Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 Oct/Nov 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) October/November 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 11_0581_23/FP © UCLES 2013 *1584534265* www.XtremePapers.com

2 0581/23/O/N/13 © UCLES 2013 For Examiner′s Use 1 Christa had a music lesson every week for one year. Each of the 52 lessons lasted for 45 minutes. Calculate the total time that Christa spent in music lessons. Give your time in hours. Answer … h [2] _____________________________________________________________________________________ 2 Three of the vertices of a parallelogram are at (4, 12), (8, 4) and (16, 16). 4 8 –8 –4 12 16 20 24 0 y x 24 20 16 12 8 4 Write down the co-ordinates of two possible positions of the fourth vertex. Answer (… , …) and (… , …) [2] _____________________________________________________________________________________ 3 Solve the equation 1 + 2x = –15 . Answer x = … [2] _____________________________________________________________________________________ 4 Write the following in order of size, smallest fi rst. cos100° tan100° 100 1 100–0.1 Answer … < … < … < … [2] _____________________________________________________________________________________

3 0581/23/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 5 Write (a) 60 square metres in square centimetres, Answer(a) … cm2 [1] (b) 22 metres per second in kilometres per hour. Answer(b) … km/h [2] _____________________________________________________________________________________ 6 In 2012 the cost of a ticket to an arts festival was $30. This was 20% more than the ticket cost in 2011. Calculate the cost of the ticket in 2011. Answer $ … [3] _____________________________________________________________________________________ 7 The solutions of the equation x2 – 6x + d = 0 are both integers. d is a prime number. Find d. Answer d = … [3] _____________________________________________________________________________________

4 0581/23/O/N/13 © UCLES 2013 For Examiner′s Use 8 m varies directly as the cube of x. m = 200 when x = 2 . Find m when x = 0.4 . Answer m = … [3] _____________________________________________________________________________________ 9 (a) Expand and simplify (a + b)2. Answer(a) … [2] (b) Find the value of a2 + b2 when a + b = 6 and ab = 7. Answer(b) … [1] _____________________________________________________________________________________

5 0581/23/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 10 15° h 628 m NOT TO SCALE Calculate the length h. Give your answer correct to 2 signifi cant fi gures. Answer h = … m [3] _____________________________________________________________________________________ 11 A = 1 3 4 - 2 f p I = 1 0 0 1 f p Work out the following. (a) AI Answer(a) AI = [1] (b) A–1 Answer(b) A–1 = [2] _____________________________________________________________________________________

6 0581/23/O/N/13 © UCLES 2013 For Examiner′s Use 12 Write the answer to the following calculations in standard form. (a) 600 ÷ 8000 Answer(a) … [2] (b) 108 – 7 × 106 Answer(b) … [2] _____________________________________________________________________________________ 13 M N D A C O B NOT TO SCALE 42° The vertices of the rectangle ABCD lie on a circle centre O. MN is a line of symmetry of the rectangle. AC is a diameter of the circle and angle ACD = 42°. Calculate (a) angle CAM, Answer(a) Angle CAM = … [2] (b) angle DCM. Answer(b) Angle DCM = … [2] _____________________________________________________________________________________

7 0581/23/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 14 (a) Simplify (64q–2) 1 2. Answer(a) … [2] (b) 57 ÷ 59 = p2 Find p. Answer(b) p = … [2] _____________________________________________________________________________________

8 0581/23/O/N/13 © UCLES 2013 For Examiner′s Use 15 A (a) Construct the locus of all the points which are 3 cm from vertex A and outside the rectangle. [2] (b) Construct, using a straight edge and compasses only, one of the lines of symmetry of the rectangle. [2] _____________________________________________________________________________________

9 0581/23/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 16 The diagram shows the entrance to a tunnel. The circular arc has a radius of 3 m and centre O. AB is horizontal and angle AOB = 120°. 120° O A B 3 m 3 m NOT TO SCALE During a storm the tunnel fi lled with water, to the level shown by the shaded area in the diagram. (a) Calculate the shaded area. Answer(a) … m2 [4] (b) The tunnel is 50 m long. Calculate the volume of water in the tunnel. Answer(b) … m3 [1] _____________________________________________________________________________________

10 0581/23/O/N/13 © UCLES 2013 For Examiner′s Use 17 (p, q) is the image of the point (x, y) under this combined transformation. p q f p = 1 0 0 1 - f p x y f p + 3 2 f p (a) Draw the image of the triangle under the combined transformation. y x 1 2 3 4 –4 –3 –2 –1 0 4 3 2 1 –1 –2 –3 –4 [3] (b) Describe fully the single transformation represented by 1 0 0 1 - f p . Answer (b) … [2] _____________________________________________________________________________________

11 0581/23/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 18 A gardener measured the lengths of 50 green beans from his garden. The results have been used to draw this cumulative frequency diagram. 5 10 15 20 25 30 35 0 50 40 30 20 10 Length of green bean (cm) Cumulative frequency Work out (a) the median, Answer(a) … cm [1] (b) the number of green beans that are longer than 26 cm, Answer(b) … [2] (c) the inter-quartile range, Answer(c) … cm [2] (d) the probability that a green bean chosen at random is more than 14 cm long. Answer(d) … [2] _____________________________________________________________________________________ Question 19 is printed on the next page.

12 0581/23/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. © UCLES 2013 For Examiner′s Use 19 f(x) = 2x + 3 g(x) = x2 (a) Find fg(6). Answer(a) … [2] (b) Solve the equation gf(x) = 100. Answer(b) x = … or x = … [3] (c) Find f –1(x). Answer(c) f –1(x) = … [2] (d) Find ff –1(5). Answer(d) … [1]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 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 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 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 Qu. Answers Mark Part Marks 1 39 2 M1 for 52 × 45 ÷ 60 oe 2 Any two of (20, 8) (–4, 0) (12, 24) 2 B1 for one correct 3 –8 2 M1 for 2x = –16 or 5.7 2 1 − = + x oe or better 4 tan 100, cos 100, 1/100, 100–0.1 2 B1 for decimals –0.1[[7..], –5.[67..], [0.01], 0.6[3..] or for three in the correct order 5 (a) 600 000 1 (b) 79.2 2 M1 for 22 × 60 × 60 ÷ 1000 oe 6 25[.00] 3 M2 for 30 × 120 100 oe or M1 for 30 associated with 120% e.g. 1.2x = 30 7 5 3 M2 for (x – 5)(x – 1) or M1 for evidence of a factorisation which gives the correct coefficient of x or positive prime constant term e.g. (x – 7)(x + 1), (x – 4)(x – 2), (x – 3)(x – 1) 8 1.6 oe 3 M1 for m = kx3 A1 for k = 25 9 (a) a2 + 2ab + b2 2 B1 for a2 [+] ab [+] ab [+] b2 or better seen (b) 22 1 10 160 3 M1 for sin 15 = 628 [] oe or better

Page 3 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 23 © Cambridge International Examinations 2013 11 (a)       − 2 4 1 3 1 (b)       − 2 4 1 2 10 1 oe 2 B1 for       d c b a 10 1 or B1 for       − 3 4 1 2 k 12 (a) 7.5 × 10–2 2 M1 for 0.075 or 40 3 or 80 6 or 0.75 × 10–1 oe (b) 9.3 × 107 2 M1 for 93 000 000 or 93 × 106 or 0.93 ×108 oe 13 (a) 24 2 M1 for MOC = 48 (b) 24 2 M1 for ACM = 66 or B1 for 48 – their (a) 14 (a) 8q–1 or q 8 2 B1 for 8qk or kq–1 (b) 1/5 or 0.2 2 M1 for 5–2, 2 5 1 or [0].04 seen oe 15 (a) Circle, radius 3 cm, centre A, not inside the rectangle 2 M1 for arc or full circle centre A radius 3 cm or for an incorrect size circle at A outside rectangle (b) One line of symmetry with correct arcs. E.g.: 2 B1 for correct ruled line (must reach or cross two sides) B1 for 2 pairs of intersecting arcs 16 (a) 8.61 or 8.609 to 8.6102 4 M1 for 120 sin 3 2 1 2 × π × × M1 for [ ] 2 3 360 30 2 × × π × M1 for area of triangle + 2 sectors (b) 430 or 431 or 430.4 to 430.41 1FT FT their (a) × 50

Page 4 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 23 © Cambridge International Examinations 2013 17 (a) triangle at (0, 3) (2, 3) and (2, 4) 3 B1 for each correct vertex If 0 scored then M1 for correct reflection in the y axis or correct translation of their first stage 3 right 2 up (b) reflection in y axis 2 B1 for reflection B1 for y axis or x = 0 18 (a) 19–19.1 1 (b) 3 2 M1 for 47 seen (c) 4.9 to 5.7 2 B1 for [UQ] 21.7 to 22.2 and [LQ] 16.5 to 16.8 (d) 50 45 oe 2 B1 for 45 seen or SC1 for 50 5 isw 19 (a) 75 2 B1 for [g(6) =] 36 (b) 3.5 –6.5 3 M1 for (2x + 3)2 = 100 M1 for 2x + 3 = [±]10 If 0 scored, SC1 for one correct value as answer (c) 2 3 − x oe final answer 2 M1 for x = 2y + 3 or y – 3 = 2x or 2 3 2 + = x y or better (d) 5 1