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

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 0581/11 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 8 printed pages. [Turn over IB13 06_0581_11/FP © UCLES 2013 *1239577507* www.XtremePapers.com

2 0581/11/M/J/13 © UCLES 2013 For Examiner's Use 1 Write 45% as a fraction in its simplest form. Answer … [1] _____________________________________________________________________________________ 2 One January day in Munich, the temperature at noon was 3°C. At midnight the temperature was –8°C. Write down the difference between these two temperatures. Answer … °C [1] _____________________________________________________________________________________ 3 (a) Calculate 5.7 – 1.032 . Write down all the numbers displayed on your calculator. Answer(a) … [1] (b) Write your answer to part (a) correct to 3 decimal places. Answer(b) … [1] _____________________________________________________________________________________ 4 Pedro and Eva do their homework. Pedro takes 84 minutes to do his homework. The ratio Pedro’s time : Eva’s time = 7 : 6. Work out the number of minutes Eva takes to do her homework. Answer … min [2] _____________________________________________________________________________________ 5 Write each of the following as a single vector. (a) 6 1 e o + 4 - 2 e o Answer(a) e o [1] (b) 4 3 - 2 e o Answer(b) e o [1] _____________________________________________________________________________________

3 0581/11/M/J/13 © UCLES 2013 [Turn over For Examiner's Use 6 50° a° 55° NOT TO SCALE Use the information in the diagram to fi nd the value of a. Answer a = … [2] _____________________________________________________________________________________ 7 Show that 1 2 1 ÷ 16 3 = 8. Do not use a calculator and show all the steps of your working. Answer [2] _____________________________________________________________________________________ 8 Sebastian ran a race in 11.4 seconds, correct to 1 decimal place. Complete the statement about the time, t seconds, that Sebastian took to run the race. Answer … Ğ t < … [2] _____________________________________________________________________________________

4 0581/11/M/J/13 © UCLES 2013 For Examiner's Use 9 Rearrange this equation to make b the subject. a = 5 b – 9 Answer b = … [2] _____________________________________________________________________________________ 10 Here are the fi rst four terms of a sequence. 4 11 18 25 Write down an expression for the nth term. Answer … [2] _____________________________________________________________________________________ 11 x and y are integers. (a) Find the value of x when –7 < x < –5 . Answer(a) x = … [1] (b) Find the value of y when 4 3 < y 16 < 8 7 . Answer(b) y = … [2] _____________________________________________________________________________________ 12 The probability of Sachin’s team winning any match is 0.45. (a) Write down the probability of Sachin’s team not winning any match. Answer(a) … [1] (b) In a season there are 40 matches. How many matches should Sachin’s team expect to win in a season? Answer(b) … [2] _____________________________________________________________________________________

5 0581/11/M/J/13 © UCLES 2013 [Turn over For Examiner's Use 13 Complete each statement with the correct mathematical term. (a) This solid is a … [1] (b) This polygon is a regular … [1] (c) Angle ABC is an … angle [1] _____________________________________________________________________________________ 14 (a) The perimeter of a square is 28 mm. Work out the length of one side of the square. Answer(a) … mm [1] (b) Calculate the volume of a cylinder with radius 5.2 cm and height 15 cm. Answer(b) … cm3 [2] _____________________________________________________________________________________ 15 Bruce invested $420 at a rate of 4% per year compound interest. Calculate the total amount Bruce has after 2 years. Give your answer correct to 2 decimal places. Answer $ … [3] _____________________________________________________________________________________ A B C

6 0581/11/M/J/13 © UCLES 2013 For Examiner's Use 16 Martina changed 200 Swiss francs (CHF) into euros (€). The exchange rate was €1 = 1.14 CHF. Calculate how much Martina received. Give your answer correct to the nearest euro. Answer € … [3] _____________________________________________________________________________________ 17 In this question use a straight edge and compasses only. Leave in all your construction arcs. (a) Construct the bisector of angle ABC. A B C [2] (b) Construct the perpendicular bisector of the line DE. E D [2] _____________________________________________________________________________________

7 0581/11/M/J/13 © UCLES 2013 [Turn over For Examiner's Use 18 (a) Which two of these have the same value? 5–2 5 2 2 2 1 c m 2 5 2 c m 0.22 Answer(a) … and … [2] (b) Simplify. (i) a6 × a3 Answer(b)(i) … [1] (ii) 24b16 ÷ 6b4 Answer(b)(ii) … [2] _____________________________________________________________________________________ 19 (a) Multiply out the brackets. 5 ( x + 3 ) Answer(a) … [1] (b) Factorise completely. 12xy – 3x2 Answer(b) … [2] (c) Solve. 5x – 24 = 51 Answer(c) x = … [2] _____________________________________________________________________________________ Question 20 is printed on the next page.

8 0581/11/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. © UCLES 2013 For Examiner's Use 20 Marco throws a six-sided dice 27 times. The bar chart shows his results. 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 Score on dice Frequency (a) Write down the mode. Answer(a) … [1] (b) Work out the probability that Marco throws a number less than 5. Answer(b) … [2] (c) Calculate the mean. Answer(c) … [3]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0581 MATHEMATICS 0581/11 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 11 © 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 Qu Answers Mark Part Answers 1 20 9 cao 1 2 11 or −11 1 3 (a) (b) 1.32656 ….. 1.327 1 1ft 4 72 2 M1 for 84 ÷ 7 5 (a) (b)       3 2       −12 8 1 1 6 105 2 M1 for 180 – 55 – 50 or B1 for 55 or 75 seen in the correct angle inside the triangle 7 correct working; e.g. 8 3 16 2 3 = × 2 M1 for and A1 for 8 3 16 2 3 = × n n k k 8 11.35, 11.45 1, 1 SC1 for both answers correct but reversed 9 [b = ] 5(a + 9) oe final answer 2 M1 for one correct step 10 7n − 3 oe 2 B1 for 7n 11 (a) (b) − 6 13 1 2 B1 for 16 12 or 16 14 or 16 13 seen 12 (a) (b) [0].55 oe 18 1 2 M1 for 40 × [0].45 oe k k 2 3

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 11 © Cambridge International Examinations 2013 13 (a) (b) (c) cuboid pentagon obtuse 1 1 1 condone [rectangular] prism 14 (a) (b) 7 1270 or 1274 or 1274.2 to 1274.4 1 2 M1 for π × 5.22 × 15 15 454.27 cao final answer 3 M1 for 2 100 4 1 420      + × oe and A1 for 454 or 454.2 to 454.3 or SC2 for answer 34.27 or SC1 for answer 34.2 to 34.3 16 175 cao final answer 3 B2 for 175.4… or M1 for 200 ÷ 1.14 17 (a) (b) correct ruled line two pairs of correct arcs correct ruled line two pairs of correct arcs 1 1 1 1 18 (a) (b) (i) (ii) 5–2 and 0.22 a9 4b12 2 1 2 M1 for any two correct decimal values seen with the correct expression e.g. 0.04, 0.4, 0.25, 0.16, 0.04 B1 for 4bk or B1 for kb12 where k is an integer ( k ≠ 0 ) 19 (a) (b) (c) 5x + 15 final answer 3x( 4y – x ) final answer 15 1 2 2 B1 for 3( 4xy – x2 ) or x( 12y – 3x ) M1 for a correct first step 20 (a) (b) (c) 4 cao 27 21 oe isw 3.33(3…) 1 2 3 M1 for 3 + 6 + 5 + 7 + 4 or 21 seen M1 for 3 × 1 + 6 × 2 + 5 × 3 + 7 × 4 + 4 × 5 + 2 × 6, allow one incorrect product or 90 seen and M1 dep for ‘their 90’ ÷ 27