Paper Reference. Paper Reference(s) 5518/18 Edexcel GCSE Mathematics B 1388 Paper 18 (Non-Calculator) Higher Tier

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1 Centre No. Candidate No. Paper Reference Surname Signature Initial(s) Paper Reference(s) 5518/18 Edexcel GCSE Mathematics B 1388 Paper 18 (Non-Calculator) Higher Tier Wednesday 4 June 2003 Afternoon Time: 1 hour 15 minutes Examiner s use only Team Leader s use only Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Items included with question papers Formulae sheet Instructions to Candidates In the boxes above, write your centre number, candidate number, your surname, initial(s), and your signature. Check that you have the correct question paper. Answer ALL the questions in the spaces provided in this question paper. Supplementary answer sheets may be used. Information for Candidates The total mark for this paper is 62. The marks for individual questions and parts of questions are shown in round brackets: e.g.. Calculators must not be used. This paper has 15 questions. There are no pages. Advice to Candidates Show all stages in any calculations. Work steadily through the paper. Do not spend too long on one question. If you cannot answer a question, leave it and attempt the next one. Return at the end to those you have left out. Printer s Log. No. M15867A W850/R1388/ /4/4/5/4/4/4 *M15867A* Turn over This publication may only be reproduced in accordance with Edexcel copyright policy. Edexcel Foundation is a registered charity Edexcel

2 Answer ALL FIFTEEN questions. Write your answers in the spaces provided. You must write down all the stages in your working. You must NOT use a calculator. 1. Using the information that = write down the value of (i) (ii) (iii) (a) Solve 22 4 = p p =... (b) Solve 7r + 2 = 5(r 4) r =... M15867A 2

3 3. (a) 2 < x 1 x is an integer. Write down all the possible values of x. (b) 2 < x 1 y > 2 y < x +1 x and y are integers. On the grid, mark with a cross ( ), each of the six points which satisfies all these 3 inequalities. y O x Page Total M15867A 3 Turn over

4 4. This table shows some expressions. The letters x, y and z represent lengths. (a) Place a tick in the appropriate column for each expression to show whether the expression can be used to represent a length, an area, a volume or none of these. Expression x + y + z xyz xy + yz + xz Length Area Volume None of these The volume of a cube is 8 m 3. (b) Change 8 m 3 to cm 3....cm 3 5. Simplify fully (i) (p 3 ) 3... (ii) 3 q 2q 3 q M15867A 4

5 6. A 12.5 cm X Diagram NOT accurately drawn. 6 cm P 15 cm B Y AB is parallel to XY. The lines AY and BX intersect at P. AB = 6 cm. XP = 12.5 cm. XY = 15 cm. Work out the length of BP....cm Page Total M15867A 5 Turn over

6 7. A 2 cm A 6 cm 2 cm Diagrams NOT accurately drawn 6cm 6 cm B 4 cm B 4 cm 18 cm 18 cm The diagram represents a large cone of height 6cm and base diameter 18cm. The large cone is made by placing a small cone A of height 2cm and base diameter 6cm on top of a frustum B. Calculate the volume of the frustum B. Give your answer in terms of π.... (4) 8. (a) Work out (b) Work out M15867A 6

7 9. (a) Explain what is meant by (i) a random sample,... (ii) a stratified sample.... The table shows some information about the members of a golf club. Age range Male Female Total Under to to Over Total number of members 454 The club secretary carries out a survey of the members. He chooses a sample, stratified both by age range and by gender, of 90 of the 454 members. (b) Work out an estimate of the number of male members, in the age range 31 to 50, he would have to sample. Page Total M15867A 7 Turn over

8 10. Work out (5 + 3)(5 3) 22 Give your answer in its simplest form. 11. A field is in the shape of a rectangle. The length of the field is 340 m, to the nearest metre. The width of the field is 117 m, to the nearest metre. Calculate the upper bound for the perimeter of the field....m M15867A 8

9 12. P Diagram NOT accurately drawn Y X R Q Triangle PQR is isosceles with PQ = PR. X is a point on PQ. Y is a point on PR. PX = PY. Prove that triangle PQY is congruent to triangle PRX. Page Total M15867A 9 Turn over

10 13. (a) Find the equation of the straight line which passes through the point (0, 3) and is perpendicular to the straight line with equation y = 2x. The graphs of y = 2x 2 and y = mx 2 intersect at the points A and B. The point B has coordinates (2, 8). y y = mx 2 y = 2x 2 B (2, 8) O A x (b) Find the coordinates of the point A. (...,...) (4) M15867A 10

11 14. A bag contains 3 black beads, 5 red beads and 2 green beads. Gianna takes a bead at random from the bag, records its colour and replaces it. She does this two more times. Work out the probability that, of the three beads Gianna takes, exactly two are the same colour.... (5) Page Total M15867A 11 Turn over

12 15. This is a sketch of the curve with equation y =f(x). It passes through the origin O. y y =f(x) O x The only vertex of the curve is at A (2, 4) (a) Write down the coordinates of the vertex of the curve with equation (i) y =f(x 3), (ii) y =f(x) 5, (iii) y = f(x), (iv) y = f(2x). The curve with equation y = x 2 has been translated to give the curve y =f(x). (b) Find f(x) in terms of x. A (2, 4) (...,...) (...,...) (...,...) (...,...) (4) f(x) =... (4) END TOTAL FOR PAPER: 62 MARKS Page Total M15867A 12

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