Cambridge IGCSE Mathematics - International 0607 — 2015 Oct/Nov Paper 1 · Variant 3

This document consists of 11 printed pages and 1 blank page. IB15 11_0607_13/FP © UCLES 2015 [Turn over *3736720442* Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/13 Paper 1 (Core) October/November 2015 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 2015 0607/13/O/N/15 Formula List Area, A, of triangle, base b, height h. A = 1 2 bh Area, A, of circle, radius r. A = πr2 Circumference, C, of circle, radius r. C = 2πr 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 prism, cross-sectional area A, length l. V =Al 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

3 © UCLES 2015 0607/13/O/N/15 [Turn over Answer all the questions. 1 Work out . 5 × 20 ÷ 4 Answer [1] 2 (a) A Shape A is drawn on a 1cm square grid. Find the perimeter of shape A. Answer(a) cm [1] (b) On the grid below, draw a different shape which has the same area as shape A. [2]

4 © UCLES 2015 0607/13/O/N/15 3 (a) Write down the value of (– 2)3. Answer(a) [1] (b) Simplify. –2 – (–8) 2 + 8 Give your answer as a fraction in its lowest terms. Answer(b) [2] 4 A farmer picks a bunch of grapes. He writes down A the colour of the grapes B the number of grapes C the weight of the grapes D which plant the grapes were picked from. (a) Which one of A, B, C or D is discrete data? Answer(a) [1] (b) Which one of A, B, C or D is continuous data? Answer(b) [1]

5 © UCLES 2015 0607/13/O/N/15 [Turn over 5 Niki began a race at 10 05. She finished the race at 16 05. (a) How many hours did Niki take to complete the race? Answer(a) h [1] (b) The distance of the race was 42 km. Work out Niki’s average speed. Answer(b) km/h [1] 6 From this list write down the irrational number. 5 7 9 2 9 7 Answer [1]

6 © UCLES 2015 0607/13/O/N/15 7 The diagram shows the graph of y = f(x). –4 –3 –2 –1 0 1 2 3 1 2 3 4 y x 4 5 –4 –3 –2 –1 –5 –6 Write down the equations of the two asymptotes of the graph. Answer [2]

7 © UCLES 2015 0607/13/O/N/15 [Turn over 8 The total cost of a holiday was $720. The pie chart shows how this money was spent. NOT TO SCALE Food Other items Hotel Travel 120° 70° 80° Find the amount of money spent on (a) food, Answer (a) $ [2] (b) other items. Answer (b) $ [2]

8 © UCLES 2015 0607/13/O/N/15 9 0 1 2 3 4 5 6 7 8 2 3 4 1 x y The diagram shows the graph of y = x2 – 4x + 8 for 0 x 4. Write down the equation of the line of symmetry of this graph. Answer [1] 10 P Draw the tangents from P to the circle. [1]

9 © UCLES 2015 0607/13/O/N/15 [Turn over 11 (a) Simplify. (i) 3x – 5 + 2x – 12 Answer(a)(i) [2] (ii) 4 × d × 2 × d Answer(a)(ii) [1] (iii) 3 x – 6 x Answer(a)(iii) [2] (b) Factorise completely. 6ab – 8a2 Answer(b) [2] (c) Solve the following equation. x + 8 = 15 Answer(c) x = [1] (d) Solve the inequality. 6x < 4x + 11 Answer(d) [2]

10 © UCLES 2015 0607/13/O/N/15 12 Data has been collected about the age (years) and the value (to the nearest $100) of the cars owned by a class of University students. Age (years) 1 2 2 3 4 4 5 7 8 Value ($) 8000 6400 5200 4000 3000 2100 1700 1200 800 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 1 2 3 4 5 6 Age (years) Value ($) 7 8 9 10 (a) Complete the scatter diagram. The first five points have been plotted for you. [2] (b) What type of correlation is shown on the scatter diagram? Answer(b) [1] (c) The mean age is 4 years. The mean value is $3600. Draw the line of best fit on your diagram. [2]

11 © UCLES 2015 0607/13/O/N/15 13 The base of this pyramid is a square of side 5 m. It has perpendicular height 12 m. Work out the volume of the pyramid. Answer m3 [3] 14 A rectangle has sides 6 cm and 8 cm. 6 cm NOT TO SCALE 8 cm Work out the length of a diagonal of this rectangle. Answer cm [2]

12 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. 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 2015 0607/13/O/N/15 BLANK PAGE

® 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 2015 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/13 Paper 1 (Core), 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 2015 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 2015 0607 13 © Cambridge International Examinations 2015 Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Question Answer Mark Part Marks 1 25 1 2 (a) 16 1 (b) Different closed shape with area 11 cm2 2 M1 for 11 seen 3 (a) –8 1 (b) 5 3 2 M1 for 10 6 seen. If zero scored, SC1 for correct simplification of their fraction. 4 (a) B 1 (b) C 1 5 (a) 6 1 (b) 7 1FT FT 42 ÷ their (a) 6 7 1 7 x = 1 y = –2 1 1 If zero, SC1 for 1 and –2 only clearly indicated 8 (a) 240 2 M1 for 120 720 360 × oe (b) 180 2 M1 for 360 – (120 + 80 + 70) seen or better 9 x = 2 1 10 Both correct ruled tangents 1 and no other lines

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2015 0607 13 © Cambridge International Examinations 2015 Question Answer Mark Part Marks 11 (a) (i) 5x – 17 Final answer 2 B1 for either 5x or –17 (ii) 8d 2 Final answer 1 (iii) 6 x oe 2 M1 for 2 6 6 x x − oe (b) 2a(3b – 4a) Final answer 2 B1 for answer 2(3ab – 4a2 ) or a(6b – 8a) If zero scored, SC1 for correct answer seen then bracket multiplied out (c) 7 1 (d) x < 5.5 oe Final answer 2 M1 for correct first step If zero scored, SC1 for answer 5.5 12 (a) Correct plots 2 B1 for 2 or 3 points plotted correctly (b) Negative 1 (c) Ruled line through (4, 3600) 1 1 Dependant on: single straight line with negative gradient 13 100 3 M1 for 25 seen and M1 for 1 25 12 3× × or better 14 10 2 M1 for [c2 = ] 62 + 82 or better