Cambridge IGCSE Mathematics - International 0607 — 2019 May/June Paper 3 · Variant 3

This document consists of 18 printed pages and 2 blank pages. DC (LEG/SG) 168253/4 © UCLES 2019 [Turn over * 7 8 1 6 4 6 7 9 5 0 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 2019 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. Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education

2 0607/33/M/J/19 © UCLES 2019 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/19 © UCLES 2019 [Turn over Answer all the questions. 1 (a) 7 8 9 10 11 12 13 From this list of numbers, write down (i) an even number, … [1] (ii) a multiple of 5, … [1] (iii) a factor of 27. … [1] (b) Write (i) 33% as a decimal, … [1] (ii) 4 3 as a decimal, … [1] (iii) 20% as a fraction, … [1] (iv) 0.9 as a percentage. …% [1] (c) Write 6.666 correct to 1 decimal place. … [1] (d) Work out 40. Give your answer correct to 2 significant figures. … [2]

4 0607/33/M/J/19 © UCLES 2019 2 (a) x y Measure angle x and angle y. x = … y = … [2] (b) a c d b e f g NOT TO SCALE In the first diagram, two lines intersect. In the second diagram, three lines meet at a point. (i) Complete each statement using one letter from either diagram. Angle … is acute. Angle … is reflex. [2] (ii) Complete each statement with a number. e = …° d + a = …° e + f + g = …° [3]

5 0607/33/M/J/19 © UCLES 2019 [Turn over 3 (a) Item Item cost ($) Number of items Cost ($) Bread 2.35 3 Milk 3.00 4 Eggs 2.82 1 Cheese 22.04 1 Total cost ($) (i) Complete the shopping bill. [2] (ii) Work out how much change there will be from $50. $ … [1] (b) A jar of coffee usually costs $7.50 . This cost is reduced by 4%. By how much is the cost reduced? $ … [1] (c) Water can be bought in a pack of 6 bottles or a pack of 10 bottles. In both packs, the bottles are the same size. Pack of 6 bottles costs $1.38 Pack of 10 bottles costs $2.20 Work out which pack is the better value. Show all your working. Pack of … bottles is the better value [3]

6 0607/33/M/J/19 © UCLES 2019 4 (a) y x – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 0 – 1 1 2 3 4 5 – 2 – 3 – 4 – 5 R P Q (i) On the grid, draw the reflection of rectangle R in the y-axis. [1] (ii) Triangle P is a reflection of triangle Q. On the grid, draw the line of reflection. [1]

7 0607/33/M/J/19 © UCLES 2019 [Turn over (b) y x – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 0 – 1 1 2 3 4 5 – 2 – 3 – 4 – 5 A C B (i) Describe fully the single transformation that maps shape A onto shape B. … … [3] (ii) Describe fully the single transformation that maps shape A onto shape C. … … [2]

8 0607/33/M/J/19 © UCLES 2019 5 (a) Ten people each invest money in a bank. The amount each person invests and their age is shown in the table. Age (years) 28 40 30 66 71 70 62 56 75 22 Amount ($ thousands) 2.5 4.5 3.5 6 8 7 7.5 6 9 3 (i) Complete the scatter diagram. The first five points have been plotted for you. Age (years) Amount ($ thousands) 20 0 1 2 3 4 5 6 7 8 9 10 30 40 50 60 70 80 [2] (ii) Work out the mean age and the mean amount. Mean age … years Mean amount $ … thousands [2] (iii) Using your answers to part (ii), draw a line of best fit on the scatter diagram. [2] (iv) Use your line of best fit to estimate how much someone aged 60 might invest. $ … thousands [1]

9 0607/33/M/J/19 © UCLES 2019 [Turn over (b) 100 other people were asked how much they had invested in the bank. The table below shows this information. Amount ($ x) Number of people x 0 1000 1 G 29 x 000 1000 2 1 G 26 x 000 000 2 3 1 G 19 x 000 000 3 4 1 G 14 x 000 000 4 5 1 G 12 (i) Write down the modal group. … x 1 G … [1] (ii) Work out an estimate of the mean. $ … [3]

10 0607/33/M/J/19 © UCLES 2019 6 (a) Simplify fully. (i) p p 6 2 - … [1] (ii) k g k g 7 5 3 + + - … [2] (b) Solve. x x 4 2 10 = + x = … [2] (c) Multiply out the brackets. x 3 9 4 - ^ h … [1] (d) A L W # = 2 2 P L W = + Work out the value of A and the value of P when L = 7 and W = 5. A = … P = … [3]

11 0607/33/M/J/19 © UCLES 2019 [Turn over (e) Write down the value of x0 . … [1] (f) Simplify. (i) t t 5 4 # … [1] (ii) p p 2 7 … [1] (g) Write down all the integer values of n that satisfy this inequality. l n 5 1 G … [1]

12 0607/33/M/J/19 © UCLES 2019 7 Some students are each asked how many cats and how many rabbits they have as pets. Each of the students has no other pets. The results are shown in the table. Example: the shaded square shows 1 student has 2 rabbits and 4 cats. Number of cats 0 1 2 3 4 Number of rabbits 0 4 3 1 2 0 1 1 1 0 1 1 2 3 2 2 2 1 3 2 1 0 2 0 4 2 2 0 0 0 (a) Find the total number of students asked. … [1] (b) Work out the number of students with (i) exactly 3 cats, … [1] (ii) exactly 4 pets, … [1] (iii) fewer than 3 pets, … [1] (iv) the same number of cats as rabbits. … [1]

13 0607/33/M/J/19 © UCLES 2019 [Turn over 8 (a) 20 cm 16 cm x cm 12 cm C A B NOT TO SCALE (i) Work out the perimeter of triangle ABC. … cm [1] (ii) Work out the area of triangle ABC. …cm2 [1] (iii) Using your answer to part (ii), find the value of x. x = … [2] (b) These two triangles are mathematically similar. 12 cm 18 cm 16 cm y cm 20 cm NOT TO SCALE Find the value of y. y = … [2]

14 0607/33/M/J/19 © UCLES 2019 9 U , , , , , , , , , 1 2 3 4 5 6 7 8 9 10 = " , , , , S 2 3 5 7 = " , , , , , T 1 3 5 7 9 = " , (a) Write down (i) n S^ h, … [1] (ii) S T + , " … , [1] (iii) S T , , " … , [1] (iv) Sl. " … , [1] (b) (i) A number is chosen at random from S. Work out the probability that it is 3. … [1] (ii) 60 students each choose a number at random from S. Find the expected number of times that 3 is chosen. … [1]

15 0607/33/M/J/19 © UCLES 2019 [Turn over 10 35 cm 95 cm NOT TO SCALE A container is made from a cylinder and a hemisphere. The cylinder has radius 35 cm and height 95 cm and the hemisphere has radius 35 cm. The container is full of water. Calculate the total volume of water in the container. Give your answer in litres. … litres [4]

16 0607/33/M/J/19 © UCLES 2019 11 The line AB is drawn on a 1 cm2 grid. 0 1 1 2 3 2 3 4 5 6 7 8 9 10 x A B y (a) Write down the co-ordinates of the midpoint of the line AB. ( … , … ) [1] (b) Find the gradient of the line AB. … [2] (c) Use Pythagoras’ Theorem to work out the length of AB. AB = … cm [3]

17 0607/33/M/J/19 © UCLES 2019 [Turn over 12 (a) (i) The mass of the Earth’s atmosphere is 5.15 × 1018 kg. When 5.15 × 1018 is written as an ordinary number, how many zeros are there in the number? … [1] (ii) 0.000 055% of the Earth’s atmosphere is hydrogen. Write 0.000 055 in standard form. … [1] (b) (i) The International Space Station travels round the Earth at a height of 450 km. Write 450 km in centimetres. Give your answer in standard form. … cm [2] (ii) The International Space Station travels at a speed of 8 km/s. Work out the distance it travels in 1 day. …km [2]

18 0607/33/M/J/19 © UCLES 2019 13 10 y x –10 0 –1 6 (a) (i) On the diagram, sketch the graph of y x x 5 2 = - for x 1 6 G G - . [2] (ii) Find the co-ordinates of the local maximum. ( … , … ) [2] (b) On the diagram, sketch the graph of y x 3 = + for x 1 6 G G - . [2] (c) Solve this equation. x x x 5 3 2 - = + x =… or x = … [2]

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20 0607/33/M/J/19 © UCLES 2019 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 Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge. BLANK PAGE

This document consists of 6 printed pages. © UCLES 2019 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 2019 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 International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the May/June 2019 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 2019 © UCLES 2019 Page 2 of 6 Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • the specific content of the mark scheme or the generic level descriptors for the question • the specific skills defined in the mark scheme or in the generic level descriptors for the question • the standard of response required by a candidate as exemplified by the standardisation scripts. GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate • marks are awarded when candidates clearly demonstrate what they know and can do • marks are not deducted for errors • marks are not deducted for omissions • answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous. GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 3 of 6 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 Question Answer Marks Partial Marks 1(a)(i) 8 or 10 or 12 1 1(a)(ii) 10 1 1(a)(iii) 9 1 1(b)(i) [0].33 1 1(b)(ii) [0].75 1 1(b)(iii) 20 100 1 or any equivalent fraction 1(b)(iv) 90 1 1(c) 6.7 1 1(d) 6.3 2 B1 for 6.32… 2(a) 60 153 2 B1 for each

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 4 of 6 Question Answer Marks Partial Marks 2(b)(i) b or d or f g 2 B1 for each 2(b)(ii) 90 180 360 3 B1 for each 3(a)(i) 7.05 12[.00] 2.82 22.04 Total 43.91 2 B1 for 7.05 or 12[.00] 3(a)(ii) 6.09 1 FT 50 – their 43.91 3(b) [0].3[0] 1 3(c) Pack of 10 with correct working 3 B1 for 0.23 oe B1 for 0.22 oe or M1 for 1.38÷6 or 2.2[0]÷10 4(a)(i) Correct reflection (–1, 1), (–3, 1), (–3, 4), (–1, 4) 1 4(a)(ii) Correct ruled line of reflection 5 y x = −− 1 4(b)(i) Rotation 90 clockwise oe About (0, 0) oe 3 B1 for each 4(b)(ii) Translation 4 5 −     −   2 B1 for each 5(a)(i) 5 points correctly plotted 2 B1 for 3 or 4 points correctly plotted 5(a)(ii) 52 5.7 2 B1 for each 5(a)(iii) Ruled line through mean point and within tolerance 2 B1 for ruled line through mean point with positive gradient outside tolerance or for ruled line within tolerance but not through mean point 5(a)(iv) 6.2 to 6.8 1 FT their straight line 5(b)(i) 0 ⩽ x < 1000 1 5(b)(ii) 2040 3 M1 for 500 × 29 + 1500 × 26 + 2500 × 19 +… M1dep for (their ∑fx) ÷ 100 6(a)(i) 4p 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 5 of 6 Question Answer Marks Partial Marks 6(a)(ii) 10k + 4g final answer 2 B1 for 10k or 4g seen 6(b) 5 2 B1 for 4x – 2x = 10 or 2x = x + 5 6(c) 27x – 12 final answer 1 6(d) [A =] 35 [P =] 24 3 B1 for [A =] 35 B2 for [P =] 24 or B1 for 14 or 10 seen 6(e) 1 1 6(f)(i) t 9 1 6(f)(ii) p5 1 6(g) 2, 3, 4, 5 1 7(a) 33 1 7(b)(i) 7 1 7(b)(ii) 6 1 7(b)(iii) 13 1 7(b)(iv) 5 or 9 1 8(a)(i) 48 1 8(a)(ii) 96 1 8(a)(iii) 9.6 2 M1 for their (a)(ii) = 20 2 × x oe 8(b) 24 2 B1 for 18 12 or 16 12 oe 9(a)(i) 4 1 9(a)(ii) 3, 5, 7 1 9(a)(iii) 1, 2, 3, 5, 7, 9 1 9(a)(iv) 1, 4, 6, 8, 9, 10 1 9(b)(i) 1 4 oe 1 9(b)(ii) 15 1 FT their (b)(i) × 60

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 6 of 6 Question Answer Marks Partial Marks 10 455 or 455.4… 4 B3 for figs 455… OR M2 for π × 352 × 95 and 3 1 4 π 35 2 3   × × ×     oe or M1 for π × 352 × 95 or 3 1 4 π 35 2 3   × × ×     oe and M1 for ÷1000 11(a) (1, 5) 1 11(b) 4 2 M1 for rise run soi by 8 2 oe 11(c) 8.25 or 8.246… 3 M2 for 2 2 8 2 + or M1 for 2 2 8 2 + 12(a)(i) 16 1 12(a)(ii) 5.5 × 10-5 1 12(b)(i) 4.5[0] × 107 2 B1 for 450 000 or 45 000 000 soi 12(b)(ii) 691 200 oe 2 M1 for [8 ×] 24 × 60 × 60 soi by 86 400 13(a)(i) Correct curve sketch 2 B1 for correct shape or for vertex in top right quadrant 13(a)(ii) (2.5, 6.25) 2 B1 for each 13(b) Correct line sketch, ruled 2 B1 for positive gradient or for y-intercept above origin 13(c) 1 and 3 2 B1 for each