Cambridge O Level
MATHEMATICS (SYLLABUS D) 4024/02
Paper 2 Calculator For examination from 2025
Maximum Mark: 100
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4024/02B Cambridge O Level – Mark Scheme For examination
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).
© Cambridge University Press & Assessment 2023 Page 2 of 10
4024/02B Cambridge O Level – Mark Scheme For examination
from 2025
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 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.
© Cambridge University Press & Assessment 2023 Page 3 of 10
4024/02B Cambridge O Level – Mark Scheme For examination
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.
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
© Cambridge University Press & Assessment 2023 Page 4 of 10
4024/02B Cambridge O Level – Mark Scheme For examination
from 2025
Question Answer Marks Partial Marks
1 20 1 Accept 2.86 or 2.857…
7 oe
2 23.5 oe 1
3 48 3 B1 for 126
84 126 108
M1 for 48 or 84 or × k where k = 72 or their 126 oe
162
4(a) 2 1
41.7 or 41.66 to 41.67 or 41
3
4(b) 140 1
4(c) 224 2 M1 for 160 ÷ 5 [× k] oe where k = 1 or 7
their (b)
or for × 160
100
5 3
− 1 oe M1 for 15 – 10x = 17 or 3 – 2x = 5
17
5
M1 for correctly isolating terms in x from their first step
6 49.5 or 49.49 to 49.50 or 35 2 4 B1 for [BE =] 32 oe
M1 for their BE ÷ 2 × 3 oe
their BE + their AF
M1 dep on at least B1 or M1 for × 7 oe
2
7(a) 0.35 2 M1 for 1 – (0.1 + 0.55)
7(b) 20 1
8(a) 60 2 360 180 (6 − 2)
M1 for or 180 – oe
6 6
8(b) 9 2 B1 for 40
360
or M1 for oe
100 − their (a)
9(a) 3 and 9 1
9(b) (A ∪ B)′ oe 1
10(a) 4.73 × 10–2 cao 1
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4024/02B Cambridge O Level – Mark Scheme For examination
from 2025
Question Answer Marks Partial Marks
10(b) [c =] 1.2 2 B1 for each
[d =] 8 2.7 # 10 4
or M1 for soi
2.25 # 10-4
11(a) 130 2 1
1500 # 2 6 [# 4]
M1 for oe
100
11(b) 4 or 4.0[0…] 3 1825
M2 for
5
oe
1500
or M1 for 1500 × k5= 1825 or better
12(a) 4x2 – x or x(4x – 1) final answer 2 B1 for 4x2 + kx or kx2 – x as final answer
or for 4x2 – x seen not as final answer
12(b) 6x 2 4x # 9y 12x ' 2a
a final answer M1 for
3y 2a
or for
9y 9y
or better
13(a) 576 cao 1
13(b) 60.40 4 B3 for $636.4[0]
or M3 for 0.32 × 1.075 × 1850 – their (a) oe
or B2 for $0.344
or M2 for 0.32 × 1.075 × 1850 oe
or M1 for 0.32 × 1.075 oe
14(a) 5 000 000 2 M1 for answer figs 5 or for 1 km = 100 000 cm soi
14(b)(i) 250 2 M1 for 180 + 70 or 360 – 110
or for correct indication of the required angle marked on
diagram
14(b)(ii) 082 3 M2 for 70 + (180 – 113 – (their (b)(i) – 195)) or better, where
their (b)(i) > 195
or for 180 – 98 oe
or M1 for angle BAC = their (b)(i) – 195 where
their (b)(i) > 195
or B1 for angle BCX = 98 (where CX is line parallel to North
line) or for angle BAC = 55
15 (–2, 7.5) 2 B1 for one coordinate correct
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4024/02B Cambridge O Level – Mark Scheme For examination
from 2025
Question Answer Marks Partial Marks
16(a) y = 6x + 3 oe three term fully simplified equation 2 B1 for 6x + 3 or y = 6x + c or y = kx + 3
16(b) 1
− 1 oe
6
17 –1, 0, 1, 2 3 B2 for 3 correct and no others or for 4 correct and one extra
or M2 for correct inequality in x, e.g. 2.5 ⩾ x > –2
or M1 for correct first step, e.g. –1 – 4 ⩽ –2x < 8 – 4 oe
18 x ⩾ –4 4 B1 for x ⩾ –4
y > x + 1 oe B1 for y > x + 1 oe
x + 2y ⩽ 4 oe B2 for x + 2y ⩽ 4 oe
or M1 for x + 2y = 4 soi
If B0 or M1 scored award instead,
SC3 for x > –4, y ⩾ x + 1 oe and x + 2y < 4 oe
or SC2 for x = –4, y = x + 1 and x + 2y = 4 soi
or SC1 for x = –4 or y = x + 1 soi
19(a)(i) –9 1
19(a)(ii) 77 2 M1 for g(35) or 7 + 2(2x2 – 3x) or better
19(a)(iii) x−7 2 y 7
oe final answer M1 for x = 7 + 2y or y – 7 = 2x or
2 2 x
= +
2
19(b) 2x2 – 27x + 90 final answer 4 M1 for 2(x – 6)2 – 3(x – 6)
B2 for 2(x2 – 6x – 6x + 36) – 3x + 18 or better
or B1 for [2] (x2 – 6x – 6x + 36) oe
19(c) − (− 3) ! M1 Condone one sign error in substituting
(− 3) 2 − 4 # 2 # −6
oe
2#2
–1.14 and 2.64 cao A2 A1 for each
or for answers –1.1 and 2.6
or for answers 1.14 and –2.64
or for –1.137… and 2.637… seen
If 0 scored SC1 for two correct answers with no working
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4024/02B Cambridge O Level – Mark Scheme For examination
from 2025
Question Answer Marks Partial Marks
20(a) 10 2 + 18 2 − 20 2 M2 M1 for 202 = 102 + 182 – 2 × 10 × 18 cos(CAD)
[cos CAD =]
2 # 10 # 18
86.17 to 86.18 A2 1
A1 for [cos CAD =] or equivalent fraction or decimal
15
Answer must be given correctly to 2.d.p. or greater accuracy for
A2 mark to be awarded
20(b) 118[.0…] 4 35 sin 27
M2 for oe
18
35 18
or M1 for = oe
sin C sin 27
A1 for 61.97… to 62
20(c) 7.75 or 7.749 to 7.751… 5 B3 for BD = 41.1 or 41.07 to 41.08…
OR
M2 for 10 2 + 35 2 − 2 # 10 # 35 # cos (BAD)
where BAD = 86.2 + 153 – their (b)
OR
M1 for 102 + 352 – 2 × 10 × 35 × cos(BAD)
A1 for 1687 to 1688
AND
M1 dep for their BD ÷ 5.3 dep at attempt at cosine rule oe
21(a) 13.5 2 k
f= oe M1 for f = oe
g3 g3
21(b) [–]87.5 3 7
B2 for 12.5 or as final answer
8
or
M1 for [1–] d n
3
1
oe soi
2
© Cambridge University Press & Assessment 2023 Page 8 of 10
4024/02B Cambridge O Level – Mark Scheme For examination
from 2025
Question Answer Marks Partial Marks
22 4 3 B1 for 5.75 or 11.5 seen
2 # (11 to 12) 2 # (12 − 0.5)
M1 for or for
5.7 + 0.05 5.7 to 5.8
23 26 6 1.44
3.27 or 3.267 to 3.268 or π M1 for [0.6 ÷] oe
25 1.44 − 0.48
M1 for 1.442 + 0.62 oe or d n + d0.6 n oe
2 2
1.44
1.5 1.5
M3 dep on at least M1 for π × 0.6 × their L – π × their 0.4 ×
their l + π × 0.62 + π × their 0.42
where L [= 1.56] is slant height of larger cone, l [= 1.04] is slant
height of smaller cone removed. their L ≠ 1.44
or M2 dep on at least M1
for π × 0.6 × their L – π × their 0.4 × their l
or M1 for π × 0.62 or π × their 0.42 or π × 0.6 × their L
or π × their 0.4 × l
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4024/02B Cambridge O Level – Mark Scheme For examination
from 2025
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