Cambridge IGCSE Mathematics - International 0607 — 2014 May/June Paper 2 · Variant 2

This document consists of 10 printed pages and 2 blank pages. IB14 06_0607_22/2RP © UCLES 2014 [Turn over *8579531881* Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 Paper 2 (Extended) May/June 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 0607/22/M/J/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 0607/22/M/J/14 [Turn over Answer all the questions. 1 (a) 6 5 4 3 2 1 –1 –2 –3 –4 –4 –3 –2 –1 1 0 2 3 4 5 6 y x B B is the point (1, 2) and =       −3 4 . Plot the point C on the grid. [1] (b) p =       3 2 q =       −1 4 . Write 2p – q as a column vector. Answer(b)         [2]

4 © UCLES 2014 0607/22/M/J/14 2 (a) Shade one small square so that this shape has exactly 1 line of symmetry. [1] (b) Shade three small squares so that this shape has exactly 2 lines of symmetry. [2] (c) Shade two small squares so that this shape has rotational symmetry of order 4. [2]

5 © UCLES 2014 0607/22/M/J/14 [Turn over 3 In a year group of a school, students study one subject from art, music or dance. The table shows the choices of the 180 students. Subject Number of students Art 85 Music 50 Dance 45 Use the circle to draw a pie chart to show this information. [3]

6 © UCLES 2014 0607/22/M/J/14 4 Write each set of numbers in order starting with the smallest. (a) 3 1 0.3 3.0 0.29 33% Answer(a) , , , , [2] smallest (b) 5 2 2 5 ( ) 3 5 5 5 Answer(b) , , , [2] smallest 5 Expand the brackets and simplify. (a) 2x2(3x + 5xy) Answer(a) [2] (b) (2a – 3b)(a – 2b) Answer(b) [3]

7 © UCLES 2014 0607/22/M/J/14 [Turn over 6 a = 34 × 52 b = 22 × 33 × 52 c = 32 × 53 × 7 (a) Find (i) a , Answer(a)(i) [1] (ii) a b . Answer(a)(ii) [1] (b) Leaving your answer as the product of prime factors, find (i) the highest common factor (HCF) of a, b and c, Answer(b)(i) [1] (ii) the lowest common multiple (LCM) of a, b and c. Answer(b)(ii) [2]

8 © UCLES 2014 0607/22/M/J/14 7 Ann, Babar, Chan and Demi each throw the same biased die. They want to find the probability of throwing a six with this die. They each throw the die a different number of times. These are their results. Ann Babar Chan Demi Number of throws 200 20 100 500 Number of sixes 60 5 30 200 (a) Complete the table below to show the relative frequencies of their results. Write your answers as decimals. Ann Babar Chan Demi Relative frequency of throwing a six [2] (b) Give a reason why Demi's result gives the best estimate of the probability of throwing a six with the biased die. Answer(b) [1] (c) Estimate the number of times that Demi could expect to get a six if he throws the die 1600 times. Answer(c) [1]

9 © UCLES 2014 0607/22/M/J/14 [Turn over 8 y is proportional to the square root of x. When x = 16, y = 10. (a) Find an equation connecting x and y. Answer(a) [2] (b) Find the value of x when y = 1. Answer(b) [2] 9 Work out the following, giving your answers in standard form. (a) (4.6 × 10–5) + (3 × 10–6) Answer(a) [2] (b) (4.6 × 10–5) × (3 × 10–6) Answer(b) [2]

10 © UCLES 2014 0607/22/M/J/14 10 Write 2 3 + x – 3 2 5 + x as a single fraction in its simplest form. Answer [3]

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CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 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 May/June 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 22 © Cambridge International Examinations 2014 1 (a) C plotted at (5, –1) 1 (b) 7 0 2 B1 for each component 2 (a) 1 (b) 2 B1 for any shape with exactly 2 lines of symmetry (c) 2 B1 for any shape with rotation symmetry of order 4 but not all square or all 4 squares in each corner shaded 3 Labelled pie chart with angles 170, 100, 90 3 Tolerance ± 2° B1 for 1 angle drawn correctly B1 for 170, 100, 90 seen 4 (a) 0.29, 0.3, 33%, 3 1 3.0 2 B1 for 1 in wrong place (b) 2 5 , 5 5 , 5 2 , 3) 5 ( 2 B1 for 1 in wrong place 5 (a) 6x³ + 10x³y 2 B1 for each term (b) 2a² – 7ab + 6b² 3 B2 for 2a² – 4ab – 3ab + 6b² B1 for above with 1 wrong / omitted term 6 (a) (i) 45 1 Accept in factor form (ii) 3 4 1 Accept 3 22 (b) (i) 3² × 5² 1 (ii) 22 × 33 × 53 × 7 2 B1 for 3 of 4 factors or B1 for 94 500

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 22 © Cambridge International Examinations 2014 7 (a) 0.3 0.25 0.3 0.4 2 M1 for dividing frequencies by number of trials, or B1 for 3 correct (b) More throws oe 1 (c) 640 1 8 (a) 2 5 x y= oe 2 M1 for y = k x (b) 25 4 oe 2 M1 for substituting y = 1 in their y = k x 9 (a) 4.9 × 10–5 2 M1 for 0.000046 + 0.000003 or 46 × 10–6 or 0.3 × 10–5 (b) 1.38 × 10–10 2 B1 for 13.8 × 10–11 10 ( )( ) 3 2 2 1 + + − x x x 3 M2 for ( ) ( ) ( )( ) 3 2 2 2 5 3 2 3 + + + − + x x x x or M1 for common denominator (x + 2)(2x + 3)