剑桥模拟试题剑桥国际高中入学
剑桥模拟试题剑桥国际高中入学
剑桥模拟试题剑桥国际高中入学The latest revision on November 22, 2020Model Test for Cambridge International SchoolSolve the following questions comprehensively.1.Three unit circles are arranged so that each touches the other two.Find the radii of the two circles which touch all three.2.Find all real numbers x such that x + 1 = |x + 3| - |x - 1|.3.(1) Given x = (1 + 1/n)n, y = (1 + 1/n)n+1, show that x y = y x.(2) Show that 12 - 22 + 32 - 42 + ... + (-1)n+1n2 = (-1)n+1(1 + 2 + ...+ n).4.All coefficients of the polynomial p(x) are non-negative and noneexceed p(0). If p(x) has degree n, show that the coefficient of x n+1 in p(x)2 is at most p(1)2/2.5.What is the maximum possible value for the sum of the absolutevalues of the differences between each pair of n non-negative real numbers which do not exceed 16.AB is a diameter of a circle. X is a point on the circle otherthan the midpoint of the arc AB. BX meets the tangent at A at P, and AX meets the tangent at B at Q. Show that the line PQ, the tangent at X and the line AB are concurrent.7.Four points on a circle divide it into four arcs. The fourmidpoints form a quadrilateral. Show that its diagonals areperpendicular.8.Find the smallest positive integer b for which 7 + 7b + 7b2 is afourth power.9.Show that there are no positive integers m, n such that 4m(m+1) =n(n+1).10.ABCD is a convex quadrilateral with area 1. The lines AD, BCmeet at X. The midpoints of the diagonals AC and BD are Y and Z.Find the area of the triangle XYZ.11. A square has tens digit 7. What is the units digit12.Find all ordered triples (x, y, z) of real numbers whichsatisfy the following system of equations:xy = z - x - yxz = y - x - zyz = x - y - z。
国际高中入学考试模拟试卷(英语)(1)
高中入学考试英语模拟试卷Paper I: Listening (15 minutes 16 marks)A.For Questions 1-10, you will hear 10 short dialogues and decide whether the followingstatements are true or false. Listen and mark “T” or “F” on the answer sheet. You’ll hear the recording TWICE.1. The driver puts the man’s bag in the trunk.2. The woman refuses the man’s suggestion.3. Lynne is having a potluck party.4. Chris is a vegetarian.5. The customer needs the salesperson’s help right now.6. The food at the restaurant was so-so.7. The man tells the woman not to do something.8. Helen feels better.9. Cindy is talking about the job that she has now.10. Bob is going to start jogging before work.B.For questions 1-6, you will hear a series of short conversations. Please write the answerto each question on the line provided. Your answer should be as brief as possible. You will hear each item TWICE.1. Where will Alberto find the tea?2. At what point exactly will the three students appear in the concert?3. When will the friends go swimming?4. Where will the tour meeting take place?5. How will teachers know who wants to attend their revision class?6. What is Lili’s problem AND how might this be resolved?Paper II: Reading (65 minutes 54 marks)A.For questions 1-10, please look at the sentences below about a journey to the Arctic onboard a ship. Read the following text to decide if each sentence is correct or incorrect.If it is correct, mark T on your answer sheet.If it is not correct, mark F on your answer sheet.Exploring the ArcticThe Arctic is one of the few places in the world untouched by pollution where you can see nature at its wildest and most beautiful. Join our ship the Northern Star from 2 to 18 July, for a 17-day voyage to the Arctic. During the voyage you are able to relax and get away from it all. There are no parties or film-shows to attend, quizzes to enter, or entertainers to watch. However, we do have specialists on board who are willing to answer any of your questions about the Arctic and who will talk about the animals and birds that you see on the trip.After setting off from Scotland, we go north along the coast of Norway to Bear Island. Along the way you'll see thousands of seabirds and wonderful scenery, with rivers of ice and huge cliffs. You will have the chance to see reindeer, polar bears, and other Arctic animals. Although we have a timetable, experience has shown that we may have to change our direction a little, depending on the weather and on which animals appear.The Northern Star is a very special ship and our past voyages have been very popular. Our cabins all have the same excellent facilities, which include a private bathroom and refrigerator. Our chefs are happy to prepare any food for people on special diets. Choose just what you want to eat from the wide variety available from the dining room buffet. There is a library, shop, clinic and plenty of space for relaxation. If you need some exercise, why not go jogging every morning around the decks, or do some swimming in the indoor pool.Prices include economy class air travel and 16 nights on board the Northern Star, all meals and excursions and all lectures.Day 1 Board the Northern Star.Days 2–7 We sail slowly north along the coast of Norway,stopping at places of interest.Day 8 Tromso. You need to get up at sunrise to see thewhales as we sail towards Tromso. Visit Tromso tosee the Arctic Museum, the cathedral and the beautifulold wooden houses. In the evening we sail away alongthe west coast to Bird Island, which is excellent forbird-watching.Days 9–10 Bear Island. We arrive here in the early evening andstay overnight. Bear Island once had an active fishingindustry, but today little of this remains. We will explorethe island, looking out for Arctic flowers.Days 11–16 Spitsbergen. A place of mountains and rivers of ice, itis home to a large variety of animals.Day 17 Leave the ship in Spitsbergen and fly to London fromTroms.B.Please read the text about behaviors on airplane and answer questions 1-8.Air rage is the current expression for aggressive or disruptive behavior of airline passengers. It comes from the term road rage, used to describe drivers whose rude and hostile attitude toward others can lead to serious accidents or violence.Major airlines are becoming increasingly concerned about air rage and are training their staff to deal with it. At the same time, they are introducing tougher policies and supporting legislation that will allow local police to arrest offenders when they land. A special agreement, known as the 1963 Tokyo Convention, allows for the arrest of troublesome passengers on landing, even if they are not citizens of that country and did not technically commit a crime there.The problem of air rage may start before passengers even board the plane and may become worse on board. Reasons for air rage include heavy traffic on the way to the airport, long check-in lines, the amount of alcohol available both in the waiting area and given out free on board the plane, and strict enforcement of no-smoking laws at the airport and on the flight itself.Airline staff are trained to spot a potential troublemaker and to deal with violent behavior by talking to the person. For more serious cases, handcuffs and straitjackets are kept on board, although these are used only as a last resort. Fortunately, incidents involving serious violence are rare, but air rage is increasingly becoming an issue of concern for all airlines.1、Air rage and road rage refer to aggressive behavior by ____________a.passengers in cars or planes.b.airline passengers and car drivers.c.car drivers and airline pilots.d.airline passengers and crews.2.According to this passage, air rage _____________a.is a more serious problem today than it was 25 years ago.b.is a problem that more and more airline companies are dealing with.c.is a problem that became very serious in the 1960s.d.occurs more on certain airlines than on others.3.The Tokyo Convention enables local police _________________a.to introduce tougher policies.b.to arrest people while flying over their country.c.to arrest aggressive passengers of any nationality.d.to use handcuffs and straitjackets to restrain aggressive passengers.4.According to this passage, which of the following factors contributes to air rage?a. a difficult journey to the airportb.smoking on boardc.restrictions on alcohold.handcuffs and straitjackets being kept on board5.From this passage we can understand that airline staff will watch out for _______________a.heavy smokers.b.heavy drinkers.c.people who are nervous about flying.d.people who start talking to aggressive passengers.6.The phrase as a last resort in the last paragraph means ______________a.in a far-away vacation spot.b.if the plane cannot return to the airport.c.after everything else has failed.d.with potential troublemakers.7.What might the airline crew do to control air rage on the plane?a.allow the passenger to smokeb.arrest the passengerc.restrain the passengerd.behave rudely to the passenger8.The writer's main purpose in this passage is to _________________a.discuss the phenomenon of air rage.b.explain the reasons for air rage.c.suggest solutions for airline staff faced with air rage.d.warn passengers about air rage.C.Please read the following article about men who hunt for birds’ nests in caves inThailand, and then answer questions 1-9 in your own words on a separate answer sheet.The Nest Hunters of Tam YaiSwiftlets are shy birds that make their nests in the remotest corners of deep caves. They have the ability to fly fast and straight like arrows around the interior of the cave walls. Like some other birds, they build their nests with their saliva, the juicy liquid from their own mouths. This juice hardens quickly to make a small nest, shaped like a cup. These nests are called “white gold”, because they can be sold for thousands of dollars in the Chinese food markets. It is these nests for which the hunters of Tam Yai are prepared to risk their lives.Tam Yai cave in southern Thailand is the largest network of caves inside a limestone mountain, known as Suwan Kuha, meaning “cave temple”. It has been given this name because it contains a large area decorated with statues of Buddhas. High above the statues, in the far corners of the cave complex, is where the nests are to be found.The nest hunters climb barefoot up dangerous bamboo poles hundreds of metres above the ground to collect these valuable nests. They rarely use safety equipment, and if they fall, they will die instantly. These nests can only be reached by the bravest and most skilled climbers, and they are often only able to reach the highest nests with the aid of a stick and a net.Nest hunting is a skill passed down in families from father to son. Because of the profits that can be made, the competition among rival climbers is fierce. There are armed guards at the entrance to the cave to protect the nests from thieves. In Tam Yai, there are also strict laws to prevent illegal hunting and to ensure proper collecting, or “harvesting”, of the nests. As a result, the birds are a protected species and the number of swiftlets is growing. Nest harvesting begins in March and if the harvest is collected at the correct time of year, each swiftlet will lay eggs three times a season. Once the young birds have hatched and flown, the nests can be collected and sold to the Chinese food industry as the vital ingredient in bird’s nest soup.The recipe for the highly valued bird’s nest soup is centuries old, and the soup is said to have a value in prolonging life. Chinese doctors often prescribe it for people who are suffering from skin conditions, lung disease and breathing problems.It is important to prepare the nests thoroughly when they arrive in the restaurant kitchens. Firstly they are washed, soaked and boiled until they have a soft, rubber-like texture. Thenthey are mixed with meat and coconut and all the ingredients are cooked together. The nest itself is not delicious, in fact it has hardly any taste. As one Chinese chef says: “It is the other ingredients which give the soup its flavour. The nest is soft and crunchy, and when you prepare it you must be careful to remove all traces of the bird, such as bones or feathers. This is because Chinese people appreciate the way it feels in their mouth rather than the taste and smell.”It is an exotic dish in a multi-million dollar market. The nests themselves are small; they weigh less than 10 grams and measure just a few centimetres. But for the nest hunters the risks are great indeed.Questions:1. What happens to the saliva when the birds build their nests?2. Why do the hunters take such great risks to collect the nests?3. Which country buys most of the birds’ nests?4. Why is Suwan Kuha regarded as a temple?5. What makes the job of nest hunting particularly dangerous? Give TWOdetails.6. According to the graph, how does the price of birds’ nests in 2008compare to that of 1968?7. How is the business of nest hunting in Tam Yai controlled? Give TWOdetails.8. How is bird’s nest soup important for health?9. How does the soup get its taste?Paper III: Use of English (20 minutes 60 marks)A.ClozeSchool’s Art SaleLast Friday parents helped collect lots of money for a school by buying children’s pictures.A primary school in Bicester used its classrooms as an art gallery for a day and (1) ............parents to come and look. All the pupils (2) ............ a work of art and (3) ............ painting went on sale at £5. Hundreds of parents and relations came and, together, they spent(4) ............ £2,000.Now the school is (5) ............ of making the exhibition bigger next year by also contacting businesses (6) ............ operate in the local area. One of the schoolchildren’s parents first had the (7) ............ after going to (8) ............ exhibitions in her home country, South Africa.The school has decided to (9) ............ the money to buy books and CD players. The Head Teacher said he was delighted to see the school (10) ............ full and he was very proud ofthe children.1 A hoped B invited C pleased D wished2 A operated B played C performed D produced3 A few B some C each D all4 A over B more C close D near5 A planning B thinking C considering D wanting6 A what B who C which D whose7 A memory B idea C habit D choice8 A same B likely C similar D equal9 A bring B add C join D use10 A so B too C such D enoughB.Grammar and Vocabulary Multiple Choices1. We don't have any milk left. _____ ?a. don't youb. are wec. do wed. have you2. I tried on two sweaters, but I didn't buy _____ of them.a. eitherb. nonec. neitherd. any3. If they ________________ the car earlier, they wouldn't have gotten stuck on the road.a. were checkedb. did checkc. had checkedd. checked4. I saw every episode in that _____________ television series.a. ten-partsb. tens-partc. tens-partsd. ten-part5. "How are you managing with the new computer program?""Not great. I ___________ to figure it out yet.'"a. can't have managedb. haven't managedc. don't managed. haven't been managing6. I've been trying ____________ Sue all morning.a. to callb. callingc. calld. to have called7. You ___________ close all the windows before you leave the house.a. needb. shouldc. oughtd. might8. He was accused ______________ stealing money from the store.a. inb. forc. byd. of9. We stayed up to watch TV ___________ it was very late.a. despiteb. in spite ofc. althoughd. even10. "I have a headache. Can you get me an aspirin?" "Sure. ________ get you one right now."a. I'm able tob. I'm goingc. I ought tod. I'll11. It will take you _______ three hours to drive to the campsite.a. greatlyb. entirelyc. approximatelyd. annually12. We didn’t get to the meeting on time __________ a traffic jam.a. causingb. because ofc. owing tod. due to13. I have to make an _________ with my dentist.a. arrangementb. assignmentc. interviewd. appointment14. The sign on the front tells you the ________ of each bus.a. resortb. destinationc. agencyd. port15. The school must be very old. When was it ___________ up?a. posedb. evolvedc. setd. founded16. I really like Jan and Dave. They’re very good ___________.a. societyb. companyc. associatesd. friendship17. The letter is okay, but you _________ a few words in the last line.a. leftb. omittedc. avoidedd. lost18. I want to move out of the city because I find __________ life exhausting.a. ruralb. remotec. urband. country19. She doesn’t talk about her feelings. She’s a very __________ person.a. insincereb. passivec. reservedd. upset20. Jim __________ his brother to lend him $ 500.a. imposedb. persuadedc. requiredd. desiredPaper IV: Writing (20 minutes 20 marks)Please write a short paragraph of about 150 words and tell us what your favorite TV program is, what it is about, and why you enjoy watching it.。
广州ulc剑桥国际高中入学考试英语真题
广州ulc剑桥国际高中入学考试英语真题1、You have coughed for several days, Bill. Stop smoking, _______ you’ll get better soon. [单选题] *A. butB. afterC. orD. and(正确答案)2、You have failed two tests. You’d better start working harder, ____ you won’t pass the course. [单选题] *A. andB. soC. butD. or(正确答案)3、Look! There are some boats ______ the river.（）[单选题] *A. on(正确答案)B. overC. betweenD. in4、—What were you doing when the rainstorm came?—I ______ in the library with Jane. （）[单选题] *A. readB. am readingC. will readD. was reading(正确答案)5、92．China is a big country ________ a long history. [单选题] *A．hasB．haveC．with(正确答案)D．there is6、4．—Let's fly a kite when you are ________ at the weekend.—Good idea. [单选题] *A．warmB．kindC．smallD．free(正确答案)7、Then the speaker _____the various factors leading to the economic crisis. [单选题] *A.went onB.went afterC.went into(正确答案)D.went for8、We have ______ homework today. （）[单选题] *A. too manyB. too much(正确答案)C. much tooD. very much9、My father?is _______ flowers. [单选题] *A. busy watering(正确答案)B. busy waterC. busy with wateringD. busy with water10、She _______ love cats, but one attacked her and she doesn’t like them anymore. [单选题]*A. got used toB. was used toC. was used forD. used to(正确答案)11、Have you done something _______ on the weekends? [单选题] *A. special(正确答案)B. soreC. convenientD. slim12、She’s _______ with her present _______ job. [单选题] *A. boring; boringB. bored; boredC. boring; boredD. bored; boring(正确答案)13、He studied harder to _______ his reading skills. [单选题] *A. improve(正确答案)B. rememberC. memorizeD. forget14、48．—________ is your new skirt, Lingling?—Black. [单选题] *A．HowB．What colour(正确答案)C．WhichD．Why15、24．Kitty’s father ______ a policeman since 2 He loves helping people. [单选题] * A．isB．wasC．has been (正确答案)D．have been16、I often _______ music from the Internet. [单选题] *A. download(正确答案)B. spendC. saveD. read17、My camera is lost. I am ______ it everywhere.（）[单选题] *A. looking atB. looking for(正确答案)C. looking overD. looking after18、Many people prefer the bowls made of steel to the _____ made of plastic. [单选题] *A. itB. ones(正确答案)C. oneD. them19、I hope to see you again _______. [单选题] *A. long long agoB. long beforeC. before long(正确答案)D. long20、73．The moonlight goes ____ the window and makes the room bright. [单选题] * A．acrossB．through(正确答案)C．overD．in21、-Do you have tickets for Friday? -Sorry, we've got _____ left. [单选题] *A. eitherB. none(正确答案)C. no oneD. neither22、_____ Lucy _____ Lily has joined the swimming club because they have no time. [单选题] *A. Not only; but alsoB. Neither; nor(正确答案)C. Either; orD. Both; and23、You _____ smoke in the library, or you will be driven away. [单选题] *A. can'tB. mustn't(正确答案)C. will notD. may not24、—Could you please make the bed?—______.（）[单选题] *A. Yes, I wasB. No, I don’tC. Sure, I’ll do it(正确答案)D. No, that’s no problem25、His remarks _____me that I had made the right decision. [单选题] *A.ensuredB.insuredC.assured(正确答案)D.assumed26、While my mother _______ the supper, my father came back. [单选题] *A. cooksB. is cookingC. was cooking(正确答案)D. has cooked27、John had planned to leave, but he decided to stay in the hotel for（）two days because of the heavy rain. [单选题] *A. otherC. another(正确答案)D. others28、1——May I help you? You seem to be having some problems.——_______ , thanks. Ithink I can manage. [单选题] *A. All rightB. No problemC. It’s all right(正确答案)D. There’s no way29、--Whose _______ are these?? ? ? --I think they are John·s. [单选题] *A. keyB. keyesC. keys(正确答案)D. keies30、We need a _______ when we travel around a new place. [单选题] *A. guide(正确答案)B. touristC. painter。
上实剑桥入学考试G1模拟卷(数学)
于点 M ，点 P 是 l1 左侧一点， P 到 l1 的距离为 b (a < b < 2a)．
（1）画出点 P 关于 l1 的对称点 P1 ，并在 PP1 上取一点 P2 ，使点 P2 、 P1 关于 l2 对称；
（保留画图痕迹，不要求写画法）
（2） PP2 与 AB 有何位置关系和数量关系？请
l1
2
2
（只需代入一个数求值）
19、（本题 6 分）
（1）在△ABC和△DCB中，
Q AB=DC,AC=DB,BC为公共边. ∴△ABC≌△DCB（SSS） ……………………………………………………2 分
（2）四边形 BNCM 为菱形……………………………………………………3 分
Q △ABC≌△DCB
∴∠DBC=∠ACB
.
1− x
10．2010 年上海世界博览会，中国馆投资 1095600000 元，将 1095600000 保留两个有效数字的近似
数应为_____ ▲__ 元．
11．如图，把一块直角三角板的直角顶点放在直尺的一边上，如果∠1＝54°，那么∠2 是 ▲ °．
12. 如图，AB 是⊙O 的直径， 点 D 在⊙O 上，∠AOD＝130°，BC∥OD 交⊙O 于 C，则∠A＝ ▲ °．
点 O 为 BC 边上的一个点，连结 OD，以 O 为圆心，BO 为半径的⊙O 分别交边 AB 于点 P，交线段
OD 于点 M，交射线 BC 于点 N，连结 MN．
（1）当 BO＝AD 时，求 BP 的长；
（2）在点 O 运动的过程中，线段 BP 与 MN 能否相等？若能，请求出当 BO 为多长时 BP＝MN；若
5
27．(10 分)某工厂用如图甲所示的长方形和正方形纸板，做成如图乙所示的竖式与横式两种长方体形 状的无．盖．纸．盒．．
上海光华剑桥入学考试样卷（高中英语卷）（学习秘籍）
PART 1 READINGYou are going to read an extract from a novel. For questions 1-8, choose the answer (A,B,C or D) which you think fits best according to the text.-------------------------------------------------------------------------------------------------------------------------------------------------------------------On Saturday mornings I worked in the family shop. I started cycling down to the shop with Dad on Saturdays as soon as I was big enough. I thought of it as giving him a hand and so I didn’t mind what I did, although it was mostly just fetching and carrying at a run all morning. I managed not to think of it as work and I looked forward to the bar of chocolate my grandmother passed me unsmilingly as I left. I tried not to look at her; I had reason to feel guilty because I’d generally already eaten some dried fruits or a sliver of cheese when no one was looking. As soon as I was fifteen, though, Dad said, ‘That’s it, our Janet. You’re of working age now and you’re not coming to work unless your grandmother pays you properly.’He did his best to make his chin look determined. ‘I shall speak to her.’The next Saturday, Gran called me into her little office behind the shop. I always hated going in there. She had an electronic heater on full blast, and the windows were always kept tightly closed whatever the weather. ‘You’re wanting to get paid, I hear,’ she said. ‘Yes, please,’ I replied. It was rather like visiting the headmistress at school, so I was very quiet and respectful. Gran searched through the mess of papers on her crowded desk, sighing and clicking her tongue. Eventually she produced an official-looking leaflet and ran her fingers along the columns of figures. ‘How old are you?’‘Fifteen…Gran,’I added for extra politeness, but she looked at me as if I had been cheeky. ‘Full-timers at your age get forty pounds for a thirty-five-hour week,’ she announced in such a way as to leave no doubt that she[15] wasn’t in favour of this. ‘No wonder there’s no profit in shopkeeping! So, Janet, what’s that per hour?’[16] Questions like that always flustered me. Instead of trying to work them out in my head, I would just stand there, unable to think straight. ‘I’ll get a pencil and paper,’ I offered. ‘Don’t bother,’ snapped Gran angrily, ‘I’ll do it myself. I’ll give you a pound an hour; take it or leave it.’‘I’ll take it, please.’‘And I expect real work for it, mind. No standing about, and if I catch you eating any of the stock, there’ll be trouble. That’s theft, and it’s a crime.’From then on, my main job at the shop was filling the shelves. This was dull, but I hardly expected to be trusted with handling the money. Once or twice, however, when Dad was extra busy, I’d tried to help him by serving behind the counter.I hated it. It was very difficult to remember the prices of everything and I was particularly hopeless at using the till. Cer tain customers made unkind remarks about this, increasing my confusion and the chances of my making a fool of myself.It was an old-established village shop, going back 150 years at least and it was really behind the times even then. Dad longed to be able to make the shop more attractive to customers, but Gran wouldn’t hear of it. I overheard them once arguing about whether to buy a freezer cabinet. ‘Our customers want frozen food,’ Dad said. ‘They see things advertised and if they can’t get them from us, they’ll go elsewhere.’‘Your father always sold fresh food,’ Gran replied. ‘People come here for quality, they don’t want all that frozen stuff.’Actually, she gave way in the end over the freezer. Mr. Timson, her great rival, installed one in his shop at the other end of the village and customers started making loud comments about how handy it was, being able to get frozen food in the village, and how good Mr. Timson’s sausages were. That really upset her because she was proud of her sausages and she ungraciously gave Dad the money to buy the freezer. Within a couple of weeks, she was eating the frozen food like the rest of us.( ) 1 How did Janet feel when she first started her Saturday morning job?A She enjoyed the work that she was given.B She was pleased to be helping her father.C She worried that she was not doing it well.D She was only really interested in the reward.( ) 2 What do we learn about her grandmother’s office in paragraph two?A It needed decorating.B It was untidy.C It had too much furniture in it.D It was dark.( ) 3 ‘This’ (line 15) refers toA shopkeepers’ profits.B a thirty-five-hour week.C Janet’s request.D the recommended wage.( ) 4 ‘Flustered’ (line 16) meansA bored.B angered.C confused.D depressed.( ) 5 Why did Janet’s grandmother react angrily to her offer to fetch a pencil and paper?A Janet was unable to answer her question.B Janet had been unwilling to help her.C Janet had made an unhelpful suggestion.D Janet had answered her rudely.( ) 6 What did Janet’s father and grandmother disagree about?A how to keep their customers loyal to the shopB the type of advertising needed to attract customersC the type of customers they needed to attractD how to get new customers to come to the shop( ) 7 What eventually persuaded Janet’s grandmother to buy a freezer?A She found that she liked frozen food after all.B A new shop opening in the village had one.C It was suggested that her products weren’t fresh.D She responded to pressure from her customers.( ) 8 What impression do we get of Janet’s feelings towards her grandmother?A She respected her fairness.B She doubted her judgement.C She disliked her manner.D She admired her determination.PART 2 WRITINGWrite an answer to one of the questions 1-3 in this part. Write your answer in 180-200 words in an appropriate style on the lined page. Put the question number in the box.1You have been doing a class project on transport. Your teacher has now asked you to write a composition about the following statement:People who are about 16 years old should go to work and take their responsibility to the society, because the nature of human being is working to create value.Write your composition.2You see this advertisement for a job in the USA.USA SUMMER CAMPSPeople of all ages needed to work in summer camps all over the USA.If you can speak English and you are cheerful, energetic and hardworking, you are the rightperson for us. Food and accommodation are provided. You just pay the air fare.You will:-look after children aged 8-12-help organize sports and evening activities-work in the kitchensWrite telling us about yourself and why you think you would be a suitable person for the job.Write your letter of application. Do not write any postal addresses.3An international student magazine is running a short story competition which you have decided to enter. The story must end with the following words:Michael closed the door and knew at that moment he had made a mistake.Write your story.4Answer one of the following two questions based on your reading of one of these set books. Write (a) or (b) as well as the number 4 in the question box, and the title of the book next to the box. Your answer must be about one of the books below.Best Detective Stories of Agatha Christie ---Longman FictionA Tale of Two Cities --- Charles DickensAnimal Farm --- George OrwellMore Tales from Shakespeare --- Charles and Mary LambWuthering Heights --- Emily BronteEither (a)‘How important is the title of a book or short story?’Your teacher has asked you to write a composition discussing this question and explaining why the writer of the book or one of the short stories you have readchose that particular title.Or (b)The English book club you belong to is producing a list of books in English which it can recommend to members. The Club Secretary has asked you to write a report on the book or short stories you have read,PART 3 USE OF ENGLISHTask 1For questions 1-15, read the text below and decide which answer best fits each space.-------------------------------------------------------------------------------------------------------------------------------------------------------------------EVERYONE’S AN ARTISTEvery year, the village of Pettineo celebrates its unique arts festival. For a few days each summer, artists from all over Europe (1)….. at this village near the north coast of Sicily to (2)….. the creative atmosphere. During their stay, the artists get (3)….. with the local people to paint a one-kilometre long picture that runs the (4)….. of the high street. (5)….. the painting is done, each visiting artist joins a local family for a big lunch and, (6)….. the meal, the family receives the (7)….. of the painting that the artist has painted. As a result, (8)….. few villagers are rich, almost every home has at least one painting by a well-known European artist. Visitors to the village are eagerly (9)….. into homes to see these paintings.The festival was the (10)….. of Antonio Presti, a local businessman who (11)….. it up four years ago. Since then, Pettineo has (12)….. a sort of domestic art museum in (13)….. any visitor can ring a doorbell, go into a house and (14)….. a painting. In addition to this exhibition of paintings in people’s homes, for those who have time to spare, there is an opportunity to (15)….. through the display of huge sculptures in the village square.( ) 1 A group B crowd C gather D combine( ) 2 A amuse B enjoy C entertain D delight( ) 3 A linked B jointly C combined D together ( ) 4 A size B measure C length D area( ) 5 A Just B Once C Soon D Only( ) 6 A in addition to B in place of C in common with D in exchange for ( ) 7 A partition B section C division D region( ) 8 A though B despite C since D even( ) 9 A persuaded B invited C requested D attracted ( ) 10 A image B purpose C thought D idea( ) 11 A set B put C got D had( ) 12 A become B advanced C grown D increased( ) 13 A what B where C whom D which( ) 14 A wonder B stare C admire D delight( ) 15 A move B step C wander D marchTask 2For questions 16-22, complete the second sentence so that it has a similar meaning to the first sentence, using the word given. Do not change the word given. You must use between two and five words, including the word given.Here is an example:You must do exactly what the manager tells you.carryYou must carry out the manager’s instructions exactly.The gap can be filled by the words ‘carry out the manager’s’.Write only the missing words on the line.------------------------------------------------------------------------------------------------------------------------------------------------------------------- 16 John is interested in knowing more about astronomy.likeJohn more about astronomy.17 Because of the parade, we weren’t allowed to park in the High Street.letBecause of the parade, the police wouldn’t in the High Street.18 ‘Did you see that film on television on Saturday?’ Susan asked me.seenSusan wanted to know that film on television on Saturday.19 ‘I’m afraid these jeans have a hole in them.’there‘I’m afraid that these jeans.’20 They cancelled the match because of the bad weather..calledThe match because of the bad weather.21 Dan never takes any notice of my advice.attentionDan never my advice.22 ‘Can I borrow your bicycle, Sarah?’ asked Frank.lendFrank asked Sarah her bicycle.Task 3For questions 23-32, read the text below. Use the word given in capitals at the end of each line to form a word that fits in the space in the same line. There is an example at the beginning. Write your answers in the space given.-------------------------------------------------------------------------------------------------------------------------------------------------------------------AIRPORTS。
XXX剑桥班入学测试卷
XXX剑桥班入学测试卷st year。
the number of deaths increased by 2%-5% compared with the year before last。
(选项A)12.The child was told to apologize for being rude to his uncle。
(选项B)13.The little girl can sing along with music。
(选项B)14.She was XXX(选项A)15.Imagine standing at the top of the hill and the wonderful view you will see。
(选项A)16.- Smoking is bad for your health。
Yes。
I know。
But I simply can't give it up。
(选项A)17.All the names of the guests are included in the list。
I don't et any of them。
(选项B)18.You are required to write each line clearly so that we can see it。
(选项B)19.The police have finally XXX.20.Perhaps we need to clear away these books to make space for our new students.21.This is the original piano on which the composer created some of his greatest works.22.In fact。
like many boys。
Jack XXX.23.According to the recent reports。
剑桥测试1 【剑桥国际高中入学资料】
剑桥冲刺班摸底测试一、单项选择题1. --- Jack bought a new mobile phone the other day.--- ________? That’s his third one in just one month.A. Had heB. Did heC. Does heD. Has he2. It is reported that the floods have left about _________ people homeless.A. two thousandB. two-thousandsC. two thousandsD. two thousands of3. --- You should apologize to her, Barry.--- ______, but it’s not going to be easy.A. I suppose soB. I feel soC. I prefer toD. I like to4. I like _____ color of your skirt. It is _____ good match for your blouse.A. a; theB. a; aC. the; aD. the; the5. Why not try your lick downtown, Bob? That’s ______ the best jobs are.A. whereB. whatC. whenD. why6. Work gets done ______ when people do it together, and the rewards are higher too.A. easilyB. very easyC. more easilyD. easier7. --- Look! He’s running so fast!--- Hard to _______ his legs were once broken.A. knowB. imagineC. realizeD. find8. Many of them turned a deaf ear to his advice, _______ they knew it to be valuable.A. as ifB. now thatC. even thoughD. so that9. The children talked so loudly at dinner table that I had to struggle ______.A. to be heardB. to have heardC. hearingD. being heard10. It _____ we had stayed together for a couple of weeks ____ I found we had a lot in common.A. was until; whenB. was until; thatC. wasn’t until; whenD. wasn’t until; that11. We firmly believe that war never settles anything. It only _____ violence.A. runs intoB. comes fromC. leads toD. begins with12. Of the seven days in the a week, Saturday is said to be the most popular ____ for a wedding in some countries.A. wayB. situationC. eventD. choice13. Would you please ______ this form for me to see if I’ve filled it in right?A. take offB. look afterC. give upD. go over14. Chan’s restaurant on Baker Street, ______ used to be poorly run, is now a successful business.A. thatB. whichC. whoD. where15. --- My cat’s really fat.--- You ______ have given her so much food.A. wouldn’tB. couldn’tC. shouldn’tD. mustn’t二、首字母填空Maybe you are more interested in sports than in history. You probably think you will never be a top student. In f_____, anyone can become a better student if he or she wants to. If you can use your time well, you may improve your study w_____ much work. Here’s how:Plan your time carefully. When you plan your week time, you should make a l_____of thing that you have to do. First write down the time for eating, sleeping, dressing, etc. Then decide on a good time for studying. Of course, studying shouldn’t take all of your time. Don’t forget to leave yourself enough _t_____ for hobbies.Find a good place to study. Look around the house _f____ a good study place. Keep this space, which may be a desk _o____just a corner of your room. No games, radio, or television! When you sit down to work, think only about the subject!Make good use of your time in class. Listen c_____to what the teacher says. Careful listening in class means less work later. You also need to take notes in class, because it can m____ it easier for you to learn well.三、Q&AIt is a Chinese traditional custom that people eat mooncakes at the time of the Mid-Autumn Festival. One 1 about it is almost 700 years old. In the 14th century, the Chinese planned a surprise attack against their enemies at the time of' the festival . The messages for the attack were put into cakes. The cakes were passed from one person to __2 __. Each person read the messages and knew when and where the attack would 3 . At last the Chinese won the victory.Mooncakes are still eaten during the Mid-Autumn Festival. However, the fillings of the mooncakes now are not messages, but foods such as meat, fruits and duck eggs. On the fifteenth day of the eighth month of eachChinese year, 4 and friends come together and enjoy the beautiful moon. Shops are crowded with people and the smell of mooncakes 5 the air. Many people go to a place where they can see the moon clearly. Large parks and the seaside are popular places. Once there, people have a picnic dinner, eat mooncakes and watch the moon rise.Chicago, Illinois, is next to a big, beautiful lake, Lake Michigan. In the summer Lake Michigan is warm and blue. People lie on the beaches and swim in the water. In the winter Lake Michigan is cold and gray. Snow covers the beaches, and ice covers the water.On a cold January day, a little boy and his father were playing in the snow on a Chicago beach. The boy was Jimmy. He was four years old. Jimmy was playing with a sled（雪橇）. He pushed the sled down a small hill. The sled went onto the ice of Lake Michigan. Jimmy ran after the sled. He ran onto the ice. Suddenly the ice broke, and Jimmy fell into the cold water. Jimmy’s father jumped into the water. He couldn’t find Jimmy. As minutes went by, he still couldn’t find Jimmy. “My kid is dead! My kid is dead!” he screamed.Men from the Chicago Fire Department arrived. Twenty minutes later they found Jimmy and pulled him out of the water. Jimmy was not breathing, and his heart was not beating. He was dead. At the beach doctors worked on Jimmy for one hour. He began to breathe, and his heart began to beat again. The doctors rushed Jimmy to the hospital. Doctors at the hospital put Jimmy on a mattress（床垫) in bed because they wanted his body to warm up slowly. They gave him some medicine because they wanted him to sleep.After eight days in the hospital, Jimmy woke up, but he couldn’t walk or talk. He stayed in the hospital for six weeks in all. Every day he got better. Then he went to another hospital. He stayed there for seven weeks. He began to walk, talk and play again.Jimmy was in the water for over 20 minutes. He couldn’t breathe in the water. He couldn’t get any oxygen. But today he is alive and healthy. How is it possible?Jimmy is alive because the water was ice cold. Usually the brain needs a lot of oxygen. But when it’s very cold, the brain slows down. It does not need much oxygen. So the cold water saved Jimmy. Jimmy’s father has another r eason. He says, “Jimmy is alive today because he is a fighter. He is a strong little boy.”1. Did Jimmy and his father play on the Chicago beach on a winter day or a summer day?__________________________________________.2. Why did Jimmy fall into the cold water?_______________________________3. Where did the doctors at the hospital put Jimmy in order to warm up his body?__________________________________________.4. What happened to Jimmy after he woke up in the hospital?_____________________________________________.5. What do you think of Jimmy?He was ___________________________________.四、作文Write about the following topic:In recent years, many young people decide to further their study abroad. What are the benefits and drawbacks of studying abroad?Give reasons for your answer and include any relevant example from your own knowledge or experience. You should write at least 250 words。
杭外剑桥国际高中入学模拟考试英语
杭外剑桥国际高中入学模拟考试英语5单项填空(共1 5小题；每小题1分，满分15分)1．Don’t talk to Simon like that. He is only _______ eleven year—old boy．A．a B．an C．the D．不填2．Ricky caught a bad cold yesterday，_________he had to stay at home．A．because B．but C．or D．so3．When traffic lights are red，we ________ stop and wait.A．may B．can C．must D．might4．How much does it cost to build the school library?Four _______ Yuan．A．million B．millions C．millions of D．millions of5．Did your parents go to climb the Zijin Mountain last Sunday?一No They _______ went to see a film．A．both B．all C．either D．every6．______ kind girl Nancy is!Yes．she is always ready to help others．A．What B．What a C．How D．How a7．Would you like to go and see a film?Sure，the TV Programmes are too_______．A．surprising B．interesting C．exciting D．boring8．I don't know ________．A．where does he come from B．what is his name.C．how old he is D．when will he leave9．Today Chinese is becoming more and more popular．It _______in many schools around the world．A．teaches B．is teaching C. has taught D．is taught10．Amy makes fewer mistakes than Frank．She does her homework______．A more carefully B．more carelessly C．more careful D．more careless11．Hello，this is Lily speaking．Could I speak to Mr. Black?…Sorry．He______ the Xuanwu Lake Park．A has been to B．went to C．has gone to D. will go to12．What about playing football this afternoon, Sam?I would rather _______ at home than _________ football．It’s too hot outside．A．stay；playing B．stay；play C. to stay；to play D. to stay；playing 13．You’d better hurry．or we’ll be late for 1he plane．Don’t worry．The plane will ____ in two hours．A．Lake in B take away C．take off D．take out14．How about going shopping on Hunan Road this evening?______,But I’ve to prepare for tomorrow’s exam．A．I can’t B．Sounds great C. That’s right D．No，I’m terribly sorry15 Now，where is my school bag?_______! We’ll be late for school．A. Just a minute B．Take it easy C. Don’t worry D．Come on完形填空(共10小题；每小题1分，满分10分)As soon as he finished his homework．Eric jumped onto his bicycle and rode off in the direction of the beach. While he was __16__ along．He thought about the whales(鲸鱼). He hoped he would see them again today．After he got to the beach．Eric __17__ his bicycle behind a bush so that no one could see it from the road．Then he ran down onto the sand．__18__ it was only four in the afternoon，the sky was already growing dark. Eric frowned(皱眉)．If it __19__ he wouldn’t be able to see the whales because they would stay in deeper water．He hurried along the beach __20__ the rocks．They were the best place to watch the whales from because of their__21__．Before Eric reached the rocks he felt a drop of water on his head．“Oh no!” he thought. “Now the whales will stay in the deep water and I won’t be able to __22__ them!” But just then he saw a large shape on the beach. It was a young whale! The whale had come too close to the shore(海岸)and got stuck(搁浅)on the __23__ ! At first the whale didn’t move at all and Eric thought it was__24__ ．Then he saw its tail move weakly．Eric turned and ran through the rain as fast as he could back to his bicycle．He had to get __25__! Unless they got the whale back in the water soon，it would die and Eric couldn’t let that happen．16．A．riding B．running C．getting D．walking17．A．sent B hid C．look D．got18．A．As B．Since C. Because D．Although19．A．shone B．snowed C. rained D．blew20．A．into B．off C. to D．from21. A．length B．size C. height D shape22．A．watch B．kill C. catch D．save23 A．soil B．beach C．grass D．water24 A．dead B．pretty C．lovely D alive25．A．care B．water C．medicine D. help阅读2x15My favorite great book is The Adventure of Tom Sawyer by Mark Twain．Tom lives with his aunt Polly in a quiet street of St. Petersburg, Missouri．He’s a lively and clever young boy，and he finds himself in many exciting adventures (冒险)．He runs away with his two friends，Huck Finn and Joe，to an island in the middle of the Mississippi River for several days．With Huck he goes looking for treasure, with Becky he gets lost in a cave．and finally，they find a box of gold．My favorite scene in the book is when everyone thinks Tom is dead．He decides to go to his own funeral．He hides and watches for a time．and then suddenly he appears．Everyone is surprised to see him but they’re also pleased to see him alive．Tom is the hero of the story，but there are other important characters．Huck is an outsider and everyone is afraid of him．Becky is pretty with fair hair，Joe is Tom’s best friend．and Injun Joe is the bad man of the story.The theme of the story is about children growing up．It describes how strangers are seen in small towns of America. Finally, it talks about freedom，social rules and how people are punished(惩罚)for bad behavior.Why do I think The Adventure of Tom Sawyer is a great book? Mark Twain wrote the story in 1876，but it's still read and loved by people all over the world today．And although it’s only a story. Twain wrote it in the everyday English of the southern states of America in the 19th century，so it sounds very real. Today it’s thought to be one of the greatest books in Americanliterature. Go on--- read it! I know you’ll enjoy it，too26．Where does Tom run away with his two friends?A．To a quiet street． B To a small town．C．To an island．D．To a forest．27．Who is the bad man in the story?A．Huck Finn． B Injun Joe．C．Becky．D．Polly．28．How did people feel when Tom appeared at his own funeral ?A．They were surprised and pleased．B．They were surprised and sadC．They were worried and excited．D．They were frightened and happy．29．The whole book is mainly about _______ ．A．freedom and social rules B．children’s bad behaviourC the growth of young children D．strangers in American small towns30．The writer writes the article to ____．A．ask us to read the bookB．tell us how popular the book is todayC．tell us when Mark Twain wrote the story D．tell us why the story sounds very realOne thing that British and Chinese cultures share is a love for fine tea．Today，when we think of Western tea culture，we often think of the English and beautiful china tea cups．Afternoon tea People believe that an English lady，Anna，first introduced the idea of afternoon tea．In the 18th and 19th centuries．the English ate only two main meals each day breakfast and a heavy supper that would last for several hours in the evening．As a result，people often got very hungry during the long wait between these two meals．To solve this problem，Anna came up with the clever idea of inviting some friends to join her for an afternoon meal between four and five o'clock．This meal included cakes and sandwiches．and tea was served(提供)to wash down the food．In order to make this afternoon meal important，fine china cups and plates，and silver teapots．knives，forks and spoons were used Soon，afternoon tea parties became popular social occasions．Today，afternoon tea parties continue to play an important part in the social life in modern Britain．Will you come for coffee'?Coffee also has an important role in British culture．People often use the words“Will you come for coffee?” to mean“Would you like to come to my home for a chat?”Normally，several different drinks such as tea, hot chocolate or a soft drink like orange Juice will be served as well as coffee．and you will be asked what you would like．However，you will not normally he offered wine at a "coffee" party.Coffeehouses and the London Stock ExchangeIn the 17th century London，coffeehouses were busy and noisy places．Businessmen and bankers went to coffeehouses to do their business, as well as to drink coffee．In fact，the London Stock Exchange(股票交易所) is believed to have started from these coffeehouses 31．Anna introduced the idea of drinking afternoon tee because she ______．A enjoyed chatting with her friends at homeB loved fine tea and beautiful china tea cupsC．wanted to share nice food with her friendsD found people felt hungry during the long wait between the two meals32．What does“social occasions”mean in Chinese?A．集体婚礼B．社交活动 C.社区表演D．公共场合33 If someone says to you“Will you come for coffee?”，youA．will be offered coffee onlyB．are asked what you would like to drinkC．will be asked to have a chat with him or herD．are invited to take part in an afternoon tea party34．From the last paragraph (段落) we can see ______.A a new business was started in coffeehousesB．coffeehouses are still used by businessmen end bankersC．businessmen and bankers went to coffeehouses just for coffeeD. most people wouldn’t like to go to coffeehouses because of the noise35．Which is the best title(标题)of the article?A．British And Chinese Cultures B．The Beginning Of Tea And CoffeeC. Coffeehouses And Business D．English Tea And Coffee CultureMass transportation revised the social and economic fabric of the American city inthree fundamental ways. It catalyzed physical expansion, it sorted out people and land uses, and it accelerated the inherent instability of urban life. By opening vast areas ofunoccupied land for residential expansion, the omnibuses, horse railways, commuter trains, and electric trolleys pulled settled regions outward two to four times more distant from city centers than they were in the premodern era. In 1850, for example, the borders of Boston lay scarcely two miles from the old business district; by the turn of the century the radius extended ten miles. Now those who would afford it could live far removed from the old city center and still commute there for work, shopping, and entertainment. The new accessibility of land around the periphery of almost every major city sparked an explosion of real estate development and fueled what we now know as urban sprawl. Between 1890 and 1920, for example, some 250,000 new residential lots were recorded within the borders of Chicago, most of them located in outlying areas. Over the same period, another 550,000 were plotted outside the city limits but within the metropolitan area. Anxious to take advantage of the possibilities of commuting, real estate developers added 800,000 potential building sites to the Chicago region in just thirty years-lots that could have housed five to six million people.Of course, many were never occupied; there was always a huge surplus of subdivided, but vacant, land around Chicago and other cities. These excesses underscore a feature of residential expansion related to the growth of mass transportation: urban sprawl was essentially unplanned. It was carried out by thousands of small investors who paid little heed to coordinated land use or to future land users. Those who purchased and prepared land for residential purposes, particularly land near or outside city borders where transit lines and middle-class inhabitants were anticipated, did so to create demand as much as to respond to it.Chicago is a prime example of this process. Real estate subdivision there proceeded much faster than population growth.36. The author mentions all of the following as effects of mass transportation on cities EXCEPTA. growth in city areaB. separation of commercial and residential districtsC. changes in life in the inner cityD. increasing standards of living37. The word "vast" in line 3 is closest in meaning toA. largeB. basicC. newD. urban38. Why does the author mention both Boston and Chicago?A. To demonstrate positive and negative effects of growthB. To show that mass transit changed many citiesC.To exemplify cities with and without mass transportationD. To contrast their rates of growth39. According to the passage, what was onedisadvantage of residential expansion?A. It was expensive.B. It happened too slowly.C. It was unplanned.D. It created a demand for public transportation.40. The author mentions Chicago in the secondparagraph as an example of a cityA. that is largeB .that is used as a model for land developmentC. where land development exceeded population growthD. with an excellent mass transportation systemHow we look and how we appear to others probably worries us more when are in our teens or early twenties than at any other time in our life. Few of us are content to accept ourselves as weare, and few are brave enough to ignore the trends of fashion.Most fashion magazines or TV advertisements try to persuade us that we should dress in a certain way or behave in a certain manner. If we do, they tell ns,we will be able to meet new people with confidence and deal with every situation confidently and without embarrassment. Changing fashion, of course, does not apply just to dress. A barber today does not cut a boy’s hair in the same way as he used to, and girls do not make up in the same way as their mothers and grandm others did. The advertisers show us the latest fashionable styles and we are constantlyunder pressure to follow the fashion in case our friends think we are odd or dull.What causes fashions to change? Sometimes convenience or practical necessity or just the fancy of an influential person can establish a fashion. Take hats,for example. In cold climates, early buildings were cold inside, so people wore hats indoors as well as outside. In recent times, the late President Kennedy caused a depression in the American hat industry by not wearing hats: moreAmerican men followed his example.There is also a cyclical pattern in fashion. In the 1920s in Europe and A merica, short skirts became fashionable. After World War Two, they dropped to ankle length. Then they got shorterand shorter the miniskirt was in fashion. After a few more years, skirts became longer again.Today, society is much freer and easier than it used to be. It is no longer necessary to dress like everyone else. Within reason, you can dress as you like or do your hair the way you like instead ofthe way you should because it is the fashion. The popularity of jeans and the “untidy” look seemsto be a reaction against the increasingly expensive fashion of the top fashion houses.At the same time, appearance is still important in certain circumstances and then we must choose our clothes carefully. It would be foolish to go to an interview for a job in a law firm wearing jeans and a sweater; and it would be discourteous to visit some distinguished scholar looking as if we were going to the beach or a night club. However, you need never feel depressed if you don’t look like the latest fashion photo. Look around you and you’ll see that no one elsedoes either!41. The author thinks that people are ___.A. satisfied with their appearanceB. concerned about appearance in old ageC. far from neglecting what is in fashionD. reluctant to follow the trends in fashion42. Fashion magazines and TV advertisements seem to link fashion to___.A. confidence in lifeB. personal dressC. individual hair styleD. personal future43. Causes of fashions are ___.A. uniformB. variedC. unknownD. inexplicable.44. Present-day society is much freer and easier because it emphasizes___.A. uniformityB. formalityC. informalityD. individuality45. Which is the main idea of the last paragraph?A. Care about appearance in formal situations.B. Fashion in formal and informal situations.C. Ignoring appearance in informal situations.D. Ignoring appearance in all situations.首字母填空0.5x10We have been in Australia for three days. We’re having a g 46 time here. Australia is the sixth largest country in the world. There is so m 47 to see that it is impossible for me to tell you everything. Sydney is a beautiful city. There are many big t 48 and beautiful flowers around the houses and they l 49 really beautiful. There are also some special a 50 in Australia, such as kangaroos and koalas. They are really lovely.During the past three days we’ve visited many p 51 of interest around Sydney. I’d like to spend more time here. But we will f 52 to another city, Cairns, to see coral beds (珊瑚礁) tomorrow. It is said that words cannot d 53 the beauty of the colourful corals. Many famous cartoon films were made there. Now we are b 54 packing our bags so that we will not lose time when we leave. We can enjoy o 55 in Cairns this time tomorrow, I’m looking forward to going there!46________47________48________49________50________51_______52________53_______ 54________55________作文30分Some people argue that the technology such as computer and mobile phone destroys social communication ,do you agree or disagree?。
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Solve the following questions comprehensively.
1.Three unit circles are arranged so that each touches the other two. Find the radii of the two circles which touch all three.
2.Find all real numbers x such that Байду номын сангаас + 1 = |x + 3| - |x - 1|.
3.(1)Given x = (1 + 1/n)n, y = (1 + 1/n)n+1, show that xy= yx.
(2) Show that 12- 22+ 32- 42+ ... + (-1)n+1n2= (-1)n+1(1 + 2 + ... + n).
13.xy = z - x - y
14.xz = y - x - z
15.yz = x - y - z
11.A square has tens digit 7. What is the units digit?
12.Find all ordered triples (x, y, z) of real numbers which satisfy the following system of equations:
4.All coefficients of the polynomial p(x) are non-negative and none exceed p(0). If p(x) has degree n, show that the coefficient of xn+1in p(x)2is at most p(1)2/2.
6.AB is a diameter of a circle. X is a point on the circle other than the midpoint of the arc AB. BX meets the tangent at A at P, and AX meets the tangent at B at Q. Show that the line PQ, the tangent at X and the line AB are concurrent.
5.What is the maximum possible value for the sum of the absolute values of the differences between each pair of n non-negative real numbers which do not exceed 1?
9.Show that there are no positive integers m, n such that 4m(m+1) = n(n+1).
10.ABCD is a convex quadrilateral with area 1. The lines AD, BC meet at X. The midpoints of the diagonals AC and BD are Y and Z. Find the area of the triangle XYZ.
7.Four points on a circle divide it into four arcs. The four midpoints form a quadrilateral. Show that its diagonals are perpendicular.
8.Find the smallest positive integer b for which 7 + 7b + 7b2is a fourth power.