Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 May/June Paper 3 · 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 104. MATHEMATICS 0581/32 Paper 3 (Core) May/June 2013 2 hours 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 16 printed pages. [Turn over IB13 06_0581_32/FP © UCLES 2013 *2662092709* www.XtremePapers.com

2 0581/32/M/J/13 © UCLES 2013 For Examiner′s Use 1 (a) 3 5 8 10 10 For the numbers above, fi nd (i) the mean, Answer(a)(i) … [2] (ii) the mode, Answer(a)(ii) … [1] (iii) the median, Answer(a)(iii) … [1] (iv) the range. Answer(a)(iv) … [1] (v) A sixth number, 11, is added to the list. Write down which one of the mean, the mode, the median and the range will stay the same. Answer(a)(v) … [1] (b) The table shows the results of asking 24 children their favourite colour. Colour Red Blue Yellow Green Pink Number of children 4 8 2 3 7 Write down the probability, as a fraction, that the favourite colour of a child chosen at random is (i) blue, Answer(b)(i) … [1] (ii) not pink. Answer(b)(ii) … [1] (c) The information in part (b) is to be shown in a pie chart. Work out the sector angle for green. Do not draw the pie chart. Answer(c) … [2] _____________________________________________________________________________________

3 0581/32/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 2 Three children have some marbles. Shireen has m marbles. Nazaneen has three times as many marbles as Shireen. Karly has 4 more marbles than Shireen. (a) Write down an expression, in terms of m, for (i) the number of marbles Nazaneen has, Answer(a)(i) … [1] (ii) the number of marbles Karly has. Answer(a)(ii) … [1] (b) The three children have a total of 84 marbles between them. (i) Write down an equation in m. Answer(b)(i) … [1] (ii) Solve your equation. Answer(b)(ii) m = … [2] (c) Shireen weighs the 84 identical marbles. Their total weight is 4.2 kg. Calculate, in grams, the weight of one marble. Answer(c) … g [2] (d) The children now decide to share the 84 marbles in the ratio Shireen : Nazaneen : Karly = 2 : 7 : 3 . Calculate the number of marbles each receives. Answer(d) Shireen … Nazaneen … Karly … [3] _____________________________________________________________________________________

4 0581/32/M/J/13 © UCLES 2013 For Examiner′s Use 3 (a) A shop has maps arranged in bookcases. (i) The length of one wall in the shop is 7.35 m. Each bookcase is 120 cm wide. Work out the maximum number of bookcases that will fi t along this wall. Answer(a)(i) … [2] (ii) Each bookcase weighs 45 kg correct to the nearest 5 kg. Write down the upper bound for the weight of a bookcase. Answer(a)(ii) … kg [1] (b) During July and August the shop sells a total of 160 maps. Some of these maps are driving maps and the rest are walking maps. (i) Complete the table below. Driving maps Walking maps Total July 15 August 65 Total 40 160 [2] (ii) Write down the fraction of the total number of walking maps that are sold in July. Give your answer in its simplest form. Answer(b)(ii) … [2]

5 0581/32/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (c) The shopkeeper buys each map for $5.50 . He sells each map for $6.60 . (i) Calculate his percentage profi t. Answer(c)(i) … % [3] (ii) Each map has a price in dollars ($) and euros (€). The price is $6.60 or €3.52 . Work out the exchange rate for €1 . Answer(c)(ii) €1 = $ … [2] (d) The shop is open for 312 days each year. The shopkeeper pays 3 employees $47.66 each per day. The total annual wage bill for the three employees is given by 3 × 312 × 47.66 . (i) Rewrite this calculation so that each number is rounded to 1 signifi cant fi gure. 3 × … × … [1] (ii) Use your answer to part (d)(i) to work out an estimate for the total annual wage bill. Answer(d)(ii) $ … [1] _____________________________________________________________________________________

6 0581/32/M/J/13 © UCLES 2013 For Examiner′s Use 4 The diagram is part of a map showing the position of two towns Anderro, A, and Bratena, B. The scale is 1 centimetre represents 10 kilometres. North North A B Scale: 1 cm to 10 km (a) Work out the distance, in kilometres, from Anderro to Bratena. Answer(a) … km [2] (b) Measure the bearing of Bratena from Anderro. Answer (b) … [1] (c) Carribon is 80 km from Anderro. The bearing of Carribon from Anderro is 304°. Mark the position of Carribon on the diagram. Label it C. [2] _____________________________________________________________________________________

7 0581/32/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 5 A B C D E (a) In this part, all constructions must be completed using a straight edge and compasses only. All construction arcs must be clearly shown. (i) Construct the perpendicular bisector of DE. [2] (ii) Mark the midpoint of DE with the letter M. [1] (iii) Construct the bisector of angle BCD. Label the point, F, where this line crosses the line you have drawn in part (a)(i). [2] (iv) Write down the mathematical name of the quadrilateral CDMF. Answer(a)(iv) … [1] (b) (i) Draw the locus of points which are 4 cm from A. [1] (ii) Draw the locus of points which are 3 cm from E. [1] (iii) Shade the region which is less than 3 cm from E and more than 4 cm from A. [1] _____________________________________________________________________________________

8 0581/32/M/J/13 © UCLES 2013 For Examiner′s Use 6 Finn is going camping. The diagram shows his tent. 2.5 m 1.5 m 1.2 m M C A B NOT TO SCALE ABC is an isosceles triangle. M is the midpoint of AC. AB = 1.5 m and BM = 1.2 m. (a) Show that AM = 0.9 m. Answer(a) [2] (b) Use trigonometry to calculate angle ABM. Answer(b) Angle ABM = … [2]

9 0581/32/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (c) The tent is a prism of length 2.5 m. The area of triangle ABC is 1.08 m2. Calculate the volume of the tent. Give the units of your answer. Answer(c) … … [2] (d) Calculate the surface area of the tent, including the base. Answer(d) … m2 [3] _____________________________________________________________________________________

10 0581/32/M/J/13 © UCLES 2013 For Examiner′s Use 7 (a) Complete the table of values for the function y = x2 – 5x + 2 . x –1 0 1 2 3 4 5 y –2 –4 –4 2 [2] (b) On the grid, draw the graph of y = x2 – 5x + 2 for –1 Ğ x Ğ=5 . y x 9 8 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 0 –1 –2 –3 –4 –5 –6 5 6 4 3 2 1 [4]

11 0581/32/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (c) (i) Write down the co-ordinates of the lowest point of the graph of y = x2 – 5x + 2 . Answer(c)(i) (… , …) [1] (ii) On the grid, draw the line y = –1 . [1] (iii) Write down the x co-ordinates of the two points where y = –1 crosses the graph of y = x2 – 5x + 2 . Answer(c)(iii) x = … and x = … [2] (d) The point (5, 2) is refl ected in the y-axis. Write down the co-ordinates of the image of the point. Answer(d) (… , …) [1] (e) Write down the equation of the line, l, drawn on the grid below. Give your answer in the form y = mx + c . y x 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 0 –1 1 2 3 4 5 –2 –3 l Answer(e) y = … [3] _____________________________________________________________________________________

12 0581/32/M/J/13 © UCLES 2013 For Examiner′s Use 8 5 4 3 2 1 0 14 10 14 20 14 30 14 40 14 50 15 00 Time 15 10 15 20 15 30 15 40 Distance (km) Sweet shop Home (a) Jono walked from his home to a sweet shop. Use the travel graph to calculate his walking speed in kilometres per hour. Answer(a) … km/h [2] (b) Jono stayed in the sweet shop for 20 minutes. He then ran home at a steady speed of 12 km/h. (i) On the grid above, complete the travel graph for Jono. [2] (ii) Write down the time Jono arrived home. Answer(b)(ii) … [1]

13 0581/32/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (c) The sweet shop owner records how much time and how much money children spend in his shop. Time in shop (min) 3 6 7 9 10 11 12 14 15 15 20 Money spent ($) 0.50 1.20 1.10 1.60 2.00 1.70 2.00 2.80 2.30 2.90 3.00 0 5 10 15 20 25 Time in shop (min) Money spent ($) 3 2 1 (i) Complete the scatter diagram. The fi rst seven points have been plotted for you. [2] (ii) What type of correlation does this scatter diagram show? Answer(c)(ii) … [1] (iii) On the grid, draw the line of best fi t. [1] (iv) A child spent $2.50 in the shop. Use your line of best fi t to estimate how long the child was in the shop. Answer(c)(iv) … min [1] _____________________________________________________________________________________

14 0581/32/M/J/13 © UCLES 2013 For Examiner′s Use 9 A family of 2 adults and 3 children are on holiday. They each hire a mountain bike from the hotel. Large mountain bike Small mountain bike First hour Each extra hour First hour Each extra hour $6 $2 $3.60 $1.20 (a) The family hire 2 large and 3 small mountain bikes for 5 hours. (i) Work out the total cost. Answer(a)(i) $ … [3] (ii) The hotel gives the family a discount of 15% on the total cost. Work out how much the family pays. Answer(a)(ii) $ … [2] (b) A wheel of a large bike has a radius of 32 cm. (i) Calculate the circumference of a wheel of a large bike. Answer(b)(i) … cm [2]

15 0581/32/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (ii) The family cross a bridge which is 24 m long. Calculate how many complete turns a wheel of a large bike makes to cross the bridge. Answer(b)(ii) … [2] (c) The diagram shows part of a wheel of a large bike. There is an angle of 9° between two metal spokes. Each spoke is 29 cm long. Calculate the total length of metal, in metres, needed to make the spokes for one wheel. Answer(c) … m [3] _____________________________________________________________________________________ Question 10 is printed on the next page. 9° NOT TO SCALE

16 0581/32/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 10 (a) (i) Find the highest common factor (HCF) of 24 and 36. Answer(a)(i) … [2] (ii) Factorise. 24x + 36y Answer(a)(ii) … [1] (b) Simplify. (i) w + 8k – 5w + 2k Answer(b)(i) … [2] (ii) (x4)5 Answer(b)(ii) … [1] (c) Here are the fi rst four terms of a sequence. 7 11 15 19 Find the nth term of this sequence. Answer(c) … [2] (d) Solve the simultaneous equations. 3x + y = 8 x + 5y = 5 Answer(d) x = … y = … [3]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0581 MATHEMATICS 0581/32 Paper 3 (Core), maximum raw mark 104 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 32 © 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 (a) (i) (ii) (iii) (iv) (v) (b) (i) (ii) (c) 7.2 oe 10 8 7 Mode 24 8 oe 24 17 45° 2 1 1 1 1 1 1 2 M1 for (3 + 5 + 8 + 10 + 10)/5 or 36/5 Must be a fraction SC1 for bi and bii both given as decimals only i.e. 0.333(…..) and 0.708(….) M1 for 360 × 3/24 or better seen 2 (a) (i) (ii) (b) (i) (ii) (c) (d) 3m m + 4 m + 3m + m + 4 = 84 oe isw 16 50 [Shireen =] 14 [Nazaneen =] 49 [Karly =] 21 1 1 1ft 2 2 1 1 1 ft m + (a)(i) + (a)(ii) = 84 if and only if (a)(i) and (a)(ii) are both in terms of m M1ft for “5”m = “80” i.e. pm = q (could be seen in bi) May be implied by a correct answer M1 for 4.2/84 × 1000 or better SC1 for figs ‘5’ or 4200 seen if M0 then M1 for 84/(2 + 7 + 3) or better and / or SC1 3 correct answers in wrong order.

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 32 © Cambridge International Examinations 2013 3 (a) (i) (ii) (b) (i) (ii) (c) (i) (ii) (d) (i) (ii) 6 cao 47.5 55 ---- 70 ---- 25 90 120 ---- --- 8 3 cao 20 1.875 cao 300, 50 45000 2 1 2 2 3 2 1 1 M1 for 735/120 oe implied by 6.125 or SC1 for figs ‘61…’ M1 for 3 or 4 correct numbers B1 for 40 15 or 8 3 seen B1 for 6.6 - 5.5 or better M1 for ‘their 1.1’ / 5.5 OR (an alternative method) M1 for 6.6/5.5 M1 for ‘their 1.2’ –1 oe M1 for 6.60/3.52, imp by 1.87 or 1.88 SC1 43200 4 (a) (b) (c) 56 to 60 [0]35 to [0]39 Correct length and bearing 2 1 2 B1 for 5.6 to 6.0 B1 for correct length 7.8 to 8.2 B1 for correct bearing 302º to 306º

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 32 © Cambridge International Examinations 2013 5 (a) (i) (ii) (iii) (iv) (b) (i) (ii) (iii) Perpendicular bisector with 2 sets of correct arcs M labelled Angle bisector with 2 sets of correct arcs Trapezium Circle centre A radius 4 cm ± 0.2 cm Circle centre E radius 3 cm ± 0.2 cm Correct region shaded cao 2 1ft 2 1 1 1 1 B1 correct line with some or no arcs Ft is intersection of their bisector with DE B1 correct line with some or no arcs 6 (a) (b) (c) (d) AM2 + 1.22 = 1.52 or [AM2] = 1.52 – 1.22 [AM=] √ (1.52 – 1.22) or √( 2.25 – 1.44) or √0.81 36.9 or 36.87 or 36.8[6…] 2.7 m3 14.2 or 14.16 M1 M1dep 2 1 1 3 M1 for cos[ABM] = 5.1 2.1 oe or better indep M2 for 2 × 0.5 × 2 × 0.9 × 1.2 + 2.5 × 2 × 0.9 + 2 × 2.5 × 1.5 or better or M1 for 2.5 × 2 × 0.9 or 2 × 2.5 × 1.5 or better if M0 then SC1 for 13.41

Page 5 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 32 © Cambridge International Examinations 2013 7 (a) (b) (c) (i) (ii) (iii) (d) (e) 8, 2, –2, 7 correctly plotted points Correct smooth curve going below y = –4 at lowest point ( 2.5cao , –4.25) y = – 1 drawn 0.5 to 0.9, 4.1 to 4.5 (– 5, 2) [y] = – 2 x + 3 2 3ft 1 1 1 1ft,1ft 1 3 B1 for 2 correct y values P2ft for 5 or 6 correctly plotted points P1ft for 3 or 4 correctly plotted points must be ruled and continuous ft is the x coordinates of the intersection of their line and their curve M2 for y = – 2 x + p or y = 2x + 3 or M1 for y = 2x + q or for attempt at rise/run even if negative not shown B1 for y = kx + 3 k≠0 8 (a) (b) (i) (b) (ii) (c) (i) (ii) (iii) (iv) 6 Line from (1450,4) to (1510,4) Line from (1510,4) to (1530,0) 1530 4 points plotted correctly Positive Correct ruled line 12< Ans <16 2 1 1ft 1ft 2 1 1 1ft M1 for 40 4 [× 60] oe Ft is (their 1510,4) to (their 1510 + 20,0) P1 for 3 correct

Page 6 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 32 © Cambridge International Examinations 2013 9 (a) (i) (ii) (b) (i) (ii) (c) 53.2[0] 45.22 201 or 201.06 to 201.1 or 2.01m 11 final answer 11.6 3 2ft 2 2 3 SC2 for 60.80 M2 for 2 × (6 + 4 × 2) + 3 × (3.60 + 4 × 1.20) or better or for 2 × 6 + 3 × 3.60 + 4(2 × 2 + 3 × 1.20) or better if M0 then B1 for 28 or 25.20 or 22.80 or 22.40 or 30.40 or 12 and 10.80 or 16 and 14.40 or 14 and 8.40 seen M1ft for ‘their ai’ × 0.85 oe M1 for 2 × π × 32 oe M1ft for bi their 2400 both in cm or bi their 24 both in m or SC1 for figs ‘119……’ M1 for 9 360 × 29 or better, implied by 1160 and M1 indep for ‘their 1160’ / 100 soi or 0.29 seen 10 (a) (i) (ii) (b) (i) (ii) (c) (d) 12 12(2x + 3y) cao 10k – 4w x20 4n + 3 oe final answer [x] = 2.5, [y] = 0.5 2 1 2 1 2 3 B1 for any other common factor other than 1 B1 for either 10k ± nw or qk – 4w p,q ≠ 0 B1 for 4n + c or kn + 3 , k ≠ 0 M1 for correct method to eliminate one variable. A1 for x or y correct.