Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 Oct/Nov 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) October/November 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 10 printed pages and 2 blank pages. [Turn over IB13 11_0581_11/FP © UCLES 2013 *1753491317* www.XtremePapers.com

2 0581/11/O/N/13 © UCLES 2013 For Examiner′s Use 1 Write in fi gures the number one hundred and twenty one thousand and forty two. Answer … [1] _____________________________________________________________________________________ 2 Write down the number of centimetres in 2 2 1 metres. Answer … cm [1] _____________________________________________________________________________________ 3 Work out 72 cents as a percentage of 83 cents. Answer … % [1] _____________________________________________________________________________________ 4 There were 41 524 people at a football match. (a) Write 41 524 correct to the nearest thousand. Answer(a) … [1] (b) One quarter of the 41 524 people left before the end of the game. Find the number of people who left before the end of the game. Answer(b) … [1] _____________________________________________________________________________________ 5 (a) Write down the order of rotational symmetry of this shape. Answer(a) … [1] (b) Draw the lines of symmetry on this shape. [1] _____________________________________________________________________________________

3 0581/11/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 6 y x 5 4 3 2 1 –1 –2 0 –1 1 2 3 4 5 –2 –3 A (a) Write down the co-ordinates of point A. Answer(a) (… , …) [1] (b) On the grid, plot the point (–1, 3). [1] _____________________________________________________________________________________ 7 Simplify the following expression. 5a – 3b – 2a – b Answer … [2] _____________________________________________________________________________________ 8 Calculate . . . . 4 89 4 07 5 27 0 93 - - . Give your answer correct to 4 signifi cant fi gures. Answer … [2] _____________________________________________________________________________________

4 0581/11/O/N/13 © UCLES 2013 For Examiner′s Use 9 55° p° NOT TO SCALE Find the value of p. Answer p = … [2] _____________________________________________________________________________________ 10 Calculate 17.5% of 44 kg. Answer … kg [2] _____________________________________________________________________________________ 11 Find the value of (a) 94, Answer(a) … [1] (b) 60. Answer(b) … [1] _____________________________________________________________________________________

5 0581/11/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 12 Solve the equation. 5 – 2x = 3x – 19 Answer x = … [2] _____________________________________________________________________________________ 13 Yim knows one angle of an isosceles triangle is 48°. He says one of the other angles must be 66°. Explain why Yim is wrong. Answer … … [2] _____________________________________________________________________________________ 14 S P A C E S One of the 6 letters is taken at random. (a) Write down the probability that the letter is S. Answer(a) … [1] (b) The letter is replaced and again a letter is taken at random. This is repeated 600 times. How many times would you expect the letter to be S? Answer(b) … [1] _____________________________________________________________________________________

6 0581/11/O/N/13 © UCLES 2013 For Examiner′s Use 15 The length, p cm, of a car is 440 cm, correct to the nearest 10 cm. Complete the statement about p. Answer … Ğ p < … [2] _____________________________________________________________________________________ 16 8 15 7 8 7 15 4 13 4 3 10 2 9 4 5 (a) Write down the mode. Answer(a) … [1] (b) Work out the median. Answer(b) … [2] _____________________________________________________________________________________ 17 Bruce invested $800 at a rate of 3% per year simple interest. Calculate the total amount he has after 6 years. Answer $ … [3] _____________________________________________________________________________________

7 0581/11/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 18 A P B C (a) On the diagram above, draw a line perpendicular to the line AB, through the point P. [1] (b) Using a straight edge and compasses only, construct the locus of points that are equidistant from A and from C. [2] _____________________________________________________________________________________

8 0581/11/O/N/13 © UCLES 2013 For Examiner′s Use 19 The diagram shows a ladder of length 8 m leaning against a vertical wall. 56° 8 m NOT TO SCALE h Use trigonometry to calculate h. Give your answer correct to 2 signifi cant fi gures. Answer h = … m [3] _____________________________________________________________________________________ 20 a = 4 3 e o b = 2 0 - e o c = 5 - 1 e o Find (a) 4a, Answer(a) f p [2] (b) b – c. Answer(b) f p [2] _____________________________________________________________________________________

9 0581/11/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 21 Do not use a calculator in this question and show all the steps of your working. Give each answer as a fraction in its lowest terms. Work out. (a) 4 3 – 12 1 Answer(a) … [2] (b) 2 2 1 × 25 4 Answer(b) … [2] _____________________________________________________________________________________ 22 (a) Factorise completely. 6ab – 24bc Answer(a) … [2] (b) Rearrange the following formula to make m the subject. j = n m – k Answer(b) m = … [2] _____________________________________________________________________________________

10 0581/11/O/N/13 © UCLES 2013 For Examiner′s Use 23 (a) Here are the fi rst four terms of a sequence. 27 23 19 15 (i) Write down the next term in the sequence. Answer(a)(i) … [1] (ii) Explain how you worked out your answer to part (a)(i). Answer(a)(ii) … [1] (b) The nth term of a different sequence is 4n – 2 . Write down the fi rst three terms of this sequence. Answer(b) … , … , … [1] (c) Here are the fi rst four terms of another sequence. –1 2 5 8 Write down the nth term of this sequence. Answer(c) … [2] _____________________________________________________________________________________

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12 0581/11/O/N/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 2013 CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 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 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 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 Qu. Part Answers Mark Part Marks 1 121 042 1 2 250 1 3 86.7 or 86.74 to 86.75 1 4 (a) (b) 42 000 10 381 cao 1 1 5 (a) (b) 2 Both lines drawn 1 1 6 (a) (b) (4, 1) Point plotted at (–1, 3) 1 1 7 3a – 4b Final Answer 2 B1 for answer 3a ± jb or ka – 4b or SC1 for answer reached in working then spoilt 8 5.293 cao 2 B1 for 5.29 or 5.292 to 5.2927 9 125 2 B1 for 55 or 125 in any other correct position on diagram or M1 for 180 – 55

Page 3 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 11 © Cambridge International Examinations 2013 10 7.7 2 M1 for 44 × 100 17.5 oe 11 (a) (b) 6561 cao 1 1 1 12 4.8 oe 2 M1 for 5 + 19 = 3x + 2x oe or better or B1 24 – 2x = 3x oe or 5 = 5x – 19 oe 13 [Other angle could be] 84 2 M1 for 180 – (48 + 48) or SC1 shows that two angles of 66 are needed to make an isosceles triangle 14 (a) (b) 6 2 oe 200 Final answer 1 1FT FT 600 × their (a) providing their (a) is a probability 15 435, 445 cao 2 B1 for one value in correct place or SC1 for both values correct but reversed 16 (a) (b) 4 7 nfww 1 2 M1 for a correctly ordered list of at least 8 numbers 17 944 cao 3 M1 for 800 × 6 ×100 3 oe A1 for 144 A1 FT Dependent on M1 scored for their 144 + 800 evaluated 18 (a) (b) Ruled perpendicular line through P Correct ruled line drawn with 2 correct sets of arcs 1 2 ± 2° B1 for correct line without correct arcs or for 2 sets of correct arcs with no line 19 6.6 cao 3 M1 for sin 56 = 8 h oe or better A1 for 6.63… A1 FT Dependent on M1 scored for their answer correctly rounded to 2sf

Page 4 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 11 © Cambridge International Examinations 2013 20 (a) (b)       12 16      − 5 3 2 2 B1 for each correct component B1 for each correct component 21 (a) 12 9 – 12 1 oe [=] 12 8 oe [=] 3 2 M1 M1 Must be shown. Both fractions must be shown (b) 2 5 × 25 4 oe Cancelling shown or 50 20 oe [=] 5 2 M1 M1 Must be shown Dependent and cancelling shown or a fraction and then 5 2 must be shown 22 (a) (b) 6b( a – 4c) Final answer n (j + k) or nj + nk oe Final answer 2 2 B1 for answer 6( ab – 4bc ) or 3b( 2a – 8c ) or 2b( 3a – 12c ) or b( 6a – 24c ) M1 for one correct step of a two-step method or SC1 for [m] = k + jn or [m] = j+ kn 23 (a) (b) (c) (i) 11 (ii) subtract 4 oe 2, 6, 10 cao 3n – 4 oe 1 1 1 2 B1 for answer 3n ± k, where k is an integer