Cambridge IGCSE Mathematics - International 0607 — 2023 Feb/March Paper 5 · Variant 2

This document has 8 pages. Any blank pages are indicated. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 Investigation (Core) February/March 2023 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 [ ]. * 4 9 9 5 1 0 6 4 9 3 * DC (CJ) 316850/2 © UCLES 2023

2 0607/52/F/M/23 © UCLES 2023 The investigation starts on page 3.

3 0607/52/F/M/23 © UCLES 2023 [Turn over Answer all the questions. INVESTIGATION SPLIT NUMBERS This investigation looks at numbers that are split into two parts. A start number is split into two parts the units, called the units and the remaining multiple of ten, called the stem. Examples start number stem units 37 30 7 125 120 5 1526 1520 6 1 (a) Complete the table for the start number 163. start number stem units 163 [1] (b) (i) For the start number 34, calculate stem - units. … [2] (ii) For the start number 125, stem2 - units2 = 1202 - 52 = 14 400 - 25 = 14 375. For the start number 34, calculate stem2 - units2. … [2] (c) For the start number 42, calculate stem2 - units2 stem - units . … [3]

4 0607/52/F/M/23 © UCLES 2023 (d) Complete the table. Use your answers to part (b) and part (c) to help you. start number stem units stem2 units2 stem2 - units2 stem - units stem2 - units2 stem - units 125 120 5 14 400 25 14 375 115 125 34 34 40 2 50 0 2500 50 1 1 22 499 151 0 49 000 000 [7] (e) What do you notice about the start number and the value of stem2 - units2 stem - units for each row of the table in part (d)? … [1] 2 For the number 125, stem + units is 120 5 125 + = . (a) Copy your answers from Question 1(d) into the shaded columns. Complete the table. start number stem units stem2 - units2 stem + units stem2 - units2 stem + units 125 120 5 14 375 125 115 34 34 40 2 42 38 50 0 50 1 22 499 0 49 000 000 [3] (b) Use your tables from Question 1(d) and Question 2(a) to complete this statement. stem2 - units2 stem + units = … [1]

5 0607/52/F/M/23 © UCLES 2023 [Turn over 3 (a) Copy your answers from Question 1(d) and Question 2(a) into the shaded columns. Complete the table. start number stem + units stem - units (stem + units) # (stem - units) 125 125 115 14 375 34 34 42 50 22 499 49 000 000 [2] (b) Use your table from Question 1(d) to help you complete this statement. (stem + units) # (stem - units) = … [1]

6 0607/52/F/M/23 © UCLES 2023 4 For the rest of the investigation, T is the stem and U is the units of any start number. (a) (i) Use algebra to show that ( )( ) T T T 5 5 52 - + = - 2 . [1] (ii) Write down the value of T for the start number 185 and use this to check the result in part (i). [3] (b) Use algebra to show that T U2 - 2 is always the product of the factors ( ) T U - and ( ) T U + . [2]

7 0607/52/F/M/23 © UCLES 2023 5 This question is about T U2 + 2 . T U + and T U - are not always factors of T U2 + 2 . (a) Use the table to help you investigate the start numbers from 35 to 40. Find whether T U + or T U - or both are factors of T U2 + 2 for these start numbers. You may not need to use all the columns. start number T U T2 U2 35 30 5 900 25 36 30 6 900 36 37 30 7 900 49 38 30 8 900 64 39 30 9 900 81 40 40 0 1600 0 [5] (b) A start number is a multiple of 10. Use algebra to explain why T U + and T U - are always factors of T U2 + 2 . [2]

8 0607/52/F/M/23 © UCLES 2023 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. BLANK PAGE

This document consists of 6 printed pages. © UCLES 2023 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core) February/March 2023 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 February/March 2023 series for most Cambridge IGCSE™, Cambridge International A and AS Level components and some Cambridge O Level components.

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2023 © UCLES 2023 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.

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2023 © UCLES 2023 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

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2023 © UCLES 2023 Page 4 of 6 Question Answer Marks Partial Marks 1(a) 160 3 1 1(b)(i) 30 – 4 C1 26 1 1(b)(ii) 302 – 42 or 900 – 16 C1 884 1 1(c) 2 2 40 2 40 2 − − C2 C1 for 402 – 22 as numerator or 40 – 2 as denominator or 1596 38 or 1600 4 38 − 42 1 1(d) start s u s2 u2 s2 – u2 s – u 2 2 s u s u − − 125 120 5 14400 25 14375 115 125 34 30 4 900 16 884 26 34 42 40 2 1600 4 1596 38 42 50 50 0 2500 0 2500 50 50 151 150 1 22500 1 22499 149 151 7000 7000 0 49 000 000 0 49 000 000 7000 7000 7 B1 for every 2 correct cells 1(e) They are the same oe 1 2(a) start s u s2 – u2 s + u 2 2 s u s u − + 125 120 5 14375 125 115 34 30 4 884 34 26 42 40 2 1596 42 38 50 50 0 2500 50 50 151 150 1 22499 151 149 7000 7000 0 49000000 7000 7000 3 FT their 884 and their 2500 B2 for 4 correct cells or B1 for 2 correct cells 2(b) stem – units oe 1

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2023 © UCLES 2023 Page 5 of 6 Question Answer Marks Partial Marks 3(a) start s + u s – u (s + u)( s – u) 125 125 115 14 375 34 34 26 884 42 42 38 1596 50 50 50 2500 151 151 149 22 499 7000 7000 7000 49 000 000 2 FT their 26 and their 38 B1 for one correct 3(b) stem2 – units2 oe 1 4(a)(i) 2 2 5 5 5 − + − T T T 1 4(a)(ii) [T =] 180 (180 – 5)(180 + 5) or 175  185 1 1802 – 52 1 32 375 seen twice 1 OR [T =] 180 (180 – 5)(180 + 5) (1) 1802 – 900 + 900 – 52 (1) 1802 – 52 (1) 4(b) (T– U)(T+ U) = T 2 + UT– UT – U 2 = T 2 – U 2 [and so (T – U) and (T + U) are always factors.] 2 B1 for (T – U)(T + U) or for T 2 + UT– UT – U 2

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2023 © UCLES 2023 Page 6 of 6 Question Answer Marks Partial Marks 5(a) Table headings including T – U and T2 + U2 C1 Correct answer in the table to a relevant division shown by the heading, or correct relevant division with answer below the table. C1 Complete their table start T – U T + U T2 + U2 2 2 T U T U + − or T–U factor 2 2 T U T U + + or T+U factor 35 25 35 925 37 or Yes or √ 26.4.. or No or X 36 24 36 936 39 or Yes or √ 26 or Yes or √ 37 23 37 949 41.26.. or No or X 25.6.. or No or X 38 22 38 964 43.8.. or No or X 25.38..or No or X 39 21 39 981 46.7.. or No or X 25.15..or No or X 40 40 40 1600 40 or Yes or √ 40 or Yes or √ 3 B2 for one correct column giving an answer to division by T + U or T – U, assuming both if a joint column seen or B1 for 4 correct cells in a division column 5(b) U will always be 0 soi 1 T 2 + U 2 = T 2 and both T + U and T – U = T. 1