Notesale: Turn your study into money

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MATHEMATICS

OCR 2024
GCSE Mathematics
J560/04 Paper 4 (Higher Tier)
With Marking Scheme Merged

Oxford Cambridge and RSA

Thursday 16 May 2024 – Morning
GCSE (9–1) Mathematics
J560/04 Paper 4 (Higher Tier)
Time allowed: 1 hour 30 minutes
You must have:
• the Formulae Sheet for Higher Tier (inside
this document)

H

You can use:
• a scientific or graphical calculator
• geometrical instruments
• tracing paper
0 *

*

J

5

6

0

2
1

Work out
...
5 182
1
...



...

9 cm

6
...
8 cm

18 cm

15 cm

Show that they have the same area
...

a

a+b

a + 2b

3a - b

The mean of these four numbers is 27
...

Find the value of a and the value of b
...


a =
...
[5]

© OCR 2024

Turn over

4
4

A school is deciding on a charity to support
...
The results are to be shown in a pie chart
...

Twice as many students voted for charity C than charity B
...


A

52°

(a) (i) Show that the sector for charity B will have an angle of 44°
...


© OCR 2024

[2]

[3]

5
(b) 39 students voted for charity A
...


(b)
...

The same results are shown in a pie chart and in a bar chart
...


...
[1]
(ii)

Give one disadvantage of using the pie chart rather than the bar chart
...



...
The diagram shows the price of each pack
...
70

3 kg
for
£32
...
90

Which pack is the best value for money?
Show how you decide
...
pack because
...


...

The interior angle of the polygon is 15 times its exterior
angle
...


n =
...

0
...



...

In a sale, the new price of the television is decreased by r %
...
1%
...

You must show your working
...
[5]

© OCR 2024

9
9

Sasha and Taylor each have a stamp collection
...

The table shows the number of stamps in each collection and the ratio UK : EU : Other
...

Are they correct?
Show how you decide
...
because
...


...

Question:
You are given
y \ x and y = 9 when x = 2
...


Solution:
y \ x so y = x + c
Substituting y = 9 and x = 2 gives
9=2+c
c=7
So, y = x + 7

Describe the error made and write out a correct solution
...


...


...


...


...

The result of each task is either “Pass” or “No pass”
...
6
...

(a) Complete the tree diagram
...
6

...

No pass


...


...
528
...


(c) x =
...

Angle SQR = 14° and angle SPQ = 62°
...


(a) Angle ROQ =
...

Not to scale
E

D

H

F
G
Line GH is a tangent to the circle at F
...

Complete these statements to prove that triangle DEF is isosceles
...

You may not need all of the lines
...
= Angle
...


...
= Angle
...


...
= Angle
...


...
= Angle
...


...
= Angle
...


...
[3]

© OCR 2024

Turn over

14
13 Function A and function B are shown below
...

Write an algebraic expression, in terms of x, for the inverse of function B
...


[2]

(b) Function C is shown below as a composite function
...


Function C: Input

Output

...

[4]

© OCR 2024

15
14 The diagram shows a circle, centre O and radius 52 cm
...

The line through T is a tangent to the circle
...

The perpendicular distance between the chord and the tangent is 72 cm
...

You must show your working
...
cm2 [6]
© OCR 2024

Turn over

16
15 (a) Solve by factorisation
...
or x =
...


(b)
...


(
...


(ii)
...
83 m / s, correct to 3 significant figures
...

(a) Use the above information to work out the shortest possible time for the lift to travel
between the ground floor and the top floor
...


(a)
...


...
[1]

17 The box plot shows the distribution of the waiting time of cars at a road junction
...


(a)
...
% [1]
(c) Given that a randomly chosen car waited for more than 30 seconds, write down
the probability that the car waited for more than 90 seconds
...

© OCR 2024

Turn over

[1]

18
18 (a) The graph shows the speed of an object during the first 20 seconds of its motion
...


(a)
...

40

30
Distance
(m)

20

10

0

0
(i)

0
...
5

2
Time (s)

3
...
m/s [2]

Use the graph to estimate the speed of this object at 3
seconds
...


(ii)
(iii)

3

Work out the average speed of this object between 2 and 4 seconds
...
5


...
Explain how you know
...

I know this because
...
[1]

Turn over for question 19
© OCR 2024

Turn over

20
19 Show that

3+2

can be written in the form

48-6

a+b 3

...


[5]

END OF QUESTION PAPER

Higher

GCSE
Mathematics - Paper 4
J560/04: Paper 4 (Higher tier)
General Certificate of Secondary Education

Mark Scheme for June 2024

Oxford Cambridge and RSA Examinations

OCR (Oxford Cambridge and RSA) is a leading UK awarding body, providing a wide range of
qualifications to meet the needs of candidates of all ages and abilities
...


It is also responsible for developing new specifications to meet national requirements and
the needs of students and teachers
...

This mark scheme is published as an aid to teachers and students, to indicate the requirements
of the examination
...
It does not
indicate the details of the discussions which took place at an examiners’ meeting before
marking commenced
...

Mark schemes should be read in conjunction with the published question papers and the
report on the examination
...


Make sure that you have accessed and completed the relevant training packages for on -screen marking: scoris assessor Online Training; OCR
Essential Guide to Marking
...


Log-in to scoris and mark the required number of practice responses (“scripts”) and the number of required standardisation responses
...


MARKING
1
...


2
...


3
...
It is essential that you meet the scoris 50% and 100% (traditional 40% Batch 1 and 1 00% Batch 2)
deadlines
...


4
...

5
...
Wh ere no alternative
response has been provided, examiners may give candidates the benefit of the doubt and mark the crossed out resp onse where legible
...
Enter a mark for each question answered into RM assessor, which will
select the highest mark from those awarded
...
)

2

J560/04

Mark Scheme
June 2024
Multiple Choice Question Responses
When a multiple choice question has only a single, correct response and a candidate provides two responses (even if one of th ese responses is
correct), then no mark should be awarded (as it is not possible to determine which was the first response selected by the candidate)
...

Contradictory Responses
When a candidate provides contradictory responses, then no mark should be awarded, even if one of the answers is correct
...
The
response space should be marked from left to right on each line and then line by line until the required number of r esponses have been considered
...
Examiners will have to apply judgement as to whether a ‘second response’ on a line is a
development of the ‘first response’, rather than a separate, discrete response
...
)
Short Answer Questions (requiring a more developed response, worth two or more marks)
If the candidates are required to provide a description of, say, three items or factors and four items or factors are provide d, then mark on a similar basis
– that is downwards (as it is unlikely in this situation that a candidate will provide more than on e response in each section of the response space
...
Examiners will need to apply professional judgement as to whether
the second (or a subsequent) response is a ‘new start’ or simply a poorly expressed continuation of the first response
...
Always check the pages (and additional objects if present) at the end of the response in case any answers have been continued there
...

7
...


Team Leaders must confirm the correct use of the NR button with their markers before live marking commences and should check this when
reviewing scripts
...


The scoris comments box is used by your team leader to explain the marking of the practice responses
...
Do not use the comments box for any other reason
...


9
...
The report should contain notes on particular strengths displayed as well as common errors or weakne sses
...


10
...

To determine the level – start at the highest level and work down until you reach the level that matches the answer
b
...
Annotations available in RM Assessor
...

Annotation

Meaning
Correct
Incorrect
Benefit of doubt
Follow through
Ignore subsequent working (after correct answer obtained), provided method has been
completed
4

J560/04

Mark Scheme

June 2024

Method mark awarded 0
Method mark awarded 1
Method mark awarded 2
Accuracy mark awarded 1
Independent mark awarded 1
Independent mark awarded 2
Misread
Special case
Omission sign
Blank page
Seen

For a response awarded zero (or full) marks a single appropriate annotation (cross, tick, M0 or ^) is sufficient, but not required
...

It is vital that you annotate standardisation scripts fully to show how the marks have been awarded
...
M marks are for using a correct method and are not lost for purely numerical errors
...
Therefore M0 A1 cannot be awarded
...

SC marks are for special cases that are worthy of some credit
...
The following abbreviations are commonly found in GCSE Mathematics mark schemes
...
You should ignore leading or trailing zeros and any decimal

point e
...
237000, 2
...
370, 0
...

isw means ignore subsequent working after correct answer obtained and applies as a default
...

oe means or equivalent
...

soi means seen or implied
...
You must check that the candidate has met all the
criteria specified for the mark to be awarded
...
The required minimum amount of
working will be defined in the guidance column and SC marks given for unsupported answers
...
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
...
Unless the command word requires that working is shown and the working required is stated in the mark scheme, then if the correct
answer is clearly given and is not from wrong working full marks should be awarded
...
e
...

16
...
For questions with FT available you must ensure that you refer back to the relevant
previous answer
...

6

J560/04 Mark Scheme June 2024 Figures or expressions that are being followed through are sometimes encompassed by single quotation
marks after the word their for clarity, e
...
FT 180 × (their ‘37’ + 16), or FT 300 – (their ‘52 + 72’)
...
g
...

17
...
e
...

18
...
Place the annotation

✓

next to the correct answer
...
Place the annotation

next to the correct answer
...
Method marks could still be awarded if there is no other method leading to the incorrect answer
...

19
...
A correct step, value or statement that is not
part of the method that leads to the given answer should be awarded M0 and/or B0
...

(iii) If more than one answer is provided on the answer line and there is more than one method provided, award marks for the
poorer response unless the candidate has clearly indicated which method is to be marked
...
In questions with no final answer line:
(i) If a single response is provided, mark as usual
...

21
...
Deduct 1 mark from any A or B marks earned and record this by using the
MR annotation
...
If a candidate corrects the misread in a later part, do not continue to follow
through, but award A and B marks for the correct answer only
...
Unless the question asks for an answer to a specific degree of accuracy, always mark at the greatest number of significant figures even if
this is rounded or truncated on the answer line
...
75, which is seen in the working
...
8, 15 or 16 on the answer line
...
75
...
Ranges of answers given in the mark scheme are always inclusive
...
For methods not provided for in the mark scheme give as far as possible equivalent marks for equivalent work
...

25
...


8

J560/04
Question
1

Mark Scheme
Answer

Marks

46
...
33[7…]
or
B1 for 99 493[
...
0625]

for B1 accept these numbers rot to at
least integers

If 0 scored SC1 for their answer to more than 4
figures correctly rounded to 4 s
...

2

M1

1

×18×6
...
g
...
8 = 57
...
8 oe

M1 for 57
...
4 = height
A1 for 6
...

2

288

[both answers =] 57
...
g
...
2

2

9

J560/04
3

Mark Scheme
[a = ] 15
...
2
with correct working

5

B4 for one correct answer with correct working
OR

June 2024
“Correct working” requires evidence of at
least M1M1 for the two equations and
M1 for some evidence of solving them

M1 for a + a + b + a + 2b + 3a – b = 27 oe
4
M1 for 3a – b – a = 24 oe

e
...
6a + 2b = 108

M1 for equating coefficients of one variable for
their linear equations

dependant on two linear equations
e
...
6a – 3b = 72 or 4a – 2b = 48
or 3a + b = 54

M1 for correct method to eliminate one variable
for their original linear equations

dependant on two linear equations
e
...
5b = 36
Allow one numerical error in each step of
solving their equations
A sign error is not an arithmetic error

If 0, M1 or M2 scored, instead award
SC3 for answers 15
...
2 with no working
or insufficient working
If 0 or M1 scored, instead award
SC2 for a = 7
...
6 with no working
or insufficient working
If 0 scored, instead award
SC1 for two answers which satisfy one of the
original conditions

10

e
...
2a – b = 24

Substitution method:
M1 and M1 for the two equations
M1 dependant on two linear equations and for rearranging
one equation to make one variable the subject e
...
=
24+

2

M1 for substituting it into their other
equation
Trials (need to see the mean or total,
and the range evaluated for each):
M1 for each correct trial up to a
maximum of 3
After three correct trials, correct final
answers score 5

J560/04
Question
4

(a)

Mark Scheme
Answer
(i)

(360 – 52) ÷ (1 + 2 + 4) or better
[= 44]

June 2024

Marks
2

Part marks and guidance
M1 for 360 – 52 or 308
or their(360 – 52)
÷(1+2+4)

better includes 308 ÷ 7

Alternative method 1 :
M2 for 7x = 360 – 52 or 7x = 308 then x = 44
or M1 for x, 2x and 4x or 360 – 52 or 308

(a)

(ii)

(b)

Correct labelled pie chart with
ruled lines and sector angles 44,
88 and 176

3

270

2

Mark the work in the answer space and if
blank, mark any work round the diagram
allow any letter

Alternative method 2 :
M2 for 52 + 44 + 2 × 44 + 4 × 44 = 360 oe
or M1 for 52 + 44 + 2 × 44 + 4 × 44 oe

For M2 and M1 accept 88 for 2 × 44 and
176 for 88 × 2

B2 for two additional correct sectors within
tolerance or a correct unlabelled/incorrectly
labelled pie chart with ruled lines or correct
labelled pie chart with unruled lines
or B1 for one correct sector within tolerance,
ignore label

Use online protractor and apply an angle
tolerance of ± 2°
...

Labels must be letters not angles

39

39

360

e
...


M1 for any correct method e
...
52 × 360 oe

or 39 +

176

52

+

88

52

3939

+

52

or

52÷360

39
44

52
52

39

condone

39

= 1
...
g
...
g
...
g
...
g
...
70 ÷ 0
...
40 ÷ 3 oe

12

See appendix for other calculations and
values
Mark their figures at the most accurate

J560/04
Question
6

Mark Scheme
Answer
32 nfww

June 2024

Marks
4

Part marks and guidance
B2 for 11
...
25 seen
OR
B1 for 15a and a or 16a
M1 for 15a + a = 180 oe
M1 for 360 ÷ their 11
...
g
...
25
180( −2)

Alternative method 1:
M2 for 15 × 360 = 180(n ─ 2) or better
or M1 for
=15×
180( −2)

360

and
M1 for 180n = 5400 + 360 oe
Alternative method 2:
Use of trials by choosing a value for n
...
Trials can be seen
from a calculation or a list
...
25
[2 × 10 -2 =] [0]
...
2 , 2-2

B1

accept answer in alternate form e
...
14 with correct working
or for answer 86 with correct working
OR
B3 for answer 0
...
161

1
...
35

1161

1350

or

1
...
161

135

1161

1
...
161

× 100

1
...
1

M3 includes

135

1350

OR
M2 for 1
...
161 or 135 and 116
...
35 or 135 or 1350
If 0 or 1 scored, instead award
SC3 for answer 14 with no working or
insufficient working
If 0 or 1 scored, instead award
SC2 for answer 0
...
86 with no working or
insufficient working

14

1−

135−116
...
14 or 86 e
...
1 –
or
oe
OR
M3 for any correct calculation that would lead
to 0
...
g
or
oe
1
...

Allow any correct method
...
35 –
1
...
161 – 1
...
189 or [1]35
– [1]16
...
161 – 1
...
9
B1 includes 1
...
1 or 1161
Alternative method :
e
...
trials needs M2 to award 5 marks,
evidence of at least 2 trials seen or M1
for each correct trial up to M3, see
appendix for figures

J560/04

Mark Scheme

Question
9

Answer

Marks

Correct statement with
supporting working
yes/correct oe
and
e
...

1533 with 1532
or
0
...
666… oe
or

5

511

766

–

2

3

Part marks and guidance
B4 for 1533 and 1532
OR
1638

M1 for

[× 9] or better

implied by 117 or 1053

M1 for
[× 8] or better
M1 for their1053 + their480 or 1638 + 660

implied by 60 or 480
implied by 1533 or 2298

9+3+2

660

8+1+2

>0

ℎ

1533
511

or

M1 for

511

June 2024

ℎ

implied by 0
...
6

2

3

766

or 1532

766

for those that sum the columns (i
...
92 or1562
...
68

25

M1 for

ℎ

or for their 2298 ×

1562
...
68 oe or 1532 or 16
...
or

3

0
...
6̇

2

[× 25]
3

M1 for 0
...
66… or 1562[
...
5x or y = 2 x oe

allow 17 and 16
...
7
See appendix
Allow any letter for k

M1 for y = kx or better e
...
9 = k × 2

2

15

can be awarded in the first statement

J560/04
Question
11 (a)

Mark Scheme
Answer
Correct tree diagram

Marks
2

(b)

They are independent oe

1

(c)

0
...
4 on missing branch in task 1
B1 for 1 – x on both missing branches in task 2

If there is more than one answer on any
branch, choose the one on the dotted
line first
Pick the best comment, see appendix

M2 for 0
...
4x = 0
...
6(1 – x) + 0
...
g
...
6 – 0
...
528
e
...
M1 for 0
...
2x
e
...
0
...
528 = 0
...
528
e
...
6x + 0
...
472

OR
M2 for 1 – 0
...
4(1 – x) = 0
...
6x – 0
...
g
...
6 – 0
...
2x or better

OR
FT their (a) if not correct for up to 3 marks
e
...
if in (a) 1 - x is replaced with e
...
0
...
6 × 0
...
4x = 0
...
6 × 0
...
4x or better
M1 for rearranging their linear equation, kx + a = b,
to make kx the subject (0< k )

e
...
0
...
528 – 0
...
4 or better

If 0 scored SC1 for any 2 branches correctly written
down and added e
...
0
...
4(1 – x)

exactly two branches

16

alternative method using trials
M1 for each correct trial up to M3 and the
correct answer from trials scores 4
marks, see appendix

J560/04
Question
12 (a)

(b)

Mark Scheme
Answer
96

Marks
3

Method 1 using angle EFH :
DEF = angle EFH
because alternate [angle]
angle

angle

EDF = angle EFH
alternate segment [thm
...
g
...
seg
...
g
...
9… or 2220 with correct
working

June 2024

Marks

Part marks and guidance
“Correct working” requires evidence of
at least M2 or M1 M1
Accept answers in the range 2217 to
2226
...


6

M2 for cos […] =

72−52

M2 implied by 67
...
76… rot
to at least an integer e
...
67, 67
...
4, 67
...
76… oe

20)2 oe or 48 and M1 for

×their96 × their20 oe

2

M2 for finding the area of the triangle
OAB implied by 960
their 134
...
2, 225
...
24
M2 for area of triangle as before or M1
for the third side e
...
48
If 0, 1 or 2 scored award SC3 for the correct
answer with insufficient working
If 0 or 1 scored award SC2 for 3179
...
718
...
718
...

followed by 3x – 2 [= 0]
(3 −2)(3 +12)

and x3+ 4 [= 0] scores M2
...

After 3x(x + 4) – 2(x + 4) or x( 3x – 2) +
4(3x – 2) followed by correct answers
award M2B1 BOD
Condone 0
...
666… or 0
...
5 and 9
...
8349[9
...
5 to 174
...
49[9
...
825 to
9
...
8349[9
...
5 and 9
...
8349[9
...
6[4…] with correct working

B1 for (x + 4)2
B2FT their (x + a)2 for their – 5
If 0 scored SC2 for ‘correct’ answer with missing
power or power written in the wrong place

e
...
(x + 11)2 – 110 scores B2FT
e
...
SC2 for (x + 4) – 5 or
(x + 42) – 5

M1 for (173
...
5) ÷ (9
...
835)
If 0 or 1 scored, instead award
SC2 for answer 17
...
g
...
g
...
33[3…] or 33[
...
g
...
g
...
g
...
0 – 16
...
If tangent is ruled
and their value is outside the range
apply FT to their tangent use accuracy
of 2 sf
Accept any correct response, accept
accelerates for increase, see appendix

1

20

J560/04

Mark Scheme

Question
19

Answer
√3+ 2

Part marks and guidance

M1

√48+6

×
√48− 6

Marks

June 2024

multiply by conjugate of denominator

√48+6

M1

√3× √48 +6√3+2√48+ 2×6

may be in a separate table
FT √

48

− 6 in both numerator and denominator

√48×√48 +6√48−6√48− 6 ×6

=4
48

√

3

soi

M1
implied by [2√48 = ] 8√3 or 14√3

√

Simplifying their fraction e
...
g
...
g
...
The figures given must be
accurate enough to differentiate between the three sizes
...
8[0]
£10
...
7[0]
£7
...
54[6] or £7
...
011
£0
...
0107[8]

Amount for £1
Amount for 1p
90[
...
90[9] to 0
...
5 to 92
...
925 to 0
...
7… g
0
...
4[0]
£32
...
90]

Amount for £7
...
70]

Alternative method 2
Allow comparison in pairs e
...

Compare 3 kg and 5 kg by working out the cost of 15 kg
3 kg is £162 and 5 kg is £161
...
46

24

Amount for £32
...
9
4
...
99… kg
5 kg

J560/04
Question 6
sides
5
...
00
7
...
00
9
...
00
11
...
00
13
...
00
15
...
00
17
...
00
19
...
00
21
...
00
23
...
00
25
...
00
27
...
00
29
...
00
31
...
00
33
...
00

interior
108
...
00
128
...
00
140
...
00
147
...
00
152
...
29
156
...
50
158
...
00
161
...
00
162
...
64
164
...
00
165
...
15
166
...
14
167
...
00
168
...
75
169
...
41

Mark Scheme
exterior
72
...
00
51
...
00
40
...
00
32
...
00
27
...
71
24
...
50
21
...
00
18
...
00
17
...
36
15
...
00
14
...
85
13
...
86
12
...
00
11
...
25
10
...
59

35
...
71

10
...
00
135
...
65
132
...
10
116
...
00

3

130
...
10

135
...
60

116
...
00
135
...
25
126
...
10
116
...
00

7

125
...
10

135
...
00

8
9

124
...
85

116
...
10

135
...
50

116
...
00
135
...
15
118
...
10
116
...
00

13

117
...
10

135
...
00

14
15

116
...
75

116
...
10

135
...
40

116
...
00
135
...
05
110
...
10
116
...
00

19

109
...
10

135
...
00

116
...
00
135
...
65
105
...
10
116
...
00

23

103
...
10

26

June 2024

J560/04
Exemplar responses for Q10

Mark Scheme

The error is……
The formula should be y = kx [not the one they use]
the formula they use is not direct proportion
He should have multiplied x and c not added
They have added the constant [instead of multiplying]
They have used the wrong equation
It should not be + [c]
They should not add
y=x+c

June 2024

Mark
1
1
1
1
1
1
1
1

They are directly proportional

0

Exemplar responses for Q11(b)
Mark
1
1
1
1
1
1
0
0
0
0

The pass before does not affect the results after
They are independent
The first task results do not affect the second
Passing first task does not affect the second task
Passing the second does not rely on passing the first
They are not linked
Same probability to pass second on both times
The probabilities of the tests do not change
The probability of passing will always stay the same
Both second tests are the same

27

J560/04
Question 11(c)

Mark Scheme

Value(x) probability
0
...
56
0
...
558
0
...
556
0
...
554
0
...
552
0
...
55
0
...
548
0
...
546
0
...
544
0
...
542
0
...
54
0
...
538
0
...
536
0
...
534
0
...
532
0
...
53
0
...
528
0
...
526
0
...
524
0
...
522
0
...
52
0
...
518
0
...
516
0
...
514
0
...
512
0
...
51

28

June 2024

J560/04
Working for Q12(a)

Mark Scheme

June 2024

Hence angle ROQ = 96° from which ORQ=OQR=42°, SRO=76°, OQS=28°
...

Mark this;
B1 for angle SPO = 14°
B1 for angle OPQ and angle OQP = 48°
B1 for angle QOP = 84° or OQR and ORQ = 42°
to maximum of B2

29

J560/04
Alternative method 2
They can draw a tangent at Q
...

B1 for SQT = 62° (alternate segment theorem),
B1 for (angle OQT = 90°) so angle OQS = 28°,
B1 for making angle OQR = 42° = angle ORQ
...
5 (e
...
174
...
835 (e
...
9

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