Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 Oct/Nov Paper 2 · Variant 2

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 0581/22 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_22/FP © UCLES 2013 *3046230711* www.XtremePapers.com

2 0581/22/O/N/13 © UCLES 2013 For Examiner′s Use 1 Write the following in order of size, smallest fi rst. 19% 5 1 .0 038 sin 11.4° 0.7195 Answer … < … < … < … < … [2] _____________________________________________________________________________________ 2 Use a calculator to work out the following. (a) 3 (– 4 × 62 – 5) Answer(a) … [1] (b) 3 × tan 30° + 2 × sin 45° Answer(b) … [1] _____________________________________________________________________________________ 3 Find the circumference of a circle of radius 2.5 cm. Answer … cm [2] _____________________________________________________________________________________ 4 Bruce plays a game of golf. His scores for each of the 18 holes are shown below. 2 3 4 5 4 6 2 3 4 4 5 3 4 3 5 4 4 4 The information is to be shown in a pie chart. Calculate the sector angle for the score of 4. Answer … [2] _____________________________________________________________________________________

3 0581/22/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 5 (a) Add one line to the diagram so that it has two lines of symmetry. [1] (b) Add two lines to the diagram so that it has rotational symmetry of order 2. [1] _____________________________________________________________________________________ 6 Rearrange the formula to make x the subject. y = x2 + 4 Answer x = … [2] _____________________________________________________________________________________

4 0581/22/O/N/13 © UCLES 2013 For Examiner′s Use 7 12 cm 10 cm 22 cm NOT TO SCALE Find the area of the trapezium. Answer … cm2 [2] _____________________________________________________________________________________ 8 A hemisphere has a radius of 12 cm. Calculate its volume. [The volume, V, of a sphere with radius r is V = 4 3 πr 3.] Answer … cm3 [2] _____________________________________________________________________________________ 9 The exterior angle of a regular polygon is 36°. What is the name of this polygon? Answer … [3] _____________________________________________________________________________________ 12 cm

5 0581/22/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 10 The table shows how the dollar to euro conversion rate changed during one day. Time 10 00 11 00 12 00 13 00 14 00 15 00 16 00 $1 €1.3311 €1.3362 €1.3207 €1.3199 €1.3200 €1.3352 €1.3401 Khalil changed $500 into euros (€). How many more euros did Khalil receive if he changed his money at the highest rate compared to the lowest rate? Answer € … [3] _____________________________________________________________________________________ 11 The speed, v, of a wave is inversely proportional to the square root of the depth, d, of the water. v = 30 when d = 400. Find v when d = 25. Answer v = … [3] _____________________________________________________________________________________ 12 A circle has a radius of 8.5 cm correct to the nearest 0.1 cm. The lower bound for the area of the circle is pπ cm2. The upper bound for the area of the circle is qπ cm2. Find the value of p and the value of q. Answer p = … q = … [3] _____________________________________________________________________________________

6 0581/22/O/N/13 © UCLES 2013 For Examiner′s Use 13 Pam wins the student of the year award in New Zealand. She sends three photographs of the award ceremony by post to her relatives. ● one of size 13 cm by 23 cm to her uncle in Australia ● one of size 15 cm by 23 cm to her sister in China ● one of size 23 cm by 35 cm to her mother in the UK Maximum lengths Australia Rest of the world 13 cm by 23.5 cm $1.90 $2.50 15.5 cm by 23.5 cm $2.40 $2.90 23 cm by 32.5 cm $2.80 $3.40 26 cm by 38.5 cm $3.60 $5.20 The cost of postage is shown in the table above. Use this information to calculate the total cost. Answer $ … [3] _____________________________________________________________________________________ 14 142° D A O C B NOT TO SCALE A, B and C are points on the circumference of a circle centre O. OAD is a straight line and angle DAB = 142°. Calculate the size of angle ACB. Answer Angle ACB = … [3] _____________________________________________________________________________________

7 0581/22/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 15 Find the co-ordinates of the point of intersection of the two lines. 2x – 7y = 2 4x + 5y = 42 Answer (… , …) [3] _____________________________________________________________________________________ 16 Solve the inequality. x 2 + x 3 2 - < 5 Answer … [4] _____________________________________________________________________________________

8 0581/22/O/N/13 © UCLES 2013 For Examiner′s Use 17 M = 2 4 1 6 f p N = 5 1 0 5 f p (a) Work out MN. Answer(a) MN = [2] (b) Find M–1. Answer(b) M–1 = [2] _____________________________________________________________________________________

9 0581/22/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 18 A (5, 23) and B (–2, 2) are two points. (a) Find the co-ordinates of the midpoint of the line AB. Answer(a) (… , …) [2] (b) Find the equation of the line AB. Answer(b) … [3] (c) Show that the point (3, 17) lies on the line AB. Answer(c) [1] _____________________________________________________________________________________

10 0581/22/O/N/13 © UCLES 2013 For Examiner′s Use 19 O E C F A D B c a O is the origin. ABCDEF is a regular hexagon and O is the midpoint of AD. = a and = c. Find, in terms of a and c, in their simplest form (a) , Answer(a) = … [2] (b) , Answer(b) = … [2] (c) the position vector of E. Answer(c) … [2] _____________________________________________________________________________________

11 0581/22/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 20 During one day 48 people visited a museum. The length of time each person spent in the museum was recorded. The results are shown on the cumulative frequency diagram. 50 40 30 20 10 0 1 2 3 4 Time (hours) 5 6 Cumulative frequency Work out (a) the median, Answer(a) … h [1] (b) the 20th percentile, Answer(b) … h [2] (c) the inter-quartile range, Answer(c) … h [2] (d) the probability that a person chosen at random spends 2 hours or less in the museum. Answer(d) … [2] _____________________________________________________________________________________ Question 21 is printed on the next page.

12 0581/22/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 21 B C A NOT TO SCALE 6 cm 4 cm 65° In triangle ABC, AB = 6 cm, BC = 4 cm and angle BCA = 65°. Calculate (a) angle CAB, Answer(a) Angle CAB = … [3] (b) the area of triangle ABC. Answer(b) … cm2 [3]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2013 series 0581 MATHEMATICS 0581/22 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 22 © 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 19% 0.7195 038 .0 sin 11.4 1/5 2 B1 for decimals [0.19], [0.2], 0.194…, 0.197…, 0.192… seen Or for four in correct order 2 (a) –447 1 (b) 2 1 3 15.7 or 15.70 to 15.71 2 M1 for 2 × π × 2.5 4 160 2 M1 for 360 18 8 × oe 5 (a) 1 (b) Some possible answers: 1 6 [±] 4 − y final answer 2 M1 for first move completed correctly M1 for second move completed correctly on answer line 7 170 2 M1 for 10 ) 22 12 ( 2 1 × + × oe 8 3619 to 3620 2 M1 for 3 12 × π × × 3 4 2 1 or better 9 decagon 3 M1 for 360 ÷ 36 oe A1 for 10 10 10.1[0] 3 M1 for 1.3199 and 1.3401 seen and M1 for 500 × 1.3199 or 500 × 1.3401 or for 500 × (their highest – their lowest) oe 11 120 3 M1 for d k v = A1 for k = 600

Page 3 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 22 © Cambridge International Examinations 2013 12 p = 71.4025 cao q = 73.1025 cao 3 B1 for 8.45 and 8.55 seen M1 for their LB2 [π] or their UB2 [π] If 0 scored, SC1 for one correct. 13 10[.00] 3 M2 for 1.90 and 2.90 and 5.20 only or M1 for two of 1.90, 2.90, 5.20 in a list of three or two values from the table or SC1 FOR 1.90, 2.90, 4.30     + 2 20 .5 40 .3 from 14 52 3 B2 for AOB = 104 or B1 for OAB or OBA = 38 15 (8, 2) 3 M1 for correctly eliminating one variable A1 for x = 8 A1 for y = 2 If 0 scored, SC2 for correct substitution and correct evaluation to find the other value. 16 x <6.8 4 B3 for 6.8 with wrong inequality or equal as answer. Or M1 for first move completed correctly and M1 for second move completed correctly and M1 for third move completed correctly 17 (a)       30 26 5 11 2 SC1 for one correct row or column (b)       − − 2 4 1 6 8 1 oe 2 B1 for       − − 2 4 1 6 k or B1 for       d c b a 8 1 18 (a) (1.5, 12.5) oe 2 B1 for either coordinate (b) y = 3x + 8 oe 3 B2 for y = mx + 8 or y = 3x + c or 3x + 8 or B1 for gradient (or m) = 3 and B1 for c = 8 If 0 scored, SC1 for 23 = their m × 5 + c or for 2 = their m × –2 + c or for 12.5 = their m × 1.5 + c (c) Most common methods: Correctly substituting P (3, 17) into y = 3x + 8 Showing the gradient of AP or BP = 3 Other methods possible. 1

Page 4 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 22 © Cambridge International Examinations 2013 19 (a) –2a – 2c oe 2 M1 for BO = –a – c or for any correct route or correct unsimplified expression (b) 2a + c 2 M1 for any correct route or correct unsimplified expression (c) –a – c oe 2FT FT their (a) or correct answer Or M1 for a correct non direct route from O to E or for correct unsimplified expression or for correct FT unsimplified 20 (a) 4.05 to 4.2 1 (b) 2.6 to 2.75 2 B1 for 9.6 seen (c) 2.05 to 2.25 2 B1 for [UQ] 5.0 to 5.1 and [LQ] 2.85 to 2.95 seen (d) 48 5 2 M1 for 5 21 (a) 37.2 or 37.17 to 37.19 3 M2 for sin[ ] = 6 65 sin 4× or M1 for 65 sin 6 sin[] 4 = oe (b) 11.7 or 11.72 to 11.74 3 M1 for [B =] 160 – 65 – their (a) M1 for 2 1 × 4 × 6 × sin their 77.8