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1 GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS C (GRADUATED ASSESSMENT) HIGHER TERMINAL PAPER SECTION A MONDAY 2 JUNE 2008 H B252A Afternoon Time: 1 hour *CUP/T52253* Candidates answer on the question paper Additional materials (enclosed): None Additional materials (required): Geometrical instruments Tracing paper (optional) INSTRUCTIONS TO CANDIDATES Write your name in capital letters, your Centre Number and Candidate Number in the boxes above. Use blue or black ink. Pencil may be used for graphs and diagrams only. Read each question carefully and make sure that you know what you have to do before starting your answer. Show your working. Marks may be given for a correct method even if the answer is incorrect. Answer all the questions. Do not write in the bar codes. Write your answer to each question in the space provided. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this Section is 50. WARNING You are not allowed to use a calculator in Section A of this paper. FOR EXAMINER S USE SECTION A SECTION B TOTAL This document consists of 15 printed pages and 1 blank page. SPA (KN) T52253/2 [100/1142/0] OCR is an exempt Charity [Turn over

2 2 Formulae Sheet Volume of prism = (area of cross-section) length crosssection length In any triangle ABC a b Sine rule = sin A sin B c = sin C b C a Cosine rule Area of triangle = a 2 = b 2 + c 2 2bc cos A 1 2 ab sin C A c B Volume of sphere = 4 3 π r 3 Surface area of sphere = 4 π r 2 r Volume of cone = 1 3 π r 2 h Curved surface area of cone = π r l l h r The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a 0, are given by x = b ± (b 2 4ac) 2a PLEASE DO NOT WRITE ON THIS PAGE

3 1 (a) Katie and Petra share their business profits. One year, Katie s share is 8000 and Petra s share is Write the ratio 8000 : as simply as possible. 3 (a)... :... [2] (b) Adam and Elias split the profits of their business in the ratio 3 : 2. One year their profits are How much does Adam receive? (b)... [2] [Turn over

4 2 The lengths shown on this shape are in centimetres Not to scale 2 (a) Calculate the area of this shape. Give the units of your answer. (a)... [3] (b) The shape is the cross-section of this prism. The length of the prism is 8 cm. P (i) How many faces does this prism have? (b)(i)... [1]

5 (ii) Draw accurately the plan view of the prism, viewed from P. 5 [2] [Turn over

6 3 Work out, giving your answers as fractions. (a) (b) (a)... [2] (b)... [2]

7 4 ABC is a triangle. DE is parallel to BA. 7 A E Not to scale x B 52 D 30 C Find angle x, giving your reasons. x =... because [3] [Turn over

8 5 The positions of two towns, Aries (A) and Benton (B), are shown on this scale drawing. Jane lives nearer to Benton than to Aries. She lives less than 6 km from Aries. Scale: 1 cm to 1 km 8 A B Using ruler and compasses only, construct and shade the region in which Jane lives. Show all your construction lines. [4]

9 6 (a) Solve. 9 (i) 2(3x 1) = 4x + 5 (a)(i)... [3] (ii) 2x + 3 > 13 (ii)... [2] (b) Factorise and solve. x 2 + 5x + 4 = 0 (b)... [3] [Turn over

10 7 Annabel and Beattie are comparing the durations (lengths of time) of their phone calls. These cumulative frequency graphs summarise the durations of their calls one month Cumulative frequency Annabel Beattie Duration (minutes) (a) Use the graph to find (i) the median duration of Annabel s phone calls, (ii) the interquartile range for the duration of Beattie s phone calls. (a)(i)... minutes [1] (ii)... minutes [2]

11 (b) Beattie says: 11 Annabel makes longer phone calls than I do. Comment on this statement. Show clearly the statistics you use in your answer [2] 8 (a) Solve algebraically these simultaneous equations. 2x + 3y = 18 y = 5 + x (a) x =... y =... [3] (b) A straight line has gradient 3 and passes though the points (0, 6) and (2, 0). Write down an equation for this line. (b)... [2] [Turn over

12 9 (a) Evaluate. 12 (i) 9 0 (a)(i)... [1] (ii) (ii)... [1] (b) Simplify. 5x y 3 2 (b)... [3]

13 13 10 A dish contains 12 sweets. 7 of them are red and 5 are green. John takes 2 sweets without looking and eats them. Calculate the probability that both his sweets are red.... [3] [Turn over

14 11 14 y y = x 2 O x The diagram shows the graph of y = x 2. (a) On the same diagram, sketch the graph of y = 1 2 x 2. [1] (b) Describe fully the single transformation which maps the graph of y = x 2 onto the graph of y = (x 3) [2]

15 15 BLANK PAGE PLEASE DO NOT WRITE ON THIS PAGE

16 16 PLEASE DO NOT WRITE ON THIS PAGE Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (OCR) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. OCR is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

17 GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS C (GRADUATED ASSESSMENT) HIGHER TERMINAL PAPER SECTION B MONDAY 2 JUNE 2008 H B252B Afternoon Time: 1 hour *CUP/T52255* Candidates answer on the question paper Additional materials (enclosed): None Additional materials (required): Geometrical instruments Tracing paper (optional) Scientific or graphical calculator INSTRUCTIONS TO CANDIDATES Write your name in capital letters, your Centre Number and Candidate Number in the boxes above. Use blue or black ink. Pencil may be used for graphs and diagrams only. Read each question carefully and make sure that you know what you have to do before starting your answer. Show your working. Marks may be given for a correct method even if the answer is incorrect. Answer all the questions. Do not write in the bar codes. Write your answer to each question in the space provided. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this Section is 50. Section B starts with question 12. You are expected to use a calculator in Section B of this paper. Use the π button on your calculator or take π to be unless the question says otherwise. FOR EXAMINER S USE SECTION B This document consists of 12 printed pages. SPA (KN) T52255/2 [100/1142/0] OCR is an exempt Charity [Turn over

18 2 Formulae Sheet Volume of prism = (area of cross-section) length crosssection length In any triangle ABC a b Sine rule = sin A sin B c = sin C b C a Cosine rule Area of triangle = a 2 = b 2 + c 2 2bc cos A 1 2 ab sin C A c B Volume of sphere = 4 3 π r 3 Surface area of sphere = 4 π r 2 r Volume of cone = 1 3 π r 2 h Curved surface area of cone = π r l l h r The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a 0, are given by x = b ± (b 2 4ac) 2a PLEASE DO NOT WRITE ON THIS PAGE

19 12 The usual price of a rugby shirt is How much does it cost in this sale? 3 SALE 12% off all prices... [3] 13 (a) Write 12G% as a fraction. Give your answer as simply as possible. (b) Calculate (a)... [2] (b)... [1] [Turn over

20 4 14 (a) Draw the graph of y = 7 2x for values of x from 0 to 5. y x [3] (b) Use your graph to find the value of x for which 7 2x = 4. (b)... [1]

21 15 y A x (a) Rotate triangle A through 90 clockwise about (2, 0). [2] (b) State one property of triangle A that is unchanged by the rotation [1] [Turn over

22 16 Year 9 did a sponsored long jump. The PE department recorded the length jumped by each of the 90 students who took part. This table summarises the results. 6 Length of jump (j metres) Frequency 2 0 < j < j < j < j < j < j (a) What is the modal class of these results? (b) One of the students who jumped is chosen at random. What is the probability that this student jumped more than 3 5 m? (a)... [1] (c) Calculate an estimate of the mean length of the jumps for the 90 students. (b)... [2] (c)...m [4]

23 17 (a) Factorise completely. 7 6x 2 + 2x (a)... [2] (b) Rearrange 5r + 2p = 6 to make p the subject. (b)... [2] [Turn over

24 18 In 2006, the population of Argentina was (a) Write as an ordinary number. 8 (a)... [1] (b) The land area of Argentina is km 2. Calculate the population density of Argentina. Give your answer to a sensible degree of accuracy. (b)...people / km 2 [3] (c) The highest point in Argentina is Cerro Aconcagua. It is 6960 m above sea level, correct to the nearest 10 metres. The highest point in Bolivia is Nevado Sajama. It is 6540 m above sea level, correct to the nearest 10 metres. Calculate the upper bound of the difference between these heights. (c)...m [3]

25 19 (a) Solve this quadratic equation. 9 3x 2 + 7x 5 = 0 Give your answers correct to 2 decimal places. (a)... [3] (b) You are given that h is inversely proportional to r 2. When h = 10, r = 5. Find h in terms of r. (b)... [3] [Turn over

26 20 (a) Joe s fish tank is a cuboid of length 34 cm, width 22 cm and height 18 cm. 10 Calculate the length of a diagonal of Joe s tank. (a)... cm [3] (b) Michael s fish tank is mathematically similar to Joe s. Michael s fish tank has twice the volume of Joe s. Calculate the height of Michael s tank. (b)... cm [3]

27 21 (a) Calculate the size of angle θ in this triangle cm θ Not to scale 4 cm (a)... [3] (b) A cone of height 7 cm and base radius 4 cm is removed from a larger cone, as shown. The larger cone has base radius 6 cm. (i) Show that the height of the larger cone is 10 5 cm. 7 cm 4 cm 6 cm [1] (ii) Calculate the volume of the remaining frustum. (b)(ii)...cm 3 [3]

28 12 PLEASE DO NOT WRITE ON THIS PAGE Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (OCR) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. OCR is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

WARNING. You are not allowed to use a calculator in Section A of this paper. This document consists of 10 printed pages and 2 blank pages.

WARNING. You are not allowed to use a calculator in Section A of this paper. This document consists of 10 printed pages and 2 blank pages. *CUP/T40907* H GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) PAPER 1 SECTION A HIGHER TIER MONDAY 4 JUNE 2007 Additional materials: Geometrical instruments Tracing paper (optional) B263A