Cambridge IGCSE Mathematics (with coursework) 0581 — 2014 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 an HB pencil for any diagrams or graphs. Do not use staples, paper clips, 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 2014 2 hours Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) This document consists of 16 printed pages. [Turn over IB14 06_0581_32/FP © UCLES 2014 *7603382359* Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education PAPA CAMBRIDGE

2 0581/32/M/J/14 © UCLES 2014 1 (a) Here is a list of numbers. 2 4 5 8 9 12 Write down all the numbers from this list which are (i) odd, Answer(a)(i) … [1] (ii) square, Answer(a)(ii) … [1] (iii) cube, Answer(a)(iii) … [1] (iv) prime. Answer(a)(iv) … [1] (b) Write one of these symbols >, < or = to make each statement true. π … 7 22 2 ^ h2 … 2 1 1 1 + … 2 (–1)2 … –1 [2] (c) Put one pair of brackets in each statement to make it true. (i) 16 + 8 ÷ 4 – 2 = 4 [1] (ii) 16 + 8 ÷ 4 – 2 = 20 [1]

3 0581/32/M/J/14 © UCLES 2014 [Turn over (d) (i) Write 84 as a product of its prime factors. Answer(d)(i) … [2] (ii) Find the highest common factor of 84 and 24. Answer(d)(ii) … [2] (iii) Find the lowest common multiple of 84 and 24. Answer(d)(iii) … [2] (e) Here are the fi rst four terms of a sequence. 3 7 11 15 (i) Write down the next term in this sequence. Answer(e)(i) … [1] (ii) Explain how you found your answer. Answer(e)(ii) … [1] (iii) Write down an expression for the n th term of this sequence. Answer(e)(iii) … [2] (iv) Explain why 125 is not in this sequence. Answer(e)(iv) … … [1] __________________________________________________________________________________________

4 0581/32/M/J/14 © UCLES 2014 2 A D C B 180 cm 120 cm 240 cm NOT TO SCALE The diagram shows the cross section ABCD of a shed. AD = 180 cm, DC = 120 cm and BC = 240 cm. (a) (i) Write down the mathematical name of the cross section ABCD. Answer(a)(i) … [1] (ii) Calculate the area of the cross section ABCD. Give the units of your answer. Answer(a)(ii) … … [3] (iii) The shed is a prism of length 2.5 metres. Calculate the volume of the shed. Give your answer in cubic metres. Answer(a)(iii) … m3 [2]

5 0581/32/M/J/14 © UCLES 2014 [Turn over (iv) Calculate the length AB. Answer(a)(iv) AB = … cm [3] (b) Here is a scale drawing of a garden, GHIJ. The scale is 1 centimetre represents 5 metres. I H G J Scale: 1 cm to 5 m The shed is placed in the garden so that it is ● nearer to GJ than to IJ and ● within 20 m of H. Using a ruler and compasses only, construct and shade the region where the shed can be placed. Show all your construction arcs. [5] __________________________________________________________________________________________

6 0581/32/M/J/14 © UCLES 2014 3 (a) Draw the line of symmetry on the shape below. [1] (b) Write down the order of rotational symmetry of the shape below. Answer(b) … [1] (c) (i) x° 157° 72° NOT TO SCALE Work out the value of x. Answer(c)(i) x = … [1] (ii) y° 49° 54° NOT TO SCALE Work out the value of y. Answer(c)(ii) y = … [2]

7 0581/32/M/J/14 © UCLES 2014 [Turn over (d) A B C O 34° NOT TO SCALE AC is a diameter of the circle, centre O. Calculate angle ACB. Answer(d) Angle ACB = … [2] (e) The diagram below shows parts of shape P and shape Q. Shape P is a regular hexagon and shape Q is another regular polygon. The two shapes have one side in common. 100° 100° Q P NOT TO SCALE Find the number of sides in shape Q. Show each step of your working. Answer(e) … [5] __________________________________________________________________________________________

8 0581/32/M/J/14 © UCLES 2014 4 Paolo’s football team played 46 games. The pictogram shows some information about the number of goals scored by Paolo’s football team. They did not score any goals in fi ve games. Number of goals Number of games 0 1 2 3 4 5 6 Key: = … games (a) (i) Complete the key. [1] (ii) Paolo’s team scored 2 goals in each of nine games. Complete the pictogram. [1] (b) (i) Write down the modal number of goals. Answer(b)(i) … [1] (ii) Find the median number of goals. Answer(b)(ii) … [1] (iii) Find the range. Answer(b)(iii) … [1] (iv) One of the 46 games is chosen at random. Work out the probability that Paolo’s team scored at least 4 goals. Answer(b)(iv) … [2]

9 0581/32/M/J/14 © UCLES 2014 [Turn over (c) The table shows the total goals scored and the total points gained by 10 teams. Team A B C D E F G H I J Goals 31 40 46 50 43 92 60 84 68 87 Points 36 35 52 56 72 78 59 70 61 75 (i) Complete the scatter diagram. The fi rst six points have been plotted for you. [2] 80 70 60 50 40 30 30 40 50 60 70 Goals 80 90 100 Points (ii) Draw the line of best fi t. [1] (iii) What type of correlation is shown? Answer(c)(iii) … [1] (iv) Use your line of best fi t to estimate the total points gained by a team scoring 75 goals. Answer(c)(iv) … [1] (v) Which team only scores a few goals but gains a lot of points? Answer(c)(v) … [1] __________________________________________________________________________________________

10 0581/32/M/J/14 © UCLES 2014 5 (a) Jasmine works for 38 hours each week and she earns $12.15 each hour. (i) Calculate her earnings in one week. Answer(a)(i) $ … [1] (ii) Jasmine pays 14% of her earnings in tax. Calculate how much money she has left after tax is paid. Answer(a)(ii) $ … [2] (iii) She pays 3 1 of the money she has left after tax in rent. Calculate how much rent she pays in one year (52 weeks). Answer(a)(iii) $ … [2] (iv) In one week she spends $140 on food and electricity in the ratio food : electricity = 3 : 2 . Calculate how much she spends on food. Answer(a)(iv) $ … [2] (b) Jasmine buys a watch for 10 000 Japanese Yen (¥). The exchange rate is $1 = ¥ 80.4 . Calculate the cost of this watch in dollars, giving your answer correct to the nearest dollar. Answer(b) $ … [3] __________________________________________________________________________________________

11 0581/32/M/J/14 © UCLES 2014 [Turn over 6 (a) Complete the table of values for y = x2 + 2x – 3 . x –4 –3 –2 –1 0 1 2 3 4 y 0 –3 –4 –3 0 5 21 [2] (b) On the grid, draw the graph of y = x2 + 2x – 3 for –4 Ğ x Ğ 4 . y x 25 20 15 10 5 –5 0 1 2 3 4 –1 –2 –3 –4 [4] (c) On the grid, draw the line y = 10 . [1] (d) Use your graphs to solve the equation x2 + 2x – 3 = 10 for –4 Y x Y 4 . Answer(d) x = … [1] __________________________________________________________________________________________

12 0581/32/M/J/14 © UCLES 2014 7 (a) 5p + 3r 7p – 6r p + 2r NOT TO SCALE Write an expression for the perimeter of this triangle. Give your answer in its simplest form. Answer(a) … [2] (b) Another triangle has a perimeter 12w – 2z . Calculate this perimeter when w = 16 and z = –3. Answer(b) … [2] (c) Solve. (i) 5a = 32 Answer(c)(i) a = … [1] (ii) 5b + 23 = 8 Answer(c)(ii) b = … [2] (iii) 5c + 7 = 2(c – 10) Answer(c)(iii) c = … [3]

13 0581/32/M/J/14 © UCLES 2014 [Turn over (d) (i) Multiply out the brackets. 8(2x + 3) Answer(d)(i) … [1] (ii) Factorise completely. 6x2 – 12x Answer(d)(ii) … [2] (e) Write each expression in its simplest form. (i) 3q4 × 5q2 Answer(e)(i) … [2] (ii) t 8 ÷ t 2 Answer(e)(ii) … [1] __________________________________________________________________________________________

14 0581/32/M/J/14 © UCLES 2014 8 (a) Work out. (i) 5 3 - 2 e o Answer(a)(i) f p [1] (ii) 5 4 - e o + 1 3 - e o Answer(a)(ii) f p [1] (b) A translation moves the point (6, 3) to the point (2, 8). Work out the vector which represents this translation. Answer(b) f p [1]

15 0581/32/M/J/14 © UCLES 2014 [Turn over (c) A point P is translated by the vector 3 4 - e o to the point (7, –2). Find the co-ordinates of P. You may use the grid below to help you. Answer(c) (… , …) [1] __________________________________________________________________________________________ Question 9 is printed on the next page.

16 0581/32/M/J/14 © UCLES 2014 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. 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. 9 A 10 9 8 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 –5 –4 –3 –2 –1 1 0 2 3 4 5 6 7 x y B (a) On the grid, draw the image of triangle A after the following transformations. (i) Refl ection in the x-axis. [1] (ii) Rotation about (0, 0) through 180°. [2] (iii) Translation by the vector 5 - 3 e o. [2] (b) Describe fully the single transformation that maps triangle A onto triangle B. Answer(b) … … [3]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 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 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. PAPA CAMBRIDGE

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 32 © Cambridge International Examinations 2014 Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Qu Answers Mark Part Answers 1 (a) (i) (ii) (iii) (iv) (b) (c) (i) (ii) (d) (i) (ii) (iii) (e) (i) (ii) (iii) (iv) 5 and 9 cao 4 and 9 cao 8 cao 2 and 5 cao < = < > (16 + 8) ÷ 4 ─ 2 = 4 16 + 8 ÷ (4 ─ 2) = 20 2 × 2 × 3 × 7 12 168 19 +4 oe 4n – 1 oe final answer accept any correct statement 1 1 1 1 2 1 1 2 2 2 1 1 2 1 B1 for 3 correct B1 for 2, 3, 7 or 2, 2, 3, 7, or 1 × 2 × 2 × 3 × 7 B1 for 2, 3, 4 or 6 or 2 × 2 × 3 or 22 × 3 or 4 × 3 or 2 × 6 seen as ans B1 for any other multiple of 168 or 2 × 2 × 2 × 3 × 7 oe any other terms must be correct e.g. add 4 B1 for 4n + k , qn – 1 q ≠ 0

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 32 © Cambridge International Examinations 2014 2 (a) (i) (ii) (iii) (iv) (b) Trapezium 25 200 cm2 6.3 134 or 134.1 to 134.2 correct angle bisector of angle J with two pairs of supporting arcs arc centre H radius 4 cm correct region shaded 1 2 1 2 3 2 2 1 SCB3 for 2.52 m2 M1 for 120 2 240 180 × +         or 180 × 120 + 2 1 × 120 × 60 or 2.1 2 4.2 8.1 × +         or 1.8 × 1.2 + 2 1 × 1.2 × 0.6 oe M1 for their (a)(ii) × 2.5 oe or figs 63 B1 for 60 seen on diagram or used M1 for 1202 + (their ‘240 – 180’) 2 or better M1 for the correct angle bisector of angle J without arcs M1 for any arc centre H dep on at least both M marks 3 (a) (b) (c) (i) (ii) (d) (e) correct mirror line 2 131 103 56 9 with supporting working 1 1 1 2 2 5 M1 for 180 – 49 – 54 or 49 + 54 or 77 seen or fully correct method M1 for 180 – 90 – 34 or better or indication of angle B = 90 M2 for internal angle of P =120 or M1 for 180 – (360 ÷ 6) or (6 – 2) × 180 ÷ 6 M1FT for 360 – their ‘120’ – 100 [= 140] M1FT for 360 ÷ (180 – their ‘140’) if M0 then answer of 9 scores SC2

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 32 © Cambridge International Examinations 2014 4 (a) (i) (ii) (b) (i) (ii) (iii) (iv) (c) (i) (ii) (iii) (iv) (v) 2 4 and a half circles 1 2 cao 6 cao 46 13 oe isw four points correctly plotted continuous ruled line of best fit positive 65 to 70 E 1 1FT 1FT 1 1 2 2 1 1 1FT 1 FT is 9 / their a(i) if their a(i) is an integer M1 for 13 seen or (6 + 5 + 2) / 46 or 6 2 1 / 23 M1 for 3 points correctly plotted dependent on at least 9 points on graph FT their continuous ruled line of best fit if positive 5 (a) (i) (ii) (iii) (iv) (b) 461.7(0) cao 397.06 or 397.1 or 397 or 397.062 6880 or 6882 or 6882.(…) 84 124 cao 1 2FT 2FT 2 3 M1FT for their (a)(i) × 0.86 oe soi M1FT for their (a)(ii) ÷ 3 soi or their (a)(ii) × 52 soi M1 for 140 × 3 ÷ (3 + 2) B2 for 124.3(…….) or 124.4 if B0 then M1 for 10 000 ÷ 80.4 B1 for rounding their answer, if decimal, to the nearest integer 6 (a) (b) (c) (d) 5 12 9 points plotted correctly correct smooth curve through all 9 correct points correct ruled line 2.7 to 2.8 2 3FT 1 1 1FT B1, B1 B2FT for 7 or 8 points correctly plotted B1FT for 5 or 6 points correctly plotted minimum length must touch y axis and curve FT their curve and ruled line

Page 5 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 32 © Cambridge International Examinations 2014 7 (a) (b) (c) (i) (ii) (iii) (d) (i) (ii) (e) (i) (ii) 13p – r Final Answer 198 6.4 or 6 5 2 –3 –9 16x + 24 6x (x – 2) 15q6 t6 2 2 1 2 3 1 2 2 1 B1 for either 13p or – r in the answer or 13p – r spoilt M1 for 12 × 16 – 2 × –3 or B1 for 192 or + 6 or – (–6) seen M1 for first correct step, i.e. 5b = 8 – 23 or better, or b + 5 23 = 5 8 or better B1 for 2c – 20 M1FT for correctly collecting cs on one side and numbers on the other, e.g. 5c – 2c = –7 – 20 or better B1 for x(6x – 12), 6(x2 – 2x), 2(3x² – 6x), 3( 2x² – 4x), 2x (3x – 6) or 3x(2x – 4) B1 for 15qn (n not 0) or kq6 ( k not 0) 8 (a) (i) (ii) (b) (c)           −15 10           −6 7          − 5 4 (3,1) 1 1 1 1 9 (a) (i) (ii) (iii) (b) correct reflection at (1,–1), (3,–1) and (3,–5) correct rotation at (–1,–1), (–3,–1) and (–3,–5) correct translation at (–4,4), (–2,4) and (–2,8) enlargement [ centre ] (0,1) [ scale factor] 2 1 2 2 1 1 1 SC1 for correct rotation any centre B1 for one direction correct, i.e. 5 left or 3 up