Cambridge IGCSE Mathematics - International 0607 — 2024 Oct/Nov Paper 5 · Variant 1

This document has 8 pages. [Turn over * 5 4 3 6 8 9 6 9 1 2 * Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/51 Paper 5 Investigation (Core) October/November 2024 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 [ ]. DC (DE/FC) 337379/1 © UCLES 2024 ,










, * 0000800000001 * ¬Oz> 4mHuOªEŠ_z5€W ¬beyW•oOrn¢FšMD¦‚ ¥••U55eUu55EE5Eu U

2 0607/51/O/N/24 © UCLES 2024 Answer all the questions. INVESTIGATION HOUSE OF CARDS This investigation looks at the number of cards in a house of cards. The diagram shows a house of cards with three rows. Rows are counted down from the top of the house. In this investigation is a horizontal card and are diagonal cards. Example 1 This house of cards has 3 rows of cards. Row 1 Row 2 Row 3 Example 2 This house of cards has 5 rows of cards. Row 1 Row 2 Row 3 Row 4 Row 5 * 0000800000002 * ,










, ĬÍú¾Ġ´íÈõÏĪÅĊÞü·þ× ĬâçúÖĩđęèÿČýîĤĝüĞĂ ĥÅąÕõÕĥµÅõĥąÅõåµåÕ DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN

3 0607/51/O/N/24 © UCLES 2024 [Turn over 1 This is Row 1 in a house of cards. There are 0 horizontal cards. There are 2 diagonal cards. There are 2 cards in total. This is Row 2 in a house of cards. There is 1 horizontal card. There are 4 diagonal cards. There are 5 cards in total. (a) This is Row 3 in a house of cards. Complete these statements for Row 3. There are … horizontal cards. There are … diagonal cards. There are … cards in total. [1] (b) (i) On the grid, draw Row 4 in a house of cards. [1] (ii) Complete these statements for Row 4. There are … horizontal cards. There are … diagonal cards. There are … cards in total. [1] * 0000800000003 * ,










, ĬÏú¾Ġ´íÈõÏĪÅĊÞú·þ× ĬâèùÎğčĩÑùõÌêĜ¹üĎĂ ĥÅõĕµµąÕÕąµąÅĕÅõµÕ DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN

4 0607/51/O/N/24 © UCLES 2024 (c) Complete the table. Use your answers to part (a), part (b)(ii) and any patterns you notice. Row (n) Number of horizontal cards Number of diagonal cards Total number of cards 1 0 2 2 2 1 4 5 part (a) 3 part (b)(ii) 4 5 [2] (d) Find an expression, in terms of n, for (i) the number of horizontal cards in Row n … [1] (ii) the number of diagonal cards in Row n … [1] (iii) the total number of cards in Row n. Give your answer in its simplest form. … [2] * 0000800000004 * ,










, ĬÍú¾Ġ´íÈõÏĪÅĊàü·Ā× ĬâèüÎĥğĠæ÷îÃȸěĬĦĂ ĥõåĕõµąõµåÅąąĕĥõåÕ DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN

5 0607/51/O/N/24 © UCLES 2024 [Turn over (e) Work out the number of horizontal cards, the number of diagonal cards and the total number of cards in Row 40. Number of horizontal cards … Number of diagonal cards … Total number of cards … [3] (f) The total number of cards in Row p is 368. Work out how many diagonal cards are in Row p. … [4] * 0000800000005 * ,










, ĬÏú¾Ġ´íÈõÏĪÅĊàú·Ā× ĬâçûÖģģĐÓāăĆÐÀ¿ĬĖĂ ĥõÕÕµÕĥĕåÕĕąąõąµµÕ DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN

6 0607/51/O/N/24 © UCLES 2024 2 The house number is the number of rows in the house. This is House 1. There are 0 horizontal cards. There are 2 diagonal cards. There are 2 cards in total. This is House 2. There is 1 horizontal card. There are 6 diagonal cards. There are 7 cards in total. (a) This is House 3. Complete these statements for House 3. There are … horizontal cards. There are … diagonal cards. There are … cards in total. [2] (b) On this grid, draw House 4. [1] * 0000800000006 * ,










, ĬÑú¾Ġ´íÈõÏĪÅĊÝú¶þ× ĬâèûÙĩċĖÛĆòï°¸ÞÄĦĂ ĥåõÕµõĥµĥµµąÅõåõĥÕ DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN

7 0607/51/O/N/24 © UCLES 2024 [Turn over (c) Complete the table. Use your answers to part (a), part (b) and any patterns you notice. House (h) Number of horizontal cards Number of diagonal cards Total number of cards 1 0 2 2 2 1 6 7 part (a) 3 part (b) 4 5 [4] (d) Write down the rule to continue the sequence for the number of horizontal cards. … [1] (e) This is an expression for the number of horizontal cards in House h. . ( ) h h 0 5 1 - Show that this expression gives the same result as your rule in part (d) when h 6 = . [3] (f) Find an expression, in terms of h, for the number of diagonal cards in House h. … [3] Questions 2(g) and 2(h) are printed on the next page. * 0000800000007 * ,










, ĬÓú¾Ġ´íÈõÏĪÅĊÝü¶þ× ĬâçüÑğćĦÞôÿºĬÀúÄĖĂ ĥåąĕõĕąÕõÅĥąÅĕŵõÕ DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN

8 0607/51/O/N/24 © UCLES 2024 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. (g) Use the expression from part (e) and your answer from part (f) to find an expression for the total number of cards in House h. Give your answer in its simplest form. … [3] (h) Lee makes a house with 100 cards. Find the number of cards in the bottom row. … [3] * 0000800000008 * ,










, ĬÑú¾Ġ´íÈõÏĪÅĊßú¶Ā× ĬâçùÑĥõģÙîĈ±ÊĤÜÔĞĂ ĥĕÕĕµĕąõĕĥĕąąĕĥµĥÕ DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN

This document consists of 7 printed pages. © Cambridge University Press & Assessment 2024 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/51 Paper 5 (Core) October/November 2024 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 2024 series for most Cambridge IGCSE, Cambridge International A and AS Level components, and some Cambridge O Level components.

0607/51 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 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 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.

0607/51 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 3 of 7 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.

0607/51 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 4 of 7 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) 2 6 8 1 1(b)(i) 1 1(b)(ii) 3 8 11 1 1(c) 3 2 6 8 4 3 8 11 5 4 10 14 2 B1 for two correct values in row 5 If 0 scored SC1 for last column = sum of previous two. 1(d)(i) n – 1 oe 1

0607/51 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 5 of 7 Question Answer Marks Partial Marks 1(d)(ii) 2n oe 1 1(d)(iii) 3n – 1 1 FT their (i) + their(ii) if expressions in n and answer in simplified form. 3n – 1 in an unsimplified form or three differences of 3 in total column C1 FT their (i) + their (ii) if expressions in n 1(e) 39 80 119 2 B1 for one correct Substitution of n = 40 into one of their expressions or their39 + their80 or 40 – 1 or 40 × 2 C1 1(f) 3p – 1 = 368 or (368 + 1)/3 C1 FT their (3n – 1) [diagonal cards = ] their p × 2 or 368 – (their p – 1) C1 their p ≠ 368 246 2 B1 for 123 or B1FT for their p × 2 or 368 – (their p – 1) oe correctly evaluated as final answer 2(a) 3 12 15 2 B1 for two correct 2(b) 1

0607/51 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 6 of 7 Question Answer Marks Partial Marks 2(c) 3 3 12 15 4 6 20 26 5 10 30 40 3 B1 for row 4 correct B2 for row 5 correct or B1 for one correct value in row 5. If 0 scored SC1 for last column = sum of previous two. 3 differences from 1, 2, 3, 4 in horizontal column or 3 differences from 4, 6, 8, 10 in diagonal column or 3 differences from 5, 8, 11, 14 in total column or House 5 drawn on grid for 2(b) C1 2(d) Add on the next consecutive number oe or Add on the last house number oe 1 2(e) 0.5×6×(6 – 1) = 15 2 B1 for 0.5 × 6 × (6 – 1) or expression evaluated to give 15 10 + 5 = 15 1 2(f) [house number] three from ×2, ×3, ×4, ×5, ×6 or next number of horizontal cards × 2 or three from 1, 4, 9, 16, 25 seen or three second differences of 2 C1 h2 + h or h(h +1) oe 2 B1 for a quadratic expression or for bad form e.g. h + 1  h 2(g) 0.5h2 – 0.5h + h2 + h C2 FT their 2(f) C1 for 0.5h(h – 1) and h(h + 1) oe 1.5h2 + 0.5h oe isw 1

0607/51 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 7 of 7 Question Answer Marks Partial Marks 2(h) 23 3 B2 for h = 8 soi or for 40 + 17 + 20 + 23 may be implied in a table or B1 for [total cards] 57, 77, 100 or 28, 72, 100 (may be 28+72=100) or their (1.5h2 + 0.5h) = 100 or sketch of t = their (1.5h2 + 0.5h) or 2 trials using their (1.5h2 + 0.5h)