Igcse-数学-历年真题

1、4400/4HEdexcel IGCSEMathematicsPaper 4HHigher TierFriday 11 June 2010- AfternoonTime: 2 hoursMaterials required for exam in ati onItems in cluded with questi on papersRuler graduated in cen timetres andNilmillimetres, protractor, compasses, pen, HB pencil, eraser, calculator.Tracing paper may be use

2、d.In struct ions to Can didatesIn the boxes above, write your centre nu mber, can didate nu mber, your sur name, in itials and sig nature.Check that you have the correct questi on paper.An swer ALL the questio ns. Write your an swers in the spaces provided in this questi on paper.You must NOT write

3、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 an swer sheets.In formatio n for Can didatesThe marks for in dividual questi ons and the parts of questi ons are show n in round brackets:

4、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 Can didatesWrite your answers neatly and in good English.N36905AIGCSE MATHEMATICS 4400FORMULA SHEET HIGHER TIERPiliagora5bof cone = | TtrhC im ed surface area of cone 利 JXf

5、alume of sphere = yn?PP oppadj = hyp x cos 0 hyp x sin （i adj x Un WIn any triangle ABCorhypBx lengthhypCosine mle: ；r= 十 P - 2加？ cts JArea of tnangle = -y ab sin CCircumference of circle = 2nrAtm of ciiclt - kiArea of a trapezium = *（乜 + t）hi*lume of cylinder = jrrhCun ed surface area of cylindtr =

6、 2 ftrhThe Quadratic EquationThe solutions of ax1+ bx + c = Q. 承 hfi亡 a 0. are given by-b- Jlr - 4acx-2aAn swer ALL TWENTY TWO questio ns.Write your an swers in the spaces provided.You must write dow n all stages in your work ing.1. Solve 6 y - 9 = 3 y + 7y =(Total 3 marks)2. The diagram shows two t

7、ow ns,A and B, on a map.(a) By measurement, find the bearing of B from A.C is ano ther tow n.The bearing of C from A is 050(b) Find the bearing of A from C.(Total 4 marks)3. A spinner can land on red or blue or yellow.The spinner is biased.The probability that it will la nd on red is 0.5The probabil

8、ity that it will la nd on blue is 0.2Imad spins the spinner on ce.(a) Work out the probability that it will la nd on yellow.Janet spins the spinner 30 times.(b)Work out an estimate for the nu mber of times the spinner will la nd on blue.(Total 4 marks)(3)4. Rosetta drives 85 kilometres in 1 hour 15

9、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

10、the cost of her journey by car.(c) Work out the cost of Rosettas journey by train. (Total 7 marks)5.(Total # marks)Diagram MOT avcurately drawnCalculate the value of x.Give your answer correct to 3 significant figures.6. A = 2, 3, 4, 5B = 4, 5, 6, 7(a) (i)List the members of A B(ii)How many members

11、are in A B? = 3, 4, 5, 6, 7P = 3, 4, 5Two other sets, Q and R each contain exactly three members.PQ = 3, 4PR = 3, 4Set Q is not the same as set R.(b) (i)Write down the members of a possible set Q(ii)Write dow n the members of a possible set R7.Recta ngular tiles have width ( x + 1) cm and height (5

12、x - 2) cm.Diagram NOT accunitely drawnSome of these tiles are used to form a large recta ngle. The large recta ngle is 7 tiles wide and 3 tiles high.widthheightDiagram iiccuratdy dravnThe perimeter of the large recta ngle is 68 cm.(a) Write dow n an equati on in x.(b)Solve this equati on to find the

13、 value ofx.(Total 6 marks)8. Show that 1 -1 - = 1 -2459. The depth of water in a reservoir in creases from 14 m to 15.75 m. Work out the perce ntage in crease.%(Total 3 marks)10. QuadrilateralsABCDa nd PQRSare similar.(1)(Total 3 marks)AB corresp onds toPQBC corresp onds toQRCD corresp onds toRSFind

14、 the value of (a) xx =(b) yy =11. Simplify fully3x(Total 3 marks)12.(a) Find the equation of the lineL.un shaded regi on show n in the(b) Find the three in equalites that defi ne the diagram below.(Total 6 marks)213.(a) Solve x - 8x + 12 = 0(3)(b) Solve the simultaneous equationsy = 2x4 x - 5y = 9y

15、= (Total 6 marks)x = (3)14.Diagram NOT accuralely drawnxThe area of the tria ngle is 6.75 cmThe angle x is acute.Find the value of x.Give your an swer correct to 1 decimal place.(Total 3 marks)15. The unfinishedhistogram shows information about the heights, h metres, ofsome trees.(a) Calculate in te

16、rval 4.5 Frequency ckrbdtyAan estimateh 10一 20 treesfor the number of trees withheightsin the(b) There are 75 trees with heights in the in terval 10 h 7(a) Find the range of f.g(x)=(c)Solve the equatio n g( x) = 1.2(d)(i) Express the inv erse fun cti on gin the form g(x)=g -1(x)=(ii)Hence write dow n gg( x) in terms of x.gg(x)=(Total 11 marks)21.OA = a and OC = c.Diagnim NOT accuralelv draun drIn the diagram(a)Find CAin terms of a and c.(1)(1)OAPCThe point B is such that AB = 1 c.(b) Give the mathematical n ame for the quadrilateralOABCThe point P is such that OP = a + kc, where k 0(c) S