Monday 10 November 2014 Morning

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1 H Monday 0 November 04 Morning GCSE METHODS IN MATHEMATICS B9/0 Methods in Mathematics (Higher Tier) * * Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical instruments Tracing paper (optional) Duration: hour minutes * B 9 0 * 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. Your quality of written communication is assessed in questions marked with an asterisk (*). The total number of marks for this paper is 60. This document consists of pages. Any blank pages are indicated. WARNING No calculator can be used for this paper OCR 04 [H/600/68] DC (RW/SW) 904/ OCR is an exempt Charity Turn over

2 Formula Sheet a Area of trapezium = (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 = b + c bc cos A Area of triangle = ab sin C A c B Volume of sphere = 4 π r Surface area of sphere = 4 π r r Volume of cone = π r h Curved surface area of cone = π r l l h r The Quadratic Equation The solutions of ax + bx + c = 0, where a = 0, are given by b ± (b 4ac) x = a OCR 04

3 Answer all the questions. = {integers from to } F = {factors of 4} M = {multiples of } (a) Complete this Venn diagram to show the sets, F and M. F M 7 [] (b) List the members of: (i) F + M (b)(i)... [] (ii) Ml. (ii)... [] OCR 04 Contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB GE. 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. OCR 04 Turn over

4 The graph of y = x + is drawn on the grid. y x 4 (a) Complete the table for y = - x. x 0 4 y = - x [] (b) Draw the graph of y = - x. [] (c) What is the x-coordinate of the point where the two graphs cross? (d) Find the gradient of the line y = - x. (c)... [] (d)... [] OCR 04

5 y 7 6 B 4 A x (a) Rotate triangle A through 90 anticlockwise about the point _, i. [] (b) Describe fully the single transformation that maps triangle A onto triangle B [] OCR 04 Turn over

6 4* Solve. 6 7_ x + i - x = _ x - i... [4] Complete the statements below using answers from this list. an equation a formula an expression none of these A = rrh + rr is... x + = x - 7 is... y + y - 8 is... y = 6 is... [] OCR 04

7 6 In the diagram AB = 8 cm, AC = 6 cm and BC = 0 cm. Angle BAC = angle ADC = 90. A 7 Not to scale 8 6 B 0 D C Find the length of AD.... cm [] OCR 04 Turn over

8 7 Dipak spins each of these fair spinners once. 8 6 (a) Dipak makes a table to show all the different pairs of numbers he could get. His score is the sum of the two numbers. Number on st spinner Number on nd spinner Score (i) Complete the table. [] (ii) Dipak says, The probability of getting a total score of is. 9 Explain why Dipak is wrong.... [] (b) Find the probability that Dipak s score is. (b)... [] OCR 04

9 9 8 Each day Jennie drinks of a carton of cranberry juice and her brother William drinks of a carton of cranberry juice. How many days will cartons of cranberry juice last them?... days [4] 9 (a) Which of these fractions have decimal equivalents which recur? Put a tick ( ) under the ones which do recur and a cross ( ) under those which do not recur [] (b) Write these decimals as fractions in their simplest form. (i) 0. (ii) 0. o (b)(i)... [] (ii)... [] OCR 04 Turn over

10 0 Find the value of x in each of these cases. 0 x (a) 0 = 0000 (a)... [] x (b) # = (b)... [] 7 x x (c) _ i ' = + (c)... [] (a) Write 4 as the product of its prime factors. (a)... [] (b) Greenford Gala is held once every 0 years. Bailey s Fair is held once every 4 years. They were last held in the same year in 0. In what year will they next both be held in the same year? OCR 04 (b)... []

11 The 0 students on a school activities trip were offered the choice of sailing or rock climbing. The choices that the boys and girls made are shown in the table. Sailing Rock climbing Total Boys 6 8 Girls Total 4 0 (a) Complete the table. [] (b) Two of the 0 students are selected at random. What is the probability that they both chose sailing? (c) Two of the students who chose rock climbing are selected at random. What is the probability that one is a boy and one is a girl? (b)... [] (c)... [] TURN OVER FOR QUESTION OCR 04 Turn over

12 A Q C a Not to scale P O b B OACB is a parallelogram. OA = a and OB = b. AQ = AC and AP = AB. (a) Find these vectors in terms of a and b. Give your answers in their simplest form. (i) OQ (a)(i)... [] (ii) PB (ii)... [] (iii) PC (iii)... [] (b) Use answers from part (a) to explain why OQ is parallel to PC [] END OF QUESTION PAPER OCR 04