Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 May/June Paper 1 · Variant 3

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. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fl uid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specifi ed in the question, and if the answer is not exact, give the answer to three signifi cant fi gures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 56. MATHEMATICS 0581/13 Paper 1 (Core) May/June 2013 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certifi cate of Secondary Education This document consists of 11 printed pages and 1 blank page. [Turn over IB13 06_0581_13/FP © UCLES 2013 *3794302449* www.XtremePapers.com

2 0581/13/M/J/13 © UCLES 2013 For Examiner′s Use 1 The table shows the distances by road, in kilometres, between some towns in New Zealand. 126 426 368 235 657 300 242 109 531 415 229 332 319 356 460 Auckland Hamilton Napier New Plymouth Rotorua Wellington Write down the distance between Rotorua and Hamilton. Answer … km [1] _____________________________________________________________________________________ 2 Find the value of 1.473. Give your answer correct to 3 decimal places. Answer … [2] _____________________________________________________________________________________ 3 The time in Lisbon is the same as the time in Funchal. A plane left Lisbon at 08 30 and arrived in Funchal at 10 20. It then left Funchal at 12 55 and returned to Lisbon. The return journey took 15 minutes more. What time did the plane arrive in Lisbon? Answer … [2] _____________________________________________________________________________________

3 0581/13/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 4 The Ocean View Hotel has 300 rooms numbered from 100 to 399. A room is chosen at random. Find the probability that the room number ends in zero. Answer … [2] _____________________________________________________________________________________ 5 Solve the equation 3x – 5 = 16 . Answer x = … [2] _____________________________________________________________________________________ 6 A television screen size, S cm, is 80 cm correct to the nearest centimetre. Complete the statement for S in the answer space. Answer … Y S I … [2] _____________________________________________________________________________________

4 0581/13/M/J/13 © UCLES 2013 For Examiner′s Use 7 Sheila can pay her hotel bill in Euros (€) or Pounds (£). The bill was €425 or £365 when the exchange rate was £1 = €1.14 . In which currency was the bill cheaper? Show all your working. Answer … [2] _____________________________________________________________________________________ 8 Without using a calculator, show that 3 5 3 ÷ 2 4 1 = 1 5 3 . You must show each step of your working. Answer [2] _____________________________________________________________________________________ 9 Factorise completely. 6xy2 – 8y Answer … [2] _____________________________________________________________________________________

5 0581/13/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 10 Use a calculator to fi nd (a) 5 24 5 , Answer(a) … [1] (b) ° 40 7 cos . Answer(b) … [1] _____________________________________________________________________________________ 11 81° 87° 63° O B C D A NOT TO SCALE (a) Calculate the size of angle AOB. Answer(a) Angle AOB = … [1] (b) What type of angle is angle AOB? Answer(b) … [1] _____________________________________________________________________________________

6 0581/13/M/J/13 © UCLES 2013 For Examiner′s Use 12 y x 6 5 4 3 2 1 –1 –2 –3 –4 0 –1 1 2 3 4 5 6 7 8 –2 –3 –4 P Q The points P and Q are marked on the grid. (a) Work out the vector . Answer(a) = f p [1] (b) = 8 1 - - e o Find the co-ordinates of the point R. Answer(b) (… , …) [1] _____________________________________________________________________________________ 13 Huy borrowed $4500 from a bank at a rate of 5% per year compound interest. He paid back the money and interest at the end of 2 years. How much interest did he pay? Answer $ … [3] _____________________________________________________________________________________

7 0581/13/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 14 4 cm 18 cm 5 cm 10 cm NOT TO SCALE The shaded shape has rotational symmetry of order 2. Work out the shaded area. Answer … cm2 [3] _____________________________________________________________________________________ 15 (a) 5x × 53 = 510 Find the value of x. Answer(a) x = … [1] (b) Simplify. 12h3 ÷ 4h–2 Answer(b) … [2] _____________________________________________________________________________________ 16 Calculate, giving your answers in standard form, (a) 2 × (5.5 × 104) , Answer(a) … [2] (b) (5.5 × 104) – (5 × 104) . Answer(b) … [2] _____________________________________________________________________________________

8 0581/13/M/J/13 © UCLES 2013 For Examiner′s Use 17 C A B F E D 6 cm 4 cm NOT TO SCALE The diagram shows a triangular prism. Triangle ABC is equilateral. AB = 4 cm and BE = 6 cm. (a) Write down the size of angle ABC. Answer(a) Angle ABC = … [1] (b) On the 1 cm2 grid, draw an accurate net of the prism. The line BE has been drawn for you. B E [3] _____________________________________________________________________________________

9 0581/13/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 18 On the fi rst day of each month, a café owner records the midday temperature (°C) and the number of hot meals sold. Month J F M A M J J A S O N D Temperature (°C) 2 4 9 15 21 24 28 27 23 18 10 5 Number of hot meals 38 35 36 24 15 10 4 5 12 20 18 32 (a) Complete the scatter diagram. The results for January to June have been plotted for you. 40 35 30 25 20 15 10 5 0 5 10 15 Temperature (°C) 20 25 30 Number of hot meals [2] (b) On the grid, draw the line of best fi t. [1] (c) What type of correlation does this scatter diagram show? Answer(c) … [1] _____________________________________________________________________________________

10 0581/13/M/J/13 © UCLES 2013 For Examiner′s Use 19 y x 0 1 2 3 4 8 7 6 5 4 3 2 1 A The point A (1, 3.5) is plotted on the grid. (a) Plot the point B (3, 6.5) and draw the straight line through A and B. [1] (b) (i) Find the gradient of the line in part (a). Answer(b)(i) … [2] (ii) Write down the equation of the line in the form y = mx + c. Answer(b)(ii) y = … [2] (c) On the grid, draw a line through the point (2, 5) that is perpendicular to the line in part (a). [1] _____________________________________________________________________________________

11 0581/13/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 20 17 cm 6 cm B C A NOT TO SCALE In the diagram, AB is a diameter of the circle and C is a point on the circumference. AB = 17 cm and AC = 6 cm. (a) Calculate the area of the circle. Answer(a) … cm2 [2] (b) (i) Explain why angle ACB = 90°. Answer(b)(i) … [1] (ii) Calculate BC. Answer(b)(ii) BC = … cm [3] _____________________________________________________________________________________

12 0581/13/M/J/13 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. BLANK PAGE © UCLES 2013

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0581 MATHEMATICS 0581/13 Paper 1 (Core), maximum raw mark 56 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 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 – May/June 2013 0581 13 © Cambridge International Examinations 2013 Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working soi seen or implied Question Answers Mark Part Marks 1 109 1 2 3.177 2 B1 for 3.176[5] or 3.17 or 3.18 3 1500 or 3 pm 2 B1 for 1h50 or 2h[0]5 or SC1 for 1255 + their 1h 50 + 15mins correctly evaluated 4 300 30 oe www 2 M1 for 30 seen or 300 k seen 5 [x =] 7 2 M1 for correct first step 3x = 16 + 5 or x − 3 5 = 3 16 6 79.5 [≤ S <] 80.5 1, 1 SC1 answers reversed 7 £ or pound[s] working must be shown 2 M1 for 425 ÷ 1.14 or 365 × 1.14 8 5 18 and 4 9 seen 5 18 × 4 9 and 45 72 or 15 24 or 5 8 oe seen M1 A1 Not essential to see 5 3 1 9 2y (3xy − 4) 2 B1 for 2 (3xy 2 − 4y) or y (6xy − 8) 10 (a) (b) [ ± ] 2.28 or 2.282 to 2.2822 0.109 or 0.1094 [3 …] 1 1 11 (a) (b) 129 Obtuse 1 1

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 13 © Cambridge International Examinations 2013 12 (a) (b) [PQ =]       −7 9 (−1 , −3) 1 1 13 ( $ ) 461.25 cao 3 M1 for 4 500 × 1.05 2 oe A1 for 4961.25 A1ft their amount − 4500 OR M2for 4500×0.05+(4500×1.05)×1.05 or M1 for 4500 × 0.05 + 4500 14 260 3 M2 for [2 × ] (4 × 10 + 18 × 5) oe or M1 for a correct area statement 15 (a) (b) [x =] 7 3h 5 1 2 B1 for 3h n (n ≠ 0) or kh 5 16 (a) (b) 1.1 × 10 5 5 × 10 3 2 2 B1 for 110 000 oe e.g.11 × 10 4 B1 for 5000 oe e.g.0.5 × 10 4 17 (a) (b) 60 Correct net 1 3 B1 for 3 rectangles and a triangle to the right and left of rectangles. B1 for 3 accurate (6 by 4) rectangles joined. B1 for 2 equilateral triangles joined in correct positions 18 (a) (b) (c) 6 points correctly plotted Correct ruled line of best fit. Negative 2 1 1 B1 for 4 or 5 correct 19 (a) (b) (i) (ii) (c) B (3 , 6.5) plotted and a ruled line A to B 1.5 oe (y = ) 1.5 x + 2 Ruled Line perpendicular to their line (±2º) and through the point (2 , 5) 1 2ft 2ft 1ft M1 for Run Rise applied to their line B1 for their (b) (i) x + a ( a ≠ 2) or b x + their 2 (b ≠ 0 or 1.5)

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 13 © Cambridge International Examinations 2013 20 (a) (b) (i) (ii) 226.98 to 227.01 Angle or triangle [in a] semi-circle 15.9 or 15.90 to 15.91 253 or 2 1 3 M1 for π × (17 ÷ 2) 2 M2 for 2 2 6 17 − or M1 for 17 2 = BC 2 + 6 2 or better.