Cambridge IGCSE™

CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/05

Paper 5 Investigation (Core) For examination from 2025
MARK SCHEME B
Maximum Mark: 40

Specimen

This document has 8 pages. Any blank pages are indicated.

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0607/05 Cambridge IGCSE – Mark Scheme For examination
SPECIMEN from 2025
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 descriptions for the question
• the specific skills defined in the mark scheme or in the generic level descriptions 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 descriptions.
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).

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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 descriptions in
mind.

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 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.

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SPECIMEN from 2025
MARK SCHEME NOTES

The following notes are intended to help with understanding of mark schemes in general, but individual mark schemes may include marks awarded for specific reasons
outside the scope of these notes.

Anything in the mark scheme which is in square brackets […] is not required for the mark to be earned, but if present it must be correct.

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.

Types of mark

M Method mark, awarded for a valid method applied to the problem.

A Accuracy mark, given 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.

C Communication mark, for clear mathematical communication and reasoning.

Abbreviations

awrt answers which round to

cao correct answer only
dep dependent on the previous mark(s)
FT follow through after error
isw ignore subsequent working (after correct answer obtained)
nfww not from wrong working
oe or equivalent
SC special case
soi seen or implied

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0607/05 Cambridge IGCSE – Mark Scheme For examination
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Question Answer Marks Partial Marks

1 4 16 25 1
2(a)(i) 81 1
2(a)(ii) 1600 1
2(b) 81 + 1600 = 1681 = 412 2 B1 for 1681 seen
3 At least three differences in the 2nd or the 3rd column C1
or
c= a 2 + b 2 or a2 + b2 = c2 used
5 B1 for first column
a b c
AND
3 4 5 In middle and last columns
5 12 13 B4 for all 6 cells correct,
or B3 for 4 cells correct,
7 24 25 or B2 for 2 cells correct,
9 40 41 or B1 for 1 cell correct.

11 60 61
13 84 85
15 112 113
17 144 145
19 180 181
21 220 221
23 264 265
25 312 313

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Question Answer Marks Partial Marks

4 Link: C1
(3, 4, 5) and (5, 12, 13)
or
(7, 24, 25) and (25, 312, 313)
(3, 4, 12, 13) 2 B1 for each

(7, 24, 312, 313)

5(a) 72 + 142 + 142 = 441 2 B1 for each statement
212 = 441
5(b) k2a2 + k2b2 + k2c2 = k2d2 M1
Evidence of dividing by k2 A1
or k2(a2 + b2 + c2) seen
leading to a2 + b2 + c2 = d2
5(c)(i) 7 1
5(c)(ii) Division by 7 seen C1
(1, 2, 2, 3) 1
5(d)(i) 6 1
5(d)(ii) (2, 6, 9, 11) 1
5(d)(iii) 22 + 62 + 92 = 121 2 FT (4, 12, 18, 22) or (6, 18, 27, 33)
B1 for each statement
112 = 121 or
B1FT their part (ii) for one correct statement
6(a)(i) 22 + 32 − 1 22 + 32 + 1 C1
or
2 2
(2, 3, 6, 7) 2 B1 for 6 or 7 correctly placed
6(a)(ii) 22 + b2 + 1 C1
= 43
2
(2, 9, 42, 43) 2 B1 for 9 or 42 correctly placed

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0607/05 Cambridge IGCSE – Mark Scheme For examination
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Question Answer Marks Partial Marks

6(b)(i) At least 3 differences in one of the columns b, c or d C1
2 B1 for one correct cell in final row or last cell in final row one more
a b c d
than the second last
2 3 6 7
2 5 14 15
2 7 26 27
2 9 42 43
2 11 62 63

6(b)(ii) d = c + 1 oe 1
6(c) a2 + b2 − 1 a2 + b2 + 1 M1
Substituting a and b both even in or
2 2
Correct answer A1
or ‘not an integer’ oe
6(d)(i) a2 + b2 + 1 1
= 23 leading to a2 + b2 + 1 = 46
2
45 + 1
or = 23
2
a2 + b2 − 1
or c = 22 and = 22 leading to a2 + b2 – 1 = 44
2

45 − 1
or c = 22 and = 22
2
6(d)(ii) (3, 6, 22, 23) B2 B1 for 3 and 6 correctly placed
B1 for 22 correctly placed

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