Cambridge IGCSE Mathematics - International 0607 — 2017 May/June Paper 3 · Variant 3

* 1 6 5 7 3 7 6 0 1 4 * This document consists of 15 printed pages and 1 blank page. DC (LK/SG) 134125/2 © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 2017 1 hour 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments Graphics Calculator 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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For r, use your calculator value. You must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 96.

2 0607/33/M/J/17 © UCLES 2017 Formula List Area, A, of triangle, base b, height h. A = bh 2 1 Area, A, of circle, radius r. A = rr2 Circumference, C, of circle, radius r. C = 2rr Curved surface area, A, of cylinder of radius r, height h. A = 2rrh Curved surface area, A, of cone of radius r, sloping edge l. A = rrl Curved surface area, A, of sphere of radius r. A = 4rr2 Volume, V, of prism, cross-sectional area A, length l. V = Al Volume, V, of pyramid, base area A, height h. V= Ah 3 1 Volume, V, of cylinder of radius r, height h. V = rr2h Volume, V, of cone of radius r, height h. V = r h 3 1 2 r Volume, V, of sphere of radius r. V = r 3 4 3 r

3 0607/33/M/J/17 © UCLES 2017 [Turn over Answer all the questions. 1 (a) A bar of chocolate costs $0.80 . Jenny buys 5 of these bars of chocolate. (i) How much does Jenny pay for these 5 bars of chocolate? $ … [1] (ii) Find how much change she receives from $5. $ … [1] (iii) One day there is a special offer on these bars of chocolate. Buy 2 bars and get 1 extra bar free. Chris wants 15 bars of chocolate. Find how much he pays using the special offer. $ … [2] (iv) Chris shares these 15 bars between himself and his brother in the ratio 3 : 2. Find how many bars his brother receives. … [2] (b) Asli buys 3 slices of pizza and 1 salad for $2.10 . Arend buys 2 slices of pizza and 2 salads for $2.20 . Find the cost of 1 slice of pizza and the cost of 1 salad. Show all your working. 1 slice of pizza = $ … 1 salad = $ … [4]

4 0607/33/M/J/17 © UCLES 2017 2 (a) (i) Write the number three million two thousand and one in figures. … [1] (ii) Work out 10 2 6 # - . … [1] (iii) Find the value of . 125 44 . … [1] (b) Complete the list of factors of 20. 1 , … , … , … , … , 20 [2] (c) (i) Calculate . . 6 1 3 42 # , giving your answer as a decimal. Write down your full calculator display. … [1] (ii) Give your answer to part (c)(i) correct to 2 decimal places. … [1] (iii) Give your answer to part (c)(i) correct to 2 significant figures. … [1]

5 0607/33/M/J/17 © UCLES 2017 [Turn over 3 (a) Simplify. a b a b 5 9 2 2 + - + … [2] (b) R M N 6 2 = + (i) Find R when M 3 =- and N 5 = . … [2] (ii) Find M when R 26 = and N 4 = . … [2] (c) Solve. x x 3 6 15 = + … [2] (d) Factorise completely. a ab 3 12 2 - … [2] (e) Simplify. x y x y 4 2 2 3 2 # … [2]

6 0607/33/M/J/17 © UCLES 2017 4 Eight friends were asked these questions. • How many minutes did you spend revising for the mathematics test? • What was your test score? The results are shown in the table. Number of minutes 60 75 100 150 180 220 270 300 Score 62 47 58 65 62 81 90 75 (a) Complete the scatter diagram. The first four points have been plotted for you. 100 90 80 70 60 50 40 30 20 10 0 0 50 100 150 Number of minutes 200 250 300 Score [2]

7 0607/33/M/J/17 © UCLES 2017 [Turn over (b) Find (i) the mean number of minutes spent revising, … [1] (ii) the mean mark scored on the mathematics test. … [1] (c) (i) Plot the mean point on the scatter graph. [1] (ii) Draw a line of best fit by eye on the scatter graph. [2] (iii) Use your line of best fit to find an estimate of the mark scored on the mathematics test by a student who spent 200 minutes revising. … [1]

8 0607/33/M/J/17 © UCLES 2017 5 30 students were asked which drink they liked best. The results are shown in the table. Drink Cola Ice tea Lemonade Orange juice Green tea Number of students 11 8 5 4 2 (a) Complete the bar chart. Number of students 12 10 8 6 4 2 0 Cola Ice tea Lemonade Drink Orange juice Green tea [2] (b) Find the probability that one of these 30 students, chosen at random, likes (i) ice tea best, … [1] (ii) orange juice or green tea best, … [1] (iii) coffee best. … [1]

9 0607/33/M/J/17 © UCLES 2017 [Turn over (c) Complete the pie chart to show the results in the table. Green tea Cola [3] 6 The distance from Breda to Amsterdam is 105 km. (a) A train from Breda to Amsterdam takes 35 minutes to complete the journey. Calculate the average speed of the train in km/h. … km/h [2] (b) Another train from Breda to Amsterdam travels at an average speed of 84 km/h. Find the time taken for this train to travel from Breda to Amsterdam. Give your answer in hours and minutes. … hours … minutes [2]

10 0607/33/M/J/17 © UCLES 2017 7 Suyeon asks each of 23 students in her class to count the number of steps in their house. The results are listed below. 23 12 16 23 18 46 32 35 15 21 16 42 41 18 34 26 41 47 23 48 23 33 37 (a) Complete the ordered stem and leaf diagram to show this information. 1 2 2 3 4 Key: … … represents … [3] (b) Find (i) the mode, … [1] (ii) the median, … [1] (iii) the interquartile range, … [2] (iv) the mean. … [1]

11 0607/33/M/J/17 © UCLES 2017 [Turn over 8 (a) Write 200 43 as a decimal. … [1] (b) Write the following fractions in order, starting with the smallest. 0 13 40 11 1 4 1 200 43 5 … , … , … , … [1] smallest (c) x 50 13 100 = Find the value of x. x = … [1] (d) Write 40 11 as a percentage. … % [1] (e) Calculate, giving each answer as a fraction. (i) 50 13 200 43 + … [1] (ii) 40 11 50 13 ' … [1] (iii) 1 4 1 200 43 # … [1]

12 0607/33/M/J/17 © UCLES 2017 9 These are the first four terms of a sequence. 64 81 98 115 (a) Write down the next two terms in this sequence. … , … [2] (b) Find an expression for the nth term of this sequence. … [2] 10 Alperen asks 30 students if they like fish (F ) or cheese (C ). 19 like fish, 24 like cheese and 2 like neither fish nor cheese. (a) Complete the Venn diagram. U F C 2 [2] (b) Write down the number of students who like fish or cheese but not both. … [1] (c) Shade the region F C + l. [1] (d) One student is chosen at random. Find the probability that this student likes cheese only. … [1]

13 0607/33/M/J/17 © UCLES 2017 [Turn over 11 y x 6 –1 –2 –3 –4 –5 –6 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 5 4 3 2 1 0 On the grid, draw the image of (a) shape after a reflection in the y-axis, [1] (b) shape after a rotation of 90° clockwise about the origin, [2] (c) shape after a translation of 6 5 - - c m. [2]

14 0607/33/M/J/17 © UCLES 2017 12 1.5 cm 0.5 cm NOT TO SCALE Tamay has 15 identical silver coins. Each coin is a cylinder of radius 1.5 cm and height 0.5 cm. (a) Find the total surface area of one coin. … cm2 [3] (b) (i) Find the total volume of all 15 coins. … cm3 [2] (ii) The 15 coins are melted down to make one large cylinder of height 3 cm. Calculate the radius of this cylinder. Give your answer correct to 1 decimal place. … cm [3]

15 0607/33/M/J/17 © UCLES 2017 13 0 20 y x –10 –3.5 3 ( ) f x x x x 6 3 2 = + - (a) On the diagram, sketch the graph of ( ) f y x = for . x 3 5 3 G G - . [2] (b) Write down the co-ordinates of the point where the graph crosses the y-axis. ( … , … ) [1] (c) Write down the co-ordinates of the points where the graph crosses the x-axis. ( … , … ) and ( … , … ) and ( … , … ) [2] (d) Write down the co-ordinates of the local minimum. ( … , … ) [2] (e) On the same diagram, sketch and label clearly the graph of (i) ( ) f y x 2 = + , [1] (ii) ( ) f y x 1 = - . [1]

16 0607/33/M/J/17 © UCLES 2017 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. 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

® IGCSE is a registered trademark. This document consists of 7 printed pages. © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 2017 MARK SCHEME Maximum Mark: 96 Published 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 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 2 of 7 MARK SCHEME NOTES The following notes are intended to aid interpretation of mark schemes in general, but individual mark schemes may include marks awarded for specific reasons outside the scope of these notes. Types of mark M Method marks, awarded for a valid method applied to the problem. A Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. For accuracy marks to be given, the associated Method mark must be earned or implied. B Mark for a correct result or statement independent of Method marks. When a part of a question has two or more ‘method’ steps, the M marks are in principle independent unless the scheme specifically says otherwise; and similarly where there are several B marks allocated. The notation ‘dep’ is used to indicate that a particular M or B mark is dependent on an earlier mark in the scheme. Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working nfww not from wrong working oe or equivalent rot rounded or truncated SC Special Case soi seen or implied

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 3 of 7 Question Answer Marks Part Marks 1(a)(i) 4[.00] 1 1(a)(ii) 1[.00] 1 FT 5 – their 4 1(a)(iii) 8[.00] 2 B1 for 10 soi or for 3 bars = 1.6[0] 1(a)(iv) 6 2 M1 for dividing by (3 + 2) soi 1(b) 6p + 2s = 4.2[0] oe M1 p = [0].5[0] A1 3×their p + 1s = 2.1[0] oe M1 s = [0].6[0] A1 If zero scored, SC1 for correct answers with no working 2(a)(i) 3 002 001 1 2(a)(ii) –2 1 2(a)(iii) 11.2 1 2(b) [1], 2, 4, 5, 10,[20] 2 B1 for 2 correct values 2(c)(i) 70.516 1 2(c)(ii) 70.52 1 FT their (c)(i) rounded to 2dp 2(c)(iii) 71 1 FT their (c)(i) rounded to 2sf 3(a) 3a + 11b final answer 2 B1 for 11ܾ or 3ܽ seen 3(b)(i) –8 2 B1 for –18 or 10 seen or M1 for 6(–3) + 2 (5) 3(b)(ii) 3 2 M1 for 26 = 6M + 2 × 4 oe 3(c) –5 2 M1 for a correct first step 3(d) 3a(a – 4b) final answer 2 M1 for 3(a2 – 4ab) or a(3a – 12b) 3(e) 8x5y3 final answer 2 B1 for 8xky3 or 8x5yk or kx5y3 4(a) 4 correct points plotted 2 B1 for 2 points correctly plotted 4(b)(i) 169.375 1 4(b)(ii) 67.5 1 4(c)(i) Correct point plotted 1 FT their (b)

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 4 of 7 Question Answer Marks Part Marks 4(c)(ii) Ruled line through their plotted mean point with positive gradient within tolerance 2 B1 for ruled line through their plotted mean point with positive gradient but not within tolerance or for ruled line within tolerance but not through their plotted mean point 4(c)(iii) 66 to 76 1 5(a) Correct bar chart 2 B1 for 2 bars correct or for all heights correct but different widths. 5(b)(i) 8 30 oe 1 5(b)(ii) 6 30 oe 1 5(b)(iii) 0 oe 1 5(c) Fully correct pie chart with labels 3 B2 for correct sectors without labels or 1 correct sector with label or B1 for 1 correct sector without label or B1 for labelled diagram with sectors in the correct order of size or M1 for 1 angle correctly calculated 6(a) 180 2 B1 for 35 60 oe or 105 35 soi 6(b) 1 hour 15 minutes 2 M1 for 105 84 oe soi 0 2 4 6 8 10 12 n u m b e r o f s t u d e n t s Drink Cola Ice tea Lemonade Orange Green tea

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 5 of 7 Question Answer Marks Part Marks 7(a) [1] [2] 5 6 6 8 8 [2] 1 3 3 3 3 6 [3] 2 3 4 5 7 [4] 1 1 2 6 7 8 2 B1 for correct table but 1 or 2 errors or for values correct but unordered E.g. 1 2 = 12 [steps] 1 7(b)(i) 23 1 7(b)(ii) 26 1 7(b)(iii) 23 2 B1 for 41 or 18 7(b)(iv) 29.1 or 29.13… 1 8(a) 0.215 1 8(b) 43 13 11 1 1 200 50 40 4 oe 1 8(c) 26 1 8(d) 27.5 1 8(e)(i) 19 40 oe 1 8(e)(ii) 55 52 oe 1 8(e)(iii) 43 160 oe 1 9(a) 132 1 149 1 FT their 132 + 17 9(b) 47 + 17n oe 2 B1 for 47 or 17n 10(a) 2 B1 for 1 number correct 10(b) 13 1 FT their Venn diagram

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 6 of 7 Question Answer Marks Part Marks 10(c) 1 10(d) 9 30 oe 1 FT their Venn diagram 11(a) Correct diagram with vertices at (–1, 3), (–1, 1), (–4, 1), (–4, 3) 1 11(b) Correct diagram with vertices at (1, –1), (3, –1), (3, –4), (1, –4) 2 B1 for correct 90° anticlockwise rotation about origin or for correct orientation, wrong position 11(c) Correct diagram with vertices at (–5, –2), (–5, –4), (–2, –2), (–2, –4) 2 B1 for translation 6 k −       or 5 k     −   or SC1 for translation 5 6 −     −   12(a) 18.8 to 18.9 3 B2 for answer 11.78 to 11.8 or M2 for 2 1.5 0.5 ×π× × + 2 2 1.5 ×π× seen or M1 for 2 1.5 0.5 ×π× × or [2 ×] π × 1.52 12(b)(i) 53[.0] or 53.01 to 53.02 2 M1 for π × 1.52 × 0.5 [× 15] 12(b)(ii) 2.4 3 B2 for 2.37… or M1 for their 53.0 = 2 3 r π× × oe soi 13(a) Correct sketch 2 B1 for maximum and minimum in correct quadrants. 13(b) (0, 0) 1 13(c) (–3, 0), ( 0, 0), (2, 0) 2 B1 for 2 correct 13(d) (1.12, 4. − 06 ) 2 B1 for each value or SC1 for (1.1, −4.1)

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 7 of 7 Question Answer Marks Part Marks 13(e)(i) Correct sketch 1 FT their (a) 13(e)(ii) Correct sketch 1 FT their (a)