# Tuesday 6 November 2012 Morning

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1 H Tuesday 6 November 2012 Morning GCSE MATHEMATICS A A501/02 Unit A (Higher Tier) *A * Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Scientific or graphical calculator Geometrical instruments Tracing paper (optional) Duration: 1 hour * A * INSTRUCTIONS TO CANDIDATES Write your name, centre number and candidate number in the boxes above. Please write clearly and in capital letters. Use black ink. HB pencil may be used for graphs and diagrams only. Answer all the questions. Read each question carefully. Make sure you know what you have to do before starting your answer. Your answers should be supported with appropriate working. Marks may be given for a correct method even if the answer is incorrect. Write your answer to each question in the space provided. Additional paper may be used if necessary but you must clearly show your candidate number, centre number and question number(s). Do not write in the bar codes. 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 paper is 60. This document consists of 16 pages. Any blank pages are indicated. You are permitted to use a calculator for this paper [A/600/3699] DC (LEO/SW) 57601/4 This paper has been pre modified for carrier language OCR is an exempt Charity Turn over

2 2 Formulae Sheet: Higher Tier a Area of trapezium = 1 2 (a + b)h h b Volume of prism = (area of cross-section) length crosssection length In any triangle ABC a sin A = b sin B = c Sine rule sin C b C a Cosine rule a 2 = b 2 + c 2 2bc cos A 1 2 Area of triangle = 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 b ± (b 2 4ac) x = 2a PLEASE DO NOT WRITE ON THIS PAGE

3 1 (a) Joe and Pam planted crocus bulbs in their gardens. They shared a bag of 250 crocus bulbs. The table shows the colour of the flower from each bulb. 3 Yellow Purple White Totals Joe Pam Totals (i) Complete the table. [3] (ii) Write the ratio 64 : 56 as simply as possible. (a)(ii) [1] (b) Sumita bought a pack of 60 crocus bulbs which produced Yellow, Purple or White flowers. The ratio Yellow : Purple : White was 7 : 5 : 3. How many of the 60 bulbs produced White flowers? (b) [3] Turn over

4 2 (a) Mandi writes a questionnaire about music. Here is one of her questions and the response boxes for it. 4 How many CDs do you own? Mandi has made two different types of error in the categories she has chosen. Explain what these errors are. 1 2 [2] (b) Mandi analyses the length of time of each track on her CDs. This table summarises the results. Length (t seconds) Frequency 0 < t < t < t < t < t < t Calculate an estimate of the mean length of time of these tracks. (b) seconds [4]

5 3 Calculate. 5 (a) (a) [1] (b) (b) [1] Turn over

6 4 (a) Find the value of 6x 2 when x = (a) [2] (b) Find the first 3 terms of the sequence whose n th term is 4n + 3. (b) [2] (c) Factorise completely. 6y 2 + 9y (c) [2]

7 (d) Solve. 7 2x + 7 = 6x 8 (d) [3] (e) Rearrange this formula to make x the subject. y = 4x + 6 (e) [2] Turn over

8 5 In this question, use a ruler and a pair of compasses. Leave in your construction lines. The scale drawing ABCD shows Neil s garden. AB is the wall of Neil s house. 8 D Scale: 1 cm represents 200 cm C A B Construct the perpendicular from D to AB. Hence find the shortest actual distance, in metres, from corner D of the garden to the house. m [4]

9 6 (a) Express 24 as a product of its prime factors. 9 (a) [2] (b) Two numbers have a highest common factor of 24 and a least common multiple of Neither of the numbers is 24. Find the two numbers, showing how you decide. (b) and [3] Turn over

10 7 A small garden table has legs 85 cm long which can be fixed in various positions. 10 (a) 64 Not to scale 85 cm h cm Calculate the height, h cm, of the table when the legs make an angle of 64 with the horizontal. (a) cm [3]

11 (b) x 11 Not to scale 85 cm 79 cm Calculate angle x when the height of the table is 79 cm. Give your answer in degrees correct to 1 decimal place. (b) [3] Turn over

12 12 8 Colin and Peter climbed Binsey Hill in the Lake District. Peter printed out this graph from his satnav Altitude (metres) Horizontal distance travelled (miles) Colin wanted to know how far they had actually walked. (a) He used this triangle to estimate the distance they walked going up Binsey Hill. Not to scale top: altitude 449 m start: altitude 170 m horizontal distance miles Calculate the distance in metres along the hypotenuse of this triangle. Use the fact that 1 mile = 1609 metres. (a) metres [5]

13 13 (b) Describe how Colin s method could be improved to calculate a better estimate of the actual distance they walked on their way up Binsey Hill. You do not need to carry out any calculations. [1] Turn over

14 14 9 This table summarises the wages of employees at a company. Wage ( w thousand) Frequency 10 < w < w < w < w < w < w 70 4 Construct a histogram to represent this distribution Wage ( w thousand) [4]

15 15 10 (a) You are given that 5a(a 1) + pa + r = 5a 2 + 7a + 9. Find the values of p and r that make this an identity. (a) p = r = [2] (b) Rearrange the following to make c the subject. 5c + 6d = cn + 9d (b) [3] TURN OVER FOR QUESTION 11

16 11 You are given that f(x) = 5x (a) Calculate f(5.2). (a) [1] (b) Work out an expression for f(2 + 3t ), writing your answer in the form at + b. (b) [3] Copyright Information OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website ( after the live examination series. If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible opportunity. For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE. 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.

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