2011 June igcse 英文数学试卷
2011年6月大学英语六级真题与答案详解完整版
2011年6月大学英语六级真题与答案详解完整版Part I Writing标准版My opinion on certificate crazeThe growing tendency among college students to get all kinds of certificates has now evolved into a craze. Just randomly ask a student what he or she is busily engaged in doing, quite possibly, you would get the answer that he or she is preparing for a certificate of some kind. So, why’s the craze? The reason behind this phenomenon is common — the enormous pressure of finding a job. Faced with a harsh job market, most students have no choice but to seek more certificates to parlay their qualifications. Another factor is that diploma and certificates still weighs heavily in terms of signifying one’s ability. For the sake of increasing their odds of landing a better job, the students ar e compelled to run from one exam to another.Though I have an open mind toward the craze on certificates, I suggest that students should be more rational when it comes to certificates, since they do not necessarily tell their ability. Instead, they should be more involved in learning and capability boosting, thus, opportunities would come quite naturally.文章点评：这是一篇“中等偏上”的学生作文。
2011年六月大学英语六级真题及答案详解
2011年6月大学英语六级真题及答案详解一、真题部分Part I writtingDirections:For this part, you are allowed 30 minutes to write a short essay o n the topic of Certificate Craze. You should write at least 150 words following the outline given below:1. 现在许多人热衷于各类证书考试2. 其目的各不相同3. 在我看来Part II R eading Comprehension (Skimming and Scanning) (15 minutes) Directions:In this part, you will have 15 minutes to go over the passage quickly and answer the questions on Answer Sheet 1. For questions 1-7, choose the best answer from the four choices marked A), B), C) and D). For questions 8-10, complete the sentences with the information given in the passage.Minority ReportAmerican universities are accepting more minorities than ever. Graduating them is another matter.Barry Mills, the president of Bowdoin College, was justifiably proud of Bowdoin's efforts to recruit minority students. Since 2003 the small, elite liberal arts school in Brunswick, Maine, has boosted the proportion of so-called under-represented minority students in entering freshman classes from 8% to 13%. "It is our responsibility to reach out and attract students to come to our kinds of places," he told a NEWSWEEK reporter. But Bowdoin has not done quite as well when it comes to actually graduating minorities. While 9 out of 10 white students routinely get their diplomas within six years, only 7 out of 10 black students made it to graduation day in several recent classes."If you look at who enters college, it now looks like America," says Hilary Pennington, director of postsecondary programs for the Bill & Melinda Gates Foundation, which has closely studied enrollment patterns in higher education. "But if you look at who walks across the stage for a diploma, it's still largely the white, upper-income population."The United States once had the highest graduation rate of any nation. Now it stands 10th. For the first time in American history, there is the risk that the rising generation will be less well educated than the previous one. The graduation rate among 25- to 34-year-olds is no better than the rate for the 55- to 64-year-olds who were going to college more than 30 years ago. Studies show that more andmore poor and non-white students want to graduate from college –but their graduation rates fall far short of their dreams. The graduation rates for blacks, Latinos, and Native Americans lag far behind the graduation rates for whites and Asians. As the minority population grows in the United States, low college graduation rates become a threat to national prosperity.The problem is pronounced at public universities. In 2007 the University of Wisconsin-Madison –one of the top five or so prestigious public universities –graduated 81% of its white students within six years, but only 56% of its blacks. At less-selective state schools, the numbers get worse. During the same time frame, the University of Northern Iowa graduated 67% of its white students, but only 39% of its blacks. Community colleges have low graduation rates generally –but rock-bottom rates for minorities. A recent review of California community colleges found that while a third of the Asian students picked up their degrees, only 15% of African-Americans did so as well.Private colleges and universities generally do better, partly because they offer smaller classes and more personal attention. But when it comes to a significant graduation gap, Bowdoin has company. Nearby Colby College logged an 18-point difference between white and black graduates in 2007 and 25 points in 2006. Middlebury College in Vermont, another top school, had a 19-point gap in 2007 and a 22-point gap in 2006. The most selective private schools – Harvard, Yale, and Princeton –show almost no gap between black and white graduation rates. But that may have more to do with their ability to select the best students. According to data gathered by Harvard Law School professor Lani Guinier, the most selective schools are more likely to choose blacks who have at least one immigrant parent from Africa or the Caribbean than black students who are descendants of American slaves."Higher education has been able to duck this issue for years, particularly the more selective schools, by saying the responsibility is on the individual student," says Pennington of the Gates Foundation. "If they fail, it's their fault." Some critics blame affirmative action – students admitted with lower test scores and grades from shaky high schools often struggle at elite schools. But a bigger problem may be that poor high schools often send their students to colleges for which they are "undermatched": they could get into more elite, richer schools, but instead go to community colleges and low-rated state schools that lack the resources to help them. Some schools out for profit cynically increase tuitions and count on student loans and federal aid to foot the bill – knowing full well that the students won't make it. "The school keeps the money, but the kid leaves with loads of debt and no degree and no ability to get a better job. Colleges are not holding up their end," says Amy Wilkins of the Education Trust.A college education is getting ever more expensive. Since 1982 tuitions have been rising at roughly twice the rate of inflation. In 2008 the net cost of attending a four-year public university – after financial aid – equaled 28% of median (中间的) family income, while a four-year private university cost 76% of median familyincome. More and more scholarships are based on merit, not need. Poorer students are not always the best-informed consumers. Often they wind up deeply in debt or simply unable to pay after a year or two and must drop out.There once was a time when universities took pride in their dropout rates. Professors would begin the year by saying, "Look to the right and look to the left. One of you is not going to be here by the end of the year." But such a Darwinian spirit is beginning to give way as at least a few colleges face up to the graduation gap. At the University of Wisconsin-Madison, the gap has been roughly halved over the last three years. The university has poured resources into peer counseling to help students from inner-city schools adjust to the rigor (严格要求) and faster pace of a university classroom–and also to help minority students overcome the stereotype that they are less qualified. Wisconsin has a "laserlike focus" on building up student skills in the first three months, according to vice provost (教务长) Damon Williams.State and federal governments could sharpen that focus everywhere by broadly publishing minority graduation rates. For years private colleges such as Princeton and MIT have had success bringing minorities onto campus in the summer before freshman year to give them some preparatory courses. The newer trend is to start recruiting poor and non-white students as early as the seventh grade, using innovative tools to identify kids with sophisticated verbal skills. Such programs can be expensive, of course, but cheap compared with the millions already invested in scholarships and grants for kids who have little chance to graduate without special support.With effort and money, the graduation gap can be closed. Washington and Lee is a small, selective school in Lexington, Va. Its student body is less than 5% black and less than 2% Latino. While the school usually graduated about 90% of its whites, the graduation rate of its blacks and Latinos had dipped to 63% by 2007. "We went through a dramatic shift," says Dawn Watkins, the vice president for student affairs. The school aggressively pushed mentoring (辅导) of minorities by other students and "partnering"with parents at a special pre-enrollment session. The school had its first-ever black homecoming. Last spring the school graduated the same proportion of minorities as it did whites. If the United States wants to keep up in the global economic race, it will have to pay systematic attention to graduating minorities, not just enrolling them.注意：此部分试题请在答题卡1上作答。
2011年Alevel数学试卷真题
*2011*UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSInternational General Certificate of Secondary EducationMATHEMATICS 0580/21 Paper 2 (Extended) May/June 20111 hour 30 minutesCandidates answer on the Question Paper.Additional Materials: E lectronic calculator Geometrical instrumentsMathematical tables (optional) Tracing paper (optional) READ THESE INSTRUCTIONS FIRSTWrite your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid.DO NOT WRITE IN ANY BARCODES.Answer all questions.If working is needed for any question it must be shown below that question.Electronic calculators should be used.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For π , use either your calculator value or 3.142.At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question.The total of the marks for this paper is 70.This document consists of 12 printed pages.IB11 06_0580_21/7RP© UCLES 2011 [Turn over *9523289317*© UCLES 20110580/21/M/J/116 ÷ ABAB1A concert hall has 1540 seats.Calculate the number of people in the hall when 55% of the seats are occupied.Answer[1]For Examiner's Use2Shade the required region on each Venn diagram.A ⋃ B' (A ⋂B )'[2]0.25−23Calculate 814 .Answer [2]4(a) Find m when 4m × 42 = 412 .Answer(a) m =[1](b) Find p when 6 p ÷ 6 5 = .Answer(b) p = [1][Turn o ver© UCLES 2011 0580/21/M/J/115A hummingbird beats its wings 24 times per second.(a) Calculate the number of times the hummingbird beats its wings in one hour.Answer(a)[1](b) Write your answer to part (a) in standard form.Answer(b)[1]For Examiner's Use6NOT TO SCALEA company makes solid chocolate eggs and their shapes are mathematically similar. The diagram shows eggs of height 2 cm and 6 cm. The mass of the small egg is 4 g. Calculate the mass of the large egg.Answerg [2]7 Find the length of the straight line from Q (−8, 1) to R (4 , 6).Answer QR =[3]6 cm2 cm© UCLES 2011 0580/21/M/J/11338Calculate the radius of a sphere with volume 1260 cm .For [The volume, V , of a sphere with radius r is V =4 πr .]3Examiner's UseAnswer cm [3]9ANOT TOSCALEDAB is parallel to CD .Calculate the value of x .Answer x =[3]10 Solve the simultaneous equations.3x + y = 30 2x – 3y = 53Answer x =y = [3]2x °BC5x ° x °[Turn o ver© UCLES 2011 0580/21/M/J/11211 A rectangular photograph measures 23.3 cm by 19.7 cm, each correct to 1 decimal place.Calculate the lower bound for(a) the perimeter,Answer(a)cm [2](b) the area.Answer(b)cm [1]For Examiner's Use12 A train leaves Barcelona at 21 28 and takes 10 hours and 33 minutes to reach Paris.(a) Calculate the time the next day when the train arrives in Paris.Answer(a)[1](b) The distance from Barcelona to Paris is 827 km.Calculate the average speed of the train in kilometres per hour.Answer(b)km/h [3]© UCLES 2011 0580/21/M/J/1122213 The scale on a map is 1: 20 000.(a) Calculate the actual distance between two points which are 2.7 cm apart on the map.Give your answer in kilometres.Answer(a)km [2]For Examiner's Use(b) A field has an area of 64 400 m . 2Calculate the area of the field on the map in cm .Answer(b) cm [2]14 Solve the equation 2x + 3x – 6 = 0.Show all your working and give your answers correct to 2 decimal places.Answer x =or x =[4][Turn o ver© UCLES 2011 0580/21/M/J/1115 A teacher asks 36 students which musical instruments they play.P = {students who play the piano} G = {students who play the guitar} D = {students who play the drums}The Venn diagram shows the results.(a) Find the value of x .Answer(a) x =[1](b) A student is chosen at random.Find the probability that this student(i) plays the drums but not the guitar,Answer(b)(i)[1](ii) plays only 2 different instruments.Answer(b)(ii)[1](c) A student is chosen at random from those who play the guitar.Find the probability that this student plays no other instrument.Answer(c)[1]For Examiner's UseD 7541 58x 2 GP© UCLES 2011 0580/21/M/J/112222 216For Examiner's Usek cmThe diagram shows a square of side k cm.The circle inside the square touches all four sides of the square.(a) The shaded area is A cm .Show that4A = 4k – πk .Answer (a)[2](b) Make k the subject of the formula 4A = 4k – πk .Answer(b) k =[3]17CNOT TOSCALEFor Examiner'sUseOB24°TAA, B and C are points on a circle, centre O.TA is a tangent to the circle at A and OBT is a straight line.AC is a diameter and angle OTA = 24°.Calculate(a)angle AOT,Answer(a) Angle AOT = [2](b)angle ACB,Answer(b) Angle ACB = [1](c)angle ABT.Answer(c) Angle ABT = [2][Turn o ver © UCLES 2011 0580/21/M/J/11© UCLES 2011 0580/21/M/J/1118For SExaminer's UseNOT TO SCALEPRIn the diagram, PQS , PMR , MXS and QXR are straight lines.PQ = 2 QS .M is the midpoint of PR . QX : XR = 1 : 3.= q and= r .(a) Find, in terms of q and r ,(i),Answer(a)(i)= [1](ii).Answer(a)(ii)=[1](b) By finding, show that X is the midpoint of MS .Answer (b)[3]QXM[Turn o ver© UCLES 20110580/21/M/J/112191510Speed (metres per second)5For Examiner's Use2 4 6 8 10 12 14Time (minutes)The diagram shows the speed-time graph of a train journey between two stations.The train accelerates for two minutes, travels at a constant maximum speed, then slows to a stop.(a) Write down the number of seconds t hat the train travels at its constant maximum speed.Answer(a)s [1](b) Calculate the distance between the two stations in metres .Answer(b)m [3](c) Find the acceleration of the train in the first two minutes .2Give your answer in m/s .Answer(c)m/s [2]Question 20 is printed on the next page.© UCLES 2011 0580/21/M/J/113–120f(x ) = xg(x ) = 2x − 3(a) Find(i) g(6),For Examiner's UseAnswer(a)(i)[1](ii) f(2x ).Answer(a)(ii)[1](b) Solve fg(x ) = 125.Answer(b) x =[3]−1(c) Find the inverse function g (x ) .Answer(c) g (x ) =[2]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 Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.。
IGCSE Maths past paper数学考试题
Q8
(Total 4 marks)
N20710RA
7
Turn over
9. The grouped frequency table gives information about the distance each of 150 people travel to work.
6
Ruler graduated in centimetres and
Nil
millimetres, protractor, compasses,
7
pen, HB pencil, eraser, calculator.
Tracing paper may be used.
8
9
Instructions to Candidates
Number
1
2
3
4
Probability
0.35
0.16
0.27
Magda is going to spin the pointer once. (a) Work out the probability that the pointer will stop on 4.
(b) Work out the probability that the pointer will stop on 1 or 3.
h b
The Quadratic Equation The solutions of ax2 + bx + c = 0 where a ≠ 0, are given by
x = −b ± b2 − 4ac 2a
N20710RA
2
Answer ALL TWENTY questions. Write your answers in the spaces provided. You must write down all stages in your working. 1. In July 2002, the population of Egypt was 69 million. By July 2003, the population of Egypt had increased by 2%. Work out the population of Egypt in July 2003.
Igcse-数学-历年真题
4400/4HEdexcel IGCSEMathematicsPaper 4HHigher TierFriday 11 June 2010 – AfternoonTime: 2 hoursMaterials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature.Check that you have the correct question paper.Answer ALL the questions. Write your answers in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).There are 22 questions in this question paper. The total mark for this paperis 100.You may use a calculator.Advice to CandidatesWrite your answers neatly and in good English.N36905AIGCSE MATHEMATICS 4400 FORMULA SHEET – HIGHER TIERAnswer ALL TWENTY TWO questions.Write your answers in the spaces provided.You must write down all stages in your working.1. Solve 6 y – 9 = 3 y + 7y = ................................(Total 3 marks) 2. The diagram shows two towns, A and B, on a map.(a) By measurement, find the bearing of B from A.....................................(2)C is another town.The bearing of C from A is 050.(b) Find the bearing of A from C.....................................(2)(Total 4 marks)3. A spinner can land on red or blue or yellow.The spinner is biased.The probability that it will land on red is 0.5The probability that it will land on blue is 0.2Imad spins the spinner once.(a) Work out the probability that it will land on yellow......................................(2)Janet spins the spinner 30 times.(b)Work out an estimate for the number of times the spinner will land on blue......................................(2)(Total 4 marks)4. Rosetta drives 85 kilometres in 1 hour 15 minutes.(a) Work out her average speed in kilometres per hour...................................... km/h(2)Rosetta drives a total distance of 136 kilometres.(b) Work out 85 as a percentage of 136................................. %(2)Sometimes Rosetta travels by train to save money.The cost of her journe y by car is £12The cost of her journey by train is 15% less than the cost of her journey by car.(c)Work out the cost of Rosetta’s journey by train.£ ...................................(3)(Total 7 marks)5.Calculate the value of x.Give your answer correct to 3 significant figures.x = ................................(Total 3 marks)6. A = {2, 3, 4, 5}B = {4, 5, 6, 7}(a)(i) List the members of A B......................................(ii) How many members are in A B?.....................................(2)ℰ = {3, 4, 5, 6, 7}P = {3, 4, 5}Two other sets, Q and R, each contain exactly three members.P Q = {3, 4}P R = {3, 4}Set Q is not the same as set R.(b)(i) Write down the members of a possible set Q......................................(ii) Write down the members of a possible set R......................................(2)(Total 4 marks)7. Rectangular tiles have width (x + 1) cm and height (5x – 2) cm.Some of these tiles are used to form a large rectangle.The large rectangle is 7 tiles wide and 3 tiles high.The perimeter of the large rectangle is 68 cm.(a) Write down an equation in x...............................................................................................................(3)(b) Solve this equation to find the value of x.x = ................................(3)(Total 6 marks)8. Show that 121 141 = 1519. The depth of water in a reservoir increases from 14 m to 15.75 m.Work out the percentage increase.................................. %(Total 3 marks)10. Quadrilaterals ABCD and PQRS are similar.AB corresponds to PQ.BC corresponds to QR.CD corresponds to RS.Find the value of(a) xx = ...............................(2)(b) yy = ...............................(1)(Total 3 marks)11. Simplify fully6x + 43x.....................................(Total 3 marks)12.(a)Find the equation of the line L......................................(3)(b) Find the three inequalites that define the unshaded region shown in the diagram below................................................................................................................(3)(Total 6 marks)13. (a) Solve x 2– 8x + 12 = 0.....................................(3)(b) Solve the simultaneous equationsy = 2x4x – 5y = 9x = ................................y = ................................(3)(Total 6 marks)14.The area of the triangle is 6.75 cm2.The angle x° is acute.Find the value of x.Give your answer correct to 1 decimal place.x = ................................(Total 3 marks)15. The unfinished histogram shows information about the heights, h metres, ofsome trees.(a) Calculate an estimate for the number of trees with heights in theinterval 4.5 < h ≤ 10.....................................(3)(b) There are 75 trees with heights in the interval 10 < h ≤ 13Use this information to complete the histogram.(2)(Total 5 marks)16. A bag contains 3 white discs and 1 black disc.John takes at random 2 discs from the bag without replacement.(a) Complete the probability tree diagram.First disc Second disc(3)(b)Find the probability that both discs are white......................................(2)All the discs are now replaced in the bag.Pradeep takes at random 3 discs from the bag without replacement.(c)Find the probability that the disc left in the bag is white......................................(3)(Total 8 marks)17. The diagram shows a sector of a circle, radius 45 cm, with angle 84°.Calculate the area of the sector.Give your answer correct to 3 significant figures.............................. cm2(Total 3 marks) 18.Calculate the length of AC.Give your answer correct to 3 significant figures................................ cm(Total 3 marks)19. A cone has slant height 4 cm and base radius r cm.The total surface area of the cone is 433π cm 2.Calculate the value of r .r = ................................(Total 4 marks)20. f(x) = (x – 1)2(a) Find f(8).....................................(1)The domain of f is all values of x where x ≥ 7(a)Find the range of f......................................(2)xg(x) =x1(c) Solve the equation g(x) = 1.2.....................................(2)(d) (i) Express the inverse function g –1 in the form g –1(x) = .......g –1(x) = ...................................(ii) Hence write down gg(x) in terms of x.gg(x) = ....................................(6)(Total 11 marks)21.In the diagram OA= a and OC= c.(a) Find CA in terms of a and c......................................(1)The point B is such that AB=1c.2(b) Give the mathematical name for the quadrilateral OABC......................................(1)The point P is such that OP= a + k c, where k ≥ 0(c) State the two conditions relating to a + k c that must be true for OAPCto be a rhombus.(2)(Total 4 marks)22. (a) Work out 5.2 × 102+ 2.3 × 104Give your answer in standard form......................................(2)a × 102 +b × 104 =c × 104(b) Express c in terms of a and b.c = ................................(2)(Total 4 marks)TOTAL FOR PAPER = 100 MARKSEND。
Igcse 数学 历年真题
4400/4HEdexcel IGCSEMathematicsPaper 4HHigher TierFriday 11 June 2010 – AfternoonTime: 2 hoursMaterials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature.Check that you have the correct question paper.Answer ALL the questions. Write your answers in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: . (2).There are 22 questions in this question paper. The total mark for this paperis 100.You may use a calculator.Advice to CandidatesWrite your answers neatly and in good English.This publication may be reproduced only in accordance with Edexcel Limited copyright policy.©2010 Edexcel Limited.Printer’s Log. No. N36905AIGCSE MATHEMATICS 4400 FORMULA SHEET – HIGHER TIERAnswer ALL TWENTY TWO questions.Write your answers in the spaces provided.You must write down all stages in your working.1. Solve 6 y – 9 = 3 y + 7y = ................................(Total 3 marks) 2. The diagram shows two towns, A and B, on a map.(a) By measurement, find the bearing of B from A.....................................(2)C is another town.The bearing of C from A is 050.(b) Find the bearing of A from C.....................................(2)(Total 4 marks)3. A spinner can land on red or blue or yellow.The spinner is biased.The probability that it will land on red isThe probability that it will land on blue isImad spins the spinner once.(a) Work out the probability that it will land on yellow......................................(2)Janet spins the spinner 30 times.(b)Work out an estimate for the number of times the spinner will land on blue......................................(2)(Total 4 marks)4. Rosetta drives 85 kilometres in 1 hour 15 minutes.(a) Work out her average speed in kilometres per hour...................................... km/h(2)Rosetta drives a total distance of 136 kilometres.(b) Work out 85 as a percentage of 136................................. %(2)Sometimes Rosetta travels by train to save money.The cost of her journey by car is £12The cost of her journey by train is 15% less than the cost of her journey by car.(c)Work out the cost of Rosetta’s journ ey by train.£ ...................................(3)(Total 7 marks)5.Calculate the value of x.Give your answer correct to 3 significant figures.x = ................................(Total 3 marks)6. A = {2, 3, 4, 5}B = {4, 5, 6, 7}(a)(i) List the members of A B......................................(ii) How many members are in A B?.....................................(2)ℰ = {3, 4, 5, 6, 7}P = {3, 4, 5}Two other sets, Q and R, each contain exactly three members.P Q = {3, 4}P R = {3, 4}Set Q is not the same as set R.(b)(i) Write down the members of a possible set Q......................................(ii) Write down the members of a possible set R......................................(2)(Total 4 marks)7. Rectangular tiles have width (x + 1) cm and height (5x – 2) cm.Some of these tiles are used to form a large rectangle.The large rectangle is 7 tiles wide and 3 tiles high.The perimeter of the large rectangle is 68 cm.(a) Write down an equation in x...............................................................................................................(3)(b) Solve this equation to find the value of x.x = ................................(3)(Total 6 marks)8. Show that 121 141 = 1519. The depth of water in a reservoir increases from 14 m to m.Work out the percentage increase.................................. %(Total 3 marks)10. Quadrilaterals ABCD and PQRS are similar.AB corresponds to PQ.BC corresponds to QR.CD corresponds to RS.Find the value of(a) xx = ...............................(2)(b) yy = ...............................(1)(Total 3 marks)11. Simplify fully6x + 43x.....................................(Total 3 marks)12.(a)Find the equation of the line L......................................(3)(b) Find the three inequalites that define the unshaded region shown in the diagram below................................................................................................................(3)(Total 6 marks)13. (a) Solve x 2– 8x + 12 = 0.....................................(3)(b) Solve the simultaneous equationsy = 2x4x – 5y = 9x = ................................y = ................................(3)(Total 6 marks)14.The area of the triangle is cm2.The angle x° is acute.Find the value of x.Give your answer correct to 1 decimal place.x = ................................(Total 3 marks)15. The unfinished histogram shows information about the heights, h metres, ofsome trees.(a) Calculate an estimate for the number of trees with heights in theinterval < h ≤ 10.....................................(3)(b) There are 75 trees with heights in the interval 10 < h ≤ 13Use this information to complete the histogram.(2)(Total 5 marks)16. A bag contains 3 white discs and 1 black disc.John takes at random 2 discs from the bag without replacement.(a) Complete the probability tree diagram.First disc Second disc(3)(b)Find the probability that both discs are white......................................(2)All the discs are now replaced in the bag.Pradeep takes at random 3 discs from the bag without replacement.(c)Find the probability that the disc left in the bag is white......................................(3)(Total 8 marks)17. The diagram shows a sector of a circle, radius 45 cm, with angle 84°.Calculate the area of the sector.Give your answer correct to 3 significant figures.............................. cm2(Total 3 marks) 18.Calculate the length of AC.Give your answer correct to 3 significant figures................................ cm(Total 3 marks)19. A cone has slant height 4 cm and base radius r cm.The total surface area of the cone is 433π cm 2.Calculate the value of r .r = ................................(Total 4 marks)20. f(x) = (x – 1)2(a) Find f(8).....................................(1)The domain of f is all values of x where x ≥ 7(a)Find the range of f......................................(2)xg(x) =x1(c) Solve the equation g(x) =.....................................(2)(d) (i) Express the inverse function g –1 in the form g –1(x) = .......g –1(x) = ...................................(ii) Hence write down gg(x) in terms of x.gg(x) = ....................................(6)(Total 11 marks)21.In the diagram OA= a and OC= c.(a) Find CA in terms of a and c......................................(1)The point B is such that AB=1c.2(b) Give the mathematical name for the quadrilateral OABC......................................(1)The point P is such that OP= a + k c, where k ≥ 0(c) State the two conditions relating to a + k c that must be true for OAPCto be a rhombus.(2)(Total 4 marks)22. (a) Work out × 102+ × 104Give your answer in standard form......................................(2)a × 102 +b × 104 =c × 104(b) Express c in terms of a and b.c = ................................(2)(Total 4 marks)TOTAL FOR PAPER = 100 MARKSEND。
2011年6月四级英语真题及答案听力原文
2011年6月大学英语四级真题试卷及答案Part II Reading Comprehension(Skimming and Scanning) (15 minutes) Directions: In this part, you will have 15 minutes to go over the passage quickly and answer the questions on Answer Sheet 1. For questions 1 - 7, choose the best answer from the four choices marked A), B), C) and D). For questions 8-10, complete the sentences with the information given in the passage.British Cuisine: the Best of Old and NewBritish cuisine(烹饪) has come of age in recent years as chefs(厨师) combine the best of old and new.Why does British food have a reputation for being so bad? Because it is bad! Those are not the most encouraging words to hear just before eating lunch at one of Hong Kong's smartest British restaurants, Alfie's by KEE, but head chef Neil Tomes has more to say."The past 15 years or so have been a noticeable period of improvement for food in England," the English chef says, citing the trend in British cuisine for better ingredients, preparation and cooking methods, and more appealing presentation. Chef such as Delia Smith, Nigel Slater, Jamie Oliver and Gordon Ramsay made the public realise that cooking - and eating - didn't have to be a boring thing. And now, most of the British public is familiar even with the extremes of Heston Blumenthal's molecular gastronomy, a form of cooking that employs scientific methods to create the perfect dish."It's no longer the case that the common man in England is embarrassed to show he knows about food," Tomes says.There was plenty of room for improvement. The problems with the nation's cuisine can be traced back to the Second World War. Before the war, much of Britain's food was imported and when German U-boats began attacking ships bringing food to the country, Britain went on rations(配给)."As rationing came to an end in the 1950s, technology picked up and was used to mass-produce food," Tomes says. "And by then people were just happy to have a decent quantity of food in their kitchens."They weren't looking for cured meats, organic produce or beautiful presentation; they were looking for whatever they could get their hands on, and this prioritisation of quantity over quality prevailed for decades, meaning a generation was brought up with food that couldn't compete with neighbouring France, Italy, Belgium or Spain.Before star chefs such as Oliver began making cooking fashionable, it was hard to find a restaurant in London that was open after 9pm. But in recent years the capital's culinary(烹饪的) scene has developed to the point that it is now confident of its ability to please the tastes of any international visitor.With the opening of Alfie's in April, and others such as The Pawn, two years ago, modern British food has made its way to Hong Kong. "With British food, I think that Hong Kong restaurant are keeping up," says David Tamlyn, the Welsh executive chef at The Pawn in Wan Chai. "Hong Kong diners are extremely responsive to new ideas or presentations, which is good news for new dishes."Chefs agree that diners in Hong Kong are embracing the modern British trend. Some restaurants are modifying the recipes(菜谱)of British dishes to breathe new life into the classics, while other are using better quality ingredients but remaining true to British traditional and tastes.Tamlyn is in the second camp. "We select our food very particulary. We use US beef, New Zealand lamb and for our custards(牛奶蛋糊) we use Bird's Custard Powder," Tamlyn says. "Some restaurants go for custard made fresh with eggs, sugar and cream, but Britishcustard is different, and we stay true to that."Matthew Hill, senior manager at the two-year-old SoHo restaurant Y orkshire Pudding, also uses better ingredients as a means of improving dishes. "There are a lot of existing perceptions about British food and so we can't alter these too much. We're a traditional British restaurant so there are some staples(主菜) that will remain essentially unchanged."These traditional dishes include fish and chips, steak and kidney pie and large pieces of roasted meats. At Alfie's, the newest of the British restaurants in town and perhaps the most gentlemen's club-like in design, Neil Tomes explains his passion for provenance(原产地). "Britain has started to become really proud of the food it's producing. It has excellent organic farms, beautifully crafted cheeses, high-quality meats."However, the British don't have a history of exporting their foodstuffs, which makes it difficult for restaurants in Hong Kong to source authentic ingredients."We can get a lot of our ingredients once a week from the UK," Tamlyn explains. "But there is also pressure to buy local and save on food miles, which means we take our vegetables from the local markets, and there are a lot that work well with British staples."The Phoenix, in Mid-Levels, offers the widest interpretation of "British cuisine", while still trying to maintain its soul. The gastro-pub has existed in various locations in Hong Kong since 2002. Singaporean head chef Tommy Teh Kum Chai offers daily specials on a blackboard, rather than sticking to a menu. This enables him to reinterpret British cuisine depending on what is available in the local markets."We use a lot of ingredients that people wouldn't perhaps associate as British, but are presented in a British way. Bell peppers stuffed with couscous, alongside ratatouille, is a very popular dish."Although the ingredients may not strike diners as being traditional, they can be found in dishes across Britain.Even the traditional chefs are aware of the need to adapt to local tastes and customs, while maintaining the Brutishness of their cuisine.At Y orkshire Pudding, Hill says that his staff asks diners whether they would like to share their meals. Small dishes, shared meals and "mixing it up" is not something commonly done in Britain, but Y orkshire Pudding will bring full dished to the table and offer individual plates for each dinner. "That way, people still get the presentation of the dishes as they were designed, but can carve them up however they like," Hill says.This practice is also popular at The Pawn, although largely for rotisseries(烤肉馆), Tamlyn says. "Some tables will arrive on Sunday, order a whole chicken and a shoulder of lamb or a baby pig, and just stay for hours enjoying everything we bring out for them."Some British traditions are too sacred(神圣的) to mess with, however, Tomes says. "I'd never change a full English breakfast."1. What is British food generally known for?A) Its unique flavor. B) Its bad taste.C) Its special cooking methods D) Its organic ingredients.2. The Second World War led to ____ in Britain.A) an inadequate supply of food B) a decrease of grain productionC) an increase in food import D) a change in people's eating habits3. Why couldn't Britain compete with some of its neighboring countries in terms of food in the post-war decades?A) Its food lacked variety. B) Its people cared more for quantity.C) It was short of well-trained chefs. D) It didn't have flavorful food ingredients.4. With culinary improvement in recent years, London's restaurants are now able to appea l to the tastes of ____.A) most young people B) elderly British dinersC) all kinds of overseas visitors D) upper-class customers5. What do Hong Kong diners welcome, according to Welsh executive chef David Tamlyn?A) Authentic classic cuisine. B) Locally produced ingredients.C) New ideas and presentations. D) The return of home-style dishes.6. While using quality ingredients, David Tamlyn insists that the dishes should ____.A) benefit people's health B) look beautiful and invitingC) be offered at reasonable prices D) maintain British traditional tastes7. Why does Neil Tomes say he loves food ingredients from Britain?A) They appeal to people from all over the world. B) They are produced on excellent organic forms.C) They are processed in a scientific way. D) They come in a great variety.8. Tamlyn says that besides importing ingredients from Britain once a week, his restaurant also buys vegetables from ____________________.9. The Phoenix in Mid-Levels may not use British ingredients, but presents its dishes ________________.10. Y orkshire Pudding is a restaurant which will bring full dishes to the table but offer plates to those diners who would like to ___________________________.Part III Listening Comprehension (35 minutes)Section ADirections:In this section, you will hear 8 short conversations and 2 long conversations. At the end of each conversation, one or more questions will be asked about what was said. Both the conversation and the questions will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A), B), C) and D), and decide which is the best answer. Then mark the corresponding letter on Answer Sheet 2 witha single line through the centre.11. A) He is careless about his appearance.B) He is ashamed of his present condition.C) He changes jobs frequently.D) He shaves every other day.12. A) Jane may be caught in a traffic jam.B) Jane should have started a little earlier.C) He knows what sort of person Jane is.D) He is irritated at having to wait for Jane.13. A) Training for the Mid-Atlantic Championships.B) Making preparations for a trans-Atlantic trip.C) Collecting information about baseball games.D) Analyzing their rivals' on-field performance.14. A) He had a narrow escape in a car accident.B) He is hospitalized for a serious injury.C) He lost his mother two weeks ago.D) He has been having a hard time.15. A) The woman has known the speaker for a long time.B) The man had difficulty understanding the lecture.C) The man is making a fuss about nothing.D) The woman thinks highly of the speaker.16. A) He has difficulty making sense of logic.B) Statistics and logic are both challenging subjects.C) The woman should seek help from the tutoring service.D) Tutoring services are very popular with students.17. A) Her overcoat is as stylish as Jill's.B) Jill missed her class last week.C) Jill wore the overcoat last week.D) She is in the same class as the man.18. A) A computer game.B) An imaginary situation.C) An exciting experience.D) A vacation by the sea.Questions 19 to 21 are based on the conversation you have just heard.19. A) Beautiful scenery in the countryside.B) Dangers of cross-country skiing.C) Pain and pleasure in sports.D) A sport he participates in.20. A) He can't find good examples to illustrate his point.B) He can't find a peaceful place to do the assignment.C) He doesn't know how to describe the beautiful country scenery.D) He can't decide whether to include the effort part of skiing.21. A) New ideas come up as you write.B) Much time is spent on collecting data.C) A lot of effort is made in vain.D) The writer's point of view often changes.Questions 22 to 25 are based on the conversation you have just heard.22. A) Journalist of a local newspaper.B) Director of evening radio programs.C) Producer of television commercials.D) Hostess of the weekly "Business World".23. A) He ran three restaurants with his wife's help.B) He and his wife did everything by themselves.C) He worked both as a cook and a waiter.D) He hired a cook and two local waitresses.24. A) He hardly needs to do any advertising nowadays.B) He advertises a lot on radio and in newspapers.C) He spends huge sums on TV commercials every year.D) He hires children to distribute ads in shopping centers.25. A) The restaurant location.B) The restaurant atmosphere.C) The food variety.D) The food price.Section BDirections: In this section, you will hear 3 short passages. At the end of each passage, you will hear some questions. Both the passage and the questions will be spoken only once. After you hear a question, you must choose the best answer from the four choices marked A), B), C) and D). Then mark the corresponding letter on Answer Sheet 2 with a single line through the centre.Passage One26. A) Its protection is often neglected by children.B) It cannot be fully restored once damaged.C) There are many false notions about it.D) There are various ways to protect it.27. A) It may make the wearer feel tired.B) It will gradually weaken the eyes of adults.C) It can lead to the loss of vision in children.D) It can permanently change the eye structure.28. A) It can never be done with high technology.B) It is the best way to restore damaged eyesight.C) It is a major achievement in eye surgery.D) It can only be partly accomplished now.Passage Two29. A) They think they should follow the current trend.B) Nursing homes are well-equipped and convenient.C) Adult day-care centers are easily accessible.D) They have jobs and other commitments.30. A) They don't want to use up all their life savings.B) They fear they will regret it afterwards.C) They would like to spend more time with them.D) They don't want to see their husbands poorly treated.31. A) Provide professional standard care.B) Be frank and seek help from others.C) Be affectionate and cooperative.D) Make use of community facilities.Passage Three32. A) Health and safety conditions in the workplace.B) Rights and responsibilities of company employees.C) Common complaints made by office workers.D) Conflicts between labor and management.33. A) Replace its out-dated equipment.B) Improve the welfare of affected workers.C) Follow the government regulations strictly.D) Provide extra health compensation.34. A) They requested to transfer to a safer department.B) They quit work to protect their unborn babies.C) They sought help from union representatives.D) They wanted to work shorter hours.35. A) To show how they love winter sports.B) To attract the attention from the media.C) To protect against the poor working conditions.D) To protect themselves against the cold weather.Section CDirections: In this section, you will hear a passage three times. When the passage is read for the first time, you should listen carefully for its general idea. When the passage is read for the second time, you are required to fill in the blanks numbered from 36 to 43 with the exact words you have just heard. For blanks numbered from 44 to 46 you are required to fill in the missing information. For these blanks, you can either use the exact words you have just heard or write down the main points in your own words. Finally, when the passage is read for the third time, you should check what you have written.Contrary to the old warning that time waits for no one, time slows down when you are on the move. It also slows down more as you move faster, which means astronauts(宇航员) someday may (36)__________ so long in space that they would return to an Earth of the (37)__________ future. If you could move at the speed of light, your time would stand still. If you could move faster than light, your time would move (38)__________ .Although no form of matter yet (39)__________ moves as fast as or faster than light,(40)__________ experiments have already confirmed that accelerated (41)__________ causes a traveler's time to be stretched. Albert Einstein (42)__________ this in 1905, when he (43)__________ the concept of relative time as part of his Special Theory of Relativity. A search is now under way to confirm the suspected existence of particles of matter (44)_________________________________________________________________________________________ .An obsession(沉迷)with time-saving, gaining, wasting, losing, and mastering it-(45)_____________________________________________________________________ ______________________________________________ . Humanity also has been obsessed with trying to capture the meaning of time. Einstein (46)_______________________________________________________________________________________________. Thus, time and time's relativity are measurable by any hourglass, alarm clock, or an atomic clock that can measure a billionth of a second. Part ⅣReading Comprehension (Reading in Depth) (25 minutes)Section ADirections:In this section, there is a passage with ten blanks. You are required to select one word for each blank from a list of choices given in a word bank following the passage. Read the passage through carefully before making your choices. Each choice in the bank is identified by a letter. Please mark the corresponding letter for each item on Answer Sheet 2 with a single line through the centre. You may not use any of the words in the bank more than once.The popular notion that older people need less sleep than younger adults is a myth, scientists said yesterday.While elderly people 47 to sleep for fewer hours than they did when they were younger, this has a(n) 48 effect on their brain's performance and they would benefit from getting more, according to research.Sean Drummond, a psychiatrist (心理医生) at the University of California, San Diego, said that older people are more likely to suffer from broken sleep, while younger people are better at sleeping 49 straight through the night.More sleep in old age, however, is 50 with better health, and most older people would feel better and more 51 if they slept for longer periods, he said."The ability to sleep in one chunk (整块时间) overnight goes down as we age but the amount of sleep we need to 52 well does not change," Dr Drummond told the American Association for the Advancement of Science conference in San Diego."It's 53 a myth that older people need less sleep. The more healthy an older adult is, the more they sleep like they did when they were 54 . Our data suggests that older adults would benefit from 55 to get as much sleep as they did in their 30s. That's 56 from person to person, but the amount of sleep we had at 35 is probably the sameDirections:There are 2 passages in this section. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A), B), C) and D). You should decide on the best choice and mark the corresponding letter on Answer Sheet 2 with a single line through the centre.Passage OneSeveral recent studies have found that being randomly (随机地) assigned to a roommate of another race can lead to increased tolerance but also to a greater likelihood (可能性) of conflict.Recent reports found that lodging with a student of a different race may decrease prejudice and compel students to engage in more ethnically diverse friendships.An Ohio State University study also found that black students living with a white roommate saw higher academic success throughout their college careers. Researchers believe this may be caused by social pressure.In a New Y ork Times article, Sam Roakye-the only black student on his freshman year floor-said that "if you're surrounded by whites, you have something to prove."Researchers also observed problems resulting from pairing interracial students in residences.According to two recent studies, randomly assigned roommates of different race are more likely to experience conflicts so strained that one roommate will move out.An Indiana University study found that interracial roommates were three times as likely as two white roommates to no longer live together by the end of the semester.Grace Kao, a professor at Penn said she was not surprised by the findings. "This may be the first time that some of these students have interacted, and lived, with someone of a different race," she said.At Penn, students are not asked to indicate race when applying for housing."One of the great things about freshman housing is that, with some exceptions, the process throws you together randomly," said Undergraduate Assembly chairman Alec Webley. "This is the definition of integration.""I've experienced roommate conflicts between interracial students that have both broken down stereotypes and reinforced stereotypes," said one Penn resident advisor (RA). The RA of two years added that while some conflicts "provided more multicultural acceptance and melding (融合)," there were also "jarring cultural confrontations."The RA said that these conflicts have also occurred among roommates of the same race.Kao said she cautions against forming any generalizations based on any one of the studies, noting that more background characteristics of the students need to be studies and explained.57. What can we learn from some recent studies?A) Conflicts between studies of different races are unavoidable.B) Students of different races are prejudiced against each other.C) Interracial lodging does more harm than good.D) Interracial lodging may have diverse outcomes.58. What does Sam Boakye's remark mean?A) White students tend to look down upon their black peers.B) Black students can compete with their white peers academically.C) Black students feel somewhat embarrassed among white peers during the freshman year.D) Being surrounded by white peers motivates a black student to work harder to succeed.59. What does the Indians Univerisity study show?A) Interracial roommates are more likely to fall out.B) Few white students like sharing a room with a black peer.C) Roommates of different races just don't get along.D) Assigning students' lodging randomly is not a good policy.60. What does Alec Webley consider to be the "definition of integration"?A) Students of different races are required to share room.B) Interracial lodging is arranged by the school for freshmen.C) Lodging is assigned to students of different races without exception.D) The school randomly assigns roommates without regard to race.61. What does Grace Kao say about interracial lodging?A) It is unscientific to make generalizations about it without further study.B) Schools should be cautious when making decisions about student lodging.C) Students' racial background should be considered before lodging is assigned.D) Experienced resident advisors should be assigned to handle the problems.Passage TwoGlobal warming is causing more than 300,000 deaths and about $125 billion in economic losses each year, according to a report by the Global Humanitarian Forum, an organization led by Kofi Annan, the former United Nations secretary general.The report, to be released Friday, analyzed data and existing studies of health, disaster, population and economic trends. It found that human-influenced climate change was raising the global death rates from illnesses including malnutrition (营养不良) and heat-related health problems.But even before its release, the report drew criticism from some experts on climate and risk, who questioned its methods and conclusions.Along with the deaths, the report said that the lives of 325 million people, primarily in poor countries, were being seriously affected by climate change. It projected that the number would double by 2030.Roger Pielke Jr., a political scientist at the University of Co lorado, Boulder, who studies disaster trends, said the Forum's report was " a methodological embarrassment" because there was no way to distinguish deaths or economic losses related to human driven global warming amid the much larger losses resulting from the growth in populations and economic development in vulnerable (易受伤害的) regions. Dr. Pielke said that "climate change is an important problem requiring our utmost attention." But the report, he said, "will harm the cause for action on both climate change and disasters because it is so deeply flawed (有瑕疵的)"However, Soren Anderasen, a social scientist at Dalberg Global Development Partners who supervised the writing of the report, defended it, saying that it was clear that the numbers were rough estimates. He said the report was aimed at world leaders, who will meet in Copenhagen in December to negotiate a new international climate treaty.In a press release describing the report, Mr. Annan stressed the need for the negotiations to focus on increasing the flow of money from rich to poor regions to help reduce their vulnerability to climate hazards, while still curbing the emissions of the heat-trapping gases. More than 90% of the human and economic losses from climate change are occurring in poor countries, according to the report.62. What is the finding of the Global Humanitarian Forum?A) Global temperatures affect the rate of economic development.B) Rates of death from illness have risen due to global warming.C) Malnutrition has caused serious health problems in poor countries.D) Economic trends have to do with population and natural disasters.63. What do we learn about the Forum's report from the passage?A) It was challenged by some climate and risk experts.B) It aroused a lot of interest in the scientific circles.C) It was warmly received by environmentalists.D) It caused a big stir in developing countries.64. What does Dr. Pielke say about the Forum's report?A) Its statistics look embarrassing.B) It is invalid in terms of methodology.C) It deserves our closest attention.D) Its conclusion is purposely exaggerated.65. What is Soren Andreasen's view of the report?A) Its conclusions are based on carefully collected data.B) It is vulnerable to criticism if the statistics are closely examined.C) It will give rise to heated discussions at the Copenhagen conference.D) Its rough estimates are meant to draw the attention of world leaders.66. What does Kofi Annan say should be the focus of the Copenhagen conference?A) How rich and poor regions can share responsibility in curbing global warming.B) How human and economic losses from climate change can be reduced.C) How emissions of heat-trapping gases can be reduced on a global scale.D) How rich countries can better help poor regions reduce climate hazards.Part ⅤCloze (15 minutes)Directions:There are 20 blanks in the following passage. For each blank there are four choices marked A), B), C) and D) on the right side of the paper. You should choose the ONE that best fits into the passage. Then mark the corresponding letter on Answer Sheet 2 with a single line through the centreWhen it comes to eating amart for your heart, stop thinking about short-term fixes and simplify your life with a straightforward approach that will serve you well for years to come.Smart eating goes beyond analyzing every bite of food you lift 67 your mouth. "In the past we used to believe that 68 amounts of individual nutrients (营养物) were the 69 to good health," says Linda V an Horn, chair of the American Heart Association's Nutrition Committee. "But now we have a 70 understanding of healthy eating and the kinds of food necessary to 71 not only heart disease but disease 72 general," she adds.Scientists now 73 on the broader picture of the balance of food eaten 74 several days or a week 75 than on the number of milligrams (毫克) of this or that 76 at each meal. Fruits, vegetables and whole grains, for example, provide nutrients and plant-based compounds 77 for good health. "The more we learn, the more 78 we are by the wealth of essential substances they 79 ," V an Horn continues, "and how they 80 with each other to keep us healthy."Y ou'll automatically be 81 the right heart-healthy track if vegetables, fruits and whole grains make 82 three quarters of the food on your dinner plate. 83 in the restaurant one quarter with lean meat or chicken, fish or eggs.The foods you choose to eat as well as those you choose to 84 clearly contribute to your well-being. Without a 85 , each of the small decisions you make in this realm can make a big 86 on your health in the years to come.67. A) between B) through C) inside D) to68. A) serious B) splendid C) specific D) separate69. A) key B) point C) lead D) center70. A) strict B) different C) typical D) natural71. A) rescue B) prevent C) forbid D) offend72. A) in B) upon C) for D) by73. A) turn B) put C) focus D) carry74. A) over B) along C) with D) beyond75. A) other B) better C) rather D) sooner76. A) conveyed B) consumed C) entered D) exhausted77. A) vital B) initial C) valid D) radical78. A) disturbed B) depressed C) amazed D) amused79. A) retain B) contain C) attain D) maintain。
2011年Alevel数学试卷真题
IB11 06_0580_21/7RP © UCLES 2011
This document consists of 12 printed p1 A concert hall has 1540 seats.
Calculate the number of people in the hall when 55% of the seats are occupied.
(a) the perimeter,
For Examiner's
Use
(b) the area.
Answer(a)
cm [2]
Answer(b)
cm2 [1]
12 A train leaves Barcelona at 21 28 and takes 10 hours and 33 minutes to reach Paris. (a) Calculate the time the next day when the train arrives in Paris.
For Examiner's
Use
Answer(a)
(b) A field has an area of 64 400 m2 . Calculate the area of the field on the map in cm2 .
km [2]
Answer(b)
14 Solve the equation 2x2 + 3x – 6 = 0. Show all your working and give your answers correct to 2 decimal places.
At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 70.
九天国际教育GCSE真题June 2011 QP - Paper 1C Edexcel Chemistry IGCSE
Turn overP38731A©2011 Edexcel Limited.1/1/1/1/*P38731A0132*Instructions• Useblack ink or ball-point pen.•Fill in the boxes at the top of this page with your name, centre number and candidate number.• Answerall questions.• Answer the questions in the spaces provided – there may be more space than you need .• Show all the steps in any calculations and state the units.Information• The total mark for this paper is 120.• The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.Advice• Read each question carefully before you start to answer it.• Keep an eye on the time.• Write your answers neatly and in good English.• Try to answer every question.•Check your answers if you have time at the end.2*P38731A0232*3*P38731A0332*Turn over*P38731A0432*2(a) Substances can be classified as elements, compounds or mixtures.5*P38731A0532*Turn over(b) Substances can also be classified as solids, liquids or gases.*P38731A0632*3 The diagram shows ammonium chloride being heated in a test tube.mixture7*P38731A0732*Turn over4Four separate food dyes (*P38731A0832*(b) During the experiment the water rises up the paper. The experiment is stopped just9*P38731A0932*Turn over(c) Each food dye has an R*P38731A01032*5 Bromine is an element in Group 7 of the Periodic Table.(ii) The formula of lead(II) bromide is PbBr6Some iron(II) sulfate (FeSO(c) A compound with the formula (NH7 Rusting occurs when iron is exposed to air and water. During rusting, iron reacts withRecord the syringe readings at the start and at the end of the experiment in the table(b) The results of the other students are shown in the table.(c) Another group of students did experiments that gave several anomalous results.8A teacher explained the different types of formula used in organic chemistry, using(b) All the compounds in part (a) belong to the same homologous series and have the(c) All the compounds in part (a) are hydrocarbons. They can undergo complete(e) When methane reacts with bromine, one of the products is hydrogen bromide.9The diagram shows how aluminium is extracted in industry.(b) The product formed at electrode(c) The uses of aluminium depend on its structure and physical properties.10Several methods are used to prepare salts. The method chosen depends on whether the(c) A soluble salt is prepared from solutions of an acid and an alkali.(d) A second student also did the titration and recorded these results:(e) A student mixed together the acid and alkali to form sodium nitrate solution. She11Hydrogen is used as a fuel. The equation for its combustion is31*P38731A03132*(c) The water formed by burning hydrogen as a fuel is often slightly acidic because it is*P38731A03232*。
九天国际教育GCSE真题June 2011 (v3) QP - Paper 1 CIE Chemistry IGCSE
This document consists of 16 printed pages.IB11 06_0620_13/FP© UCLES 2011[Turn over*8339598569*UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary EducationCHEMISTRY 0620/13Paper 1 Multiple Choice May/June 201145 MinutesAdditional Materials: Multiple Choice Answer Sheet Soft clean eraserSoft pencil (type B or HB is recommended)READ THESE INSTRUCTIONS FIRSTWrite in soft pencil.Do not use staples, paper clips, highlighters, glue or correction fluid.Write your name, Centre number and candidate number on the Answer Sheet in the spaces provided unless this has been done for you.There areforty questions on this paper. Answer all questions. For each question there are four possibl e answers A , B , C and D .Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.Read the instructions on the Answer Sheet very carefully.Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet. A copy of the Periodic Table is printed on page 16. You may use a calculator.© UCLES 20110620/13/M/J/111 The diagrams show the arrangement of particles in three different physical states of substance X.state 1state 2state 3Which statement about the physical states of substance X is correct? A Particles in state 1 vibrate about fixed positions. B State 1 changes to state 2 by diffusion.C State 2 changes directly to state 3 by condensation.D The substance in stage 3 has a fixed volume.2 In the diagrams, circles of different sizes represent atoms of different elements. Which diagram represents hydrogen chloride gas?BACD3 The diagram shows part of the Periodic Table.ACBDWhich element is correctly matched with its electronic structure?electronicstructure A 2,8,1 B 2,4 C 2,8,2 D 2,84An aqueous solution is coloured.Which method of separation would show that the solution contains ions of different colours?A chromatographyB crystallisationC distillationD filtration5 The table gives the solubility of four substances in ethanol and in water.A mixture containing all four substances is added to ethanol, stirred and filtered.The solid residue is added to water, stirred and filtered.The filtrate is evaporated to dryness, leaving a white solid.Which is the white solid?solubility inethanol waterA insoluble insolubleB insoluble solubleC soluble insolubleD soluble soluble6Which two elements react together to form an ionic compound?structureelement electronicW 2,4X 2,8Y 2,8,1Z 2,8,7A W and XB X and YC Y and ZD Z and W© UCLES 2011 0620/13/M/J/11 [Turn over7Electricity is passed through concentrated aqueous sodium chloride, as shown.What is the test for the gas formed at the positive electrode?A bleaches damp litmus paperB ‘pops’ with a lighted splintC relights a glowing splintD turns damp red litmus paper blue8Electricity from a power station passes through overhead cables to a substation and then to a school where it is used to electrolyse concentrated hydrochloric acid using inert electrodes.Which substances are used for the overhead cables and for the electrodes?overheadcables electrodesA aluminium copperB aluminium platinumC copper platinumD platinum aluminium9The nucleon number and proton number of the lithium atom are shown by the symbol Li73.What is the correct symbol for the lithium ion in lithium chloride?A 62Li− B 63Li+ C 73Li+ D 73Li−© UCLES 2011 0620/13/M/J/1110Three processes are listed.burning methane in airradioactive decay of 235Ureacting hydrogen with oxygen.Which statements about these processes are correct?1 Hydrogen and methane are being used as fuels.2 All the processes involve oxidation.3 All the processes are used to produce energy.A 1 and 2 onlyB 1 and 3 onlyC 2 and 3 only D1, 2 and 311 Which statement about the electrolysis of molten lead(II) bromide is correct?A A colourless gas is seen at the cathode.B A grey metal is seen at the anode.C A red/brown gas is seen at the anode.D A red/brown metal is seen at the cathode.12What is the relative molecular mass (M r) of HNO3?A 5B 31C 32D 6313The equation for the effect of heat on hydrated sodium carbonate is as shown.Na2CO3.10H2O(s) Na2CO3(s) + 10H2O(g)Statements made by four students about the reaction are given.P Anhydrous sodium carbonate is formed.Q Steam is formed.R There is a colour change from blue to white.S The reaction is reversible.Which students’ statements are correct?A P, Q and R onlyB P, Q and S onlyC Q, R and S onlyD P, Q, R and S© UCLES 2011 0620/13/M/J/11 [Turn over© UCLES 2011 0620/13/M/J/11For which two reactions would the apparatus be suitable?reaction 1 AgNO 3(aq) + HC l (aq) → AgC l (s) + HNO 3(aq) reaction 2 2H 2O 2(aq) → 2H 2O(l) + O 2(g)reaction 3 MgO(s) + 2HC l (aq) → MgC l 2(aq) + H 2O(l)reaction 4ZnCO 3(s) + 2HC l (aq) → ZnC l2(aq) + CO 2(g) + H 2O(l)A 1 and 2B 1 and 3C 2 and 4D 3 and 415 A student investigates the rate of reaction between magnesium and excess sulfuric acid.The volume of hydrogen given off in the reaction is measured over time.The graph shows the results of two experiments, R and S.volume of hydrogen given offtimeWhich change in conditions would cause the difference between R and S?A A catalyst is added in S.B The acid is more concentrated in R than in S.C The magnesium is less finely powdered in R than in S.D The temperature in R is lower than in S.© UCLES 2011 0620/13/M/J/11[Turn over16 Butane, ethanol and hydrogen are fuels.Which substances produce both carbon dioxide and water when used as a fuel?butane ethanolhydrogen A B C D17 X is a monatomic gas.gas XWhich statement about X is correct? A X burns in air. B X is coloured. C X is unreactive.D X will displace iodine from potassium iodide.18 The equation shows the reaction between a halogen and aqueous bromide ions.X 2 +2Br –(aq) → 2X –(aq) + Br 2…1… …2……3…Which words correctly complete gaps 1, 2 and 3?1 2 3 A chlorine brown colourless B chlorine colourless brown C iodine brown colourless D iodine colourless brown19Carbon dioxide is an acidic oxide that reacts with aqueous calcium hydroxide.Which type of reaction takes place?A decompositionB fermentationC neutralisationD oxidation20 A solution contains barium ions and silver ions.What could the anion be?A chloride onlyB nitrate onlyC sulfate onlyD chloride or nitrate or sulfate21 A mixture containing two anions was tested and the results are shown below.test result dilute nitric acid added effervescence of a gas whichturned limewater milkydilute nitric acid added, followedyellow precipitate formedby aqueous silver nitrateWhich anions were present?A carbonate and chlorideB carbonate and iodideC sulfate and chlorideD sulfate and iodide22 Which is not a typical property of an acid?A They react with alkalis producing water.B They react with all metals producing hydrogen.C They react with carbonates producing carbon dioxide.D They turn litmus paper red.© UCLES 2011 0620/13/M/J/11© UCLES 2011 0620/13/M/J/11[Turn over23 The diagram shows a section of the Periodic Table.WVXZYI II III IV V VI VII 0Which elements will conduct electricity at room temperature? A V, W and XB V, Y and WC W, X and ZD Y and Z24 Water from a reservoir flows to the water works where purification processes 1 takes placefollowed by process 2.What are purification processes 1 and 2?purification process 1purification process 2A chlorination filtrationB filtration chlorinationC fractional distillationfiltrationDfiltration fractional distillation25 The properties of a metal are important in deciding its use.Which row lists a property that is not correct for the use given?use of the metalmetal property neededA aluminium in aircraft wings low densityB aluminium in food containers resists corrosionC mild steel in car bodies high densityD stainless steel in cutlerydoes not rust© UCLES 2011 0620/13/M/J/1126 Brass is an alloy of copper and zinc.Which statement is correct?A Brass can be represented by a chemical formula.B Brass is formed by a chemical reaction between copper and zinc.C The alloy will dissolve completely in dilute hydrochloric acid.D The zinc in the alloy will dissolve in dilute hydrochloric acid.27 Which statement is correct for the element of proton number 19?A It is a gas that dissolves in water.B It is a hard metal that is not very reactive with water.C It is a non-metal that burns quickly in air.D It is a soft metal that is highly reactive with water.28 Which row describes the conditions used to make steel from the iron produced by a blastfurnace?calcium oxide(lime)oxygen heat A B C D29The table shows the results of adding three metals, P, Q and R, to dilute hydrochloric acid and to water.metal dilute hydrochloric acid waterP hydrogen produced hydrogen producedQ no reaction no reactionR hydrogen produced no reactionWhat is the order of reactivity of the metals?mostreactive least reactiveAP R QBP Q RC R QPD RP Q30Which substance is a metal?electrical conductivity(solid) electrical conductivity(molten)A high highB high lowC low highD low low31Greenhouse gases may contribute to climate change.Two of these gases are emitted into the atmosphere as a result of processes within animals.Gas ……1…… is produced by process ……3…… .Gas ……2…… is produced by process ……4…… .Which words correctly complete gaps 1, 2, 3 and 4?1 2 3 4A CO C2H6 digestion respirationB CO C2H6 respiration digestionC CO2 CH4 digestion respirationD CO2 CH4 respiration digestion32The diagram shows the composition by volume of air.XWhat is X?A argonB carbon dioxideC nitrogenD oxygen33The table gives the composition of the atmosphere of four newly discovered planets.planet composition of atmosphereW argon, carbon dioxide and oxygenX argon, nitrogen and oxygenY argon, carbon dioxide and methaneZ methane, nitrogen and oxygen On which planets is the greenhouse effect likely to occur?A W onlyB W, X and ZC W and Y onlyD W, Y and Z34Which two substances, when reacted together, would form a salt that contains two of the essential elements provided by fertilisers?A potassium hydroxide and nitric acidB potassium hydroxide and sulfuric acidC sodium hydroxide and nitric acidD sodium hydroxide and sulfuric acid35Statement 1: Alloying iron with other materials to form stainless steel prevents iron from rusting by excluding oxygen.Statement 2: Painting, oiling and electroplating are all methods of preventing iron from rusting.Which is correct?A Both statements are correct and statement 2 explains statement 1.B Both statements are correct but statement 2 does not explain statement 1.C Statement 1 is correct but statement 2 is incorrect.D Statement 2 is correct but statement 1 is incorrect.36What is the main constituent of natural gas?A carbon dioxideB ethaneC hydrogenD methane37 What is not essential for the formation of ethanol by fermentation?A lightB sugarC yeastD water38Which industrial process is shown in the diagram?crudeoil vapourA crackingB fermentationC fractional distillationD polymerisation39The diagram shows the structures of three compounds.OCH HOHCH HCHHHHOC CHHCHWhy do these three compounds belong to the same homologous series?A They all contain carbon, hydrogen and oxygen.B They all contain the same functional group.C They are all carbon based molecules.D They are all flammable liquids.40Compounds containing five carbon atoms in a molecule may have names beginning with ‘pent…’.What is the name of the compound shown?key= carbon= oxygen= hydrogenA pentaneB pentanoic acidC pentanolD pentene16Per mission to r epr oduce items wher e thir d-par ty owned mater ial pr otected by copyr ight is included has been sought and clear ed wher e possible. Ever y 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 Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.G r o u p140C eC e r i u m 58141P rP r a s e o d y m i u m 59144N d N e o d ym i u m 60P mP r o m e t h i u m61150S mS a m a r i u m62152E uE u r o p i u m63157G dG a d o l i n i u m64159T bT e r b i u m65162D yD y s p r o s i u m66165H oH o l m i u m67167E rE r b i u m68169T mT h u l i u m69173Y bY t t e r b i u m70175L uL u t e t i u m71232T hT h o r i u m 90P aP r o t a c t i n i u m 91238UU r a n i u m92N pN e p t u n i u m93P uP l u t o n i u m94A mA m e r i c i u m95C mC u r i u m96B kB e r k e l i u m97C fC a l i f o r n i u m98E sE i n s t e i n i u m99F mF e r m i u m100M dM e n d e l e v i u m101N oN o b e l i u m102L rL a w r e n c i u m1031HH y d r o g e n17L iL i t h i u m 323N aS o d i u m 1124M gM a g n e s i u m1240C aC a l c i u m 2045S c S c a n d i u m 2148T i T i t a n i u m2251V V a n a d i u m 2352C r C h r o m i u m 2455M n M a n g a n e s e 2556F e I r o n 2659C o C o b a l t 2759N i N i c k e l 2864C u C o p p e r 2965Z n Z i n c3070G aG a l l i u m3127A l A l u m i n i u m1311B B o r o n 512C C a r b o n614NN i t r o g e n716OO x y g e n819FF l u o r i n e928S iS i l i c o n1431PP h o s p h o r u s1532SS u l f u r1635.5C lC h l o r i n e1740A rA r g o n1820N eN e o n104H eH e l i u m273G eG e r m a n i u m3275A sA r s e n i c3379S eS e l e n i u m3480B rB r o m i n e3584K rK r y p t o n3639KP o t a s s i u m 1988S rS t r o n t i u m 3889Y Y t t r i u m 3991Z r Z i r c o n i u m4093N b N i o b i u m 4196M o M o l y b d e n u m 42T c T e c h n e t i u m 43101R u R u t h e n i u m 44103R h R h o d i u m 45106P d P a l l a d i u m 46108A g S i l v e r47112C dC a d m i u m48115I nI n d i u m49119S nT i n50122S bA n t i m o n y51128T eT e l l u r i u m52127II o d i n e53131X eX e n o n54137B aB a r i u m 56139L a L a n t h a n u m 57*178H fH a f n i u m72181T a T a n t a l u m 73184W T u n g s t e n 74186R e R h e n i u m 75190O s O s m i u m 76192I rI r i d i u m 77195P t P l a t i n u m78197A uG o l d79201H gM e r c u r y80204T lT h a l l i u m81207P bL e a d82209B iB i s m u t h83P oP o l o n i u m84A tA s t a t i n e85R nR a d o n86F rF r a n c i u m 87227A cA c t i n i u m899B eB e r y l l i u m4II I I I II V V V I V I I 085R bR u b i d i u m 37133C sC a e s i u m 55226R a R a d i u m 88T h e v o l u m e o f o n e m o l e o f a n y g a s i s 24d m 3a t r o o m t e m p e r a t u r e a n d p r e s s u r e (r .t .p .).a Xb a = r e l a t i v e a t o m ic m a s sX = a t o m i c s y m b o lb = p r o t o n (a t o m ic ) n u m b e rK e y *58-71 L a n t h a n o i d s e r i e s 90-103 A c t i n o i d s e r i e s D A T A S H E E T T h e P e r i o d i c T a b l e o f t h e E l e m e n t sPMT。
Igcse-数学-历年真题-2
4400/4HEdexcel IGCSEMathematicsPaper 4HHigher TierFriday 11 June 2010 – AfternoonTime: 2 hoursMaterials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature.Check that you have the correct question paper.Answer ALL the questions. Write your answers in the spaces provided in this question paper.You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets.Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).There are 22 questions in this question paper. The total mark for this paperis 100.You may use a calculator.Advice to CandidatesWrite your answers neatly and in good English.This publication may be reproduced only in accordance with Edexcel Limited copyright policy.©2010 Edexcel Limited.Printer’s Log. No. N36905AIGCSE MATHEMATICS 4400 FORMULA SHEET – HIGHER TIERAnswer ALL TWENTY TWO questions.Write your answers in the spaces provided.You must write down all stages in your working.1. Solve 6 y – 9 = 3 y + 7y = ................................(Total 3 marks) 2. The diagram shows two towns, A and B, on a map.(a) By measurement, find the bearing of B from A.....................................︒(2)C is another town.The bearing of C from A is 050︒.(b) Find the bearing of A from C.....................................︒(2) (Total 4 marks)3. A spinner can land on red or blue or yellow.The spinner is biased.The probability that it will land on red is 0.5The probability that it will land on blue is 0.2Imad spins the spinner once.(a) Work out the probability that it will land on yellow......................................(2)Janet spins the spinner 30 times.(b)Work out an estimate for the number of times the spinner will land on blue......................................(2)(Total 4 marks)4. Rosetta drives 85 kilometres in 1 hour 15 minutes.(a) Work out her average speed in kilometres per hour...................................... km/h(2)Rosetta drives a total distance of 136 kilometres.(b) Work out 85 as a percentage of 136................................. %(2)Sometimes Rosetta travels by train to save money.The cost of her journey by car is £12The cost of her journey by train is 15% less than the cost of her journey by car.(c)Work out the cost of Rose tta’s journey by train.£ ...................................(3)(Total 7 marks)5.Calculate the value of x.Give your answer correct to 3 significant figures.x = ................................(Total 3 marks)6. A = {2, 3, 4, 5}B = {4, 5, 6, 7}(a)(i) List the members of A ⋂B......................................(ii) How many members are in A ⋃B?.....................................(2)ℰ = {3, 4, 5, 6, 7}P = {3, 4, 5}Two other sets, Q and R, each contain exactly three members.P ⋂Q = {3, 4}P ⋂R = {3, 4}Set Q is not the same as set R.(b)(i) Write down the members of a possible set Q......................................(ii) Write down the members of a possible set R......................................(2)(Total 4 marks)7. Rectangular tiles have width (x + 1) cm and height (5x – 2) cm.Some of these tiles are used to form a large rectangle.The large rectangle is 7 tiles wide and 3 tiles high.The perimeter of the large rectangle is 68 cm.(a) Write down an equation in x...............................................................................................................(3)(b) Solve this equation to find the value of x.x = ................................(3)(Total 6 marks)8. Show that 121 141 = 1519. The depth of water in a reservoir increases from 14 m to 15.75 m.Work out the percentage increase.................................. %(Total 3 marks) 10. Quadrilaterals ABCD and PQRS are similar.AB corresponds to PQ.BC corresponds to QR.CD corresponds to RS.Find the value of(a) xx = ...............................(2)(b) yy = ...............................(1)(Total 3 marks)11. Simplify fully6x + 43x.....................................(Total 3 marks)12.(a)Find the equation of the line L......................................(3)(b) Find the three inequalites that define the unshaded region shown in the diagram below................................................................................................................(3)(Total 6 marks)13. (a) Solve x 2– 8x + 12 = 0.....................................(3)(b) Solve the simultaneous equationsy = 2x4x – 5y = 9x = ................................y = ................................(3)(Total 6 marks)14.The area of the triangle is 6.75 cm2.The angle x° is acute.Find the value of x.Give your answer correct to 1 decimal place.x = ................................(Total 3 marks)15. The unfinished histogram shows information about the heights, h metres, ofsome trees.(a) Calculate an estimate for the number of trees with heights in theinterval 4.5 < h ≤ 10.....................................(3)(b) There are 75 trees with heights in the interval 10 < h ≤ 13Use this information to complete the histogram.(2)(Total 5 marks)16. A bag contains 3 white discs and 1 black disc.John takes at random 2 discs from the bag without replacement.(a) Complete the probability tree diagram.First disc Second disc(3)(b)Find the probability that both discs are white......................................(2)All the discs are now replaced in the bag.Pradeep takes at random 3 discs from the bag without replacement.(c)Find the probability that the disc left in the bag is white......................................(3)(Total 8 marks)17. The diagram s hows a sector of a circle, radius 45 cm, with angle 84°.Calculate the area of the sector.Give your answer correct to 3 significant figures.............................. cm2(Total 3 marks) 18.Calculate the length of AC.Give your answer correct to 3 significant figures................................ cm(Total 3 marks)19. A cone has slant height 4 cm and base radius r cm.The total surface area of the cone is 433π cm 2.Calculate the value of r .r = ................................(Total 4 marks)20. f(x) = (x – 1)2(a) Find f(8).....................................(1)The domain of f is all values of x where x ≥ 7(a)Find the range of f......................................(2)xg(x) =x1(c) Solve the equation g(x) = 1.2.....................................(2)(d) (i) Express the inverse function g –1 in the form g –1(x) = .......g –1(x) = ...................................(ii) Hence write down gg(x) in terms of x.gg(x) = ....................................(6)(Total 11 marks)21.In the diagram = a and = c.(a) Find CA in terms of a and c......................................(1)The point B is such that AB=1c.2(b) Give the mathematical name for the quadrilateral OABC......................................(1)The point P is such that = a + k c, where k ≥ 0(c) State the two conditions relating to a + k c that must be true for OAPCto be a rhombus.(2)(Total 4 marks)22. (a) Work out 5.2 × 102+ 2.3 × 104Give your answer in standard form......................................(2)a × 102 +b × 104 =c × 104(b) Express c in terms of a and b.c = ................................(2)(Total 4 marks)TOTAL FOR PAPER = 100 MARKS END。
剑桥IGCSE课程数学科目试卷四
UCLES 2007
Answer(c)
0607/04/SP/10
minutes [3] [Turn over
4 2 f(x) = 5 .
1− x (a) Find f(–9).
For Examiner's
Use
(b) Solve f(x) = 2.
Answer(a)
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, highlighters, glue or correction fluid. You may use a pencil for any diagrams or graphs.
For Examiner's
Use
Answer(a)
km/h [2]
(b) One day, the train departed at 08 50 but, due to delays, the average speed was reduced by 10%. Calculate (i) the new arrival time,
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education
CAMBRIDGE INTERNATIONAL MATHEMATICS Paper 4 (Extended) SPECIMEN PAPER
初2011级第六学期第一学月考试英语试题11.3.15
初2011级第六学期第一学月考试英语试题(11.3.15)初2011级第六学期第一学月考试英语试题第一部分听力部分（每小题1分，共20分）第一节、１．What do people do when they meet for the first time in the girl’s country?２．What is the weather like today? ３．How did they go to work today?４．What are they eating now? ５．What is the girl’s favorite animal?第二节、６．When should the man get to Bill’s birthday party?A．At 6:05. B．At 6:00. C．At 5:55. ７．What animals does the man like better?A．Pandas. B．Tigers. C．Koalas. ８．What is the woman looking for?A．A pay phone. B．A bank. C．A hospital.９．What do both the man and the women like to do?A．Read newspapers. B．Listen to soft music. C．Watch TV.10．What did the boy forget to do?A．Turn off the light. B．Lock the door.C．Turn off the water.第三节、听第一段对话，回答11至12题。
11．Who made Mr Jin angry this morning?A．Simon and Tom. B．Jack and Simon. C．Tom and Jack.12．What would the boys never do again?A．Eat in class. B．Stay out late to play football. C．Talk with each other in class.听第二段对话，回答13至15题。
英国高中数学 C1 - 2011(试卷)
Paper Reference(s)6663/01Edexcel GCECore Mathematics C1Advanced SubsidiaryMonday 10 January 2011 MorningTime: 1 hour 30 minutesMaterials required for examination Items included with question papersMathematical Formulae (Pink)NilCalculators may NOT be used in this examination.Instructions to CandidatesWrite the name of the examining body (Edexcel), your centre number, candidate number, the unit title (Core Mathematics C1), the paper reference (6663), your surname, initials and signature.Information for CandidatesA booklet ‘Mathematical Formulae and Statistical Tables’ is provided.Full marks may be obtained for answers to ALL questions.The marks for the parts of questions are shown in round brackets, e.g. (2).There are 11 questions in this question paper. The total mark for this paper is 75.Advice to CandidatesYou must ensure that your answers to parts of questions are clearly labelled.You must show sufficient working to make your methods clear to the Examiner.Answers without working may not gain full credit.H35402A This publication may only be reproduced in accordance with Edexcel Limited copyright policy.©2011 Edexcel Limited.H35402A21. (a ) Find the value of 4116-.(2)(b ) Simplify 4412⎪⎪⎭⎫ ⎝⎛-xx . (2)2.Find⎜⎠⎛+-x x x x d )4312(3125,giving each term in its simplest form.(5)3.Simplify13325-√√-,giving your answer in the form p + q √3, where p and q are rational numbers.(4)4.A sequence 1a , 2a , 3a , ... is defined by1a = 2,1+n a = n a 3– cwhere c is a constant.(a ) Find an expression for 2a in terms of c .(1)Given that ∑=31i i a = 0,(b ) find the value of c .(4)H35402A3 Turn over5.Figure 1Figure 1 shows a sketch of the curve with equation y = f(x ) wheref(x ) = 2-x x, x ≠ 2.The curve passes through the origin and has two asymptotes, with equations y = 1 and x = 2, as shown in Figure 1.(a ) In the space below, sketch the curve with equation y = f(x − 1) and state the equations of theasymptotes of this curve.(3) (b ) Find the coordinates of the points where the curve with equation y = f(x − 1) crosses thecoordinate axes.(4)6.An arithmetic sequence has first term a and common difference d . The sum of the first 10 terms of the sequence is 162.(a ) Show that 10a + 45d = 162.(2) Given also that the sixth term of the sequence is 17,(b ) write down a second equation in a and d ,(1)(c ) find the value of a and the value of d .(4)H35402A47. The curve with equation y = f(x ) passes through the point (−1, 0).Given thatf ′(x ) = 12x 2 − 8x + 1,find f(x ).(5)8.The equation x 2 + (k − 3)x + (3 − 2k ) = 0, where k is a constant, has two distinct real roots.(a ) Show that k satisfiesk 2 + 2k − 3 > 0.(3)(b ) Find the set of possible values of k .(4)9. The line 1L has equation 2y − 3x − k = 0, where k is a constant.Given that the point A (1, 4) lies on 1L , find(a ) the value of k ,(1)(b ) the gradient of 1L .(2)The line 2L passes through A and is perpendicular to 1L .(c ) Find an equation of 2L giving your answer in the form ax + by + c = 0, where a , b and c areintegers.(4)The line 2L crosses the x -axis at the point B .(d ) Find the coordinates of B .(2) (e ) Find the exact length of AB .(2)H35402A510. (a ) Sketch the graphs of(i) y = x (x + 2)(3 − x ),(ii) y = –x2.showing clearly the coordinates of all the points where the curves cross the coordinate axes.(6)(b ) Using your sketch state, giving a reason, the number of real solutions to the equationx (x + 2)(3 – x ) + x2= 0.(2)11. The curve C has equationy = 321x – 239x + x 8+ 30, x > 0.(a ) Find xyd d .(4)(b ) Show that the point P (4, –8) lies on C .(2)(c ) Find an equation of the normal to C at the point P , giving your answer in the form ax + by + c= 0 , where a, b and c are integers.(6)TOTAL FOR PAPER: 75 MARKSEND。
2011年6月份全国四级考试真题word绝情版
2011年6月份全国四级考试真题word绝情版Part I Writing (30 minutes) Directions: For this part, you are allowed 30 minutes to write a short essay on the topic of Online Shopping. You should write at least 120 words followingthe outline given below:1．现在网上购物已成为一种时尚2．网上购物有很多好处，但也有不少问题3．我的建议Online Shopping注意：此部分试题在答题卡1上。
Part II Reading Comprehension (Skimming and Scanning) (15 minutes)Directions: In this part, you will have 15 minutes to go over the passage quickly and answer the questions on Answer Sheet 1. For questions 1-7, choose thebest answer from the four choices marked A), B), C) and D). For questions8-10, complete the sentences with the information given in the passage.British Cuisine: the Best of Old and NewBritish cuisine (烹饪) has come of age in recent years as chefs (厨师) combine the best of old and new.Why does British food have a reputation for being so bad? Because it is bad! Those are not the most encouraging words to hear just before eating lunch at one of Hong Kong's smartest British restaurants, Alfie's by KEE, but head chef Neil Tomes has more to say."The past 15 years or so have been a noticeable period of improvement for food in England," the English chef says, citing the trend in British cuisine for better ingredients, preparation and cooking methods, and more appealing presentation. Chefs such as Delia Smith, Nigel Slater, Jamie Oliver and Gordon Ramsay made the public realise that cooking - and eating - didn't have to be a boring thing. And now, most of the British public is familiar even with the extremes of Heston BlumenthaPs molecular gastronomy, a form of cooking that employs scientific methods to create the perfect dish."It's no longer the case that the common man in England is embarrassed to show he knows about food," Tomes says.There was plenty of room for improvement. The problems with the nation's cuisine can be traced back to the Second World War. Before the War, much of Britain's food was imported and when German U-boats began attacking ships bringing food to the country, Britain went on rations (配给)."As rationing came to an end in the 1950s, technology picked up and was used to mass-produce food," Tomes says. "And by then people were just happy to have a decent quantity of food in their kitchens."They weren't looking for cured meats, organic produce or beautiful presentation; they were looking for whatever they could get their hands on, and this prioritisation of quantity over quality prevailed for decades, meaning a generation was brought up with food that couldn't compete with neighbouring France, Italy, Belgium or Spain.Before star chefs such as Oliver began making cooking fashionable, it was hard to find a restaurant in London that was open after 9pm. But in recent years the capital's culinary (烹饪的) scene has developed to the point that it is now confident of its ability to please the tastes of any international visitor.With the opening of Alfie's in April, and others such as The Pawn, two years ago, modern British food has made its way to Hong Kong. "With British food, I think that Hong Kong restaurants are keeping up," says David Tamlyn, the Welsh executive chef at The Pawn in Wan Chai. "Hong Kong diners are extremely responsive to new ideas or presentations, which is good news for new dishes."Chefs agree that diners in Hong Kong are embracing the modern British trend. Some restaurants are modifying the recipes (菜谱) of British dishes to breathe new life into the classics, while others are using better quality ingredients but remaining true to British traditions and tastes.Tamlyn is in the second camp. "We select our food very particularly. We use US beef, New Zealand lamb and for our custards (牛奶蛋糊)we use Bird's Custard Powder," Tamlyn says. "Some restaurants go for custard made fresh with eggs, sugar and cream, but British custard is different, and we stay true to that."Matthew Hill, senior manager at the two-year-old SoHo restaurant Yorkshire Pudding, also uses better ingredients as a means of improving dishes. "There are a lot of existing perceptions about British food and so we can't alter these too much. We're a traditional British restaurant so there are some staples (主菜) that will remain essentially unchanged."These traditional dishes include fish and chips, steak and kidney pie and large pieces of roasted meats. At Alfie's, the newest of the British restaurants in town and注意：此部分试题请在答题卡1上作答。
2011年6月份全国四级考试真题word绝情版
2011年6月份全国四级考试真题word绝情版Part I Writing (30 minutes) Directions: For this part, you are allowed 30 minutes to write a short essay on the topic of Online Shopping. You should write at least 120 words followingthe outline given below:1．现在网上购物已成为一种时尚2．网上购物有很多好处，但也有不少问题3．我的建议Online Shopping注意：此部分试题在答题卡1上。
Part II Reading Comprehension (Skimming and Scanning) (15 minutes)Directions: In this part, you will have 15 minutes to go over the passage quickly and answer the questions on Answer Sheet 1. For questions 1-7, choose thebest answer from the four choices marked A), B), C) and D). For questions8-10, complete the sentences with the information given in the passage.British Cuisine: the Best of Old and NewBritish cuisine (烹饪) has come of age in recent years as chefs (厨师) combine the best of old and new.Why does British food have a reputation for being so bad? Because it is bad! Those are not the most encouraging words to hear just before eating lunch at one of Hong Kong's smartest British restaurants, Alfie's by KEE, but head chef Neil Tomes has more to say."The past 15 years or so have been a noticeable period of improvement for food in England," the English chef says, citing the trend in British cuisine for better ingredients, preparation and cooking methods, and more appealing presentation. Chefs such as Delia Smith, Nigel Slater, Jamie Oliver and Gordon Ramsay made the public realise that cooking - and eating - didn't have to be a boring thing. And now, most of the British public is familiar even with the extremes of Heston BlumenthaPs molecular gastronomy, a form of cooking that employs scientific methods to create the perfect dish."It's no longer the case that the common man in England is embarrassed to show he knows about food," Tomes says.perhaps the most gentlemen's club-like in design, Neil Tomes explains his passion for provenance (原产地)."Britain has started to become really proud of the food it's producing. It has excellent organic farms, beautifully crafted cheeses, high-quality meats."However, the British don't have a history of exporting their foodstuffs, which makes it difficult for restaurants in Hong Kong to source authentic ingredients."We can get a lot of our ingredients once a week from the UK," Tamlyn explains. "But there is also pressure to buy local and save on food miles, which means we take our vegetables from the local markets, and there are a lot that work well with British staples."The Phoenix, in Mid-Levels, offers the widest interpretation of "British cuisine", while still trying to maintain its soul. The gastro-pub has existed in various locations in Hong Kong since 2002. Singaporean head chef Tommy Teh Kum Chai offers daily specials on a blackboard, rather than sticking to a menu. This enables him to reinterpret British cuisine depending on what is available in the local markets."We use a lot of ingredients that people wouldn't perhaps associate as British, but are presented in a British way. Bell peppers stuffed with couscous, alongside ratatouille, is a very popular dish."Although the ingredients may not strike diners as being traditional, they can be found in dishes across Britain.Even the traditional chefs are aware of the need to adapt to local tastes and customs, while maintaining the Britishness of their cuisine.At Yorkshire Pudding, Hill says that his staff asks diners whether they would like to share their meals. Small dishes, shared meals and "mixing it up" is not something commonly done in Britain, but Yorkshire Pudding will bring full dishes to the table and offer individual plates for each diner. "That way, people still get the presentation of the dishes as they were designed, but can carve them up however they like," Hill says.This practice is also popular at The Pawn, although largely for rotisseries (烤肉馆), Tamlyn says. "Some tables will arrive on a Sunday, order a whole chicken and a shoulder of lamb or a baby pig, and just stay for hours enjoying everything we bring out for them."Some British traditions are too sacred (神圣的)to mess with, however, Tomes says. "I'd never change a full English breakfast."注意：此部分试题请在答题卡1上作答。
Igcse数学历年真题
4400/4HEdexcel IGCSEMathematicsPaper 4HHigher TierFriday 11 June 2010 – AfternoonTime: 2 hoursMaterials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature.Check that you have the correct question paper.Answer ALL the questions. Write your answers in the spaces provided in this question paper. You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit.If you need more space to complete your answer to any question, use additional answer sheets. Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: e.g. (2). There are 22 questions in this question paper. The total mark for this paper is 100.You may use a calculator.Advice to CandidatesWrite your answers neatly and in good English.This publication may be reproduced only in accordance withEdexcel Limited copyright policy.©2010 Edexcel Limited.Printer’s Log. No. N36905AIGCSE MATHEMATICS 4400 FORMULA SHEET – HIGHER TIERAnswer ALL TWENTY TWO questions.Write your answers in the spaces provided.You must write down all stages in your working.1. Solve 6 y – 9 = 3 y + 7y = ................................(Total 3 marks) 2. The diagram shows two towns, A and B, on a map.(a) By measurement, find the bearing of B from A.....................................︒(2)C is another town.The bearing of C from A is 050︒.(b) Find the bearing of A from C.....................................︒(2)(Total 4 marks)3. A spinner can land on red or blue or yellow.The spinner is biased.The probability that it will land on red is 0.5The probability that it will land on blue is 0.2Imad spins the spinner once.(a) Work out the probability that it will land on yellow......................................(2)Janet spins the spinner 30 times.(b) Work out an estimate for the number of times the spinner will land on blue......................................(2)(Total 4 marks)4. Rosetta drives 85 kilometres in 1 hour 15 minutes.(a) Work out her average speed in kilometres per hour...................................... km/h(2)Rosetta drives a total distance of 136 kilometres.(b) Work out 85 as a percentage of 136................................. %(2)Sometimes Rosetta travels by train to save money.The cost of her journey by car is £12The cost of her journey by train is 15% less than the cost of her journey by car.(c)Work out the cost of Rose tta’s journey by train.£ ...................................(3)(Total 7 marks)5.Calculate the value of x.Give your answer correct to 3 significant figures.x = ................................(Total 3 marks)6. A = {2, 3, 4, 5}B = {4, 5, 6, 7}(a)(i) List the members of A ⋂B......................................(ii) How many members are in A ⋃B?.....................................(2)ℰ = {3, 4, 5, 6, 7}P = {3, 4, 5}Two other sets, Q and R, each contain exactly three members.P ⋂Q = {3, 4}P ⋂R = {3, 4}Set Q is not the same as set R.(b)(i) Write down the members of a possible set Q......................................(ii) Write down the members of a possible set R......................................(2)(Total 4 marks)7. Rectangular tiles have width (x + 1) cm and height (5x – 2) cm.Some of these tiles are used to form a large rectangle.The large rectangle is 7 tiles wide and 3 tiles high.The perimeter of the large rectangle is 68 cm.(a) Write down an equation in x...............................................................................................................(3)(b) Solve this equation to find the value of x.x = ................................(3)(Total 6 marks)8. Show that 121 141 = 1519.The depth of water in a reservoir increases from 14 m to 15.75 m. Work out the percentage increase.................................. %(Total 3 marks)10. Quadrilaterals ABCD and PQRS are similar.AB corresponds to PQ.BC corresponds to QR.CD corresponds to RS.Find the value of(a) xx = ...............................(2)(b) yy = ...............................(1)(Total 3 marks)11. Simplify fully6x + 43x.....................................(Total 3 marks)12.(a)Find the equation of the line L......................................(3)(b) Find the three inequalites that define the unshaded region shown in the diagram below................................................................................................................(3)(Total 6 marks)13. (a) Solve x 2– 8x + 12 = 0.....................................(3)(b) Solve the simultaneous equationsy = 2x4x – 5y = 9x = ................................y = ................................(3)(Total 6 marks)14.The area of the triangle is 6.75 cm2.The angle x°is acute.Find the value of x.Give your answer correct to 1 decimal place.x = ................................(Total 3 marks)15. The unfinished histogram shows information about the heights, h metres, of some trees.(a) Calculate an estimate for the number of trees with heights in the interval 4.5 < h ≤ 10.....................................(3)(b) There are 75 trees with heights in the interval 10 < h ≤ 13Use this information to complete the histogram.(2)(Total 5 marks)16. A bag contains 3 white discs and 1 black disc.John takes at random 2 discs from the bag without replacement.(a) Complete the probability tree diagram.First disc Second disc(3)(b)Find the probability that both discs are white......................................(2)All the discs are now replaced in the bag.Pradeep takes at random 3 discs from the bag without replacement.(c)Find the probability that the disc left in the bag is white......................................(3)(Total 8 marks)17. The diagram shows a sector of a circle, radius 45 cm, with angle 84°.Calculate the area of the sector.Give your answer correct to 3 significant figures.............................. cm2(Total 3 marks) 18.Calculate the length of AC.Give your answer correct to 3 significant figures................................ cm(Total 3 marks)19. A cone has slant height 4 cm and base radius r cm.The total surface area of the cone is 433π cm 2.Calculate the value of r .r = ................................(Total 4 marks)20. f(x) = (x – 1)2(a) Find f(8).....................................(1)The domain of f is all values of x where x ≥ 7(a)Find the range of f......................................(2)xg(x) =x1(c) Solve the equation g(x) = 1.2.....................................(2)(d) (i) Express the inverse function g –1 in the form g –1(x) = .......g –1(x) = ...................................(ii) Hence write down gg(x) in terms of x.gg(x) = ....................................(6)(Total 11 marks)21.In the diagram OA= a and OC= c.(a) Find CA in terms of a and c......................................(1)The point B is such that AB=1c.2(b) Give the mathematical name for the quadrilateral OABC......................................(1)The point P is such that OP= a + k c, where k ≥ 0(c) State the two conditions relating to a + k c that must be true for OAPC to be a rhombus.(2)(Total 4 marks)22. (a) Work out 5.2 × 102 + 2.3 × 104Give your answer in standard form......................................(2)a × 102 +b × 104 =c × 104(b) Express c in terms of a and b.c = ................................(2)(Total 4 marks)TOTAL FOR PAPER = 100 MARKSEND。
IGCSE数学样题May-June 2010_2
1.5 2.5
For Examiner's
Use
8
[3]
© UCLES 2010
0580/12/M/J/10
9
16 Daniel invested $2500 for 2 years at 5.5% per year compound interest. Calculate how much interest he received.
Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES.
At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 56.
12 (a) 1 = 3x .
27
Write down the value of x.
(b) Simplify (i) p7 × p-2 ,
(ii) m3 ÷ m7.
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This document consists of 19 printed pages and 1 blank page.IB11 06_0580_43/4RP© UCLES 2011[Turn over*8044643715*UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary EducationMATHEMATICS 0580/43Paper 4 (Extended) May/June 20112 hours 30 minutesCandidates answer on the Question Paper.Additional Materials: Electronic calculatorGeometrical instrumentsMathematical tables (optional)Tracing paper (optional)READ THESE INSTRUCTIONS FIRSTWrite your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES.Answer all questions.If working is needed for any question it must be shown below that question. Electronic calculators should be used.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π use either your calculator value or 3.142.At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 130.© UCLES 20110580/43/M/J/11For Examiner's Use1 Lucy works in a clothes shop.(a) In one week she earned $277.20.(i) She spent 81of this on food.Calculate how much she spent on food. Answer(a)(i) $ [1](ii) She paid 15% of the $277.20 in taxes. Calculate how much she paid in taxes. Answer(a)(ii) $ [2](iii) The $277.20 was 5% more than Lucy earned in the previous week. Calculate how much Lucy earned in the previous week. Answer(a)(iii) $ [3](b) The shop sells clothes for men, women and children.(i) In one day Lucy sold clothes with a total value of $2200 in the ratio men : women : children = 2 : 5 : 4. Calculate the value of the women’s clothes she sold. Answer(b)(i) $ [2](ii) The $2200 was 7344of the total value of the clothes sold in the shop on this day. Calculate the total value of the clothes sold in the shop on this day. Answer(b)(ii) $ [2]© UCLES 2011 0580/43/M/J/11[Turn overUsex(a) (i) Draw the reflection of shape X in the x -axis. Label the image Y . [2](ii) Draw the rotation of shape Y , 90° clockwise about (0, 0). Label the image Z . [2](iii) Describe fully the single transformation that maps shape Z onto shape X .Answer(a)(iii)[2](b) (i) Draw the enlargement of shape X , centre (0, 0), scale factor21. [2](ii) Find the matrix which represents an enlargement, centre (0, 0), scale factor 21.Answer(b)(ii)[2](c) (i) Draw the shear of shape X with the x -axis invariant and shear factor –1.[2](ii) Find the matrix which represents a shear with the x -axis invariant and shear factor –1.Answer(c)(ii)[2]© UCLES 20110580/43/M/J/11Use(x + 5) cm2x cmx cmNOT TO SCALEThe diagram shows a square of side (x + 5) cm and a rectangle which measures 2x cm by x cm. The area of the square is 1 cm 2 more than the area of the rectangle.(a) Show that x 2 – 10x – 24 = 0 . Answer(a) [3]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(b) Find the value of x . Answer(b) x = [3](c) Calculate the acute angle between the diagonals of the rectangle. Answer(c) [3]© UCLES 2011 0580/43/M/J/11For Examiner's Use4NOT TO SCALEThe circle, centre O , passes through the points A , B and C . In the triangle ABC , AB = 8 cm, BC = 9 cm and CA = 6 cm. (a) Calculate angle BAC and show that it rounds to 78.6°, correct to 1 decimal place. Answer(a) [4](b) M is the midpoint of BC .(i) Find angle BOM . Answer(b)(i) Angle BOM = [1]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(ii) Calculate the radius of the circle and show that it rounds to 4.59 cm, correct to 3 significantfigures.Answer(b)(ii) [3](c) Calculate the area of the triangle ABC as a percentage of the area of the circle. Answer(c) % [4]© UCLES 2011 0580/43/M/J/11ForExaminer's Use5 (a) Complete the table of values for the function f(x ), where f(x ) = x 2 + 21x , x ≠ 0 .xO 3 O 2.5 O 2 O 1.5 O 1 O 0.50.5 1 1.5 2 2.5 3 f(x ) 6.41 2.69 4.25 4.252.69 6.41[3](b) On the grid, draw the graph of y = f(x ) for O 3 Y x Y O 0.5 and 0.5 Y x Y 3 .[5]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(c) (i) Write down the equation of the line of symmetry of the graph.Answer(c)(i)[1](ii) Draw the tangent to the graph of y = f(x ) where x = O 1.5. Use the tangent to estimate the gradient of the graph of y = f(x ) where x = O 1.5. Answer(c)(ii) [3](iii) Use your graph to solve the equation x 2 + 21x= 3.Answer(c)(iii) x = or x = or x = or x = [2](iv) Draw a suitable line on the grid and use your graphs to solve the equation x 2 + 21x = 2x .Answer(c)(iv) x =or x =[3]© UCLES 2011 0580/43/M/J/11For Examiner's Use6CumulativefrequencyMass (kilograms)mThe masses of 200 parcels are recorded. The results are shown in the cumulative frequency diagram above.(a) Find(i) the median, Answer(a)(i) kg [1](ii) the lower quartile, Answer(a)(ii) kg [1](iii) the inter-quartile range, Answer(a)(iii) kg [1](iv) the number of parcels with a mass greater than 3.5 kg. Answer(a)(iv) [2]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(b) (i) Use the information from the cumulative frequency diagram to complete the groupedfrequency table.Mass (m ) kg0 I m Y 44 I m Y 66 I m Y 77 I m Y 10Frequency 36 50[2](ii) Use the grouped frequency table to calculate an estimate of the mean. Answer(b)(ii) kg [4](iii) Complete the frequency density table and use it to complete the histogram.Mass (m ) kg 0 I m Y 4 4 I m Y 6 6 I m Y 7 7 I m Y 10Frequency density916.7FrequencydensityMass (kilograms)m[4]© UCLES 20110580/43/M/J/11ForExaminer's Use7 Katrina puts some plants in her garden.The probability that a plant will produce a flower is107. If there is a flower, it can only be red, yellow or orange.When there is a flower, the probability it is red is 32 and the probability it is yellow is 41.(a) Draw a tree diagram to show all this information. Label the diagram and write the probabilities on each branch. Answer(a) [5](b) A plant is chosen at random. Find the probability that it will not produce a yellow flower. Answer(b) [3](c) If Katrina puts 120 plants in her garden, how many orange flowers would she expect? Answer(c) [2]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use8A(a) Draw accurately the locus of points, inside the quadrilateral ABCD , which are 6 cm from thepoint D . [1](b) Using a straight edge and compasses only, construct(i) the perpendicular bisector of AB , [2](ii) the locus of points, inside the quadrilateral, which are equidistant from AB and from BC . [2](c) The point Q is equidistant from A and from B and equidistant from AB and from BC .(i) Label the point Q on the diagram. [1](ii) Measure the distance of Q from the line AB . Answer(c)(ii) cm [1](d) On the diagram, shade the region inside the quadrilateral which is• less than 6 cm from Dand• nearer to A than to Band• nearer to AB than to BC . [1]© UCLES 2011 0580/43/M/J/11For Examiner's Use9 f(x ) = 3x + 1 g(x ) = (x + 2)2(a) Find the values of(i) gf(2), Answer(a)(i)[2](ii) ff(0.5). Answer(a)(ii)[2](b) Find f –1(x ), the inverse of f(x ). Answer(b)[2](c) Find fg(x ). Give your answer in its simplest form. Answer(c)[2]© UCLES 2011 0580/43/M/J/11[Turn overFor Examiner's Use(d) Solve the equation x 2 + f(x ) = 0. Show all your working and give your answers correct to 2 decimal places. Answer(d) x = or x =[4]UseBABCD is a parallelogram.DC, M is the midpoint of BC and N is the midpoint of LM.pq.(i)Find the following in terms ofp and q, in their simplest form.(a)Answer(a)[1](b)Answer(a)[2](c)Answer(a)[2] (ii) N lies on the line AC.Answer(a)(ii) [1]© UCLES 2011 0580/43/M/J/11© UCLES 2011 0580/43/M/J/11[Turn overUseEH J2x°75°(x + 15)°NOT TO SCALEEFG is a triangle. HJ is parallel to FG . Angle FEG = 75°. Angle EFG = 2x ° and angle FGE = (x + 15)°.(i) Find the value of x . Answer(b)(i) x = [2](ii) Find angle HJG . Answer(b)(ii) Angle HJG = [1]© UCLES 2011 0580/43/M/J/11For Examiner's Use11 (a) (i) The first three positive integers 1, 2 and 3 have a sum of 6. Write down the sum of the first 4 positive integers. Answer(a)(i) [1](ii) The formula for the sum of the first n integers is21)(+n n . Show the formula is correct when n = 3. Answer(a)(ii) [1](iii) Find the sum of the first 120 positive integers. Answer(a)(iii) [1](iv) Find the sum of the integers121 + 122 + 123 + 124 + …………………………… + 199 + 200.Answer(a)(iv)[2](v) Find the sum of the even numbers 2 + 4 + 6 + …………………………+ 800.Answer(a)(v)[2]© UCLES 20110580/43/M/J/11For Examiner's Use(b) (i) Complete the following statements about the sums of cubes and the sums of integers.13 = 1 1 = 113 + 23 = 9 1 + 2 = 3 13 + 23 + 33 =1 +2 +3 =13 + 23 + 33 + 43 =1 +2 +3 +4 =[2](ii) The sum of the first 14 integers is 105. Find the sum of the first 14 cubes. Answer(b)(ii) [1](iii) Use the formula in part(a)(ii) to write down a formula for the sum of the first n cubes. Answer(b)(iii) [1](iv) Find the sum of the first 60 cubes. Answer(b)(iv) [1](v) Find n when the sum of the first n cubes is 278 784. Answer(b)(v) n = [2]BLANK PAGEPer mission to r epr oduce items wher e thir d-par ty owned mater ial pr otected by copyr ight is included has been sought and clear ed wher e possible. Ever y 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 Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.© UCLES 2011 0580/43/M/J/11。