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Examiners use only Team Leaders use only Paper Reference(s) 4400/3H London Examinations IGCSE Mathematics Paper 3H Higher Tier Monday 10 May 2004 Morning Time: 2 hours Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Centre No. Candidate No. Paper Reference 4 4 0 0 3 H Surname Initial(s) Signature Turn over Instructions to Candidates In the boxes above, write your centre number and candidate number, your surname, initial(s) and signature. The paper reference is shown at the top of this page. Check that you have the correct question paper. Answer ALL the questions in the spaces provided in this question paper. Show all the steps in any calculations. Information for Candidates There are 20 pages in this question paper. All blank pages are indicated. The total mark for this paper is 100. The marks for parts of questions are shown in round brackets: e.g. (2). You may use a calculator. Advice to Candidates Write your answers neatly and in good English. Printers Log. No. N20710RA This publication may only be reproduced in accordance with London Qualifications Limited copyright policy. 2004 London Qualifications Limited. W850/R4400/57570 4/4/4/1/3/1/3/1/3/1000 *N20710RA* Page Leave Numbers Blank 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Total N20710RA 2 IGCSE MATHEMATICS 4400 FORMULASHEET HIGHER TIER Pythagoras Theorem adj = hyp cos opp = hyp sin opp = adj tan or opp tan adj = adj cos hyp = opp sin hyp = Circumference of circle = 2r Area of circle = r 2 Area of a trapezium= (a+b)h 1 2 b a opp adj hyp b a h length section cross a 2 +b 2 =c 2 Volume of prism = area of cross section length Volume of cylinder = r 2 h Curved surface area of cylinder = 2rh h r Volume of cone = r 2 h Curved surface area of cone = rl 1 3 r l r h Volume of sphere = r 3 Surface area of sphere = 4r 2 4 3 r In any triangle ABC Sine rule Cosine rule a 2 =b 2 +c 2 2bccosA Area of triangle = absinC 1 2 sin sin sin abc ABC = C a b c BA The Quadratic Equation The solutions of ax 2 +bx+c=0 where a0, are given by 2 4 2 b b ac x a = c AnswerALLTWENTY 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. . million (Total 3 marks) 2. (a) Expand 3(2t+1) . (1) (b) Expand and simplify (x+5)(x3) . (2) (c) Factorise 10p15q . (1) (d) Factorise n 2 +4n . (1) (Total 5 marks) Leave blank N20710RA 3 Turn over Q2 Q1 Leave blank N20710RA 4 3. A circle has a radius of 4.7cm. (a) Work out the area of the circle. Give your answer correct to 3 significant figures. . cm 2 (2) The diagram shows a shape. (b) Work out the area of the shape. . cm 2 (4) (Total 6 marks) Q3 Diagram NOT accurately drawn 7cm 6cm 3cm 11cm 2cm Diagram NOT accurately drawn 4.7cm Leave blank N20710RA 5 Turn over Q4 4. The diagram shows a pointer which spins about the centre of a fixed disc. When the pointer is spun, it stops on one of the numbers 1, 2, 3 or 4. The probability that it will stop on one of the numbers 1 to 3 is given in the table. Magda is going to spin the pointer once. (a) Work out the probability that the pointer will stop on 4. . (2) (b) Work out the probability that the pointer will stop on 1 or 3. . (2) Omar is going to spin the pointer 75 times. (c) Work out an estimate for the number of times the pointer will stop on 2. . (2) (Total 6 marks) Number 1 2 3 4 Probability 0.35 0.16 0.27 Leave blank N20710RA 6 Q6 5. (a) Express 200 as the product of its prime factors. . (2) (b) Work out the Lowest Common Multiple of 75 and 200. . (2) (Total 4 marks) 6. Two points, A and B, are plotted on a centimetre grid. A has coordinates (2, 1) and B has coordinates (8, 5). (a) Work out the coordinates of the midpoint of the line joining A and B. (. , .) (2) (b) Use PythagorasTheorem to work out the length of AB. Give your answer correct to 3 significant figures. . cm (4) (Total 6 marks) Q5 7. A = 1, 2, 3, 4 B = 1, 3, 5 (a) List the members of the set (i) A B, . (ii) A B. . (2) (b) Explain clearly the meaning of 3A. . (1) (Total 3 marks) 8. (i) Solve the inequality 3x+71 . (ii) On the number line, represent the solution to part (i). (Total 4 marks) Leave blank N20710RA 7 Turn over Q8 Q7 4 3 2 1 0 1 2 3 4 9. The grouped frequency table gives information about the distance each of 150 people travel to work. (a) Work out what percentage of the 150 people travel more than 20km to work. . % (2) (b) Work out an estimate for the mean distance travelled to work by the people. . km (4) (c) Complete the cumulative frequency table. (1) Leave blank N20710RA 8 Distance travelled (dkm) Frequency 0d5 34 5d10 48 10d15 26 15d20 18 20d25 16 25d30 8 Distance travelled (dkm) Cumulative frequency 0d5 0d10 0d15 0d20 0d25 0d30 (d) On the grid, draw a cumulative frequency graph for your table. (2) (e) Use your graph to find an estimate for the median of the distance travelled to work by the people. Show your method clearly. . km (2) (Total 11 marks) Leave blank N20710RA 9 Turn over 160 140 120 100 80 60 40 20 Cumulative frequency 10 20 30 O Distance travelled (dkm) Q9 10. The diagram shows a shape. AB is an arc of a circle, centre O. Angle AOB=90. OA=OB=6cm. Calculate the perimeter of the shape. Give your answer correct to 3 significant figures. . cm (Total 4 marks) 11. The distance between the Earth and the Sun is 150000000km. (a) Write the number 150000000 in standard form. . (1) The distance between Neptune and the Sun is 30 times greater than the distance between the Earth and the Sun. (b) Calculate the distance between Neptune and the Sun. Give your answer in standard form. . km (2) (Total 3 marks) Leave blank N20710RA 10 Q11 Q10 6cm A OB6cm Diagram NOT accurately drawn 12. (a) Find the gradient of the line with equation 3x4y=15 . (3) (b) Work out the coordinates of the point of intersection of the line with equation 3x4y=15 and the line with equation 5x+6y=6 (. , .) (4) (Total 7 marks) 13. A body is moving in a straight line which passes through a fixed point O. The displacement, s metres, of the body from O at time t seconds is given by s=t 3 +4t 2 5t (a) Find an expression for the velocity, vm/s, at time t seconds. v = . (2) (b) Find the acceleration after 2 seconds. . m/s 2 (2) (Total 4 marks) Leave blank N20710RA 11 Turn over Q13 Q12 14. The unfinished table and histogram show information from a survey of women about the number of calories in the food they eat in one day. (a) (i) Use the information in the table to complete the histogram. (ii) Use the information in the histogram to complete the table. (3) (b) Find an estimate for the upper quartile of the number of calories. You must make your method clear. . (2) (Total 5 marks) Leave blank N20710RA 12 Q14 Number of calories (n) Frequency 0n1000 90 1000n2000 2000n2500 140 2500n4000 Frequency density 1000 2000 30000 Number of calories (n) 4000 15. The length of a side of a square is 6.81cm, correct to 3 significant figures. (a) Work out the lower bound for the perimeter of the square. . cm (2) (b) Give the perimeter of the square to an appropriate degree of accuracy. You must show working to explain how you obtained your answer. . cm (2) (Total 4 marks) 16. Express the algebraic fraction as simply as possible. . (Total 3 marks) 2 2 2320 16 xx x Leave blank N20710RA 13 Turn over Q16 Q15 17. An electrician has wires of the same length made from the same material. The electrical resistance, Rohms, of a wire is inversely proportional to the square of its radius, rmm. When r=2, R=0.9 (a) (i) Express R in terms of r. R = . (ii) On the axes, sketch the graph of R against r. (4) One of the electricians wires has a radius of 3 mm. (b) Calculate the electrical resistance of this wire. . ohms (1) (Total 5 marks) Leave blank N20710RA 14 Q17 R O r 18. A, B, C and D are four points on the circumference of a circle. The chords AC and BD intersect at E. AE=3.6cm, CE=2.8cm, DE=2.4cm and AD=4.9cm. (a) Calculate the length of BE. . cm (3) (b) Calculate the size of angle AED. Give your answer correct to 3 significant figures. . (3) (Total 6 marks) Leave blank N20710RA 15 Turn over Q18 Diagram NOT accurately drawn A 2.4cm3.6cm E C D 4.9cm B 2.8cm 19. f:x6 2x1 g:x6 , x0 (a) Find the value of (i) f(3), . (ii) fg(6). . (2) (b) Express the inverse function f 1 in the form f 1 :x6. . (2) (c) (i) Express the composite function gf in the form gf:x6. . (ii) Which value of x must be excluded from the domain of gf? x = . (2) (Total 6 marks) 3 x Leave blank N20710RA 16 Q19 20. Q, R, S and T are points on the circumference of a circle. PU is a tangent to the circle at T. PQR is a straight line. Angle PQT=108. Angle STR=44. Work out the size of angle STU. You must give a reason for each step in your working. . (Total 5 marks) TOTALFOR PAPER: 100 MARKS END Leave blank N20710RA 17 Q20 Diagram NOT accurately drawn P S 44 R 108 Q T U BLANK PAGE N20710RA 18
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