Cambridge IGCSE Mathematics - International 0607 — 2014 Oct/Nov Paper 2 · Variant 1

This document consists of 8 printed pages. IB14 11_0607_21/RP © UCLES 2014 [Turn over *5669966743* Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended) October/November 2014 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. 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 40.

2 © UCLES 2014 0607/21/O/N/14 Formula List For the equation ax2 + bx + c = 0 x = 2 _ ± 4 2 _ b b ac a Curved surface area, A, of cylinder of radius r, height h. A = 2πrh Curved surface area, A, of cone of radius r, sloping edge l. A = πrl Curved surface area, A, of sphere of radius r. A = 4πr2 Volume, V, of pyramid, base area A, height h. V= 1 3 Ah Volume, V, of cylinder of radius r, height h. V = πr2h Volume, V, of cone of radius r, height h. V = 1 3 πr2h Volume, V, of sphere of radius r. V = 4 3 πr3 = = sin sin sin a b c A B C a2 = b2 + c2 – 2bc cos A Area = 1 2 bc sin A A a B C b c

3 © UCLES 2014 0607/21/O/N/14 [Turn over Answer all the questions. 1 Insert brackets in these calculations so that the answers are correct. (a) 10 – 4 + 3 + 2 = 5 [1] (b) 10 – 5 × 7 + 2 = 45 [1] 2 h° g° NOT TO SCALE The diagram shows a regular hexagon and a regular pentagon. (a) Find g. Answer(a) g = [3] (b) Find h. Answer(b) h = [2]

4 © UCLES 2014 0607/21/O/N/14 3 Find the value of (a) 50, Answer(a) [1] (b) 3 2 8 −. Answer(b) [2] 4 (a) 3023 is a prime number. Write down the factors of 3023. Answer(a) [1] (b) p and q are prime numbers. (i) Write down the highest common factor (HCF) of p and q. Answer(b)(i) [1] (ii) Write down an expression, in terms of p and q, for the lowest common multiple (LCM) of p and q. Answer(b)(ii) [1]

5 © UCLES 2014 0607/21/O/N/14 [Turn over 5 (a) Solve this inequality. 3(x + 2) > 5x – 2 Answer(a) [3] (b) Show your answer to part (a) on this number line. –3 –2 –1 0 1 2 3 4 5 6 7 x [2] 6 Sanjay asks a random sample of 200 students how they travel to school. These are his results. Method of travel Walk Cycle Bus Car Train Frequency 52 47 62 27 12 (a) Find the relative frequency of a student travelling by bus. Answer(a) [1] (b) The school has 1200 students. (i) Explain why it is reasonable to use your answer to part (a) as the probability that a student chosen at random from the school travels by bus. Answer(b)(i) [1] (ii) Estimate the number of students in the school who travel by bus. Answer(b)(ii) [1]

6 © UCLES 2014 0607/21/O/N/14 7 31 students took a test which was marked out of 70. The stem and leaf diagram shows their results. 1 3 3 4 7 2 4 4 7 8 9 Key 2 4 = 24 marks 3 3 3 4 6 7 8 4 0 2 5 5 8 9 9 5 3 4 6 7 8 6 2 5 5 7 (a) Find the median. Answer(a) [1] (b) Another student took the test later. What mark did this student get if (i) the median and range do not change, Answer(b)(i) [1] (ii) the median and range both increase by 1? Answer(b)(ii) [1] 8 In standard form, x = a × 105 and y = b × 107 where a < b. In standard form, y x = c × 10d where 1 Y c < 10. (a) Find the value of d. Answer(a) [1] (b) Find c in terms of a and b. Answer(b) c = [2]

7 © UCLES 2014 0607/21/O/N/14 [Turn over 9 Here are the sketches of four graphs. y A x 0 y B x 0 y C x 0 y D x 0 Each of the graphs represents one of these equations. y = x² + 3x y = 3 – 2x y = 3 – x² y = 2x + 3 y = x² y = – 3x y = x² – 3 y = 3x From the equations above, write down which one represents each graph. Answer Graph A y = Graph B y = Graph C y = Graph D y = [4] Questions 10 and 11 are printed on the next page.

8 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 (UCLES) 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. Cambridge International Examinations 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. © UCLES 2014 0607/21/O/N/14 10 (a) Factorise completely. 8a2 – 50b2 Answer(a) [3] (b) Write as a single fraction, simplifying your answer. 5 3 3 2 2 − + − x x Answer(b) [3] 11 (a) Find log28 . Answer(a) [1] (b) Find p when log 3 + 2log 5 = log p. Answer(b) p = [2]

® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 2014 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended), maximum raw mark 40 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2014 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0607 21 © Cambridge International Examinations 2014 1 (a) ( ) 10 4 3 2 5 − + + = 1 (b) ( ) ( ) 10 5 7 2 45 − × + = 1 2 (a) 108 3 M2 for 5 180 ) 2 5 ( × − or 5 360 180 − or M1 for (5 – 2) × 180 soi by 540 or M1 for 5 360 (b) 132 2FT M1 for 360 – their 108 – 120 or their 72 + 60 3 (a) 1 1 (b) 4 1 or 0.25 2 M1 for 2 or 64 seen or reciprocal at any stage 4 (a) 1, 3023 1 (b) (i) 1 1 (ii) pq 1 5 (a) x < 4 final answer 3 B1 for 3x + 6 > 5x – 2 M1 FT for isolating terms M1 FT for completion correctly to answer space If 0 scored SC1 for x = 4 (b) Correct diagram 2FT B1FT 4 marked and arrow/line to left or for circle at 4 6 (a) 200 62 oe 1 (b) (i) Large sample oe 1 (ii) 372 1FT 7 (a) 40 1 (b) (i) 40 1 (ii) 68 1 8 (a) –3 1 (b) b a 10 2 M1 for 2 10 a b − × seen

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0607 21 © Cambridge International Examinations 2014 9 A y = 2x + 3 B y = – 3x C 2 3 y x = − D 2 3 y x = − 4 B1 each 10 (a) 2(2a + 5b)(2a – 5b) final answer 3 B2 for (4a + 10b)(2a – 5b) or (2a + 5b)(4a – 10b) or B1 for ( ) 2 2 2 4 25 a b − (b) ) 5 )( 3 2 ( 19 8 − − − x x x final answer 3 Accept 2 2 13 15 x x − + M2 for ) 5 )( 3 2 ( )3 2 (3 ) 5 ( 2 − − − + − x x x x or M1 for common denominator (2x – 3)(x – 5) 11 (a) 3 1 (b) 75 2 B1 for [log] 25 seen