Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 May/June Paper 3 · 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 104. MATHEMATICS 0581/31 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 20 printed pages. [Turn over IB13 06_0581_31/FP © UCLES 2013 *1470714761* www.XtremePapers.com

2 0581/31/M/J/13 © UCLES 2013 For Examiner′s Use 1 (a) On a map, the height of Hillibar Station is 1047 m and the height of Sular Junction is 297 m. (i) Calculate the difference in these heights. Answer(a)(i) … m [1] (ii) The temperature falls by 1°C for every 100 m increase in height. One day the temperature in Sular Junction is 19°C. Work out the temperature at Hillibar Station. Answer(a)(ii) … °C [1] (iii) Write 297 correct to the nearest ten. Answer(a)(iii) … [1] (iv) Write 1047 correct to the nearest hundred. Answer(a)(iv) … [1] (b) (i) Kim arrives at Hillibar Station at 12 35. The taxi to her hotel takes 27 minutes. Work out the time Kim arrives at her hotel. Answer(b)(i) … [1] (ii) Henry takes 17 minutes to walk from his home to Sular Junction. He must arrive there by 10 43. Work out the latest time he can leave home. Answer(b)(ii) … [1]

3 0581/31/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (c) Here is part of a train timetable. Each journey from Sular Junction to Hillibar Station takes the same time. Sular Junction departs 10 59 12 32 14 48 Hillibar Station arrives 12 35 14 08 (i) Complete the timetable. [2] (ii) The distance between Sular Junction and Hillibar Station is 64 km. Calculate the average speed, in kilometres per hour, of a train between these two stations. Answer(c)(ii) … km/h [2] (iii) Joel arrives at Sular Junction at 11 48. At what time is the next train to Hillibar Station due to depart? Answer(c)(iii) … [1] _____________________________________________________________________________________

4 0581/31/M/J/13 © UCLES 2013 For Examiner′s Use 2 (a) 43° 108° p° A B NOT TO SCALE AB is a straight line. Find the value of p. Answer(a) p = … [1] (b) 123° 107° 88° q° NOT TO SCALE Find the value of q. Answer(b) q = … [1] (c) 48° r° s° NOT TO SCALE D C B A DCB is a straight line and AB = AC. Find the values of r and s. Answer(c) r = … s = … [2]

5 0581/31/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (d) NOT TO SCALE B A t° 130° The straight line AB crosses two parallel lines. Find the value of t. Answer(d) t = … [1] (e) NOT TO SCALE u° 124° C A B O A and B lie on a circle, centre O. AC and BC are tangents to the circle. Find the value of u. Answer(e) u = … [2] _____________________________________________________________________________________

6 0581/31/M/J/13 © UCLES 2013 For Examiner′s Use 3 (a) On each of the following shapes draw any lines of symmetry. (i) [1] (ii) [2] (b) Complete this shape by shading one square so that it has rotational symmetry of order 2. [1]

7 0581/31/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (c) 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 –6 –7 –5 –4 –3 –2 –1 1 0 2 3 4 5 6 7 y x B A T On the grid, draw the image of triangle T after a (i) refl ection in the line x = 4, [2] (ii) translation by the vector 4 5 - - e o , [2] (iii) rotation, centre (4, 1) through 180°. [2] (d) Describe fully the single transformation that maps (i) triangle T onto triangle A, Answer(d)(i) … [3] (ii) triangle T onto triangle B. Answer(d)(ii) … [2] _____________________________________________________________________________________

8 0581/31/M/J/13 © UCLES 2013 For Examiner′s Use 4 The table shows a summary of the types of employment for 90 people. Employment Frequency Pie chart sector angle Retail 18 72° Leisure industry 12 48° Public service 35 Other 25 (a) (i) Complete the table. [2] (ii) Complete the pie chart and label the sectors. Retail Leisure industry [2]

9 0581/31/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (b) Here are the ages of the people working in the leisure industry. 16 17 19 23 23 24 27 31 33 40 45 56 (i) Work out the range. Answer(b)(i) … years [1] (ii) Calculate the mean. Answer(b)(ii) … years [2] (iii) Sabrina wants to interview someone working in the leisure industry. She chooses one person at random. Write down the probability that the person chosen is under 30 years old. Answer(b)(iii) … [1] _____________________________________________________________________________________

10 0581/31/M/J/13 © UCLES 2013 For Examiner′s Use 5 The table shows the height, in metres, above sea-level and the temperature, in °C, at midday for some places on a mountain. Height above sea-level (m) 420 540 660 820 960 1100 1240 1580 Temperature (°C) 29.8 28.3 27.7 27.2 25.4 25.0 24.2 21.0 (a) Complete the scatter diagram for these results. The fi rst four points have been plotted for you. 30 29 28 27 26 25 24 23 22 21 20 400 600 800 1000 Height (m) 1200 1400 1600 Temperature (°C) [2] (b) What type of correlation does this scatter diagram show? Answer(b) … [1] (c) On the grid, draw the line of best fi t. [1] (d) Use your line of best fi t to estimate the temperature at a height of 1400 m. Answer(d) … °C [1] _____________________________________________________________________________________

11 0581/31/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 6 (a) (i) Write down all the factors of 22. Answer(a)(i) … [2] (ii) Write down a multiple of 13 between 30 and 50. Answer(a)(ii) … [1] (b) 1 2 6 9 15 17 19 21 27 (i) Write down all the prime numbers in this list. Answer(b)(i) … [2] (ii) Write down a cube number from this list. Answer(b)(ii) … [1] (c) (i) Write 0.0035 in standard form. Answer(c)(i) … [1] (ii) Calculate (6.3 × 106) ÷ (1.5 × 102). Write your answer in standard form. Answer(c)(ii) … [2] _____________________________________________________________________________________

12 0581/31/M/J/13 © UCLES 2013 For Examiner′s Use 7 B A 82 km 27 km C North NOT TO SCALE The diagram shows the positions of three towns A, B and C. B is 27 km north of A and the distance between A and C is 82 km. (a) Calculate BC. Answer(a) BC = … km [2] (b) Write down the three fi gure bearing of C from A. Answer(b) … [1] (c) (i) Use trigonometry to calculate angle ABC. Answer(c)(i) Angle ABC = … [2] (ii) Work out the bearing of C from B. Answer(c)(ii) … [1]

13 0581/31/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (d) (i) Calculate the area of triangle ABC. Answer(d)(i) … km2 [2] (ii) The land forming the triangle ABC is valued at $8400 for each square kilometre. Calculate the value of this land. Answer(d)(ii) $ … [1] _____________________________________________________________________________________

14 0581/31/M/J/13 © UCLES 2013 For Examiner′s Use 8 Ben and Ruth own a company. (a) The company’s profi ts of $43 680 are shared in the ratio Ben : Ruth = 2 : 5 . Calculate Ruth’s share of the profi ts. Answer(a) $ … [2] (b) Ruth invests $15 000 at a rate of 4% per year simple interest. Calculate how much her investment is worth at the end of 3 years. Answer(b) $ … [3] (c) The company employs 450 people. 14% of these people work in sales. Calculate the number of people who work in sales. Answer(c) … [2]

15 0581/31/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (d) Every year Ben travels 32 000 km on business. (i) Car-rent Cost ($) = 600 + 0.35d where d is the distance travelled in kilometres Calculate the cost of hiring a car from Car-rent to travel 32 000 km. Answer(d)(i) $ … [2] (ii) Drive-easy Cost = $100 plus $4 for every 10 km travelled Calculate the cost of hiring a car from Drive-easy to travel 32 000 km. Answer(d)(ii) $ … [2] _____________________________________________________________________________________

16 0581/31/M/J/13 © UCLES 2013 For Examiner′s Use 9 (a) (i) Complete the table of values for y = x2 + x . x –3 –2 –1 0 1 2 3 y 6 0 0 6 [2] (ii) On the grid, draw the graph of y = x2 + x for –3 Ğ x Ğ 3 . y x 14 13 12 11 10 9 8 7 6 5 4 3 2 1 –1 –2 0 1 2 3 –1 –2 –3 [4] (iii) On the grid, draw the line y = 10. [1] (iv) Use both your graphs to solve x2 + x = 10 for –3 Ğ x Ğ 3 . Answer(a)(iv) x = … [1]

17 0581/31/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (b) Another line, L, has the equation y = 3 2 x – 5 . (i) Write down the gradient of L. Answer(b)(i) … [1] (ii) Write down the equation of a straight line that is parallel to L. Answer(b)(ii) … [1] (c) y x 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 0 –1 1 2 3 4 –2 K Write the equation of the line, K, in the form y = mx + c . Answer(c) y = … [3] _____________________________________________________________________________________

18 0581/31/M/J/13 © UCLES 2013 For Examiner′s Use 10 (a) In 2001 Arnold was x years old. Ken is 34 years younger than Arnold. (i) Complete the table, in terms of x, for Arnold’s and Ken’s ages. 2001 2013 Arnold’s age x Ken’s age [3] (ii) In 2013 Arnold is three times as old as Ken. Write down an equation in x and solve it. Answer(a)(ii) x = … [4]

19 0581/31/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (b) Solve the simultaneous equations. 3x + 2y = 18 2x – y = 19 Answer(b) x = … y = … [3] _____________________________________________________________________________________ Question 11 is printed on the next page.

20 0581/31/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 11 (a) Calculate the area of a circle of radius 6 cm. Answer(a) … cm2 [2] (b) 6 cm NOT TO SCALE Each circle in this rectangle has a radius of 6 cm. The circles fi t exactly in the rectangle. Calculate the shaded area. Answer(b) … cm2 [4]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0581 MATHEMATICS 0581/31 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 31 © 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 Answers 1 (a) (i) (ii) (iii) (iv) (b) (i) (ii) (c) (i) (ii) (iii) 750 11, 11.5 or 12 300 1000 13 02 10 26 16 24 40 cao 12 32 1 1ft 1 1 1 1 2 2 1 B1 for 1 (h) 36 or 2 (h) 16 or 3 (h) 49 or 96 or 136 or 229 or 4.24(pm) soi. M1 for 64 ÷ their time (e.g. 1(h) 36(m) ) 2 (a) (b) (c) (d) (e) 29 42 [r =] 66 and [s =] 114 50 56 1 1 1,1ft 1 2 Ft is s = 180 – their r M1 for either angle at A or B indicated as 90 soi

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 31 © Cambridge International Examinations 2013 3 (a) (i) (ii) (b) (c) (i) (ii) (iii) (d) (i) (ii) one correct line only two correct lines correct square correct reflection correct translation correct rotation rotation centre (0,0) angle 90° [anticlockwise] translation      − 3 6 1 2 1 2 2 2 1 1 1 1 1 B1 for either correct line with at most one incorrect B1 for reflection in x = k or y = 4 B1 for 5 left or 4 down SC for translation of       − − 5 4 B1 for a correct rotation about the wrong centre 4 (a) (i) (ii) (b) (i) (ii) (iii) 140 100 correct labelled pie chart 40 29.5 12 7 oe 1 1 2ft 1 2 1 if 0 scored SC1 for their total = 240 B1 ft for correct sectors drawn B1 for correct labelling consistent with table M1 for (attempt to add ) ÷ 12 isw 5 (a) (b) (c) (d) 4 points plotted correctly negative correct ruled line 22.4 – 22.8 2 1 1 1ft B1 for 3 points plotted correctly Ft from their (c) if ruled and negative gradient

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 31 © Cambridge International Examinations 2013 6 (a) (i) (ii) (b) (i) (ii) (c) (i) (ii) 1, 2, 11, 22 39 2,17,19 1 or 27 3.5 × 10–3 4.2 × 104 2 1 2 1 1 2 B1 for just three of these or 3 correct with 1 extra or all four and up to 2 extras or 1 × 22 and 2 × 11 B1 for just two of these or all three and an extra one M1 for 42 000 oe 7 (a) (b) (c) (i) (ii) (d) (i) (ii) 86.3 or 86.33075….. 090 cao 71.8 or 71.77492….. 108.2 or 108 1107 9 298 800 2 1 2 1ft 2 1ft M1 for [BC =] 2 2 82 27 + or 6724 729+ or 7453 M1 for tan [x=] (82÷27) or better oe M1 for 27×82÷2 or better, imp by 1110 8 (a) (b) (c) (d) (i) (ii) 31 200 16 800 63 11 800 12 900 2 3 2 2 2 M1 for (43 680 ÷ 7) × 5 or 6240 × 5 M2 for 15 000 + 15 000 × 0.04 × 3 oe or M1 for 15 000 × 0.04 × 3 oe, imp by 1800 M1 for 450 × [0].14 oe M1 for 600 + 0.35 × 32 000 or better M1 for 100 + 4 × 32 000 ÷ 10 or better

Page 5 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 31 © Cambridge International Examinations 2013 9 (a) (i) (ii) (iii) (iv) (b) (i) (ii) (c) 2 and 2 12 7 points correctly plotted correct curve through the 7points correct line 2.6 – 2.8 3 2 y = 3 2 x + c [y =] 2x – 3 1 1 3ft 1 1 1ft 1 1 3 all in the correct places P2ft for 5 or 6 points correctly plotted P1ft for 3 or 4 points correctly plotted Must be ruled and continuous ft their curve and their line c not –5 M2 for y = 2x + p or M1 for attempt at gradient i.e. run rise B1 for y = qx – 3 q≠0 10 (a) (i) (ii) (e) x +12 x – 34 x − 22 x +12 = 3(x – 22) 39 cao 3 8 − 1,1,1 1ft 3 3 in each part allow correct unsimplified terms accept x +12 = 3x – 66 or (x+12) / 3 = x – 22 M1 for their 3x – 66 seen M1 for correctly collecting terms from ax + b = cx + d a,b,c,d ≠ 0 M1 for correct method to eliminate one variable. A1 for x or y correct. 11 (a) (b) 113 or 113.09 to 113.112 185 or 186 or 185.76 or 185.328 to 185.42 2 4 M1 for π × 62 or better M1 for their (a) × 6 M1 for 24 × 36 soi, imp by 864 M1 for their (24 × 36) – their (their (a) × 6) ft their (a) for M3