Excel / Education. GCSE Mathematics. Paper 2B (Calculator) Higher Tier. Time: 2 hours. Turn over

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1 Excel / Education GCSE Mathematics Paper 2B (Calculator) Higher Tier Time: 2 hours 2B 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 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 100. The marks for questions and parts of questions are shown in round brackets: e.g.. Calculators may be used. Advice to Candidates Show all your working.

2 1. Convert 2m 2 into cm 2 2. (a) Write the number 60 as a product of its prime factors.. cm 2 (b) Write the number 80 as a product of its prime factors. (c) Hence or otherwise find the highest common factor of 60 and The following diagram represents a garden with a square pond in the corner. 2 m Pond x 10 m x

3 (a) Write down an expression, in terms of x, for the shortest side of the garden. (b) Write down AND SIMPLIFY an expression, in terms of x, for the perimeter of the garden. The perimeter of the garden is 30m (c) Work out the value of x 4. (a) Given that x is an integer and -1 x < 4. Write down all the values that x could take. (b) Solve the inequality 5x 3-1..

4 5. Solve these simultaneous equations; 3x + y = 13 2x + 3y = 11 x =. y =. (4) 6. Steven and Mike are trying to find out what kind of tv programmes people of their age enjoy the most. (a) Design a questionnaire they could use for this purpose. (b) They ask everyone in their Maths class to fill in the questionnaire. State one reason why this might give inaccurate results (1)

5 7. The graph of y = x 2 6x + 8 is to be plotted. (a) Complete the following table for y = x 2 6x + 8 x y (b) On the grid below, plot the graph of y = x 2 6x + 8 (4) y x (c) Factorise x 2 6x + 8.

6 (d) Using your answer to part (c) or otherwise, solve the equation; x 2 6x + 8 = Solve the following equations; (a) 5x 9 = 46 (b) 9x 2 = 5x (c) 3x! 7 2 =!8. (d) 3x! 7 2 = 4! x..

7 9. Give that a, b, c and d are lengths. Tick the appropriate boxes to indicate which expressions could represent volumes. a 2 b + cd 2 4πd 2 a b 3 (c + 5) πb 3 + c 3 (a + b) d 2(a 2 + b 2 ) 2 d 10. y C D A x B

8 Describe fully the transformation that takes shape A to; (a) Shape B.... (b) Shape C.... (c) Shape D.... (d) Describe the single transformation that takes shape B to shape D A school has 1700 students in five year groups as follows; Year group Students Year 7 50 Year Year Year Year A stratified sample of 68 students is to be taken. Calculate how many students from each year group should be in the sample.... (4)

9 12. The diagram shows the graph of y = cos x. 0 x 360 o (a) On the grid below sketch the graph of y = 3 cos x. 3 y x

10 3 (b) On the grid below sketch the graph of y = - cos x. y x (c) (i) On the grid below sketch the graph of y = cos 2x. y x

11 (ii) Use your graph in (c)(i) to solve the equation; cos 2x = 0 0 x 360 o 13. The probability that James completes his homework on time is p The probability that Shuma completes her homework on time is p ¼ Their probabilities are assumed to be independent.... Given that the probability they both complete their homework is 1 / 3, show that p = (3 d p) (6) 14. Find the area of this sector of a circle. 20 o 8cm..

12 15. The diagram shows a regular hexagon ABCDEF. OA = a and OB = b. F A a E O b B D C (a) Find, in terms of a and b; (i) CF (ii) EC.. (b) Show that AB is parallel to FC..

13 16. (a) Write x 2-4x + 1 in the form (x + p) 2 + q where p and q are integers to be found. (b).. Hence or otherwise, solve x 2-4x + 1 = 0. Leave your answer in surd form... End of Questions (Total Marks: 100)

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