# THIS IS A LEGACY SPECIFICATION

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1 THIS IS A LEGACY SPECIFICATION H GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) Paper Section A (Higher Tier) B9A * OCE / 1 795* Candidates answer on the question paper. OCR supplied materials: None Other materials required: Geometrical instruments Tracing paper (optional) Friday 1 January 011 Morning Duration: 1 hour * B 9 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. Pencil may be used for graphs and diagrams only. Read each question carefully. Make sure 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. 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). Answer all the questions. 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 Section is 50. This document consists of 1 pages. Any blank pages are indicated. WARNING No calculator can be used for Section A of this paper DC (CW/DJ) 1795/6 OCR is an exempt Charity Turn over

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

3 1 Anil does this calculation on his calculator He writes down the numbers shown on his calculator display as , but forgets to put in the decimal point. (a) Use estimation to decide where the decimal point should go. You must show your working. (b) Write the correct answer, accurate to 3 significant figures. (a)... [3] (b)... [1] Turn over

4 In this question leave in all the construction arcs you use. The diagram shows the sketch of a field. B 5 m A 110 m Not to scale 70 m (a) Make an accurate scale drawing of the field. Use a scale of 1 cm to represent 10 m. The line DC has been drawn for you. D 95 m C D C [3] (b) A mobile phone mast is to be erected in the field. The mast must be the same distance from B as it is from D at least 65 m from A. On your drawing, use ruler and compasses only to construct all the possible positions for the mast. Show your answer clearly. []

5 3 y A x 3 (a) Enlarge rectangle A by scale factor 1 with centre (0, 0). [] (b) Translate rectangle A by the vector ( 7 ). [] Turn over

6 Write each of the following as a single power of 5. 5 (a) (b) 1 5 (a)... [] (b)... [1] (c) the square root of five cubed (c)... [1] 5 At Barney s Diner a three-course meal costs more than a two-course meal. A group of people go to the Diner. Three of them have two-course meals and the rest have three-course meals. The total cost is 16. Let x be the cost of a two-course meal. Write down an equation in x and solve it to find the cost of a two-course meal.... [5]

7 6 7 Carol chooses two of these cards at random and places them side by side. She notes whether each is a vowel or a consonant. (a) Complete the probability tree diagram for Carol s choices. 1st Card nd Card 3 9 vowel vowel consonant consonant vowel consonant [] (b) Calculate the probability that at least one of her cards is a consonant. (b)... [3] Turn over

8 7 Mr Gill drives regularly from Manchester to London. He records the time, t hours, it takes on 0 of these journeys. His results are summarised in the table below. Time (t hours) Number of journeys Time (t hours) Cumulative frequency.75 < t 3 t 3 3 < t t < t t < t t < t 1 t < t.5 6 t.5 0 (a) Complete the table of cumulative frequencies. [1] (b) On the grid below draw a cumulative frequency diagram to show these data Cumulative frequency Time (hours) [] (c) (i) Find the median time. (c)(i)... hours [1] (ii) Find the interquartile range of the times. (ii)... hours []

9 (d) Mr Badley also travels from Manchester to London. He travels by train. The median time for his journeys is 3.7 hours and the interquartile range is 0. hours. Make two comparisons between Mr Gill s journeys and Mr Badley s journeys [] D A O B C The lines AB and CD bisect each other at O. (a) Prove that triangles AOC and BOD are congruent.... [3] (b) Prove that CA is parallel to BD.... [] Turn over

10 9 The sketch shows the graph of y = f(x). 10 y x On the given axes, sketch the graphs of these functions. (a) y = f(x) y x [1] (b) y = f(x) y x [1]

11 (c) y = f(x + ) 11 y x [1] 10 (a) Simplify (5 + )(5 ). (a)... [] (b) Expand (3 + 3 )( + 3 ). Write your answer in the form a + b 3 where a and b are integers. (b)... [3]

12 1 PLEASE DO NOT WRITE ON THIS PAGE 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 CB 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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