Cambridge IGCSE Mathematics - International 0607 — 2020 Oct/Nov Paper 5 · Variant 3

Cambridge IGCSE™ DC (MB) 207018 © UCLES 2020 [Turn over This document has 8 pages. Blank pages are indicated. * 1 8 9 3 7 5 5 3 7 0 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/53 Paper 5 Investigation (Core) October/November 2020 1 hour 10 minutes You must answer on the question paper. No additional materials are needed. 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, including sketches, to gain full marks for correct methods. ● In this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. INFORMATION ● The total mark for this paper is 36. ● The number of marks for each question or part question is shown in brackets [ ].

2 0607/53/O/N/20 © UCLES 2020 Answer all the questions. INVESTIGATION AREA OF RIGHT-ANGLED TRIANGLES This investigation looks at finding the area of a right-angled triangle using its perimeter. In this investigation all lengths are in centimetres. w b h w is the hypotenuse of the triangle, b is the base of the triangle, h is the height of the triangle. Perimeter, P, of this triangle. b h w P = + + Area, A, of this triangle. A bh 2 1 = 1 (a) This right-angled triangle is drawn on a 1 cm2 grid. (i) Measure and write down the length of the hypotenuse. … [1] (ii) Show that the perimeter is 12. [1] (iii) Find the area of the triangle. … [1]

3 0607/53/O/N/20 © UCLES 2020 [Turn over (b) 10 8 6 NOT TO SCALE (i) Find the perimeter of this triangle. … [2] (ii) Find the area of this triangle. … [2]

4 0607/53/O/N/20 © UCLES 2020 (c) w NOT TO SCALE b h Complete the table for right-angled triangles with sides b, h and w. b h w Perimeter, P Area, A 12 5 13 30 30 84 13 85 24 25 56 84 60 11 132 [5]

5 0607/53/O/N/20 © UCLES 2020 [Turn over 2 (a) NOT TO SCALE 26 24 10 This triangle has perimeter P = 60. Show that the calculation 2 60 2 60 26 # - b l gives the correct area for this triangle. [3] (b) NOT TO SCALE 50 48 This triangle has perimeter P = 112. Show that the calculation 2 112 2 112 50 # - b l gives the correct area for this triangle. [3]

6 0607/53/O/N/20 © UCLES 2020 3 (a) Complete the table. b h w P A Calculation 24 10 26 60 120 2 60 2 60 26 # - b l = 120 12 9 15 36 54 2 2 36 36 15 # - b l = 54 48 50 112 2 2 112 112 50 # - b l = 15 8 17 60 = 60 21 29 70 210 = 12 37 210 = [8] (b) Write an expression for the area of a right-angled triangle in terms of P and w. … [1]

7 0607/53/O/N/20 © UCLES 2020 [Turn over (c) w b h Pythagoras’ Theorem w b h 2 2 2 = + NOT TO SCALE 56 33 Use your expression from part (b) to find the area of this triangle. … [4] Question 4 is printed on the next page.

8 0607/53/O/N/20 © UCLES 2020 4 (a) w b h NOT TO SCALE This is a rhombus. Use Question 3(b) to write down an expression for the area of this rhombus in terms of P and w. … [1] (b) Use your expression from part (a) to find the area of this rhombus when w = 41 and b = 40. … [4] 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.

This document consists of 6 printed pages. © UCLES 2020 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/53 Paper 5 (Core) October/November 2020 MARK SCHEME Maximum Mark: 36 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 October/November 2020 series for most Cambridge IGCSE™, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 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.

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 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

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 4 of 6 Question Answer Marks Partial Marks 1(a)(i) 5 1 1(a)(ii) 3 + 4 + 5 [= 12] 1 1(a)(iii) 6 1 1(b)(i) 6 + 10 + 8 C1 24 B1 1(b)(ii) 1 8 6 2 × × or 1 6 8 2 × × or 6 8 2 × C1 24 B1 1(c) A relevant calculation C1 b h w P A 12 5 13 30 30 84 13 85 182 546 24 7 25 56 84 60 11 61 132 330 B4 B3 for 4 correct white cells or B2 for 3 correct white cells or B1 for 2 correct white cells 2(a) 1 24 10 2 × × M1 30(30 – 26) or 30 × 4 M1 120 seen twice from correct formulae A1 2(b) 112 – 50 – 48 or 2 2 50 48 − or 2 2 50 48 − C1 1 48 14 336 2 × × = B1 56(56 – 50) = 336 or 56 × 6 = 336 B1

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 5 of 6 Question Answer Marks Partial Marks 3(a) 372 = b2 + 122 or better or 1 12 210 2 × × = b or better C1 b h w P A Calculation 24 10 26 60 120 60 60 26 2 2   × −     = 120 12 9 15 36 54 36 36 15 2 2   × −     = 54 48 14 50 112 336 112 112 50 2 2   × −     = 336 15 8 17 40 60 40 40 17 2 2   × −     = 60 21 20 29 70 210 70 70 29 2 2   × −     [=210] 35 12 37 84 210 84 84 37 2 2   × −     [=210] B7 B1 for each white cell correct FT their 35 for finding P only in last row. 3(b) 2 2   × −     P P w oe, isw 1 3(c) 2 2 56 33 + or 2 2 56 33 + soi C1 33 + 56 + their 65 C1 154 154 65 2 2   × −     their C1 FT their (b) in P and w FT their 154 and their 65 924 B1 4(a) 4 × their 3(b), oe isw 1

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 6 of 6 Question Answer Marks Partial Marks 4(b) 412 – 402 or 2 2 41 40 − soi C1 [P=] 90 soi M1 FT 81 + their h 720 B2 B1 for 90 90 4 41 2 2   × × −     or for correct substitution of 41 and their 90 in their part (a)