Igcse 數(shù)學(xué) 歷年真習(xí)題 2

1、4400/4HEdexcel IGCSEMathematics Paper 4HHigher TierFriday 11 June 2010 AfternoonTime: 2 hoursMaterials required for examination Items included with question papersRuler graduated in centimetres andNilmillimetres, protractor, compasses,pen, HB pencil, eraser, calculator.Tracing paper may be used.Inst

2、ructions 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

3、. 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 questi

4、ons 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.N36905AIGCSE MATHEMATICS 4400FORMULA SHEET HIGHER TIERAnswer ALL TWENTY TWO questions.Write your answers in the spaces provided.You must write d

5、own 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

6、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 estima

7、te 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 t

8、ravels 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 Rosettas journey by train.£ .(3)(Total 7 marks)5.Calculate the value of x.Give your answer correct to 3 significant f

9、igures.x = .(Total 3 marks)6. A = 2, 3, 4, 5B = 4, 5, 6, 7(a) (i) List the members of A Ç B.(ii) How many members are in A È B.(2) = 3, 4, 5, 6, 7P = 3, 4, 5Two other sets, Q and R, each contain exactly three members.P Ç Q = 3, 4P Ç R = 3, 4Set Q is not the same as set R.(b) (i)

10、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 th

11、e 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 that1 ¸ 1 = 19. 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

12、 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 fully + .(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 d

13、iagram below.(3)(Total 6 marks)13. (a) Solve x 2 8x + 12 = 0.(3)(b) Solve the simultaneous equationsy = 2x 4x 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. T

14、he 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)(Tot

15、al 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

16、 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(

17、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 cm2.Calculate the value of r.r = . (Total 4 marks)20. f(x) = (x 1)2(a) Find f(8).(1)The domain o

18、f f is all values of x where x 7(a) Find the range of f.(2)g(x) = (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 in terms of a and c.(1)The point B is such that = c.(b) Give the mathematical name for the quadrilateral OABC.(1)The point P is such that = a + kc, where k 0(c) State the two conditions rel