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Cambridge International AS LevelMATHEMATICS 9709/22 Paper 2 Pure Mathematics March 2020 MARK SCHEMEMaximum Mark: 50PublishedThis mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers.Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.Cambridge International will not enter into discussions about these mark schemes.Cambridge International is publishing the mark schemes for the March 2020 series for most Cambridge IGCSE™, Cambridge International A and AS Level components and some Cambridge O Level components.This document consists of 11 printed pages.© UCLES 2020 [Turn overGeneric Marking PrinciplesThese general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles.GENERIC MARKING PRINCIPLE 1:Marks must be awarded in line with:•the specific content of the mark scheme or the generic level descriptors for the question•the specific skills defined in the mark scheme or in the generic level descriptors for the question•the standard of response required by a candidate as exemplified by the standardisation scripts.GENERIC MARKING PRINCIPLE 2:Marks awarded are always whole marks (not half marks, or other fractions).GENERIC MARKING PRINCIPLE 3:Marks must be awarded positively:•marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate•marks are awarded when candidates clearly demonstrate what they know and can do•marks are not deducted for errors•marks are not deducted for omissions•answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous.GENERIC MARKING PRINCIPLE 4:Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5:Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen).GENERIC MARKING PRINCIPLE 6:Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.© UCLES 2020 Page 2 of 11Mathematics-Specific Marking Principles1 Unless a particular method has been specified in the question, full marks may be awarded for any correct method. However, if a calculation is requiredthen no marks will be awarded for a scale drawing.2 Unless specified in the question, answers may be given as fractions, decimals or in standard form. Ignore superfluous zeros, provided that the degree ofaccuracy is not affected.3 Allow alternative conventions for notation if used consistently throughout the paper, e.g. commas being used as decimal points.4 Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw).5 Where a candidate has misread a number in the question and used that value consistently throughout, provided that number does not alter the difficulty orthe method required, award all marks earned and deduct just 1 mark for the misread.6 Recovery within working is allowed, e.g. a notation error in the working where the following line of working makes the candidate’s intent clear.© UCLES 2020 Page 3 of 11Mark Scheme NotesThe following notes are intended to aid interpretation of mark schemes in general, but individual mark schemes may include marks awarded for specific reasons outside the scope of these notes.Types of markM Method mark, awarded for a valid method applied to the problem. Method marks are not lost for numerical errors, algebraic slips or errors in units.However, it is not usually sufficient for a candidate just to indicate an intention of using some method or just to quote a formula; the formula or idea must be applied to the specific problem in hand, e.g. by substituting the relevant quantities into the formula. Correct application of a formulawithout the formula being quoted obviously earns the M mark and in some cases an M mark can be implied from a correct answer.A Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. Accuracy marks cannot be given unless the associated methodmark is earned (or implied).B Mark for a correct result or statement independent of method marks.DM or DB When a part of a question has two or more “method” steps, the M marks are generally independent unless the scheme specifically says otherwise;and similarly, when there are several B marks allocated. The notation DM or DB is used to indicate that a particular M or B mark is dependent onan earlier M or B (asterisked) mark in the scheme. When two or more steps are run together by the candidate, the earlier marks are implied and full credit is given.FT Implies that the A or B mark indicated is allowed for work correctly following on from previously incorrect results. Otherwise, A or B marks are given for correct work only.© UCLES 2020 Page 4 of 11AbbreviationsAEF/OE Any Equivalent Form (of answer is equally acceptable) / Or EquivalentAG Answer Given on the question paper (so extra checking is needed to ensure that the detailed working leading to the result is valid)CAO Correct Answer Only (emphasising that no “follow through” from a previous error is allowed)CWO Correct Working OnlyISW Ignore Subsequent WorkingSOI Seen Or ImpliedSC Special Case (detailing the mark to be given for a specific wrong solution, or a case where some standard marking practice is to be varied in the light of a particular circumstance)WWW Without Wrong WorkingAWRT Answer Which Rounds To© UCLES 2020 Page 5 of 11© UCLES 2020 Page 6 of 11© UCLES 2020 Page 7 of 11© UCLES 2020 Page 8 of 11© UCLES 2020 Page 9 of 11© UCLES 2020 Page 10 of 119709/22 CambridgeInternational AS Level – Mark SchemeMarch 2020PUBLISHED© UCLES 2020 Page 11 of 11。
高二英语数学建模方法练习题30题带答案1. The number of apples is twice as many as the number of bananas. If the number of bananas is \(x\), then the number of apples is _.A. \(x + 2\)B. \(2x\)C. \(x - 2\)D. \(x/2\)答案：B。
解析：在这个句子中，“twice as many as”是关键的英语表述，表示倍数关系。
根据数学原理，如果香蕉的数量是\(x\)，苹果的数量是香蕉数量的两倍，那么就是\(2\times x = 2x\)。
这里主要涉及到简单的倍数关系的数学概念以及对“twice as many as”这个英语短语的理解。
2. There are \(y\) students in a class. If the number of boys is one - third of the total number of students, then the number of boys is _.A. \(y/3\)B. \(3y\)C. \(y + 3\)D. \(y - 3\)答案：A。
解析：“one - third of”这个英语短语表示三分之一。
根据数学原理，总数是\(y\)，男孩数量是总数的三分之一，就是\(y\times\frac{1}{3}=\frac{y}{3}\)。
这里考查了分数关系的数学概念和对这个英语短语的理解。
3. The price of a book is \(p\) dollars. If the price of a pen is \(20\%\) less thanthe price of the book, then the price of the pen is _.A. \(0.8p\)B. \(1.2p\)C. \(p - 20\)D. \(p + 20\)答案：A。
雅思考试全题模拟试题(1)ListeningTIME ALLOWED: 30 minutesNUMBER OF QUESTION: 40InstructionYou will hear a number of different recordings and you will have to answer questions on what you hear.There will be time for you to read the instructions and questions, and you will have a chance to check you work.All the recordings will be played ONCE only.The test is in four sections. Write your answers in the listening question booklet. At the end of the test you will be given ten minutes to transfer your answers to an answer sheet.Now turn to Section 1 on page 2.SECTION 1 Question1-9Question 1-6Listen to conversation between friend and the housing officer and complete the list below.Write NO MORE THAN THREE WORDS OR NUMBERS for each answer.HOUSING LISTHOUSING LISTAddress Number of rooms Price per week Additional informationMr. J Devenport 82Salisbury Road Brighton BN 16 3 AN Tel 01273 884673 2 bedrooms sitting room kit. bath Example ￡120 UnfurnishedMrs E.S. Jarvis2Wicken Street Brighton BN 15 4JH Tel 01273 771621 (1) sitting room kit.bath (2)First floorMrs. E.C. Sparshott 180Silwood Road Brighton BN 14 9RY Tel (3)2 large rm/s shared kit and bath ￡35 Nice area (4)Mr A Nasiry 164 Preston Road Brighton BN5 7RT Tel 01273 703865 large bedroom sitting room with kitchenette.bath. (5)Ground floor Central(6) 2 harrow Road Brighton BN9 9HK Tel 01273 745621 2 large rooms kit bath ￡86 No petsQuestions 7-9Write NO MORE THAN THREE WORDS for each answer7.When is the accommodation available?8.Where is the telephone?9.How is the flat heated?SECTION 2 Questions 10-20Questions 10-14Circle the correct letters A-D10.How many conventions have already been held ?A. 2B. 3C. 4D. 511.Where is the convention being held?A. BrisbaneB. MelbourneC. CanberraD. Sydney12.How long is the convention forA 2 days B.5 days C.6 days D. 7 days13.How many Australian speakers will be attending the convention?A.20B.25C.30D.3514.Which countries are the guest speakers from?A. Britain and CanadaB. Canada and the USC. Britain and the USD. Britain, Canada and the USQuestion 15-17Listen to the directions and match the places in questions 15-17 to the appropriate letters A-G on the map.Example Peroni's Answer ( A )15. Jumbo Sandwich Shop ( )16. Slim's Vegetarian ( )17. The Geneva Bistro ( )Questions 18-20Look at this page from the program. Tick ( √ ) if the information is correct or write in the changes.CONVENTION PROGRAMExampleAfternoon sessions Answerstart at 2.00pm 2.30finish at 4.00pm ______________TALKS“Marketing” by Jane Howard (18)Blue Room (19)“Distribution of Goods” by Sara Moore” Barbara MooreRed Room (20)“Advertising” by Peter NewsteadOrange Room cancelledSECTION 3 Questions 21——32Questions 21_24Complete the table showing the prices and types of coffee sold Common Room.I = InstantR = RealE = EspressoEuropean Development studies Arts "C"Building American StudiesType of coffee Example I (21)E (24)Price of coffee Example 20P (22)(23)25PQuestions 25-32Complete the table showing the number of points 1,2or3 awarded to the food offered by eachCommon Room.Arts "c" Building European Refectory American StudiesMatthew (28)Alice (25)Example 1 (29)(31)Jenny (26)(27)(30)(32)SECTION 4 Questions 33-40Questions 33-35Look at Question 33-35 below and the grid . Tick ( √ )the relevant boxes in each column.COUNTRY 33. Which countries are affected by Britain's pollution? 34.Which country relies heavily on nuclear power? 35. Which countries use lime filtering to reduce the amount of chemical pollutant released into the atmosphere?AustraliaBelgiumDenmarkFranceGermanyHollandJapanSwedenUSAQuestions 36-40Write NO MORE THAN THREE WORDS for each answer.36. When did fish stock there begin to decline?37. What did scientists inject into the land ?38. Has the situation improved?39. How effective is the use of limestone slurry?40. what is one of the major disadvantages of using limestone slurry?reading1TIME ALLOWED :1 HourNUMBER OF QUESTIONS :38InstructionsALL ANSWERS MUST BE WRITTEN ON THE ANSWER SHEETThe test is divided as follow :Reading passage 1 questions 1-11Reading passage 2 questions12-25Reading passage 3 questions26-38Start at the beginning of the test and work through it .you should answer all the questions. if you cannot do a particular question leave it and go on to the next .you can return to it later.Section 1 question 1-14Question 1-4There are six job advertisements A-F on the opposite pageAnswer the questions below by writing the letters of the appropriate advertisements in boxes 1-4 on your answer sheet .Example answerWhich job is in a travel agent's ? D1. which job is in a hotel?2. Which job for someone to look after a child?3. Which WTO advertisements are for waiters?4. Which WTO jobs would particularly like a German speaker?RestaurantSupervisorWaiting staffTelephonist__________the ideal candidates must have relevant experience gained in a high quality hotel .please call personnel on 071-722-77333, or send your CV to :Regents Park Hilton , Lodge Road , LondonNW8 7JTLONDONREGENTS PARKHILTONB..USE YOURLANGUAGES AND EARN450-1200 P.W.we are one of the largest business publishers in Europe and have limited vacancies for intelligent young people in our London advertisement sales office. Enquiries from German Spanish and eastern European speakers especially welcome. Phone Andrew Warburton on 071 753 4300C.SECRETARYBusy charteredAccountants require experienced /efficient secretary ,accounts ,typing experience and an excellent telephone manner essential shorthand useful.Please send CV to :box no .9246 c/o evening standard classified , 2 derry street ,kensington W8 5EE.D.TRAVELCOMPANYVacancy for self-confident person to look after bookings for our Caribbean hotels .salary based on applicant's experience &suitability .please send CV to Ian Taplin , MRI LTD, 9 Galena Road , London , WG OLXE.NANNY WANTEDFor 9 month old handful .Artistle /Prof household Ntting Hill , 3 days per week .some hours flexibility req'd .knowledge German/Hungarian advantage not essential 071 221 7375F.JOIN THE STARS!FOOD SERVERSThe biggest and busiest restaurant in London is seeking additional stars for its team of dedicated professionals .if you have experience in high volume restaurantsand are looking for a challenge ,then come on down for an audition.Interview day is on Friday , 6th MAY from 12 noon to 7 pm .planet Hollywood is located at 13 Coventry Street , London. W1.Questions 5-10Read the page from a UK telephone directory on the opposite page.Answer the questions below by writing the appropriate telephone numbers in boxes 5-10 on your answer sheet.What should you dial ifExampleYou want to speak to the international operator? answer1235 .there is something wrong with your telephone?6. there has been an accident and you want to call an ambulance?7. you want to find out a number in a foreign country ?8.you want to know how much telephone calls cost?9.you want to purchase an answer-phone machine?10. you want to use a credit card to pay for a telephone call?Operator services 101The operator is there to help you if you have difficulty making a call or if you want to use any of our special call service .these include: ALARM CALLS ADVICE OF DURATION CHARGE CREDIT CARD CALLS FLXED TIME CALLS FREEFONE CALLS PERSONAL CALLS TRANSFERRED CHARGE CALLS SUBSCRIBER CONTROLLED TRANSFER .for details of charges see our free leaflet , Dial 101 and ask for financial services.International operator 123See section 3 (international )for details.Directory Enquiries 142Tell the operator the town you require .have paper and pencil ready. International directory enquiries 130Emergency 010Tell the operator what service you want .Faults 166Any fault should be reported to the local fault repair service.Sales 170Telemessage 190If you have something special to say and prefer to say it in writing . International telemessage 191International telegrams 192You can send a telegram to most other countries.Maritime service 200SHIP'S TELEGRAM SERVIE SHIP'S TELEPHONE SERVICE INMARSAT SATELLITE SERVICE (DIAL 177) .you can call or send a message to someone aboard ship by using our maritime services .for known .for INMARSAT (maritime satellite) service dial 178 .give the ship's name ,its identification number and ocean region , if known, satellite service and provide the number .Any other call enquiries 111Question 11-14Read the following noticeUsing NO MORE THAN THREE WORDS from the passage answer the questions below. Write your answer in boxes 11-14 on your answer sheet.FIRE NOTICEIn the event of life , the ALARM will ring .on hearing the fire alarm ,all those in the West Wing should evacuate the building by staircase J.Rooms 1 to 199 are in the west wing .all others should use staircase A. The assembly area for occupants of west wing is the staff car park at the rear of the building .all others assemble in the front courtyard.Evacuate the building even if the alarm stops.If you discover a fire ,shout fire and operate the nearest fire alarm .attack the fire with an extinguisher but do not take any risks .inform reception by dialling 3333.ExampleWhere is room 1 answerthe west wing11.you are in room 101 .which staircase should you use to evacuate the building ?12. you are in room 201.where should you wait outside after evacuating the building ?13 what should you do if the alarm stops?14.who should you contact if you discover a fire?SECTION 2 Questions 15-27Questions 15-20Read “Information for New Students” below and answer the questions that follow. Write your answers in boxes 15-20 on your answer sheet.HILTON ENGLISH LANGUAGE CENTREINFORMATION FOR NEW STUDENTSCLASS TIMES9.00 am – 10.30 am 11.00 am – 12.30 pm 1.30 pm – 3.00 pmThe Language Centre is open Monday to Friday. Each class has one afternoon free per week. On the first day go to the lecture hall to check your timetable.SELF-ACCESSThe language laboratory (Room 1110) is open Monday to Friday from 3.15 pm to 5.oo pm for all full-time students. You can learn how to use the computers for language games or word-processing.There are cassettes for students to borrow to practise their English. Go in and ask the teacher to show you.If you plan to take public examinations, there are dictation and listening comprehension cassettes for you to practise with. There are cloze exercises on the computers. Ask your class teacher for a list of past exam essays. Students can borrow cassettes to take home but they must be returned after two days. ATTENDANCEAll students on student visas are expected to attend classes regularly. Students who do not attend classes will be reported to oss. Eighty per cent attendance is required for students to receive their certificate on completion of their course. It is also required by oss for an extension to your visa.BOOKSIf students are given course books, the books are their responsibility.If a book is lost, the student will be expected to pay for it. If students wish to buy books, there is a bookshop in the college specialising in English books (Room 3520).15.when do classes begin and end on a full day?16.How many afternoons does a class meet each week?17.Where are the timetables displayed?18.Who can use the language laboratory after classes?19.Who is available in the self-access centre to help the students?20.How much of a course must you attend according to visa restrictions?Questions 21-27Read the passage below about a college in the city of Bath, written in 1985, and answer the questions that follow.The CollegeThe college has the advantage of location in one of the most attractive cities in the country. Within the city of Bath it occupies modern buildings in a landscaped garden on Sion hill, Lansdown and an adjacent Georgian Crescent, Somerset Crescent, which includes teaching and residential accommodation for post-graduate studies. It also occupies three houses in Sydney Place, which are used for studio and workshop accommodation for part-time courses in the Visual Arts and for the Foundation Course in Art and Design.The Newton Park site is situated four miles west of Bath between the villages of Newton St Loe and Corston. Within the grounds are a Georgian mansion, where thecollege’s sentral administration is located, an Elizabethan dairy, stables and the tower of a medieval manor house; all these older buildings have been adapted to present-day use. A new purpose-built Home Economics block was opened in January 1985. During 1986 a new Sports Hall will be completed and new residential blocks are under construction to be completed ready for the start of the academic year in September 1986; a new music Block will be completed in 1987.The Art and Design degree courses which are currently accommodated at Corsham, about nine miles east of Bath, will be moved to the Sion Hill site in Bath by September 1986 thus reinforcing Faculty and Course links.The college courses are designed to take advantage of the special opportunities and circumstances provided by its environment. Students have available such resources as the Costume and Fashion Research Centre, the Royal Photographic Centre and the Museum of American Domestic Life at Claverton. Concerts and recitals, including some given by staff and students, take place throughout the year in the Assembly Rooms. The college uses buildings in five different places. Where are the following things located?In boxes 21-27 on your answer sheet writeNP if something is located in Newton ParkC if something is located in CorshamSH if something is located in Sion HillSC if something is located in Somerset CrescentSP if something is located in Sydney PlaceExampleA landscaped garden AnswerSH21.Central Administration22.Home Economics Block23.Art and Design Foundation Course24.Art and Design Degree Course after 198625.Post-graduate Residences26.Sports Hall27.Music BlockSECTION 3 Questions 28-38Read the passage below and answer questions 28-38WINTER SPORTSIce,danger and exhilarationThe 17th Winter Games, held in Norway in 1994, are part of an Olympic tradition which goes back almost 3,000 years. For more than Games were held, every four years, on hallowed ground near Mount Olympus, where the Greek gods were said to live.The ‘Olympics’ brought together men from war-torn tribes and states in Greece and its colonies. A sacred truce was declared to allow men to travel to the games in safety. Women could not take part and were forbidden, on pain of death, even to attend the Games.The ancient Olympics were abolished by the Roman Emperor Theodosius in 393 AD, after Greece had lost its independence. But the idea never died and the Frenchman Baron Pierre de Coubertin, an educator and scholar, founded the modern Olympics,his aim was to bring together, once every four years, athletes from all countries on the friendly fields of amateur sport. No account was to be taken of national rivalries, nor politics, race, religion, wealth or social status.The first modern Games were held in Athens in 1896, and four years later, in Paris, women began to take part. Although the winter Olympics did not begin until 1924, figure skating was part of the 1908 London summer Olympics; both skating and ice hockey were included in the Antwerp Games in 1920. But generally winter sports were felt to be too specialized. Only cold weather countries had much experience of activities such as skiing-a means of transport overland across ice and snow during long winters.The Scandinavians, for whom skiing is a part of everyday life, had objected to a winter fames. They feared it would threaten their own Nordic Games, which had been held every four years since 1901. But the international Olympic Committee (IOC) agreed to stage an International Sports Week in Chamonix, France, in 1924.It was a success and the Scandinavians won 28 of the 43 medals, including nine golds. They dropped their objections and the event was retrospectively named the First Olympic Winter Games.Apart from the Second World War period the Winter Olympics were held every four years, a few months before the summer Olympics. But in 1986 the IOC changed the schedule so that the summer and winter games would be held in different years. Thus, for the only time in history, the Lillehammer (Norway) Games took place just two years after the previous Winter Olympics which were held in Albertville, France.Since the Winter Games began, 55 out of 56 gold medals in the men’s nordic skiing events have been won by competitors from Scandinavia or the former Soviet Union. For teams from warm weather countries, cross-country skiing can pose problems. At the Calgary Games in 1988, one competitor in the 50-kilometre event was so slow that race officials feared he was lost and sent out a search party. Roberto Alvarez of Mexico had never skied more than 20 kilometres before and finished 61st and last 52 minutes behind the 60th place.Questions 28-31Complete the table below. Write a date for each answer.Write your answers in boxes 28-31 on your answer sheetDATE EVENT(28)Ancient Olympics came to an end(29)First women’s eventsExample: 1901 First Nordic Games(30)First winter team game included in Olympics(31)学 海 无 涯- - 11 First Winter Olympic GamesQuestions 32-38Look at the following statements. In boxes 32-38 on your answer sheet write TRUEFALSENOT GIVEN if the statement is trueif the statement is falseif the information is not given in the passage32.The spectators, as well as the participants, of the ancient Olympics were all male.33.Only amateur athletes are allowed to compete in the modern Olympics.34.The modern Olympics have always demonstrated the political neutrality intended by their founder.35.The Antwerp Games proved that winter sports were too specialized.36.Cross-country skiing events are a specialty of cold-weather countries.37.Only Scandinavians have won gold medals in men ’s winter Olympics nordic skiing events.38.One Winter Olympics has succeeded another every four years since 1924 with a break only for the Second World War.WRITING TASK 1You should spend on more than 20 minutes on this task.You live in a room in college which you share with another student. You find it very difficult to work there because he or she always has friends visiting. They have parties in the room and sometimes borrow your things without asking you.Write a letter to the Accommodation Officer at the college and ask for a new room next term. You would prefer a single room.Explain your reasons.You should write at least 150 words.You do NOT need to write your own address.Begin your letter as follows:Dear Sir/Madam,。
昆明环球雅思测试题答案听力部分第一部分：填空题1. 答案：A2. 答案：B3. 答案：C4. 答案：A5. 答案：B第二部分：选择题6. 答案：C7. 答案：A8. 答案：B9. 答案：D10. 答案：A第三部分：配对题11. 答案：E12. 答案：A13. 答案：D14. 答案：B15. 答案：C第四部分：地图题16. 答案：A17. 答案：C18. 答案：B19. 答案：D20. 答案：E阅读部分第一部分：判断题21. 答案：True22. 答案：False23. 答案：Not Given24. 答案：True25. 答案：False第二部分：选择题26. 答案：C27. 答案：A28. 答案：D29. 答案：B30. 答案：E第三部分：摘要填空题31. 答案：environmental32. 答案：pollution33. 答案：technology34. 答案：recycling35. 答案：legislation写作部分小作文：柱状图描述The bar chart illustrates the percentage of individuals in different age groups who participated in regular physicalactivities in a European country in the year 2010.It is apparent that the highest percentage of physically active individuals was in the 15-24 age bracket, accounting for approximately 70%. The 25-34 and 35-44 age groups had similar participation rates, both around 60%. The 45-54 age group showed a notable decrease in activity levels, with just over 50% engaging in regular exercise. The 55-64 age group had the lowest rate of physical activity, with just under 40% of individuals participating.Overall, the data suggests that younger age groups were more likely to engage in regular physical activities compared to their older counterparts.大作文：议论文The advancement of technology has had a profound impact on the way people live and work. Some argue that it has madelife more convenient, while others believe that it has led to a loss of interpersonal skills and a sense of community. This essay will discuss both views and provide a balanced conclusion.On the one hand, technology has indeed made our lives easier in many ways. For instance, the internet has revolutionized communication, allowing people to connect with others instantly across the globe. Online shopping and digital banking have also simplified daily tasks, saving time and effort. Furthermore, automation and artificial intelligence have increased productivity in various industries, leading to economic growth and improved living standards.On the other hand, critics argue that technology has also had negative effects on society. The over-reliance on digital communication has been blamed for the decline in face-to-face interactions, which are essential for building strong relationships and a sense of community. Additionally, the constant use of smartphones and social media has been linked to mental health issues such as anxiety and depression, particularly among young people.In conclusion, while technology has undoubtedly brought about significant conveniences, it is crucial to be mindful of its potential drawbacks. It is the responsibility of individuals and society as a whole to use technology wisely and maintain a healthy balance between the digital and physical worlds.口语部分第一部分：自我介绍Examiner: Good morning/afternoon. My name is [Examiner's name]. How are you today?Candidate: Good morning/afternoon, [Examiner's name]. I'm doing well, thank you. My name is [Candidate's name], and I'm from [Candidate's hometown].第二部分：个人话题Examiner: Let's talk about an interesting place you've been to. Can you describe this place and explain why you found it interesting?Candidate: Certainly. The most interesting place I've visited recently is the ancient town of Lijiang in Yunnan Province.It's a UNESCO World Heritage site known for its well-preserved traditional architecture and unique Naxi culture. The cobblestone streets, ancient bridges, and the surrounding beautiful landscapes make it a truly captivating destination. What I found most fascinating was the fusion of different cultures and the harmonious way of life of the local people.第三部分：深入讨论Examiner: Do you think technology has more advantages or disadvantages for society?Candidate: I believe that technology has more advantages than disadvantages for society. While it's true that it can lead to some negative outcomes, such as privacy concerns andsocial isolation, the benefits are undeniable. Technology has improved healthcare, education, and communication, and it has also created numerous job opportunities. It。
UNIVERSITY OF CAMBRIDGE INTERNA TIONAL EXAMINA TIONSGeneral Certificate of Education Advanced LevelMATHEMATICS9709/03Paper3Pure Mathematics3(P3)May/June20061hour45minutes Additional Materials:Answer Booklet/PaperGraph paperList of Formulae(MF9)READ THESE INSTRUCTIONS FIRSTIf you have been given an Answer Booklet,follow the instructions on the front cover of the Booklet.Write your Centre number,candidate number and name on all the work you hand in.Write in dark blue or black pen on both sides of the paper.Y ou may use a soft pencil for any diagrams or graphs.Do not use staples,paper clips,highlighters,glue or correctionfluid.Answer all the questions.Give non-exact numerical answers correct to3significantfigures,or1decimal place in the case of angles in degrees,unless a different level of accuracy is specified in the question.The use of an electronic calculator is expected,where appropriate.Y ou are reminded of the need for clear presentation in your answers.The number of marks is given in brackets[]at the end of each question or part question.The total number of marks for this paper is75.Questions carrying smaller numbers of marks are printed earlier in the paper,and questions carrying larger numbers of marks later in the paper.At the end of the examination,fasten all your work securely together.This document consists of4printed pages.©UCLES2006[Turn over1Given that x =4 3−y ,express y in terms of x .[3]2Solve the inequality 2x >|x −1|.[4]3The parametric equations of a curve are x =2θ+sin 2θ,y =1−cos 2θ.Show that d y d x =tan θ.[5]4(i)Express 7cos θ+24sin θin the form R cos (θ−α),where R >0and 0◦<α<90◦,giving theexact value of R and the value of αcorrect to 2decimal places.[3](ii)Hence solve the equation7cos θ+24sin θ=15,giving all solutions in the interval 0◦≤θ≤360◦.[4]5In a certain industrial process,a substance is being produced in a container.The mass of the substancein the container t minutes after the start of the process is x grams.At any time,the rate of formation of the substance is proportional to its mass.Also,throughout the process,the substance is removed from the container at a constant rate of 25grams per minute.When t =0,x =1000and d x d t=75.(i)Show that x and t satisfy the differential equationd x d t=0.1(x −250).[2](ii)Solve this differential equation,obtaining an expression for x in terms of t .[6]6(i)By sketching a suitable pair of graphs,show that the equation 2cot x =1+e x ,where x is in radians,has only one root in the interval 0<x <12π.[2](ii)Verify by calculation that this root lies between 0.5and 1.0.[2](iii)Show that this root also satisfies the equation x =tan −121+e x .[1](iv)Use the iterative formula x n +1=tan −1 21+e x n,with initial value x 1=0.7,to determine this root correct to 2decimal places.Give the result of each iteration to 4decimal places.[3]©UCLES 20069709/03/M/J/067The complex number2+i is denoted by u.Its complex conjugate is denoted by u*.(i)Show,on a sketch of an Argand diagram with origin O,the points A,B and C representing thecomplex numbers u,u*and u+u*respectively.Describe in geometrical terms the relationship between the four points O,A,B and C.[4](ii)Express uu*in the form x+i y,where x and y are real.[3](iii)By considering the argument ofuu*,or otherwise,prove thattan−1 43=2tan−1 12.[2]8The diagram shows a sketch of the curve y=x12ln x and its minimum point M.The curve cuts the x-axis at the point(1,0).(i)Find the exact value of the x-coordinate of M.[4](ii)Use integration by parts tofind the area of the shaded region enclosed by the curve,the x-axis and the line x=4.Give your answer correct to2decimal places.[5]9(i)Express10(2−x)(1+x2)in partial fractions.[5](ii)Hence,given that|x|<1,obtain the expansion of10(2−x)(1+x2)in ascending powers ofx,up toand including the term in x3,simplifying the coefficients.[5]©UCLES20069709/03/M/J/06[Turn over10The points A and B have position vectors,relative to the origin O,given by−−→OA= −135and−−→OB=3−1−4.The line l passes through A and is parallel to OB.The point N is the foot of the perpendicular from B to l.(i)State a vector equation for the line l.[1](ii)Find the position vector of N and show that BN=3.[6] (iii)Find the equation of the plane containing A,B and N,giving your answer in the form ax+by+c =d.[5]Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible.Every reasonable effort has been made by the publisher(UCLES)to trace copyright holders,but if any items requiring clearance have unwittingly been included,the publisher will be pleased to make amends at the earliest possible opportunity.University of Cambridge International Examinations is part of the University of Cambridge Local Examinations Syndicate(UCLES),which is itself a department of the University of Cambridge.©UCLES20069709/03/M/J/06。
雅思口语Part1范文答案解析：Math 数学数学类的题目在雅思口语Part One中最近又浮出了水面，上次考到还是在多年以前的事情了。
该话题难度适中，也是我们大家在学习生涯中比较熟悉的科目，因此在问题上面不会感到特别陌生。
不过雅思小编需要提醒大家的是，即便碰到熟悉的题目也不可掉以轻心，尽量减少表达错误。
平时练习过程中，可以看到下面的题目后，自己先回答一番，然后再进结合原创范文进行行学习和巩固练习。
Do you often use a calculator? 你经常使用计算器吗？Yes, I use it a lot. I usually use it when I am doing math assignments or sitting for an exam that allows me to take a calculator. I honestly find it quite useful as it helps me save my?time.是的，我经常用的。
我通常情况下会在做数学题或者参加一场可以允许我携带计算器的考试里使用它。
老实讲，我还是觉得计算器非常实用的，它能帮助我节省我的时间。
Are girls generally good at mathematics? 总得来说女孩子们擅长数学吗？No, I don’t think they are generally. I don’t think mathematics is what they are good at. But, don’t get me wrong. The reason why I think so is that most girls just somehow don’t find any interest in it.不，我不觉得。
我不觉得他们擅长数学。
但是别无误，我觉得他们不擅长数学的原因是因为他们不知怎么的就是对数学不感兴趣。
Turn over P43410A©2014 Pearson Education Ltd.5/5/5/*P43410A0124*Instructionst Use black ink or ball-point pen.t Fill in the boxes at the top of this page with your name,centre number and candidate number.t Answer all questions.t A nswer the questions in the spaces provided– there may be more space than you need.t Calculators may be used.t I f your calculator does not have a ʌ button, take the value of ʌ to be3.142 unless the question instructs otherwise.Informationt The total mark for this paper is 80t T he marks for each question are shown in brackets– use this as a guide as to how much time to spend on each question.t Q uestions labelled with an asterisk (*) are ones where the quality of yourwritten communication will be assessed.Advicet Read each question carefully before you start to answer it.t Keep an eye on the time.t Try to answer every question.tCheck your answers if you have time at the end.2*P43410A0224*3*P43410A0324*Turn overAnswer ALL questions.Write your answers in the spaces provided.You must write down all stages in your working.1 Ann and Ben each have 20 cards. Ann gives 5 of her cards to Ben. Ben gives 8 of his cards to Ann.How many cards does each person have now?Ann ............................Ben ............................(Total for Question 1 is 3 marks)4*P43410A0424*2 Here are some triangles drawn on a grid.Two of these triangles are congruent.(a) Write down the letters of these triangles.............................and ............................(1)One of the triangles is similar to triangle B .(b) Write down the letter of this triangle.............................(1)(Total for Question 2 is 2 marks)ABCD E FG H I5*P43410A0524*Turn over3 Here is a polygon.(a) Write down the mathematical name of the polygon....................................................................................(1)(b) Draw a sketch of a hexagon.(1)(c) In the space below, draw accurately a rectangle with a length of 5 cmand a width of 3 cm.(2)(Total for Question 3 is 4 marks)6*P43410A0624*4 Sarah and Greta were in a diving competition. Here are the scores for each girl’s three dives. Sarah 8.8 9.0 9.3 Greta 9.0 9.0 9.0Who got the higher total score, Sarah or Greta?You must show your working........................................................(Total for Question 4 is 2 marks)5 Howard is going to paint a wall. He needs to buy some tins of paint. The area of the wall is 58 m 2.Each tin of paint will cover an area of 12 m 2.Work out the smallest number of tins of paint Howard needs to buy.............................(Total for Question 5 is 2 marks)7*P43410A0724*Turn over8*P43410A0824*7 138 people are going on a school trip.Each person will travel by coach or by minibus. Steve gets 3 coaches for the trip.Each coach has seats for 35 passengers. Steve also needs some minibuses for the trip. Each minibus has seats for 10 passengers.Work out the smallest number of minibuses Steve needs.........................................................(Total for Question 7 is 3 marks)9*P43410A0924*Turn over10*P43410A01024*9 Kimona is going to cook some meat.She uses this rule to work out the cooking time in minutes.cooking time in minutes = weight of meat in kg × 40 and then add 15Kimona wants to finish cooking the meat at 1 pm. The weight of the meat is 1.5 kg.Work out the latest time Kimona can start to cook the meat........................................................(Total for Question 9 is 3 marks)11 (a) Work out +8 í 6.............................(1)out í5 í 4(b)Work.............................(1)out í12 · +4Work(c).............................(1)(Total for Question 11 is 3 marks)12P = n + 2tn = 4t = 5Work out the value of P.P = .............................(Total for Question 12 is 2 marks)13The information in the table can be used to change between Euros (€) and Pounds (£).Pounds (£)1020100400Euros (€)12.5025125500(a) Change £25 to Euros.€.............................(2)In France a coat costs €100In England an identical coat costs £90*(b) In which country is the coat cheaper?(3)(Total for Question 13 is 5 marks)17Fadiq is going to make some dresses.She needs 675 centimetres of thread for each dress.Fadiq wants to make 8 dresses.She has 50 metres of thread.Does Fadiq have enough thread for the 8 dresses?You must show how you got your answer.(Total for Question 17 is 3 marks)*Here is information about two investments.18Investment A Invest £2400 for 3 years and get £8 each month.Investment B Invest £2400 for 3 years at a rate of 3.5% per year simple interest.Which is the better investment?You must show your working.(Total for Question 18 is 5 marks)19 The side elevation and the front elevation of a cuboid are drawn on the centimetre grid.On the grid, draw an accurate plan of the cuboid.(Total for Question 19 is 2 marks)side elevationfront elevation20Glen buys four tickets for a concert.Each ticket costs £54Glen also has to pay a booking fee.The booking fee is 5% of the total price of the tickets.Work out the total amount Glen has to pay.£..............................................................(Total for Question 20 is 3 marks)21* Tea bags are sold in three sizes of box.A small box of 50 tea bags costs £2.15 A medium box of 80 tea bags costs £3.29 A large box of 125 tea bags costs £5.17Which size of box is the best value for money?(Total for Question 21 is 4 marks)Small 50 bags £2.15Medium 80 bags £3.29Large 125 bags £5.1722 Stephanie is x years old.Tobi is twice as old as Stephanie.Ulrika is 3 years younger than Tobi.The sum of all their ages is 52 years.that 5x – 3 = 52Show(a)(3)(b) Work out the value of x.x = .............................(2)(Total for Question 22 is 5 marks)25 Make h the subject of the formula x = 5h + 8.......................................................(Total for Question 25 is 2 marks)TOTAL FOR PAPER IS 80 MARKS。
1/6/2018 The maps show changes of a school in 1985 and now. Summarise information and make comparisons when necessary.People in many countries today have a wide range of householdgoods(e.g. television, microwave ovens and rice cookers) than everbefore. Is it a positive or negative development?1/13/2018 The graphs below show the changes in age structure of population in a European country from 1901 to 1981 and a projection in 2021.Some people believe that employers should not be concerned aboutdress, while others think the working quality is the most important. Towhat extent do you agree or disagree?1/18/2018 The chart below shows amount (in tonnes) of coffee and tea importedto four countries in 2007.Lectures were used in the past with many students. With moderntechnology available for education, there is no justification for this wayof teaching. To what extent do you agree or disagree?1/20/2018 The graphs show the number of yearly visits from France and North America to the U.K., for holiday and business reasons.People are now surrounded by advertising. This both affects whatpeople think is important and has a negative impact on people’s lives.To what extent do you agree or disagree?2/1/2018 混合型：折线+柱状折线图：布里斯班和堪培拉平均最高气温和最低气温对比柱状图：布里斯班和堪培拉平均降水天数的对比Figures show that in some countries, there is an ever-increasingproportion of population aged 15 or younger. What do you think theeffect of current and future in those countries?2/3/2018The restoration of old buildings in major cities in the world spendsnumerous government expenditures. This money should be used in newhousing and road development. To what extent do you agree ordisagree?2/10/2018 The graphs show the size of ozone layer hole in Antarctic and the production of three kinds of ozone-damaging gases from 1980 to 2000.Some people think that people who prefer to read for pleasure will havebetter imagination and language skills than people who like watchingTV. To what extent do you agree or disagree?2/24/2018 The pie chart illustrates what the residential water used for in the years1988 and 2008.More and more people buy and use their own car. Do you think theadvantages of this trend for individuals outweigh its disadvantages forenvironment?3/3/2018 The following charts illustrate the information about players ofelectronic games in South Korea in 2003.Write a passage about thecharts.In many countries, prison is the most common solution to the problemof crime. However, another effective way is to provide people withbetter education so that they can not become criminals. To what extentdo you agree or disagree?3/10/2018 The chart below shows the depth of snow(cm) in a particular ski resort in Canada in three individual years.Some people think that one of the best ways to solve environmentalproblems is to increase the cost of fuels for cars and other vehicles. Towhat extent do you agree or disagree with this statement?3/15/2018 The bar chart shows the percentage and exact time (weekly) males and females spent on house tasks in 2010 of a country. Summarise theinformation by selecting and reporting the main features and makecomparisons where relevant.Many country invest money to prepare competitors to join topcompetitions like Olympic Game and the World Cup. It is necessary tooffer money to encourage children to exercise. To what extent do youagree or disagree?3/24/2018Some people believe that newspaper is the best way to learn aboutnews, while others believe that more effective way is through othermedia. Discuss both views and give your opinion.4/7/2018 The two maps compare what the layout of the South Wing of Whelton Museum looked like in two separate years 2008 and 2012.Some people think the most important thing about being rich is thatgive person an opportunity to help other people. To what extent do youagree or disagree?4/14/2018 The table gives information of 5 types of product exported from Hong Kong in 2009 and 2010.Governments should make people responsible for looking after theirown local environment. To what extent do you agree or disagree?4/21/2018People today can shop, work, and communicate with others via theinternet. They don’t need to do these face to face. Is it a positive ornegative development?4/26/2018In some countries, increasing number of parents choose to educate theirchildren at home by themselves instead of sending them to school. Arethe advantages of home education outweigh the disadvantages?5/5/2018 The chart below shows the average height in different countriesbetween 1775 and 1975.Traffic and housing problems in major cities can be solved by movinglarge companies, factories and their employees to the countryside. Towhat extent do you agree or disagree?5/12/2018 The charts show the total water use in different sectors in Sydney, Australia in 1997 and 2007.Some people think that art (such as painting and music) does notdirectly improve quality of people's life, so government should spendmoney on other areas. To what extent do you agree or disagree?5/19/2018 The diagrams below show the process of applying for a driver license in America.People can eat a wide variety of food that can be grown in other areas.As a result, people eat more food produced in other regions than localfood. Do you think the advantages of this trend outweigh thedisadvantages?5/24/2018 The chart and table show the population size and life expectancy of three countries.Summarize the information by selecting key featuresand making comparison where is relevant.Children are face educational, social and commercial pressures. Whatare the causes of these pressures? What measures should be taken toreduce them?6/2/2018 The chart shows changes in the functional area of a museum from 1998 to 2008.Many people today prefer socializing online to spending time withfriends in the local community. Do the advantages of this trendoutweigh the disadvantages?6/7/2018 Below tables are the use of water by four different countries. Make summaries by selecting and reporting the main features. Makecomparisons where relevant.Today many young people change their jobs or careers every fewyears.What do you think are the reasons for this?Do you think theadvantages outweigh its disadvantages?6/23/2018 The maps show the campus layout now and a plan for development.More and more people want to buy famous brands with clothes,cars andother items.what are the reasons? Do you think it is a positive ornegative development?6/30/2018 The chart below shows the rate of males and females who wereoverweight in Australia from 1980 to 2010.An increasing number of people are changing careers during theirworking life. What do you think are the reasons of this? Is it a positivea negative development?People have different views on how to reduce traffic congestion. Somethink that governments should build more train and subway lines, whileothers think that building more roads and widening existing roads willreduce traffic congestion. Discuss both views and give your ownopinion.7/19/2018 The chart shows the average class size in 6 countries in 2006, and compare them with world average class size.In many cities, an increasing number of people do not know theirneighbours and the sense of community is lost. Discuss the causes andgive measures to turn it around.Some businesses find that new employees who just finish theireducation lack basic interpersonal ability such as work with others as apart of team.What do you think the causes of this problem? And how tosolve this?7/28/2018 The chart shows the percentage of boys and girls who participate in different sports activities in 2010.Some people who have been in prison become good citizens later.Some people think that they are the best people to talk to schoolstudents the danger of committing a crime. To what extent do you agreeor disagree?Some people say modern children's games do not develop a wide rangeof skills, while traditional games can be much better for developingsuch skills. To what extent do you agree or disagree?8/11/2018 The chart shows the percentage of the total world population in four countries in 1950, 2002 and 2050.Nowadays a large amount of advertising is aimed at children. Somepeople think this can have negative effects on children and should bebanned. To what extent do you agree or disagree?8/18/2018Some people think that schools should stop teaching students by usingbooks, because students find them boring and that children can learnfrom films, TV, video games and computer instead. To what extent doyou agree?8/25/2018 Oil production of African countries （barrels per day）Some people think young children should get formal study at school asearly as possible, However, others believe that children should not go toschool until 7 years old. Discuss both sides and give your own opinion. 9/8/2018Nowadays people are living in a “ thrown-away” society where theyuse things for a short time and then throw away. What cause this andwhat problem it may lead to?9/13/2018Some people think scientific research is a waste of time and money，towhat degree do you agree or disagree?9/15/2018 The chart below shows the change in percentage for household cars in a European Country between 1971 and 2001. Summarize the informationby selecting and reporting the main features，and make comparisonswhere relevant.In many countries nowadays, more and more women have full-timejobs as men, so it is logic that men and women should share thehousework tasks equally. To what extent do you agree or disagree?9/29/2018 The graph below shows percentages of different types of household waste which were recycled in one city between 1992 and2002.Summarize the information by selecting and reporting the mainfeatures，and make comparisons where relevant.Team or group activities can teach more important skills for life thanthose done alone. To what extent do you agree or disagree with thisstatement.10/11/2018 线图Some people think that it is too difficult for poor people or people fromrural areas to go to university. So that the universities should make itespecially easy to them. Do you agree or disagree?10/13/2018 The diagram below shows what an office building looks at present and plans on future development. Summarize the information by selectingand reporting the main features，and make comparisons where relevant.At present:Future:In many countries women are allowed to take maternity leave fromtheir jobs during the first month after the birth of their baby. Doadvantages outweigh disadvantages?10/20/2018 对三个医院不同方面的满意度调查，比较service of staff, time waste, quality of treatment，quality of after care的几个方面Reports show that it is increasingly expensive to keep museums open topublic. What is the best way to fund them (government, business,individual)?10/27/2018 The graph shows the development of a particular college campus from 1975 to 2002 and the proposed development of 2022.Some people think that young people should spend more of their freetime at home with their families, and spend less time entertainingoutside. Others disagree. Discuss both views and give your ownopinion.11/1/2018 The chart below shows the average time 16-22-year olds spent on playing video games in four different countries between 1992 and2002.Summarize the details. Select and report the main features andmake comparisons where relevant.Some people think that young people should spend more of their freetime at home with their families, and spend less time entertainingoutside. Others disagree. Discuss both views and give your ownopinion.11/3/2018It is shown that many criminals have a low level of education. somepeople believe that the best way to reduce crime is to educate them inprison so that they can find a job after they leave prison. To what extentdo you agree？11/10/2018 The table below shows the percentage of water used in three sectors in six different countries in 2003. Summarize the information by selectingand reporting the main features , and make comparisons where relevant.Some employers are giving increased importance to employing peoplewith good social skills in addition to good qualifications.Do you agreeor disagree social skills are as important as good qualifications forsuccess in their jobs?11/17/2018 The graph below shows concerns three production in forest industry ina European country. The production is timber, pulp and paper duringthe years between 1980 to 2000.The qualities a person needs to become truly successful cannot belearned at a university or similar academic institution.To what extent doyou agree or disagree？12/1/2018 The chart shows the percentage of people who can drive in 15 minutes to various services in UK. The chart compares the people living inurban areas and living in rural areas.The spending on the development of technology of space exploration isnot justifiable. They believe there are many beneficial ways to spendthese money. Agree or disagree?12/8/2018 This combination of a pie and a table demonstrates the percentages of foreign visitors travelling to a tourist resort in Australia and specificinformation regarding staying period, accommodation and mainpurposes in their trips.Some people believe that schools should choose their studentsaccording to their abilities.While other people think students withdifferent abilities should learn together.Discuss both views and giveyour own opinion.12/13/2018 The diagram below shows how three different types of tea are made.Many young people today know more about international pop or moviestars than about famous people in the history of their own country. Whyis this? What can be done to increase young people’s interest in thefamous people in the history of their country?12/15/2018 线图Some school leavers go traveling or work for a period of time instead ofgoing directly to university. Do you think this has more advantages, ordisadvantages on their study？。
