Cambridge IGCSE™
CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/42
Paper 4 (Extended) February/March 2022
MARK SCHEME
Maximum Mark: 120
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 2022 series for most
Cambridge IGCSE™, Cambridge International A and AS Level components and some Cambridge O Level
components.
This document consists of 8 printed pages.
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0607/42 Cambridge IGCSE – Mark Scheme February/March 2022
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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.
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.
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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
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Question Answer Marks Partial Marks
1(a) 3 2 M1 for isolating y oe
− oe
4
6 1
1(b)(i) 5−3 M1
[grad = ] oe
8−4
Substitution of (4, 3) or (8, 5) into M1
y = (their m)x + c or y – y1 = m(x – x1)
1 A1
y= x + 1 or 2y – 6 = x – 4 or
2
2y – 10 = x – 8 leading to 2y – x = 2
without error or omission
1(b)(ii) 1 2 1
[ y =] x + 7 B1 for [ y =] x + k , k ≠ 1
2 2
or for [y =] jx + 7, j ≠ 0
2(a) 15 1
2(b) 47.5[0] 2 19
M1 for × 250 oe
100
2(c) 15 3 500 × 1.5 × y
M2 for 500 + = 612.50 oe
100
500 × 1.5 × y
or M1 for oe
100
or for one year’s interest = 7.5[0]
2(d)(i) 13629 cao 3 B2 for 13630 or 13629. ...
3
12
or M1 for 20000 × 1 − oe
100
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Question Answer Marks Partial Marks
2(d)(ii) 24 nfww 4 B3 for 23.4 or 23.43...
OR
12 1000
M3 y log 1 − = log oe
100 20000
or correct trials reaching 23 and 24
or good sketch indicating value between 23 and 24
y
12 1000
or M2 for 1 − = oe
100 20000
or at least 3 correct trials
or suitable graph with y > 1
y
12
or M1 for 20000 × 1 − = 1000 oe soi by at
100
least 2 correct trials with n > 3
2(e) 9[.00] or 8.999 to 9.000... 3 4673
M2 for 10
12000
or M1 for 12 000 × (.....)10 = 4673
3(a)(i) 7 1
3(a)(ii) 4 1
3(a)(iii) 5.5 1
3(a)(iv) 5 1
3(b) 115.65 2 M1 for mid-values soi
3(c) 17 4 B3 for 25n + 845 = 25.4n + 838.2 oe or better
or M2 for 3 × 5 + 11 × 15 + n × 25 + 19 × 35
= 25.4(n + 3 + 11 + 19) oe
or M1 for 3 × 5 + 11 × 15 + n × 25 + 19 × 35 oe
or 25.4(n + 3 + 11 + 19)
or for correct trial with integer value of n
4(a) [ a = ] 65 3 B1 for each
[ b = ] 85
[ c = ] 95
4(b) [u = ] 70 6 B1 for each
[v = ] 30
[w = ] 80 FT 180 – their u – their v
[x = ] 20
[y = ] 50 FT 150 – their x – their w
[ z = ] 60 FT 110 – their y
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Question Answer Marks Partial Marks
5(a)(i) 4 x 2 + 12 x + 9 final answer 2 B1 for three of 4x2, 6x, 6x, 9 or for correct answer
seen
5(a)(ii) 4 1 FT their 9 – 5
5(a)(iii) 2 x + 3 = ± their 4 M1 their 4 > 0
1 1 B1
−2 , − oe
2 2
5(b)(i) 6 2 k
final answer M1 for [x = ] oe
w −1 w −1
5(b)(ii) 4 1 FT only incorrect k
5(b)(iii) 36 36 + x 2 6
2 3 M1 for correct multiplication of term in w
2
+ 1 or 2
or + 1 M1 for correct squaring
x x x M1 for correctly isolating w
final answer Max M2 if incorrect answer
6(a) (5x + 1)(2x – 1) – 7(13 – x) = 84 oe M1 Correct first statement without brackets expanded
10x2 – 5x + 2x – 1 B1
– 91 + 7x B1 on LHS or 91 – 7x on RHS
10 x 2 + 4 x − 176 = 0 oe A1
leading to 5 x 2 + 2 x − 88 = 0 with no errors
or omissions
6(b) ( 5 x + 22 )( x − 4 ) 2 B1 for (5x + a)(x + b) with ab = –88 or a + 5b = 2
or for 5x(x – 4) + 22(x – 4)
or for x(5x + 22) – 4(5x + 52)
6(c) 63 2 M1 for solving their factorised quadratic, allowing
omission of negative root.
FT (13 – their positive root) × 7
1
if < x < 13
2
7(a) Correct sketch 2
10
5
M1 for a modulus graph or
4 -2
0
0 2 4
for graph of y = 4 – x2
-5
-10
7(b) –2, 2 2 B1 for each
If 0 scored, SC1 for (2, 0) and (–2, 0)
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Question Answer Marks Partial Marks
7(c) (0, 4) 1
7(d) 1 or 2 or 3 1
7(e)(i) Correct sketch 1
10
0
4 -2 0 2 4
-5
-10
7(e)(ii) 1.24 or 1.236..., 3.24 or 3.236... 2 B1 for each
or B1 for both seen
e.g. 1.24 ⩽ x ⩽ 3.24 or with y coords included
or for 1.23 and 3.23
7(e)(iii) Two correct regions above x-axis and 2 B1 for one correct and no wrong or for one correct
below both graphs and one incomplete
8(a)(i) 25 1
8(a)(ii) –47 1 FT 3 – 2 × their 25
8(b) 1 2 M1 for 2x + 1 = 3 – 2x or better
oe
2
8(c) 7 – 4x final answer 2 M1 for 2(3 – 2x) + 1
8(d) 3− x 2 M1 for y + 2x = 3 or better
oe final answer
2 y 3
or = −x
2 2
or x = 3 – 2y
8(e) 99 2 M1 for log( x + 1) = 2(0.5) + 1 or better
8(f) 10 x − 1 2 M1 for 10 y = x + 1 or x = log( y + 1)
9(a) 6.22 or 6.222 to 6.223 3 4
M2 for oe
sin 40
4
or M1 for sin 40 = oe
x
9(b)(i) 49.5 or 49.45 to 49.46 3 92 + 102 − 82
M2 for [cos=] oe
2.9.10
or M1 for 82 = 92 + 102 – 2 × 9 × 10 cos(...)
9(b)(ii) 5.85 or 5.845 to 5.851... 3 BT
M2 for = cos(their(b)(i)) oe or better
9
or M1 for CT drawn and right angle at T
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Question Answer Marks Partial Marks
9(c) 21[.0] or 20.98 to 21.00 5 12sin 35
M2 for
7
7 12
or M1 for = oe
sin 35 sin P
A1 for 79.5 or 79.50 to 79.51
M1 for 180 – their 79.5
If 0 scored, SC1 for diagram showing the two angles
10(a) 4 3
oe B1 for each pair of branches
5
7 3
, oe
10 10
9 1
, oe
10 10
10(b)(i) 18 2 4 9
oe M1 for their ×their
25 5 10
10(b)(ii) 43 2 1 7
oe M1 for their(b)(i) + ×their oe
50 5 10
10(c)(i) 36 2 M1 for their(b)(ii) × p = their(b)(i) or better
oe
43
10(c)(ii) their(b)(ii), 1 – their (b)(ii) oe 3 B1 for each pair of branches
their (c)(i), 1 – their(c)(i) oe
4 3
, oe
7 7
11(a) 114.6 or 114.5 to 114.6 3 y
M2 for × 2πr = 2r oe
360
y
or M1 for × 2πr oe
360
11(b)(i) x 1 M2 x 1
× π × 82 − × 82 × sin x = A M1 for × π × 82 or × 82 × sin x
360 2 360 2
11(b)(ii) 18.3 or 18.26 to 18.27... 1
11(b)(iii) Correct sketch of curve and line B2 B1 for correct shape of curve
6
0
0 20 40 60 80
58.9 or 58.90 to 58.92 1
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