Cambridge IGCSE Mathematics - International 0607 — 2024 Oct/Nov Paper 6 · Variant 2

This document has 12 pages. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/62 Paper 6 Investigation and Modelling (Extended) October/November 2024 1 hour 40 minutes You must answer on the question paper. No additional materials are needed. INSTRUCTIONS ● Answer both part A (Questions 1 to 4) and part B (Questions 5 to 10). ● 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 60. ● The number of marks for each question or part question is shown in brackets [ ]. * 1 3 3 7 1 6 3 8 7 2 * DC (PQ/CGW) 337383/4 © UCLES 2024 ,










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2 0607/62/O/N/24 © UCLES 2024 Answer both parts A and B. A INVESTIGATION (QUESTIONS 1 TO 4) REVERSE DIFFERENCES (30 marks) You are advised to spend no more than 50 minutes on this part. This investigation looks at what happens when you reverse the digits of a number and then find the difference between the new number and the original number. This is called the reverse difference. STEP 1 Write down a 2-digit number. STEP 2 Reverse the digits of the number. STEP 3 Find the positive difference between the two numbers. Example 1 Example 2 STEP 1 Write a number 52 STEP 1 13 STEP 2 Reverse the digits 25 STEP 2 31 STEP 3 Find the difference 52 25 27 - = STEP 3 31 13 18 - = 1 (a) Complete the three steps for each 2-digit number in the table. STEP 1 12 13 14 15 16 17 18 STEP 2 21 31 41 51 STEP 3 18 45 63 [2] (b) Complete this table of 2-digit numbers and their reverse differences. Use part (a) and any patterns you notice to help you. Number Reverse difference Number Reverse difference Number Reverse difference Number Reverse difference 10 9 20 18 30 27 40 36 11 21 9 31 18 41 27 12 22 32 9 42 13 18 23 9 33 43 14 24 34 44 15 25 27 35 45 16 45 26 36 36 46 17 27 45 37 36 47 18 63 28 54 38 45 48 19 29 63 39 54 49 45 [3] * 0000800000002 * ,










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3 0607/62/O/N/24 © UCLES 2024 [Turn over (c) Complete the statement with the largest number possible. The reverse difference is always a multiple of … [1] (d) The table in part (b) is extended to the right. These two columns are part of the extended table. Number Reverse difference A 9 What is the value of the 2-digit number A? … [2] * 0000800000003 * ,










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4 0607/62/O/N/24 © UCLES 2024 2 You can find reverse differences for 3-digit numbers using the same steps. Example STEP 1 Write a number 138 STEP 2 Reverse the digits 831 STEP 3 Find the difference 831 138 693 - = (a) The table continues to the right until 199. Complete the first column of reverse differences. Number Reverse difference Number 100 99 110 101 0 111 102 103 198 104 297 105 396 106 107 108 693 109 792 [2] (b) Explain why each column of reverse differences has the same sequence of reverse differences. … … [1] * 0000800000004 * ,










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5 0607/62/O/N/24 © UCLES 2024 [Turn over (c) Complete the statement with the largest number possible. The reverse difference is always a multiple of … [1] (d) A 3-digit number abc has first digit a, second digit b and third digit c. In this part a c 2 . So the number 601 has a 6 = , b 0 = and c 1 = . (i) Anna says that a is the hundreds digit, b is the tens digit and c is the units digit. She says the value of abc is a b c 100 10 + + . Anna writes the value of the reverse number cba. c b a 100 10 + + She writes the difference between the two numbers. ( ) ( ) a b c c b a 100 10 100 10 + + - + + Complete Anna’s working and factorise the result. … [2] (ii) A 3-digit number has a 8 = and a reverse difference of 594. Find three possible 3-digit numbers. … [2] * 0000800000005 * ,










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6 0607/62/O/N/24 © UCLES 2024 3 Use your result from Question 2(d)(i) to answer both parts of this question. Anna uses 3-digit numbers to find reverse differences. (a) The reverse difference for a 3-digit number is 99. Comment on the values of each of the three digits. … … [3] (b) The table in Question 2(a) is extended to 999. Find all the possible reverse differences for 3-digit numbers. … [2] 4 (a) Find an expression for the reverse difference for the 5-digit number abcde, where a e 2 . … [3] * 0000800000006 * ,










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7 0607/62/O/N/24 © UCLES 2024 [Turn over (b) The 5-digit number a158e has a reverse difference of 33 066 and a e 2 . (i) Find the connection between a and e. … [4] (ii) Find all the 5-digit numbers a158e with a reverse difference of 33 066. … [2] * 0000800000007 * ,










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8 0607/62/O/N/24 © UCLES 2024 B MODELLING (QUESTIONS 5 to 10) NEWSPRINT (30 marks) You are advised to spend no more than 50 minutes on this part. This task looks at the amount of newsprint in a newspaper and the number of trees used to make the newspaper. Newsprint is the amount of paper that makes a newspaper. Newsprint is always rectangular. 5 A sheet of newsprint measures 560 mm by 430 mm. Each square metre of newsprint has a mass of 42 g. (a) Show that the mass of one sheet of newsprint is 0.0101 kilograms, correct to 3 significant figures. [3] (b) A newspaper uses 20 sheets of newsprint. Work out the mass of this newspaper in kilograms. … [1] (c) Give a practical reason why your answer to part (b) is slightly less than the actual mass of the newspaper. You may assume all measurements are accurate. … [1] * 0000800000008 * ,










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9 0607/62/O/N/24 © UCLES 2024 [Turn over (d) Circulation is the number of copies of a newspaper made in a day. The newspaper has an average circulation of 950 000. (i) Use your answer to Question 5(b) to work out the total mass of these newspapers. Give your answer in tonnes. … [2] (ii) The newspaper is made every day from Monday to Friday each week. Work out the mass of newsprint, in tonnes, used in a year of 52 weeks. Give your answer correct to the nearest thousand. … [2] 6 There are different sizes of newsprint. A sheet of newsprint measures L mm by W mm. The mass of one square metre of newsprint is d grams. Each newspaper has S sheets of newsprint. The circulation is C newspapers per day, Monday to Friday. (a) Write a model for the mass of newsprint, M tonnes, that is used to make the newspaper in a year. … [2] (b) The company that makes the newspaper now uses newsprint with a mass of 43 g per square metre. All other figures remain the same as in Question 5. Calculate the mass, in tonnes, of newsprint that the company now uses in a year. … [2] * 0000800000009 * ,










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10 0607/62/O/N/24 © UCLES 2024 7 Newsprint is made from the wood of fast-growing fir trees. There are four stages to make newsprint: • Cut down the tree. • Saw off the branches to leave the trunk. • Grind down the trunk to make wood pulp. • Turn the wood pulp into newsprint. trunk (a) Complete this statement. The best mathematical shape to model the trunk of a fir tree is a cone because … … [1] (b) Trees are cut down when the diameter at the base is 21 cm. The average height of the trunk is 14 metres. The mass of one cubic metre of wood is 530 kg. Volume, V, of cone of radius r, height h. V r h 3 1 2 r = Show that it takes approximately 12 trees to make one tonne of wood pulp. [5] * 0000800000010 * ,










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11 0607/62/O/N/24 © UCLES 2024 [Turn over 8 Trees are usually planted in grids to make them easier to look after. This is part of a plan showing some planted trees. Each dot is a tree. D The distance between a tree and its nearest neighbour is D metres. Find a model, in terms of D, for the number of trees, N, in a 100 m by 100 m square. … [3] Questions 9(a), 9(b) and 10 are printed on the next page. * 0000800000011 * ,









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12 0607/62/O/N/24 © UCLES 2024 9 (a) Sketch your model from Question 8, for values of D between 0 and 10. 3000 0 0 10 N D [2] (b) An internet site recommends a distance of 4.2 m between trees. A company plants a grid of 620 trees in a 100 m by 100 m square. Use your graph to find if the company has used the recommended distance between trees. … [2] 10 When wood pulp is turned into newsprint the mass remains the same. 12 trees make 1 tonne of wood pulp. There are 620 trees in each 100 m by 100 m square. The company needs the mass of newsprint in Question 6(b). Work out the area of trees that the company needs. … [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 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. * 0000800000012 * ,









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This document consists of 10 printed pages. © Cambridge University Press & Assessment 2024 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/62 Paper 6 (Extended) October/November 2024 MARK SCHEME Maximum Mark: 60 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 2024 series for most Cambridge IGCSE, Cambridge International A and AS Level components, and some Cambridge O Level components.

0607/62 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 2 of 10 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 descriptions 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.

0607/62 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 3 of 10 Mathematics-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, non-integer 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 or sign 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 A or B 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.

0607/62 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 4 of 10 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) 12 13 14 15 16 17 18 21 31 41 51 61 71 81 9 18 27 36 45 54 63 2 B1 for 4 correct

0607/62 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 5 of 10 Question Answer Marks Partial Marks 1(b) N RD N RD N RD N RD 10 9 20 18 30 27 40 36 11 0 21 9 31 18 41 27 12 9 22 0 32 9 42 18 13 18 23 9 33 0 43 9 14 27 24 18 34 9 44 0 15 36 25 27 35 18 45 9 16 45 26 36 36 27 46 18 17 54 27 45 37 36 47 27 18 63 28 54 38 45 48 36 19 72 29 63 39 54 49 45 2 B1 for 5 rows correct One correct subtraction seen or 3 differences of 9 seen or 3 examples of 9 × positive difference C1 1(c) 9 1 1(d) 80 1 Three from column 72, 63, 54, 45, 36, 27, 18, 9,0 leading to 9 in bottom row or bottom row [72, 63, 54, 45] 36, 27, 18 or 89 in bottom left cell and 98 – 89 = 9 or 12, 23, 34, 45, … or difference in digits is 1 C1

0607/62 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 6 of 10 Question Answer Marks Partial Marks 2(a) N RD N RD 100 99 105 396 101 0 106 495 102 99 107 594 103 198 108 693 104 297 109 792 1 One correct subtraction seen or 3 differences of 99 seen or 3 examples of 99 × positive difference C1 2(b) First and third digits are [always] the same oe or [only] second digit changes [which doesn’t affect the Reverse Difference] oe 1 2(c) 99 1 2(d)(i) 100a + 10b + c – 100c – 10b – a or 99a – 99c 1 99(a – c) 1 2(d)(ii) 594  99 oe or difference [between a and c] = 6 oe or 99c = 99 × 8 –594 or 3 correct trials with a = 8 C1 FT their 99 Three correct numbers of the form 8 ... 2 1 3(a) 99(a – c) = 99 or a correct example resulting in 99 C1 FT their 99(a – c) The difference between the first and third digits must be 1 oe 1 The second digit can be any digit 1

0607/62 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 7 of 10 Question Answer Marks Partial Marks 3(b) Min c = 0, max a = 9 so 0 to 9 = 10 [digits] or correct example showing RD of 891 or one of 0  99 or 1  99, ..., 9  99 or c – a = 9 oe C1 0, 99, 198, 297, 396, 495, 594, 693, 792, 891 1 4(a) 10 000a + 1000b + 100c + 10d + e or 10 000e + 1000d + 100c + 10b + a C1 9999a + 990b – 990d – 9999e isw oe 2 B1 for two terms correct 4(b)(i) 9999a + 990b – 990d – 9999e = 33 066 or one correct trial of a158e – e851a with a > e C1 FT their 4(a) 9999a + 990 [× 1] – 990 × 8 – 9999e or a second correct trial of a158e – e851a with a > e C1 FT their 4(a) iff b and d terms 9999a – 9999e = 39 996 oe or a third correct trial of a158e – e851a with a > e and with result of 33 066 C1 a – e = 4 oe 1 4(b)(ii) 41 580 51 581 61 582 71 583 81 584 91 585 2 FT their a – e if single digit integer B1 for five correct with no errors

0607/62 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 8 of 10 Question Answer Marks Partial Marks Modelling 5(a) 560 430 42 1000 1000 1000     oe leading to 0.0101[1... 3 M2 for 560 430 1000 1000   oe or M1 for figs 560  figs 430 5(b) 0.202 or 0.2022 to 0.2023 kg 1 5(c) Any added quantity – Ink/print or staples/binding 1 5(d)(i) 0.202 × 950 000 C1 FT their answer to 5(b) If C0 scored SC1 for 0.0101… × 950 000 192 or 191.9 or 192.1 to 192.2 1 5(d)(ii) 50 000 1 (192 or 191.9 or 192.1 to 192.2) × 5 × 52 C1 FT their 5(d)(i) 6(a) 260 1000 1000 1000 1000 =    L W d S C M oe isw 2 FT their 260 in 5(d)(ii) B1 for 260 1000 1000 1000 1000 =    LWdSC M oe with one error or omission 6(b) 51 000 to 51 200 tonnes 1 If 0 scored SC1 for 70000 to 71900 Correct substitution 260 560 430 43 20 950 000 1000 1000 1000 1000         oe or 50 000  43 42 C1 FT their 6(a) answer if first method used FT their 5(d)(ii) answer if second method used 7(a) Circular base/cross section/cylindrical [and] apex/vertex i.e. Radius/diameter narrows as it gets taller oe 1

0607/62 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 9 of 10 Question Answer Marks Partial Marks 7(b) 0.21 or 0.105 seen or correct change to m3 at some stage 1 ( ) 2 105 14 3   figs figs 1 ( ) 2 105 14 530 3    figs figs figs or ( ) 2 105 14 1000 530 3    figs figs 1 11.67... leading to 12 2 B1 for 85.7 or 85.6 to 85.86 or B1 for 11.67… 8 2 100   =     N D oe isw 2 B1 for 2 100       D Diagram with at least one vertical D or one more horizontal D shown or 1 = areaof square N area for tree oe or 1 row = 100  D C1 9(a) Correct sketch 2 Correct shape and B1 for passing through approx. (10, 100) and B1 for passing through approx. (1.8, 3000)

0607/62 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 10 of 10 Question Answer Marks Partial Marks 9(b) If model is 2 100   =     N D then No oe and 4.02 or No oe and 567 OR If model is 2 100 1   = +     N D then No oe and 4.18 or Yes oe and 4.18 rounds to 4 or No oe and 615[.5…] or 616 or Yes oe and 615 rounds to 620 1 Horizontal line on graph at approx. N = 620 or Vertical line at D = 4.2 C1 10 51 200 12 620  or 51 200 620 12 C2 FT their 51 200 in 6(b) C1FT for 620 their 6(b) or their 6(b)  12 or for 620 12 990 or 9 900 000 1 990 [lots of] 100 m by 100 m squares or hectares or 9 900 000 m2 C1 FT their 990 or FT their 9 900 000