Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 May/June Paper 3 · 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 104. MATHEMATICS 0581/33 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 15 printed pages and 1 blank page. [Turn over IB13 06_0581_33/FP © UCLES 2013 *7790623406* www.XtremePapers.com

2 0581/33/M/J/13 © UCLES 2013 For Examiner′s Use 1 (a) Kasem earns $900 each month. 14% of this amount is deducted for tax and insurance. Show that he receives $774 each month. Answer(a) [2] (b) He pays 9 2 of the $774 in rent. Calculate the amount of rent he pays. Answer(b) $ … [1] (c) Kasem spends $480 each month on food, entertainment and clothes. He shares this in the ratio food : entertainment : clothes = 9 : 3 : 4. Calculate how much he spends on food each month. Answer(c) $ … [2] (d) Kasem saves the rest of his money. Work out the amount he saves as a percentage of $774. Answer(d) … % [2] _____________________________________________________________________________________

3 0581/33/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 2 (a) 2 12 144 40 .6 25 110 11 4 80 0.25 From this list of numbers, write down (i) a two-digit odd number, Answer(a)(i) … [1] (ii) a square number, Answer(a)(ii) … [1] (iii) the value of 2–2, Answer(a)(iii) … [1] (iv) an irrational number, Answer(a)(iv) … [1] (v) the lowest common multiple of 8 and 10, Answer(a)(v) … [2] (vi) the cube root of 8. Answer(a)(vi) … [1] (b) (i) Find the smallest factor, apart from 1, of 2013. Answer(b)(i) … [1] (ii) Write 2013 as the product of its prime factors. Answer(b)(ii) … × … × … [2] _____________________________________________________________________________________

4 0581/33/M/J/13 © UCLES 2013 For Examiner′s Use 3 A B 9 8 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 –8 –9 –6 –7 –8 –5 –4 –3 –2 –1 1 0 2 3 4 5 6 7 8 y x (a) Write down the order of rotational symmetry of shape A. Answer(a) … [1] (b) Describe fully the single transformation which maps shape A onto shape B. Answer(b) … [2] (c) (i) Translate shape A by the vector . Label the image C. [2] (ii) Rotate shape A through 90° clockwise about the origin. Label the image D. [2] 5 7 - - e o

5 0581/33/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (d) Triangle LMN is drawn on the 1 cm2 grid below. (i) Enlarge triangle LMN by scale factor 3 from the centre P. L M N P [2] (ii) Write down the length of the base, LM, and the height of triangle LMN. Answer(d)(ii) LM = … cm Height = … cm [2] (iii) Calculate the area of triangle LMN. Answer(d)(iii) … cm2 [2] (iv) Find the area of the enlarged triangle. Answer(d)(iv) … cm2 [2] _____________________________________________________________________________________

6 0581/33/M/J/13 © UCLES 2013 For Examiner′s Use 4 (a) The table shows some values of y = x2 – 2x – 1. x –3 –2 –1 0 1 2 3 4 y 14 2 –1 –2 7 (i) Complete the table. [2] (ii) On the grid, draw the graph of y = x2 – 2x – 1 for –3 Y x Y 4. y x 16 14 12 10 8 6 4 2 –2 –4 0 1 2 3 4 –1 –2 –3 [4]

7 0581/33/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (b) Write down the equation of the line of symmetry of the graph. Answer(b) … [1] (c) The point with co-ordinates (–3, 7) lies on the line y = –x + 4 . (i) Write down the co-ordinates of two other points on this line. Use x co-ordinates so that –3 < x Y 4 . Answer(c)(i) (… , …) and (… , …) [2] (ii) On the grid, draw the line y = –x + 4 for –3 Y x Y 4 . [1] (iii) Use both graphs to fi nd the solutions of the equation x2 – 2x – 1 = –x + 4 . Answer(c)(iii) x = … or x = … [2] _____________________________________________________________________________________

8 0581/33/M/J/13 © UCLES 2013 For Examiner′s Use 5 (a) North North B C D A Scale: 1 cm to 12 km The diagram shows four towns, A, B, C and D, joined by straight roads AB, BC and BD. The scale is 1 centimetre represents 12 kilometres. (i) Measure the bearing of B from A. Answer(a)(i) … [1] (ii) Work out the distance in kilometres from A to B. Answer(a)(ii) … km [2] (iii) Saraswati takes 1 hour 30 minutes to drive from A to B. Calculate her average speed, in kilometres per hour, for this journey. Answer(a)(iii) … km/h [1]

9 0581/33/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (b) At B, Saraswati follows another straight road which is equidistant from BC and BD. Using a straight edge and compasses only and leaving in all your construction lines, construct the line of this road on the diagram. [2] (c) Another motorist, Leah, leaves C and drives on a bearing of 165° to meet Saraswati at town E. Town E is on the road in part (b). Show Leah’s journey on the diagram and mark the town E. [1] (d) Saraswati travelled from B to E at an average speed of 55 km/h. Calculate the time, in hours and minutes, that she took. Answer(d) … h … min [4] (e) There is a speed limit of 50 km/h on all roads within 30 km of town D. On the diagram, show the boundary of the region where this speed limit applies. [2] _____________________________________________________________________________________

10 0581/33/M/J/13 © UCLES 2013 For Examiner′s Use 6 Felix rolls two fair dice, each numbered from 1 to 6, and adds the numbers shown. He repeats the experiment 70 times and records the results in a frequency table. The fi rst 60 results are shown in the tally column of the table. The last 10 results are 6, 8, 9, 2, 6, 4, 7, 9, 6, 10 . Total Tally Frequency 2 3 4 5 6 7 8 9 10 11 12 (a) (i) Complete the frequency table to show all his results. [2] (ii) Write down the relative frequency of a total of 5. Answer(a)(ii) … [1]

11 0581/33/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (b) (i) Write down the mode. Answer(b)(i) … [1] (ii) Write down the range. Answer(b)(ii) … [1] (iii) Work out the median. Answer(b)(iii) … [2] (iv) Calculate the mean. Answer(b)(iv) … [3] (c) (i) Complete this table showing how different totals can be made when rolling two dice. Dice 2 Dice 1 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 3 4 7 5 7 9 6 12 [1] (ii) Explain why 7 is the most likely total. Answer(c)(ii) … [1] _____________________________________________________________________________________

12 0581/33/M/J/13 © UCLES 2013 For Examiner′s Use 7 (a) B C D A h 8.4 cm 12.5 cm 5.5 cm 70° NOT TO SCALE In the quadrilateral ABCD, BC is parallel to AD. AB = 5.5 cm, BC = 8.4 cm, AD = 12.5 cm and angle BAD = 70°. The height of the quadrilateral is h. (i) Write down the mathematical name of the quadrilateral ABCD. Answer(a)(i) … [1] (ii) Use trigonometry to show that h = 5.2 cm, correct to 1 decimal place. Answer(a)(ii) [2] (iii) Calculate the area of the quadrilateral ABCD. Answer(a)(iii) … cm2 [2]

13 0581/33/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use (iv) The quadrilateral forms the cross section of a prism with length 6.8 cm. Calculate the volume of the prism. Give your answer correct to 2 signifi cant fi gures. Answer(a)(iv) … cm3 [2] (b) C B A E D y° z° w° x° 64° 95° NOT TO SCALE The diagram shows a pentagon, ABCDE. AB is parallel to DC. A straight line, parallel to ED, passes through the vertex C. (i) Find the values of w, x and y. Answer(b)(i) w = … x = … y = … [3] (ii) The sum of the angles of a pentagon is 540°. Find the value of z. Answer(b)(ii) z = … [2] _____________________________________________________________________________________

14 0581/33/M/J/13 © UCLES 2013 For Examiner′s Use 8 (a) Simplify the following expressions. (i) 3m – 5m + 6m Answer(a)(i) … [1] (ii) 5e – 4f – 3e – 6f Answer(a)(ii) … [2] (b) s = u + at (i) Calculate the value of s when u = 27, a = –2 and t = 15. Answer(b)(i) s = … [2] (ii) Make t the subject of the formula s = u + at. Answer(b)(ii) t = … [2] (c) Solve the simultaneous equations. 5x + 2y = 4 4x – y = 11 Answer(c) x = … y = … [3] _____________________________________________________________________________________

15 0581/33/M/J/13 © UCLES 2013 [Turn over For Examiner′s Use 9 (a) Write down the next term and the rule for fi nding the next term for the following sequences. (i) 3, 9, 27, 81, ... Answer(a)(i) Next term … rule … [2] (ii) 2, 3, 6, 11, 18, ... Answer(a)(ii) Next term … rule … [2] (iii) 4, 2, 1, 2 1 , ... Answer(a)(iii) Next term … rule … [2] (iv) 5, –10, 20, –40, ... Answer(a)(iv) Next term … rule … [2] (b) (i) Write down the next two terms of this sequence. 5, 13, 21, 29, … , … [2] (ii) Write down the nth term of this sequence. Answer(b)(ii) … [2] (iii) Find the 100th term. Answer(b)(iii) … [1] _____________________________________________________________________________________

16 0581/33/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. BLANK PAGE © UCLES 2013

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0581 MATHEMATICS 0581/33 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 33 © 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) 900 × 86 ÷ 100 = 74 2 M1 for 900 × 14 ÷ 100 A1 for 900 – 126 = 774 (b) [$] 172 1 (c) [$] 270 2 M1 for 480 ÷ (9 + 3 + 4) (d) 15.8 or 15.76(...) 2ft B1 for 774 – their (b) – 480 B1 Or 294 – their (b) SC1 for 38 or 37.9 2 (a) (i) 11 1 (ii) 144 or 4 or 0.25 1 (iii) 0.25 1 (iv) 12 1 (v) 40 cao 2 B1 for 80 or any common multiple of 40 (vi) 2 1 (b) (i) 3 1 (ii) 3 [×] 11 [×] 61 2 B1 for two of 3, 11 and 61 seen

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 33 © Cambridge International Examinations 2013 3 (a) 2 1 (b) Reflection x = –1 1 1 (c) (i) Translation       − − 5 7 2 B1 for 7 left or 5 down SC1 for translation       − − 7 5 (ii) Rotation 90° clockwise about the origin shown. 2 B1 for any other rotation of 90° about other point (d) (i) Correct enlargement shown 2 B1 for an enlargement with any correct scale factor and/or correct shape incorrect position (ii) 3, 2 1, 1 SC1 for 2, 3 (iii) 3 2ft M1 their LM × their height ÷ 2 (iv) 27 2ft M1 their base × their height ÷ 2 from their enlarged triangle. 4 (a) (i) 7, –1, 2 2 B1 for any 2 correct (ii) 8 points plotted Correct smooth curve 3ft 1 P2ft for 6 or 7 correct P1ft for 4 or 5 correct (b) x = 1 1 (c) (i) Two correct points 1,1 x –2 –1 –0 –1 –2 –3– 4 y –6 –5 –4– 3– 2 –1 –0 (ii) Correct line drawn 1 Must be ruled and continuous (iii) –1.9 to –1.7, 2.7 to 2.9 2ft 1 for each correct 5 (a) (i) (0)35 to (0)39 1 (ii) 117.6 to 122.4 [km] 2 B1 for (10 ± 0.2) cm seen (iii) 80 or 78.4 to 81.6 1ft ft their (a)(ii) ÷ 1.5 (b) Bisector of angle CBD with 2 correct pairs of arcs. 2 B1 correct line (±2°), some or all arcs absent (c) Ruled line from C to BD on a bearing of 165° 1 (d) 1 [h] 18 [min] to 1 [h] 26 [min] www 4 B1ft measure BE M1 change to kilometres. M1 for their distance ÷ 55 (e) Circle, centre D, with radius 2.5 ± 0.2 cm 2 M1 for 2.5 ± 0.2 soi. SC1 for circle, centre D, incorrect radius or freehand ‘correct’ circle

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 33 © Cambridge International Examinations 2013 6 (a) (i) Frequency table completed 2 M1 for 8 correct frequencies SC1 for all correct tallies if no frequencies. OR SC1 for all correct frequencies in tally column (ii) 70 3 oe 1 ft ft their table (b) (i) 6 1 (ii) 10 1 (iii) 6 2 M1 for clear recognition of mid values used (iv) 6.43 to 3sf 3 M1 for total of freq × their result M1 dep for division by their 70 (c) (i) All totals filled in 1 Allow 1 error or omission (ii) More ways of getting 7 1 Any equivalent explanation 7 (a) (i) Trapezium 1 (ii) 5.5 h = sin 70 or better 5.17 or 5.16(8...) seen M1 A1 (iii) 54.3 or 54.34 or 54.(0...) 2 M1 for 0.5 (8.4 + 12.5) × 5.2 oe (iv) 370 2ft B1ft Their (a)(iii) × 6.8 not correctly rounded to 2sf (b) (i) 64 21 116 1 1ft 1 ft 85 – their (b)(i) (ii) 154 2ft M1 for 540 – (90 + 95 + 64 + their x + their y) 8 (a) (i) 4m 1 (ii) 2e – 10f 2 B1 for ae – 10f or 2e ± bf (a,b ≠ 0) (b) (i) –3 2 M1 for 27 + (–2) × 15 or better (ii) [t=] a u s − or a s − a u 2 M1 first step correct SC1 for s – u ÷ a www (c) [x =] 2, [y =] –3 3 M1 for correct method to eliminate one variable. A1 for x or y correct

Page 5 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0581 33 © Cambridge International Examinations 2013 9 (a) (i) 243 Multiply by 3 oe 1 1 (ii) 27 Add next odd number oe 1 1 Add 1 first and keep adding 2 more each time (iii) 4 1 or 0.25 1 Halve or divide by 2 1 (iv) 80 Multiply by –2 oe 1 1 (b) (i) 37, 45 1, 1ft ft is (ans) + 8 (ii) 8n – 3 oe final answer 2 B1 for 8n + a or B1 for bn – 3 (b ≠ 0) (iii) 797 1ft Only follow through a linear expression