；（2）()432f x x ax bx cx d =++++，()110f =，()220f =，()330f =，求()()106f f +-．15、我们学过直线与圆的位置关系，根据材料完成问题（1）（2）类似给出背景知识：平面:0Ax By Cz D α+++=；球：()()()2222x a y b z c R -+-+-=；点(),,a b c 到平面:0Ax By Cz D α+++=的距离公式：d =；球心到平面的距离为d ，当d R <时，球与平面相交，当d R =时，球与平面相切，当d R>时，球与平面相离；问题（1）：若实数m 、n 、k 满足1m n k ++=，求222m n k ++的最小值；问题（2）()12x y z =++．2019年交大附中自招数学试卷一、填空题1、求值：cos30sin 45tan 60⋅⋅=.2、反比例函数1y x =与二次函数243y x x =-+-的图像的交点个数为.3、已知210x x --=，则3223x x -+=.4、设方程()()()()()()11111211210x x x x x x ++++++++=的两根为1x ，2x ，则()()1211x x ++=.5、直线y x k =+（0k <）上依次有,,,A B C D 四点，它们分别是直线与x 轴、双曲线k y x=、y 轴的交点，若AB BC CD ==，则k =.6、交大附中文化体行设施齐全，学生既能在教室专心学习，也能在操场开心运动，德智体美劳全面发展，某次体育课，英才班部分学生参加篮球小组、其余学生参加排球小组。
2018年上海市交通大学附属中学自招物理真题卷和解析
2018年交大附中自招真题卷整理【例1】已知甲、乙、丙三个电荷，依次排列在同一直线上，且都处于静止状态，由此可以判断（）A. 甲、乙、丙带同种电荷B. 甲、丙带同种电荷，甲、乙带异种电荷C. 甲、丙带同种电荷，甲、乙可能带同种电荷，也可能带异种电荷D. 无论甲、乙、丙带何种电荷，均可能使它们同时静止【例2】如图所示，作用在杠杆一端且始终与杠杆垂直的力F，将杠杆缓慢地由位置A拉至位置B，在这个过程中，力F的大小（）A.变小B. 不变C. 变大D.先变大后变小【例3】人们常常用充气泵为金鱼缸内的水补充氧气，如图所示为充气泵气室的工作原理图。
设大气压强为P0，气室中的气体压强为P，气体通过阀门S1、S2与空气导管相连接，下列选项中正确的是（）A. 当橡皮碗被拉伸时，P>P0，S1开通,S2关闭B. 当橡皮碗被拉伸时，P<P0，S1开通，S2关闭C. 当橡皮碗被压缩时，P>P0，S1关闭，S2开通D. 当橡皮碗被压缩时，P<P0，S1关闭，S2开通【例4】如图所示，静止的传送带上有一木块A正在匀速下滑,当传送带突然向上开动时，木块滑到底部所需的时间t与传送带静止不动时所需时间t0相比（）A.t=t0B.t>t0C.t<t0D. 无法判断【例5】某旅客在火车车厢内以1.5米/秒的速度行走。
当车厢静止时，他从车厢头走到车厢尾需要20秒。
当火车以10米/秒的速度向前匀速行驶时，则他从车厢头走到车厢尾需要的时间是______秒，站在地面上的人看见该旅客通过的路程为______米。
【例6】如图所示，将一块重为3N，体积为100cm3的石块，用细线系着浸没在装有水的圆柱形容器中，容器中水的深度由10cm上升到12cm。
则石块所受浮力大小为______牛；细线松动，石块沉到容器底静止后，容器对水平地面的压强为______帕(容器的重力和容器壁的厚度，g=10N/kg)。
【例7】把一根粗糙的木棒按图所示的方式放在分开的两手的食指上。
2018年上海交大附中自主招生数学试卷(无答案)-教育文档
交大附中自主招生试卷2019.03第一部分1. 已知13x x +=-，求3311000x x ++. 2. 11(1)x x x t x x x x +++=++有增根，求所有可能的t 之和. 3. AB ∥CD ，15AB =，10CD =，3AD =，4CB =，求ABCD S .4. 346y x x =-+，若a x b ≤≤时，其中x 的最小值为a ，最大值为b ，求a b +.5. 22(2)y x m =-+，若抛物线与x 轴交点与顶点组成正三角形，求m 的值.6. DE 为BC 的切线，正方形ABCD 边长为200，BC 以BC 为直径的半圆，求DE 的长.7. 在直角坐标系中，正ABC ∆，(2,0)B ，9(,0)2C 过点O 作直线DMN ，OM MN =， 求M 的横坐标.8. 四圆相切⊙B 与⊙C 半径相同，⊙A 过⊙D 圆心，⊙A 的半径为9，求⊙B 的半径.9. 横纵坐标均为整数的点为整点，（12m a <<），y mx a =+（1100x ≤≤），不经过整 点，求a 可取到的最大值.10. G 为重心，DE 过重心，1ABC S ∆=，求ADE S ∆的最值，并证明结论.第二部分（科学素养）1. 已知直角三角形三边长为整数，有一条边长为85，求另两边长（写出10组）.2. 阅读材料，根据凸函数的定义和性质解三道小题，其中第（3）小题为不等式证明（1）14b =；（2）13b =.（注：选（1）做对得10分，选（2）做对得20分） 3. 请用最优美的语言赞美仰晖班（80字左右）（17分）4. 附加题（25分）（2 points ） solve the following system of equations for 2122.2221w x y z w x y z w w x y z w x y z +++=⎧⎪+++=⎪⎨+++=⎪⎪+++=⎩ （4 points ）Compute 98∞（6 points ）Solve the equation 1=.Express your answer as a reduced fraction with the numerator written in their prime factorization.The gauss function []x denotes the greatest less than or equal to xA ）（3 points ）Compute 2018!2015!2017!2016!+⎡⎤⎢⎥+⎣⎦B ）（4points ）Let real numbers 12,,,n x x x ⋅⋅⋅ be the solutions of the equation 23[]40x x --=，find the value of 22212n x x x ++⋅⋅⋅+ C ）（6 points ）Find all ordered triples (,,)a b c of positive real that satisfy ：[]3a bc =，[]4a b c =，and []5ab c =。
2017-2018学年上海市交大附中英语自招练习 (六)
交大附中自招练习（六）TEST ONE(A)"Dining out" and “eating out" are phrases people use in Britain when they eat in a restaurant. Eating out is more popular in Britain today than it 1 (ever be) In 2006. for the first time ever. British people spent more on eating out in restaurants than on cooking for themselves and eating at home. It seems that many British people 2 (become ) increasingly interested in how good their food tastes and how healthy it is. 3 ,eating out can also be expensive. so British people do not dine out every night. Eating in a restaurant is often seen as 4 special occasion. When 5 (go) on a first date,or if celebrating an anniversary or a birthday, many people like to go to a restaurant, and people often eat in a restaurant 6 going to the cinema or the theater.Naturally, restaurants vary greatly in quality and price. However, almost all British cities have a vast range of cuisines to choose 7 as well as traditional British food. In fact. When asked 8 was their favorite food, more British people said an Indian curry than any other dish!As well as dining in a restaurant, 9 people are too tired l0 (cook)after work they often get a "take-away." This means that they order from a take-away (or take-out) restaurant by phone, and then go to collect it and take it home to eat. Many take-out restaurants also deliver to your house. The most popular take-out foods are pizza (Italian). Indian and Chinese-- and then all you have to do is open the door, pay, and eat!(B)An earthquake rumbles; a building collapses ...Almost before the dust settles. search andrescue (SAR) dogs and handler teams are there searching for victims alive and dead. With a sense of smell far 1 (powerful ) than man's and an ability to probe nooks (角落）and crannies that humans cannot get 2 ,these dogs save lives and bring comfort to those who are anxiously waiting to hear about 3 loved ones. But it's not just about smell-dogs' superior hearing and night vision also come into play.Time is always an issue in search and rescue. In an avalanche situation. for instance, approximately 90 percent of victims 4 alive 15 minutes after burial; 35 minutes after burial, only 30 percent of victims are alive. 5 most avalanche victims don't survive. their chances increase greatly when dogs are in on the search. Even in cases 6 victims are presumed dead, dogs are invaluable assets-they locate the bodies so family members can give their loved one a proper burial.Dogs must be trained in certain ways for them to be qualified as SAR d02s. SAR training ensures that dogs 7 complete their tasks of finding human scent in all conditions regardless of weather or distractions.With the proper trainings, SAR dogs can do a lot of amazing things. including rappeling down（绕绳下降）mountainsides with their handler, locating a human being 8 a 5000-meter radium, finding a dead body 9 in water. climbing ladders and walking across an unstable beam a collapsed building, but it's all toward a single end human scent!TEST TWO(A)Several years ago. I was training at the Olympic Training Center in Colorado Springs, Colorado. During my early moming workout, I noticed a guy _l_ (quart-walk) around the track with a tire full of sand around his neck. It was obviously very heavy.I didn't know 2_ the guy was or wbat he did as an athlete. Finally, one day at lunch I happened to be sitting _3_ the table from him We began talking. His name was Eric."I see you doing the squat-walking every morning. That's incredible What sport do you do?" I said. "I'm a skater. you know, a speed skater." Eric answered. He seemed to be a very unassuming (低调的) person.We met a few more times at lunch and one day I asked him. "How are you going to do at the Winter Olympics?" "I think I'm going to win five gold medals," he said, _4_ a trace of arrogance "Five gold medals! The guy is crazy!" I said to myselfI asked 5 he thought he would win five gold medals. His answer was simple but impressive: "Because I train harder than anyone else in the world."I thought his answer gave _6_ a rational reason for the seemingly irrational belief7 he could win five gold medals. 8 he continued training hard, he'd be giving himself permission 9 ( believe) he could win.He is Eric Heiden. who 10 (participate) in the 1980 Winter Olympics and did win five gold medals.(B)Although Alexander Bell is 9 (often) associated with the invention of the telephone, he also created many other wonderful things.Bell's interests were extremely varied. His work ranged across the scientific landscape and he often went to bed 10_ (read) the Encyclopedia Britannica. searching it for new areas of interest.Bell's inventive genius 11 (honor) only in part (部分地）by the eighteen patents granted in his name alone and the twelve 12 shared with his co-workers. These included fourteen for the telephone and telegraph. four for the photophone. one for the phonograph, five for aerial vehicles, four for hydroairplanes(永上飞机) and two for selenium cells(硒光电管).Bell's inventions covered a wide range of interests, including a metal jacket to assist in breathing, an instrument to detect minor hearing problems. a device to locate icebergs. investigations on how 13 (separate) salt from seawater. and work on 14 (find) new energy to replace fuels.He also invented the metal detector in 1881, _ 15 _ was used in an attempt _16_ (find) the assassin's bullet in the body of U.S. President James Garfield!TEST TRREE(A)He has had countless articles written about him and has even been the subject of a feature on Oprah Winfrey's talk show.A 29-year-old ape, Kanzi is able to understand and communicate with humans and is believed to understand around 450 words-30 to 40 of l he uses daily.Kanzi has been famous 2 the late 1980s when his astonishing ability to communicate _ 3 _ (frrst discover). He lives at the Great Ape Trust in Iowa, U.S.A., where expert Dr. Sue Savage-Rumbaugh has been teaching him to "speak" 4 _ pointing at symbols on a computer.Kanzi speaks by pressing a symbol on the computer which then repeats the word out loud Sue says that he is even able to put together two-word sentences and create new phrases. "When Iowa was hit by storm and 5 _ (flood), he would point out 'big water.' He had a hard time6 (chew) the kale（甘蓝），so he pointed at 'slow lettuce.' For the word 'pizza, ' he pointed at' 'cheese, ' 'tomato' and 'bread. ,,,Sue says she taught Kanzi to communicate 7 same way she taught her son to speak.The Trust also takes care of Teco. Kanzi's 3-month-old son. Teco is also learning to communicate and Sue believes he may one day surpass his father as he . 8 _ (be) around humans since birth.(B)Two people are taken into custody（监禁）for a Crime. The police are aware that evidence is insufficient. so the prisoners are separated and questioned individually. Each prisoner is told that if he speaks and tums the other prisoner in 9 .that prisoner remains silent, he will go free while the silent prisoner will do jail tune. If both prisoners speak up, they will both do some jail time, although the sentence will be shorter than 10 for a prisoner who remains silent while another speaks. If both prisoners remain silent, they will each be given a very short prison sentence.What should the prisoners do? By remaining silent. a prisoner runs the risk of _11_ (hit) with a long sentence while the other prisoner walks. By speaking. a prisoner can hope that the other prisoner stays silent, in which case he goes free. Of course. when both prisoners speak, they both get some jail time, but the risk of remaining silent is far _12_ (great) than the risk of speaking.This is the prisoner's dilemma, a concept in game theory. Game theorists have determined that speaking up is always _13_ answer for both parties in this case. The reason for this is that each party must assume that the other will act with only self-interest in mind.The prisoner's dilemma plays on the idea that people caught in challenging situations usually try to guess what other people will do. Many people use the prisoner's dilemma to show 14 situations can escalate(升级）through a series of seemingly rational options. For example. . people stuck in dense traffic often choose to take selfish actions in the hopes of getting ahead, rather than 15_ (cooperate) with the collective. As a result. gridlock often emerges; witheveryone -1 6_ (lose) in the situation.TEST FOUR(A )For most American teenagers over the age of sixteen, owning a car seems to be a must. Cars have become as much l status symbol for young drivers as they are for many adults.A decade ago, American teenagers would be very excited when their parents gave them a car 2 a high school graduation present. Now, it has become much 3 (easy) for them to get the four-wheel vehicle they want-they can find it 4 (wrap) in ribbon on the street outside their homes on their sixteenth birthday.Young people love to have a car because it will be very convenient to go anywhere in the car. And it seems that owning a car has developed another meaning over time-the person who owns a car 5 (appear) to be independent and cool, and the one 6 doesn't lose face. That's why we always see in American movies and TV series teenagers who don't own a car beg their parents to lend them their car. You know. 7 is a shame arriving at a friend's party by getting dropped off by parents. No wonder Hannah Montana feels embarrassed once she had to be dropped off at a party by her dad 8 she lost her driver's license!(B)Lena. Bridget. Tibby. and Carmen 9 (be) best friends since they were little kids. Now they have just finished their freshman year of high school. Just 10 they are about to spend their frrst summer apart, they discover a pair of jeans that miraculously fits all of them. 11their different physiques (体格) . And not just fit-the pants make each girl look and feel beautiful and confident. In a solemn midnight ceremony. the girls make up a contract about the magical pants, part of 12 is that they'll send them back and forth among themselves throughout the summer. They don't know it yet. but they'll need the confidence that 13 (come) with the pants during a summer that will test them. 14 in different ways.That is the story The Sisterhood of the Traveling Pants tells. The friendship that the four girls share is the kind every teen 15 (long) for: rock solid and dependable, with no rivalries or pettiness (狭隘）to spoil it. filled only with kindness. love and understanding. The author. Ann Brashares, is a great storyteller. She builds a reservoir of affection for each character that makesthe climax of each of their stories effective.16 (publish) in 2001. the book stayed on the New York Times Best Seller list (《组约时报》畅销书榜) for over a year. The movie of the same name, based on the novel. was also a hit.TEST FIVE(A)Rod Allbright is a sixth grader. He goes to school like any other normal kid. Unfortunately, the class bully, a naughty boy called Billy Becker, always picks on him l he is overweight.While Rod's working on his science homework. tiny aliens come 2 (crash) through his bedroom window in a spaceship. They come to the Earth to capture another alien an evil one named BKR. He is known in other galaxies 3 his cruelties. The aliens eat Rod's homework and force him to help them.Rod is 4 honest boy. So when his science teacher asks him 5 his homework is, Rod answers, "Aliens ate my homework." Of course. no one believes him, so they don't bother 6 (ask) him why the aliens are here.Rod helps the tiny aliens to return to their normal size. Later, he finds out that Billy Becker is BKR and he skips school to search his house with the aliens. They get caught when BKR 7 (come) home from school He traps them in a storing device 8 he keeps his alien items. They break free of the device and escape from the house with some difficulty.Finally they defeat BKR through efforts and Rod learns many important lessons about life along the way.(B)A daughter complained to her father about her life and how things were so hard for her. It seemed that when one problem was solved a new one 9 (arise). She did not know how she was going to cope and wanted to give up.Her father, a chef took her to the kitchen. He filled three pots with water and put in them carrots, eggs and coffee beans respectively. He then placed each pot on a high fire and let them sit and boil, 10 saying a word. The daughter waited impatiently, 11 (wonder)what he wasdoing. In about twenty minutes, the pots came to a boil. The father turned off the fire and took out the carrots. the eggs and the coffee beans. He placed them in three bowls and turned to his daughter."Sweetheart, what do you see?" he asked."Carrots. eggs. and coffee," she replied.He asked her to feel the carrots. She did and noted that they were soft. He then asked her to take an egg and break 12 . After pulling off the shell, she observed the hard-boiled egg. Finally, he asked her to sip the coffee. She smiled as she tasted its rich flavor.The daughter was still a bit confused and asked. "What does this mean, dad?""Though the carrots, the eggs and the coffee beans all faced the same adversity---boiling water-they reacted differently," explained the father.The carrots 13 (go) in strong and lard but after being boiled 14 (soften) and became weak. The eggs had been fragile; their thin outer shells had protected their liquid interior. But after boiling. their inside became hardened. The coffee beans were unique, however. 15 put in the boiling water, they changed the water."Which are you." the father asked his daughter. "When adversity knocks on your door, 16 do you respond? Are you a carrot, an egg, or a coffee bean?”KEYS:TEST ONE A) has ever been are becoming However a going before from which because to cookB) more powerful to the are while where can in in FindingTEST TWO A) quart-walking who at for if out that As long as to believe participatedB) often to read honored is to separate finding which to findTEST THREE A) which in was discovered for flood to chew in has beenB) any hit greater the the cooperation lostTEST FOUR A) of to easier wrapped appears who what whenB) are as with it comes but longs PublishedTEST FIVE A) as crashing for an what to ask came whenB) arised for wondered down went softened Before how。
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2018年上海交通大学自主招生考试 1.
设点0)P
，已知曲线y x =
≤≤上存在n 个点12,,,n A A A ，使得
12,,
,n PA PA PA
构成公差为1(5d ∈的等差数列，求n 的最大值；
2.已知△ABC 的面积为1
4，外接圆半径R
=1
111a b c
++的大小
3.已知等差数列{}n a ，满足22
11n a a a ++≤，试求1221n n n a a a +++++
+的最大值
4.
记6的小数部分为
t
，求t 6
)的值 5.已知2113
,12
n n n a a a a +==-+，求
12
2017
111a a a +++
的整数部份
6.设X 为全集，A X ⊂,定义1,0,S A S A
f S A ∈⎧=⎨∉⎩
，对X 的真子集A 和B ，下列错误的是（ ）
A . S S
B A B A f f ⊆⇒≤ B .若B A ⋂≠φ，则S S S B S B A f f f ⋂≤≤
C .忘记
D . S S S B S B A f f f ⋃=≤
7.在四面体中不同长度的棱长至少有______条
8.在一个平面内，一条抛物线把平面最多分成2部分，两条抛物线把平面最多分成7部分，问四条抛物线把平面最多分成几部分？
9.已知22(,)(53cos )(2sin )g a b a b a b =+-+-，求(,)g a b 的最小值 10.已知133a =，12n n a a n +-=，则当
n
a n
取最小值时，n =________ 11.已知动点A 在椭圆22
12516
x y +=上，动点B 在圆22(6)1x y -+=上，求AB 的最大
值
12.若100!12(*)n M M Z =∈，则当n 取最大值时，M 是否能被2,3整数
13.设光线从点A （1,1）出发，经过y 轴反射到圆22(5)(7)1x y -+-=上一点P ，若光线从点A 到点P 经过的路程为R ，求R 的最小值
14.正整数列1,2,3……，将其中的完全平方数和完全立方数都划去，求将剩下的数按照从小到大排列的第500个数是多少？。