Cambridge IGCSE Mathematics - International 0607 — 2022 May/June Paper 3 · Variant 2

[Turn over DC (NF/SW) 214443/2 © UCLES 2022 This document has 16 pages. * 5 2 1 4 5 9 4 0 0 3 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2022 1 hour 45 minutes You must answer on the question paper. You will need: Geometrical instruments INSTRUCTIONS ● Answer all questions. ● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. ● Write your name, centre number and candidate number in the boxes at the top of the page. ● Write your answer to each question in the space provided. ● Do not use an erasable pen or correction fluid. ● Do not write on any bar codes. ● You should use a graphic display calculator where appropriate. ● You may use tracing paper. ● You must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. ● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. ● For r, use your calculator value. INFORMATION ● The total mark for this paper is 96. ● The number of marks for each question or part question is shown in brackets [ ]. Cambridge IGCSE™

2 0607/32/M/J/22 © UCLES 2022 Formula List Area, A, of triangle, base b, height h. A = bh 2 1 Area, A, of circle, radius r. A = r2 r 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 = r 4 2 r 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 = r h 2 r 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 0607/32/M/J/22 © UCLES 2022 [Turn over Answer all the questions. 1 (a) 21 22 23 24 25 26 27 28 29 From this list of numbers, write down (i) an even number, … [1] (ii) a multiple of 6, … [1] (iii) a factor of 100, … [1] (iv) a prime number. … [1] (b) Find the value of (i) , 841 … [1] (ii) . 63 … [1] (c) Work out. . . . 5 2 13 25 35 51 + Give your answer correct to 2 decimal places. … [2]

4 0607/32/M/J/22 © UCLES 2022 2 2 0 y x 2 4 1 3 5 4 1 3 5 6 A D B C Quadrilateral ABCD is drawn on a 1 cm square grid. (a) Write down the mathematical name of quadrilateral ABCD. … [1] (b) Write down the coordinates of point B. ( … , …) [1] (c) Work out the area and the perimeter of quadrilateral ABCD. Area … cm2 Perimeter … cm [2] (d) On the diagram, draw the lines of symmetry of quadrilateral ABCD. [2]

5 0607/32/M/J/22 © UCLES 2022 [Turn over 3 (a) These are the first four terms of a sequence. 4 8 12 16 (i) Write down the next two terms of this sequence. … , … [1] (ii) Write down the rule for continuing this sequence. … [1] (iii) Find the nth term of this sequence. … [1] (b) Look at the patterns of numbers in this table. Row 1 20 19 39 2 2 - = Row 2 1 3 19 8 7 2 2 - = Row 3 3 18 17 5 2 2 - = Row 4 1 3 17 6 3 2 2 - = Row 5 Row 8 (i) Complete Row 5 of the table. [1] (ii) Complete Row 8 of the table. [2] (iii) Find the nth term of this sequence. 39 37 35 33 … [2]

6 0607/32/M/J/22 © UCLES 2022 4 108° NOT TO SCALE y° x° Q B C P A In the diagram, AQB and PBC are straight lines and . PQ PB = (a) What type of triangle is BPQ? … [1] (b) Find the value of x. x = … [3] (c) Find the value of y. y = … [1] (d) AB and BC are two sides of a regular polygon. Work out the number of sides of this polygon. … [2]

7 0607/32/M/J/22 © UCLES 2022 [Turn over 5 (a) The table shows the melting point, in °C, of some metals. Metal Melting point (°C) Zinc 420 Gold 1063 Silver 893 Copper 1084 Aluminium 660 (i) Write these five temperatures in order of size starting with the smallest. … , … , … , … , … [1] smallest (ii) Write 1063 correct to the nearest 10. … [1] (iii) Write 1084 in words. … [1] (b) Brass can be made by combining copper and zinc in this ratio. copper : zinc = 13 : 7 Work out the mass of copper and the mass of zinc used to make 60 kg of brass. copper … kg zinc … kg [2]

8 0607/32/M/J/22 © UCLES 2022 6 (a) (i) A train travels from Amsterdam to Brussels in 2 hours 15 minutes. It leaves Amsterdam at 11 10. Work out the time the train arrives in Brussels. … [1] (ii) On its return journey, the train leaves Brussels at 14 50. It arrives in Amsterdam at 17 15. Work out the length of time this journey took. Give your answer in hours and minutes. … h … min [1] (b) One day, the adult train fare from Amsterdam to Brussels is 75 euros. (i) The fare for a child is 5 3 of the adult fare. Work out the child fare for the journey. … euros [1] (ii) On another day the adult fare of 75 euros is increased by 12%. Work out the adult fare on this day. … euros [2] (c) The train from Amsterdam to Brussels travels 180 km in 2 hours 15 minutes. Work out the average speed of the train in kilometres per hour. … km / h [2]

9 0607/32/M/J/22 © UCLES 2022 [Turn over 7 The graph shows the cost, y dollars, of printing x cards. 0 0 10 20 30 40 10 20 30 Number of cards Cost ($) 40 50 y x (a) (i) Find the cost of printing 45 cards. $ … [1] (ii) Find the largest number of cards that can be printed for $28. … [1] (b) (i) Find the equation of the line in the form . y mx c = + y = … [3] (ii) Any number of cards can be printed. Steffi needs 100 cards. Use your equation from part (b)(i) to find how much these will cost. $ … [2]

10 0607/32/M/J/22 © UCLES 2022 8 y x 20 – 5 – 4 0 3 (a) On the diagram, sketch the graph of y x x 3 2 = + for . x 4 3 G G - [2] (b) On the diagram, sketch the graph of y x 2 6 = + for . x 4 3 G G - [2] (c) Find the coordinates of each point of intersection of y x x 3 2 = + and . y x 2 6 = + ( … , … ) and ( … , … ) [2] 9 (a) Complete each of these statements using 1 or 2 . 11 … 7 11 - … 7 - [1] (b) Simplify. (i) x x x 3 5 + + … [1] (ii) p t p t 6 2 4 3 - - + … [2]

11 0607/32/M/J/22 © UCLES 2022 [Turn over (c) Factorise fully. x xy 12 3 + … [2] (d) Solve. (i) x 5 5 = x = … [1] (ii) x x 7 3 3 5 + = + x = … [2] (e) y x 6 2 = (i) Find the value of y when x = 5. y = … [1] (ii) Find the value of x when y = 294. x = … [2] (iii) Rearrange the formula y = 6x2 to make x the subject. x = … [2]

12 0607/32/M/J/22 © UCLES 2022 10 A garage sells used cars. The table shows the selling price, in $, and the distance travelled, in km, of eight used cars. All cars are of the same make and model. Distance travelled (km) 8000 15 000 25 000 22 000 34 000 2000 40 000 46 000 Selling price ($) 7300 5000 3900 5500 4000 6000 2000 2300 (a) Complete the scatter diagram. The first four points have been plotted for you. 0 0 2000 4000 6000 8000 1000 3000 5000 7000 10 000 20 000 30 000 Distance travelled (km) Selling price ($) 40 000 50 000 [2] (b) What type of correlation is shown in the scatter diagram? … [1] (c) The mean distance travelled is 24 000 km and the mean selling price is $4500. On the scatter diagram, draw a line of best fit. [2] (d) Another used car of this make and model had travelled a distance of 30 000 km. Use your line of best fit to estimate the selling price of this car. $ … [1]

13 0607/32/M/J/22 © UCLES 2022 [Turn over 11 B A D E C 68° 54 mm 35 mm 45 mm NOT TO SCALE The diagram shows three right-angled triangles ABC, BCD and CDE. , AC 54mm = , CD 45mm = CE 35mm = and angle °. BAC 68 = (a) Use trigonometry to show that , BC 134mm = correct to the nearest mm. [2] (b) Use trigonometry to find angle BCD. Angle BCD = … [2] (c) Use Pythagoras’ Theorem to find DE. DE = … mm [2]

14 0607/32/M/J/22 © UCLES 2022 12 The table shows the frequency distribution for the masses, in kg, of 100 students. Mass (m kg) m 30 40 1 G m 0 0 4 5 1 G m 0 0 5 6 1 G m 0 0 6 7 1 G m 0 0 7 8 1 G m 0 0 8 9 1 G Frequency 16 23 28 18 11 4 (a) Complete the cumulative frequency table. Mass (m kg) m 40 G m 0 5 G m 0 6 G m 0 7 G m 0 8 G m 0 9 G Cumulative frequency [2] (b) On the grid below, draw the cumulative frequency curve for this data. 30 0 20 40 60 80 10 30 50 70 100 90 50 70 90 Mass (m kg) Cumulative frequency 40 60 80 [3]

15 0607/32/M/J/22 © UCLES 2022 [Turn over (c) Use your cumulative frequency curve to find an estimate of (i) the median, … kg [1] (ii) the interquartile range. … kg [2] (d) Use your cumulative frequency curve to find an estimate for the number of students with a mass of less than 68 kg. … [1] Question 13 is printed on the next page.

16 0607/32/M/J/22 © UCLES 2022 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 Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. 13 (a) A cube has edges of length 3 cm. NOT TO SCALE 3 cm (i) Find the volume of the cube. … cm3 [2] (ii) Find the total surface area of the cube. … cm2 [2] (b) NOT TO SCALE 15 cm 20 cm 30 cm Some cubes, each with edges of length 3 cm, are placed in a box. The box is a cuboid with dimensions 30 cm by 20 cm by 15 cm. Work out the greatest number of these cubes that can be placed in the box. … [3]

This document consists of 6 printed pages. © UCLES 2022 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2022 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 2022 series for most Cambridge IGCSE, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 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.

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 3 of 6 Maths-Specific Marking Principles 1 Unless a particular method has been specified in the question, full marks may be awarded for any correct method. However, if a calculation is required then no marks will be awarded for a scale drawing. 2 Unless specified in the question, answers may be given as fractions, decimals or in standard form. Ignore superfluous zeros, provided that the degree of accuracy is not affected. 3 Allow alternative conventions for notation if used consistently throughout the paper, e.g. commas being used as decimal points. 4 Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw). 5 Where a candidate has misread a number in the question and used that value consistently throughout, provided that number does not alter the difficulty or the method required, award all marks earned and deduct just 1 mark for the misread. 6 Recovery within working is allowed, e.g. a notation error in the working where the following line of working makes the candidate’s intent clear. 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

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 4 of 6 Question Answer Marks Partial Marks 1(a)(i) 22 or 24 or 26 or 28 1 1(a)(ii) 24 1 1(a)(iii) 25 1 1(a)(iv) 23 or 29 1 1(b)(i) 29 1 1(b)(ii) 216 1 1(c) 9.38 2 B1 for 9.376 to 9.377 2(a) rectangle 1 2(b) (5, 4) 1 2(c) [A =] 8 [P =] 12 2 B1 for each If 0 scored, SC1 for correct answers reversed 2(d) Two correct lines and no others 2 B1 for one correct line and no others or for two correct lines and one incorrect line 3(a)(i) 20, 24 1 3(a)(ii) +4 oe 1 3(a)(iii) 4n 1 3(b)(i) 162 – 152 = 31 1 3(b)(ii) 132 – 122 = 25 2 B1 for 132 – 122 or [=] 25 3(b)(iii) −2n + 41 oe 2 B1 for −2n + k any k or jn + 41 j ≠ 0 4(a) isosceles 1 4(b) 36 3 B1 for PBQ or PQB = 72 M1 for 180 – 2 × their72 4(c) 108 1 FT 180 – their PQB 4(d) 5 2 M1 for 360 ÷ their PBQ 5(a)(i) 420, 660, 893, 1063, 1084 1 5(a)(ii) 1060 1 5(a)(iii) One thousand [and] eighty four 1 5(b) [C =] 39 [Z =] 21 2 B1 for each or M1 for 60÷20 soi

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 5 of 6 Question Answer Marks Partial Marks 6(a)(i) 13 25 or 1 25 pm 1 6(a)(ii) 2h 25m 1 6(b)(i) 45 1 6(b)(ii) 84 2 M1 for 75 × 12 100 oe 6(c) 80 2 M1 for 180 ÷ their time 7(a)(i) 36 1 7(a)(ii) 25 1 7(b)(i) 0.4x + 18 oe 3 M1 for their rise ÷ their run B1 for 0.4x + c or mx + 18 oe m≠0, c≠0 7(b)(ii) 58 2 FT their mx + c from (b)(i) for 2 marks M1 for x = 100 in their mx + c from (b)(i) 8(a) Correct curve 2 B1 for correct shape or for vertex in correct quadrant 8(b) Correct straight line 2 B1 for straight line with positive gradient or for straight line with positive intercept 8(c) (–3, 0) (2, 10) 2 B1 for each 9(a) > < 1 9(b)(i) 9x final answer 1 9(b)(ii) 2p + [1]t final answer 2 B1 for 2p or [+] [1]t 9(c) 3x(4 + [1]y) final answer 2 B1 for x(12 + 3y) or 3 (4x + [1] xy) 9(d)(i) 25 1 9(d)(ii) ½ or 0.5 or 2/4 2 M1 for 7x – 3x or 3x – 7x seen or for 5 – 3 or 3 – 5 seen 9(e)(i) 150 1 9(e)(ii) 7 2 M1 for 294 ÷ 6 9(e)(iii) √( y÷6) oe 2 M1 for 6 y = x2 10(a) 4 points correctly plotted 2 B1 for 2or 3 points correctly plotted 10(b) Negative 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 6 of 6 Question Answer Marks Partial Marks 10(c) Ruled straight line through the mean point and within tolerance 2 B1 for Ruled straight line through the mean point but not within tolerance Or Ruled straight line within tolerance but not through the mean point 10(d) 3600 to 4200 1 FT their straight line with negative gradient 11(a) tan 68 = 54 BC or better M1 133.6… or 133.7 A1 11(b) 70.3 or 70.4 or 70.32 to 70.38 2 M1 for cos[ ] = 45 134 oe 11(c) 57.0 or 57.00 to 57.01 2 M1 for 352 + 452 12(a) 16, 39, 67, 85, 96, 100 2 M1for 4 correct values FT one addition error 12(b) Correct curve 3 B2 for 5 or 6 correct points correctly plotted or B1 for 3 or more of their points correctly plotted M1 for increasing curve through their 6 points 12(c)(i) 52 to 54 1 12(c)(ii) 16 to 22 2 B1 for LQ = 43 to 46 or UQ = 62 to 65 12(d) 80 to 84 1 13(a)(i) 27 2 M1 for 3×3×3 13(a)(ii) 54 2 M1 for 3×3 soi 13(b) 300 3 M2 for 10,5 and 6 soi or M1 for 10 or 5 or 6 seen If 0 scored, SC1 for 333 or (30×20×15)÷their (a)(i)