Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 May/June Paper 2 · 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 70. MATHEMATICS 0581/23 Paper 2 (Extended) May/June 2013 1 hour 30 minutes 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 12 printed pages. [Turn over IB13 06_0581_23/FP © UCLES 2013 *1411986028* www.XtremePapers.com

2 0581/23/M/J/13 © UCLES 2013 For Examiner′s Use 1 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] _____________________________________________________________________________________ 2 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] _____________________________________________________________________________________ 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 0581/23/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 4 Use a calculator to fi nd (a) 5 24 5 , Answer(a) … [1] (b) ° 40 7 cos . Answer(b) … [1] _____________________________________________________________________________________ 5 Write the following in order of size, smallest fi rst. 3 .1 5 2 ^ h 1.5 3 2 c m 1.5 - 3 2 c m 3 3 2 - 2 c m Answer … < … < … < … [2] _____________________________________________________________________________________ 6 The volumes of two similar cones are 36π cm3 and 288π cm3. The base radius of the smaller cone is 3 cm. Calculate the base radius of the larger cone. Answer … cm [3] _____________________________________________________________________________________

4 0581/23/M/J/13 © UCLES 2013 For Examiner′s Use 7 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] _____________________________________________________________________________________ 8 The mass, m, of a sphere varies directly with the cube of its radius, r. m = 160 when r = 2. Find m when r = 5. Answer m = … [3] _____________________________________________________________________________________

5 0581/23/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 9 Calculate, giving your answers in standard form, (a) 2 × (5.5 × 104) , Answer(a) … [2] (b) (5.5 × 104) – (5 × 104) . Answer(b) … [2] _____________________________________________________________________________________ 10 Find the value of 2x + y for the simultaneous equations. 3x + 5y = 48 2x – y = 19 Answer 2x + y = … [4] _____________________________________________________________________________________

6 0581/23/M/J/13 © UCLES 2013 For Examiner′s Use 11 The sum of the prime numbers less than 8 is equal to 17. (a) Find the sum of the prime numbers less than 21. Answer(a) … [2] (b) The sum of the prime numbers less than x is 58. Find an integer value for x. Answer(b) x = … [2] _____________________________________________________________________________________ 12 Two spinners have sections numbered from 1 to 5. Each is spun once and each number is equally likely. The possibility diagram is shown below. 1 1 2 3 4 5 2 3 4 5 Second spinner First spinner 1 2 3 4 5 1 2 3 4 5 Find the probability that (a) both spinners show the same number, Answer(a) … [2] (b) the sum of the numbers shown on the two spinners is 7. Answer(b) … [2] _____________________________________________________________________________________

7 0581/23/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 13 Write as a single fraction in its simplest form. 3 x x x x 3 1 1 + + - - - Answer … [4] _____________________________________________________________________________________ 14 (a) Solve 3n + 23 < n + 41. Answer(a) … [2] (b) Factorise completely ab + bc + ad + cd. Answer(b) … [2] _____________________________________________________________________________________

8 0581/23/M/J/13 © UCLES 2013 For Examiner′s Use 15 A B C y x 12 – x 15 – x 20 – x 14 13 8 The Venn diagram shows the number of elements in sets A, B and C. (a) n(A ∪ B ∪ C ) = 74 Find x. Answer(a) x = … [2] (b) n( ) = 100 Find y. Answer(b) y = … [1] (c) Find the value of n((A ∪ B )' ∩ C ). Answer(c) … [1] _____________________________________________________________________________________

9 0581/23/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 16 f(x) = x + x 2 – 3, x ¸ 0 g(x) = 2 x – 5 Find (a) fg(18), Answer(a) … [2] (b) g–1(x). Answer(b) g–1(x) = … [2] _____________________________________________________________________________________ 17 M = 2 3 3 6 e o N = 2 1 1 7 5 2 e o (a) Work out MN. Answer(a) [2] (b) Find M–1, the inverse of M. Answer(b) [2] _____________________________________________________________________________________

10 0581/23/M/J/13 © UCLES 2013 For Examiner′s Use 18 O A B 120° 5 cm NOT TO SCALE A and B lie on a circle centre O, radius 5 cm. Angle AOB = 120°. Find the area of the shaded segment. Answer … cm2 [4] _____________________________________________________________________________________

11 0581/23/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 19 C O E A D B c b OABCDE is a regular polygon. (a) Write down the geometrical name for this polygon. Answer(a) … [1] (b) O is the origin. = b and = c. Find, in terms of b and c, in their simplest form, (i) , Answer(b)(i) = … [1] (ii) , Answer(b)(ii) = … [2] (iii) the position vector of E. Answer(b)(iii) … [1] _____________________________________________________________________________________ Question 20 is printed on the next page.

12 0581/23/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 (a) y = x 8 + 4 Find y when x = 2. Give your answer correct to 4 decimal places. Answer(a) y = … [2] (b) Rearrange y = x 8 + 4 to make x the subject. Answer(b) x = … [4]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0581 MATHEMATICS 0581/23 Paper 2 (Extended), maximum raw mark 70 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 23 © 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 Marks 1 £ or pound[s] Correct working must be shown 2 M1 for 425 ÷ 1.14 or 365 × 1.14 2 oe www 2 M1 for 30 seen or 300 k seen 3 1500 or 3 pm 2 B1 for 1h50 or 2h[0]5 or SC1 for 1255 + their 1h50 + 15mins correctly evaluated 4 (a) (b) [ ± ] 2.28 or 2.282 to 2.2822 0.109 or 0.1094[3…] 1 1 5 5.1 3 2       3 2 3 2      − ( )3 2 5.1 5.1 3 2 −       2 M1 for at least 2 correct decimals seen 1.3[1..] 0.5[4..] 1.8[3..] or 1.84 0.7[6..] 6 6 3 M2 for 3 36 288 3 π π × or M1 for 3 36 288 3 π π × or 3 288 36 3 π π × 7 260 3 M2 for [2 × ](4 × 10 + 18 × 5) oe or M1 for a correct area statement 8 2500 3 M1 for 3 kr m = A1 for k = 20 9 (a) (b) 1.1 × 105 5 × 103 2 2 B1 for 110 000 oe e.g.11 × 104 B1 for 5000 oe e.g. 0.5 × 104 30 300

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 23 © Cambridge International Examinations 2013 10 25 4 M1 for correct method to eliminate one variable A1 for x = 11 A1 for y = 3 B1 FT for 2 × their x + their y correctly evaluated 11 (a) (b) 77 either 18 or 19 or both 2 2FT M1 for 11,13,17,19 clearly identified, ignore numbers less than 8 with no other numbers greater than or equal to 8 besides possibly an extra 17 M1 for 11,13,17 clearly identified, ignore numbers less than 8 with no other numbers greater than or equal to 8 besides possibly an extra 17 or for their (a) − 58 12 (a) (b) 25 5 oe 25 4 oe 2 2 B1 for answer k 5 or 25 k B1 for answer k 4 or 25 k 13 )1 )( 3 ( 8 + − x x x 4 B1 for common denominator (x – 3)(x + 1) seen B1 for (x + 3)(x + 1) – (x – 1)(x – 3) soi B1 for x2 + 3x + x + 3 or x2 – 3x – x + 3 soi 14 (a) (b) n < 9 (b + d)(a + c) 2 2 M1 for 2n < 18 or 2n – 18 < 0 oe If 0 scored SC1 for 9 with incorrect inequality. B1 for b(a + c) + d(a + c) or a(b + d) + c (b + d) 15 (a) (b) (c) 4 26 8 2 1FT 1 M1 for attempt at sum of all numeric and x terms equated to 74 =18 + 2 × their (a) 16 (a) (b) 1.5 2(x + 5) or 2x + 10 2 2 B1 for [g(18) =] 4 M1 for correct first step e.g. 5 5 − = y x or 5 2 + = y x or 2y = x – 10

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 23 © Cambridge International Examinations 2013 17 (a) (b)       27 45 12 16 23 7       − − 2 3 3 6 3 1 2 2 B1 for any one row or column correct, must be in a 2 by 3 matrix B1 for       − − 2 3 3 6 k or       d c b a 3 1 18 15.4 or 15.35 to 15.36 4 M1 for 2 5 360 120 × ×π oe M1 for 120 sin 5 2 1 2 × × oe M1 for 120 sin 5 2 1 5 360 120 2 2 × × − × ×π oe 19 (a) (b) (i) (ii) (iii) hexagon −b + c b − 1 2 c −b + c 1 1 2 1FT B1 for OB + BA or any correct route = their (b)(i) 20 (a) (b) [ ± ] 3.1623 cao 8 4 2 − y oe final answer 2 4 M1 for √10 seen M1 first move completed correctly M1 second move completed correctly M1 third move completed correctly M1 final move completed correctly on answer line