Cambridge IGCSE Mathematics - International 0607 — 2020 May/June Paper 3 · Variant 2

Cambridge IGCSE™ This document has 20 pages. Blank pages are indicated. DC (ST/CT) 183469/2 © UCLES 2020 [Turn over * 1 3 8 3 4 4 6 5 0 4 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2020 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 [ ].

2 0607/32/M/J/20 © UCLES 2020 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/20 © UCLES 2020 [Turn over Answer all the questions. 1 (a) Write down a multiple of 7. … [1] (b) Here are the factors of 99. 1 3 9 11 33 99 Write down the factors that are prime. … [2] (c) Write down all of the factors of 20. … [2] (d) Write 54 as a product of its prime factors. … [2] (e) For an activity, students are split into groups. The students can be split exactly either into groups of 15 or into groups of 21. Work out the smallest number of students taking part in the activity. … [2]

4 0607/32/M/J/20 © UCLES 2020 2 (a) The temperature, in °C, in each of five cities is listed in the table. City Temperature (°C) Amsterdam −4 Dublin 5 Oslo −11 Venice 6 Warsaw 9 (i) Write down which city is the coldest. … [1] (ii) Work out the difference in temperature between Amsterdam and Warsaw. … °C [1] (iii) Work out the difference in temperature between Amsterdam and Oslo. … °C [1] (b) Chris climbs from Kathmandu to the top of Mount Everest. He uses this formula to find the temperature, T °C, at different heights, H metres, above sea level. . T H 0 008 30 # =- + (i) The top of Mount Everest is 8850 m above sea level. Show that the temperature at the top of Mount Everest is -40.8 °C. [1]

5 0607/32/M/J/20 © UCLES 2020 [Turn over (ii) Kathmandu is 1400 m above sea level. Work out the temperature in Kathmandu. … °C [1] (iii) The temperature at Everest Base Camp is −12.4 °C. Work out the height of Everest Base Camp above sea level. … m [2] (iv) Rearrange this formula to make H the subject. . T H 0 008 30 # =- + H = … [2]

6 0607/32/M/J/20 © UCLES 2020 3 (a) y x – 3 – 4 – 5 – 2 – 1 – 1 1 2 3 4 5 – 2 – 3 – 4 – 5 1 2 3 4 5 0 C A B The diagram shows a hexagon drawn on a 1cm2 grid. (i) Write down the coordinates of (a) point A, ( … , …) [1] (b) point B, ( … , …) [1] (c) point C. ( … , …) [1] (ii) On the grid, draw the reflection of the hexagon in the x-axis. [2]

7 0607/32/M/J/20 © UCLES 2020 [Turn over (b) (i) Write down the order of rotational symmetry of this shape. … [1] (ii) On the shape above, draw all the lines of symmetry. [2] 4 (a) Use the correct mathematical word to complete each sentence. (i) The distance around the edge of a circle is the … . [1] (ii) A straight line which touches the edge of a circle once only is a … . [1] (iii) A straight line from the edge of a circle to its centre is a … . [1] (b) 6 cm 18 cm NOT TO SCALE This shape is a rectangle joined to two semicircles. Work out the total area of this shape. Give the units of your answer. … … [5]

8 0607/32/M/J/20 © UCLES 2020 5 (a) The bar chart shows the numbers of girls and boys in a village school and their ages. Key Girls Boys Number of students 0 2 12 13 14 Age (years) 15 16 4 6 8 10 12 14 16 18 20 22 24 26 (i) There are 19 boys aged 16 in the school. Complete the bar chart. [1] (ii) For students aged 13, work out how many more boys than girls there are. … [1] (iii) Find the total number of students aged 12. … [1] (iv) Find the total number of girls in the school. … [1] (v) Which age has the largest total number of students? … [1]

9 0607/32/M/J/20 © UCLES 2020 [Turn over (b) In a country there are 11.5 million children. The probability that one of these children has measles is 0.2 . Work out the expected number of these children that have measles. … million [2] (c) In a town, the probability that a student aged 17 has passed their driving test is 0.7 . Two students aged 17 are chosen at random from the town. (i) Complete the tree diagram. Has passed Has not passed Has not passed Has passed Has passed Has not passed 0.7 … … … … … First student Second student [2] (ii) Work out the probability that both students have not passed their driving test. … [2]

10 0607/32/M/J/20 © UCLES 2020 6 (a) Write each of these ratios in its simplest form. (i) 6 : 30 … : … [1] (ii) 75 cents : 2 dollars … : … [2] (b) (i) One year, Amir earns $85 000. He pays 5 1 of this in tax. Work out how much Amir pays in tax. $ … [1] (ii) The next year, the $85 000 that Amir earns is increased by 3%. Work out how much Amir now earns. $ … [2]

11 0607/32/M/J/20 © UCLES 2020 [Turn over (iii) Another year, Amir receives a bonus of $8400. He decides to use this bonus for savings and for pleasure in the ratio savings : pleasure = 1 : 5. Work out how much of the bonus Amir uses for savings and how much he uses for pleasure. Savings $ … Pleasure $ … [2]

12 0607/32/M/J/20 © UCLES 2020 7 The table shows the height and the shoe size of each of eight children. Height (cm) 57 79 102 100 92 81 109 60 Shoe size 21 23 25.5 24 25 24 27.5 22 (a) Complete the scatter diagram. The first four points have been plotted for you. 20 1550 60 70 80 Height (cm) 90 100 110 25 30 Shoe size [2] (b) What type of correlation is shown in the scatter diagram? … [1] (c) (i) Work out the mean height and the mean shoe size. Mean height = … cm Mean shoe size = … [2] (ii) On the scatter diagram, draw a line of best fit. [2] (d) Use your line of best fit to estimate the shoe size of a child with height 70 cm. … [1]

13 0607/32/M/J/20 © UCLES 2020 [Turn over 8 (a) (i) 7 × 7 × 7 × 7 × 7 × 7 = 7n Write down the value of n. n = … [1] (ii) Write down the value of 70. … [1] (b) Simplify fully. (i) x 7 2 4 3 # … [2] (ii) x x 7 2 ' … [3]

14 0607/32/M/J/20 © UCLES 2020 9 (a) y x – 3 – 4 – 5 – 2 – 1 – 1 1 2 3 4 5 – 2 – 3 – 4 – 5 1 2 3 4 5 0 Rotate the triangle by 90° clockwise about (0, 0). [2] (b) 12 cm 8.4 cm 5 cm x cm NOT TO SCALE These two triangles are mathematically similar. Work out the value of x. x = … [2]

15 0607/32/M/J/20 © UCLES 2020 [Turn over (c) y x – 3 – 4 – 5 – 2 – 1 – 1 1 2 3 4 5 – 2 – 3 – 4 – 5 1 2 3 4 5 0 B A Describe fully the single transformation that maps triangle A onto triangle B. … … [3]

16 0607/32/M/J/20 © UCLES 2020 10 (a) Solve. (i) x 3 6 = x = … [1] (ii) x 2 5 4 H - … [2] (b) Solve the simultaneous equations. You must show all your working. x y 3 13 + = x y 2 12 - = x = … y = … [2] (c) Multiply out the brackets and simplify. ( )( ) x x 1 4 + - … [2]

17 0607/32/M/J/20 © UCLES 2020 [Turn over 11 y x 30 – 20 – 5 5 0 (a) (i) On the diagram, sketch the graph of y x x 2 8 2 = + - for x 5 5 G G - . [2] (ii) Find the coordinates of the local minimum. ( … , …) [1] (b) On the diagram, sketch the graph of y x 3 2 = - for x 5 5 G G - . [2] (c) Find the x-coordinate of each point of intersection of y x x 2 8 2 = + - and y x 3 2 = - . x = … and x = … [2]

18 0607/32/M/J/20 © UCLES 2020 12 (a) North A B Scale: 1 cm to 10 km A boat sails from A to B. (i) Measure the bearing of B from A. … [1] (ii) Work out the actual distance from A to B. … km [2]

19 0607/32/M/J/20 © UCLES 2020 (b) x° y m 8 m 2 m 4.5 m NOT TO SCALE The boat has two triangular sails. (i) Find the value of x. x = … [2] (ii) Find the value of y. y = … [2]

20 0607/32/M/J/20 © UCLES 2020 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 7 printed pages. © UCLES 2020 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2020 MARK SCHEME Maximum Mark: 96 Published Students did not sit exam papers in the June 2020 series due to the Covid-19 global pandemic. This mark scheme is published to support teachers and students and should be read together with the question paper. It shows the requirements of the exam. The answer column of the mark scheme shows the proposed basis on which Examiners would award marks for this exam. Where appropriate, this column also provides the most likely acceptable alternative responses expected from students. Examiners usually review the mark scheme after they have seen student responses and update the mark scheme if appropriate. In the June series, Examiners were unable to consider the acceptability of alternative responses, as there were no student responses to consider. Mark schemes should usually be read together with the Principal Examiner Report for Teachers. However, because students did not sit exam papers, there is no Principal Examiner Report for Teachers for the June 2020 series. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the June 2020 series for most Cambridge IGCSE™ and Cambridge International A & AS Level components, and some Cambridge O Level components.

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 2 of 7 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 2020 © UCLES 2020 Page 3 of 7 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 2020 © UCLES 2020 Page 4 of 7 Question Answer Marks Partial Marks 1(a) Any multiple of 7 1 1(b) 3, 11 only 2 B1 for each 1(c) 1, 2, 4, 5, 10, 20 2 B1 for 4 correct values 1(d) 2 × 3 × 3 × 3 or 2 × 33 2 M1 for any correct product for 54 or B1for 2, 3, 3, 3 1(e) 105 2 M1 for checking at least 3 multiples of 15 and 21 or for 3 × 5 and 3 × 7 seen 2(a)(i) Oslo 1 2(a)(ii) 13 1 2(a)(iii) 7 1 2(b)(i) −0.008 × 8850 + 30 seen 1 2(b)(ii) 18.8 1 2(b)(iii) 5300 2 B1 for −12.4 – 30 [= −0.008H ] or better 2(b)(iv) 30 0.008 T − − oe 2 B1 for T – 30 = −0.008H 3(a)(i)(a) (2, 4) 1 3(a)(i)(b) (0, 2) 1 3(a)(i)(c) (−2, 3) 1 3(a)(ii) Correct reflection 2 B1 for correct reflection in any horizontal line If 0 scored, SC1 for correct reflection in y-axis 3(b)(i) 2 1 3(b)(ii) 2 correct lines of symmetry 2 B1 for 1 correct line, no incorrect or for 2 correct lines, 1 or more incorrect 4(a)(i) Circumference 1 4(a)(ii) Tangent 1 4(a)(iii) Radius 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 5 of 7 Question Answer Marks Partial Marks 4(b) 136 or 136.2 to 136.3 4 M3 for π × 32 + 18 × 6 oe or M2 for 2 1 3 2   × π×     and 18 × 6 or M1 for 2 1 3 2   × π×     or 18 × 6 cm2 1 5(a)(i) Bar, height 19 1 5(a)(ii) 11 1 5(a)(iii) 29 1 5(a)(iv) 78 1 5(a)(v) 15 1 5(b) 2.3 2 B1 for figs 23 or M1 for 11.5 × 0.2 5(c)(i) Correct tree diagram 2 M1 for 0.3 correctly placed once 5(c)(ii) 0.09 2 M1 for their0.3 × their0.3 6(a)(i) 1 : 5 1 6(a)(ii) 3 : 8 2 M1 for 75[c] : 200[c] or for [$]0.75 : [$] 2 6(b)(i) 17 000 1 6(b)(ii) 87 550 2 M1 for 85 000 × 3 1 100   +     oe 6(b)(iii) [Savings] 1400 [Pleasure] 7000 2 M1 for 8400 ÷ (1 + 5) soi by 1400 7(a) 4 points correctly plotted 2 B1 for 2 or 3 points correctly plotted 7(b) positive 1 7(c)(i) [Height] 85 [Shoe size] 24 2 B1 for each 7(c)(ii) Ruled straight line through mean point and within tolerance 2 B1 for ruled straight line with positive gradient through mean point but not within tolerance or for ruled straight line not through mean point but within tolerance 7(d) 22 to 23 1 FT their positive gradient ruled line

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 6 of 7 Question Answer Marks Partial Marks 8(a)(i) 6 1 8(a)(ii) 1 1 8(b)(i) 3 14 x 2 M1 for multiplying tops and bottoms soi by 6 28 x or for cancelling 2 and 4 8(b)(ii) 2 7 3 B2 for 2 7 x x or M1 for 2 7 x x ×   9(a) Correct rotation (3, 4) (3, 0) (1, 3) 2 B1 for correct orientation, wrong position or for correct rotation 90 anticlockwise 9(b) 3.5 2 M1 for 8.4 5 12 x = oe or for s.f. 0.7 or 1.42 to 1.43 9(c) Enlargement s.f. 3 [centre] (−4, 1) 3 B1 for each 10(a)(i) 18 1 10(a)(ii) x ⩾ 4.5 or 1 4 2 2 B1 for 2x ⩾ 4 + 5 or x – 2.5 ⩾ 2 10(b) [x =] 5 [y =] −2 2 B1 for each If 0 scored, SC1 for correct substitution to find the other variable 10(c) x2 – 3x – 4 2 B1 for any three of x2 , –4x, (+)1x, –4 seen 11(a)(i) Correct sketch 2 B1 for correct shape or for vertex in correct quadrant

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 7 of 7 Question Answer Marks Partial Marks 11(a)(ii) (−1, −9) 1 11(b) Correct sketch 2 B1 for ruled line with positive gradient or for ruled line crossing y-axis below origin 11(c) 3 and −2 2 B1 for each 12(a)(i) [0]55 1 12(a)(ii) 45 2 B1 for AB = 4.3 to 4.7 cm oe 12(b)(i) 60.6 or 60.64… 2 M1 for [ ][ ] 8 tan 4.5 x = 12(b)(ii) 8.25 or 8.246… 2 M1 for 82 + 22