Cambridge IGCSE Mathematics - International 0607 — 2013 Oct/Nov Paper 1 · Variant 1

This document consists of 11 printed pages and 1 blank page. IB13 11_0607_01/4RP © UCLES 2013 [Turn over *2859125547* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/01 Paper 1 (Core) October/November 2013 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, highlighters, glue or correction fluid. You may use a 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. www.XtremePapers.com

2 © UCLES 2013 0607/11/O/N/13 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 2013 0607/11/O/N/13 [Turn over For Examiner's Use 1 Write 8572 (a) correct to the nearest 10 , Answer (a) [1] (b) correct to the nearest 100 . Answer (b) [1] 2 Put one of + – × ÷ in the box to make the following correct. 3 × (11 5) = 18 [1] 3 Write the following in order, starting with the smallest. 25 52 33 Answer I I [2]

4 © UCLES 2013 0607/11/O/N/13 For Examiner's Use 4 On the shape draw the line of symmetry. [1] 5 (a) Work out 4 3 of $120 . Answer (a) $ [1] (b) A sum of money is divided between Stefan and Tomas in the ratio Stefan : Tomas = 1 : 3. (i) What fraction of the money does Stefan receive? Answer (b)(i) [1] (ii) What percentage of the money does Tomas receive? Answer (b)(ii) % [1]

5 © UCLES 2013 0607/11/O/N/13 [Turn over For Examiner's Use 6 (a) Jean plays golf. Here are her best 10 scores. 69 71 68 70 71 66 71 72 69 70 (i) What is the range of her scores? Answer (a)(i) [1] (ii) Find Jean’s modal score. Answer (a)(ii) [1] (b) Anya records the shoe size of 10 of her friends. This frequency table shows her results. Shoe size Frequency 3 4 4 2 5 3 6 1 Find the mean shoe size. Answer (b) [3]

6 © UCLES 2013 0607/11/O/N/13 For Examiner's Use 7 In the diagram BE is the diameter of the circle and AC is a tangent to the circle at B. D E B C A NOT TO SCALE (a) Write down the size of angle BDE. Answer (a) [1] (b) Write down the size of angle CBE. Answer (b) [1] (c) Which word is the mathematical name for the line DE? diameter radius sector chord circumference centre Answer (c) [1]

7 © UCLES 2013 0607/11/O/N/13 [Turn over For Examiner's Use 8 (a) The diagram shows the graph of y = x 1 . –4 –3 –2 –1 0 1 2 3 4 –4 –3 –2 –1 1 2 3 4 y x Write down the equations of the two asymptotes of the graph of y = x 1 . Answer (a) [2] (b) The diagram shows the graph of y = f(x). 1 –1 –1 1 2 3 y x –2 –3 2 0 (i) Write down the domain. Answer (b)(i) [1] (ii) Write down the range. Answer (b)(ii) [1] (iii) On the diagram, sketch the graph of y = f(x) + 1 . [1]

8 © UCLES 2013 0607/11/O/N/13 For Examiner's Use 9 Jimmi’s pencil case only contains 3 pens and 12 pencils. (a) He chooses an object at random from his pencil case. Find the probability that the object is a pencil. Answer (a) [1] (b) Jimmi chooses an object at random from his pencil case and then replaces it. He repeats this 100 times. How many times do you expect Jimmi to choose a pen? Answer (b) [2]

9 © UCLES 2013 0607/11/O/N/13 [Turn over For Examiner's Use 10 (a) Solve the following equations. (i) 6 + 5w = 41 Answer (a)(i) w = [2] (ii) 7 (3x – 4) = 35 Answer (a)(ii) x = [3] (b) Write down two integers which satisfy the inequality 4a – 1 < 10 . Answer (b) [2]

10 © UCLES 2013 0607/11/O/N/13 For Examiner's Use 11 A is the point (2, –1) and B is the point (4, 5). 0 y x NOT TO SCALE A B (a) Find the co-ordinates of the midpoint of AB. Answer (a) ( ) [1] (b) (i) Find the gradient of AB. , Answer (b)(i) [2] (ii) Find the equation of the line AB. Answer (b)(ii) [2] (c) Write down the equation of a line parallel to AB. Answer (c) [1]

11 © UCLES 2013 0607/11/O/N/13 For Examiner's Use 12 15 mm 12 mm 9 mm NOT TO SCALE x y Write down (a) tan x, Answer (a) [1] (b) cos y. Answer (b) [1]

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. University of 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 2013 0607/11/O/N/13 BLANK PAGE

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2013 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/01 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 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. www.XtremePapers.com

Page 2 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0607 01 © Cambridge International Examinations 2013 1 (a) (b) 8570 8600 1 1 2 – 1 3 52 33 25 accept any clear indication 2 B1 for 2 of 32, 25, 27 seen 4 Correct line drawn 1 5 (a) (b) (i) (ii) 90 4 1 75% 1 1 1FT FT their 4 1 6 (a) (i) (ii) (b) 6 71 4.1 1 1 3 M1 for ∑fx (= 41) M1 for their 41 ÷ 10 7 (a) (b) (c) 90° 90° Chord 1 1 1 8 (a) (b) (i) (ii) (iii) x = 0 oe y = 0 oe –2 < x < 1 0 < f(x) < 2 Correct translation 1 1 1 1 1 Condone strict inequalities 9 (a) (b) 15 12 oe 20 1 2 M1 for their 15 3 × 100 soi

Page 3 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0607 01 © Cambridge International Examinations 2013 10 (a) (b) (c) 7 3 Any 2 integers a < 2 2 3 2 M1 for correct first step M1 for correct first step and M1 FT for correct second step B1 each 11 (a) (b) (i) (ii) (c) (3, 2) 3 y = 3x –7 y = 3x + c 1 2 2FT 1FT M1 for y increase/x increase B1FT for y = their 3x + k or for y = ax –7, a ≠ 0 or for their 3x –7 FT their (b)(i), c ≠ their k 12 (a) (b) 9 12 oe 15 12 oe 1 1