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MATHEMATICS

OCR 2024
GCSE Mathematics
J560/06 Paper 6 (Higher Tier)
With Marking Scheme Merged

Oxford Cambridge and RSA

Monday 10 June 2024 – Morning
GCSE (9–1) Mathematics
J560/06 Paper 6 (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

*

J

5

6

0

0

6

*

Please write clearly in black ink
...


Centre number

Candidate number

First name(s)
Last name
INSTRUCTIONS
• Use black ink
...

• Write your answer to each question in the space provided
...

• Answer all the questions
...
Marks might
be given for using a correct method, even if your answer is wrong
...
142 unless the question says
something different
...

• The marks for each question are shown in brackets [ ]
...

ADVICE
• Read each question carefully before you start your answer
...

Graph 1

Graph 2

y

y

O

x

O

Graph 3
y

x

O

x

Graph 4

Graph 5

Graph 6

y

y

y

O

x

O

x

O

x

For each description below, write down the number of the graph that best represents
the relationship between x and y
...
8x + 32
...


x: average speed when running 200 m
y: time taken to run 200 m
...


x: mass of a solid object made from clay
y: volume of the same solid object
...

[3]

3
2

The graph shows a household’s average daily electricity usage, in kilowatt hours (kWh)
...

Reason 1:
...

Reason 2:
...
[2]

3

The word MATHEMATICS is spelt using tiles
...

One at a time, 99 children each take a tile at random from the bag
...

Work out how many times the letter M is expected to be taken from the bag
...
[3]
© OCR 2024

Turn over

4
4

1 cm on a map represents 150 km in real life
...

Scale: 1 cm represents 150 km
City B
City A

Heidi is planning to walk from City A to City B for charity
...
Heidi says she will walk from City A to City B at an average speed of 2
...

(i)

Use this information to work out how many days Heidi needs to complete the walk
from City A to City B
...
days [4]

Explain why the information used in part (i) is likely to give an underestimate for
the number of days Heidi needs to complete the walk
...


...

Explain Yoshi’s error and write the scale correctly in the form 1 : n
...


...
[2]
© OCR 2024

5
5

The diagram shows a regular pentagon made using ten congruent right-angled triangles
...


Not to scale

12 cm
2
(a) Show that the area of the pentagon is 247
...


[6]

(b) The regular pentagon is the base of a pyramid
...

The perpendicular height of the pyramid is h cm
...

[The volume of a pyramid is

1
3 # area of base # perpendicular height
...

© OCR 2024

Turn over

[3]

6
6

(a) Two numbers, A and B, are written as the product of their prime factors
...

Give your answer as an ordinary number
...


[2]

(b) A number, R, is written as the product of its prime
factors
...

The highest common factor (HCF) of R and another number, P, is
26
...


(b) k =
...

In bag X, the ratio of apples to bananas is 5 : 7
...


(a) Finley says
Bag X and bag Y contain the same number of apples
...

Finley is definitely correct
Finley might be correct, or might not be correct
Finley is definitely not correct

Show how you decided
...


...


...

The ratio of apples to bananas is now 11 :
14
...

© OCR 2024

Turn over

[3]

8
8 (a) Complete this table for

3
2
y = x - 3x
...

y
20

15

10

5

–2

–1

0

1

2

3

4

x

–5

–10

–15

–20
[3]
(c) Use the graph to solve the equation x3 - 3x2 = 5
...


(c)
...
The sector has an angle of 30°
...

The perpendicular distance between BC and AD is 6 cm
...
7 cm2 , correct to 3 significant figures
...


(b)
...

Start

top half
bottom half

End

(a) Kareem writes the numbers 5 to 12 in the grid
...


© OCR 2024

[1]

11
(b) Use algebra to prove that for any set of eight consecutive numbers written in this grid in the
same way, the sum of the numbers in the top half of the grid is 16 less than the sum of the
numbers in the bottom half of the grid
...

He records whether
•
•

the train is on time or late
there are seats available or no seats available
...

Seats
available

On time

Late

No seats
available

Seats
available

No seats
available

13

6

5

4

(a) Find the relative frequency of there being no seats available on Jack’s train journey
...


[2]

(b) Jack says
If the train is late, travellers are less likely to find seats available than if the train was
on time
...



...


...
[3]

© OCR 2024

13

12 The region R is shown on this grid
...

The first inequality is given below
...

yH0
2y
...


© OCR 2024

[3]

Turn over

14
13 A group of students record the time taken to travel to school
...

Some of their results are recorded on this histogram
...

(a) How many students took less than 20 minutes to travel to school?

(a)


...

Add these students’ results to the histogram
...

y
Not to scale

10

O

x

The distance from the point (0, 10) to a point (12, t) is 12
...

Work out the two possible values of t
...


t =
...
[5]
© OCR 2024

Turn over

16
3
15 y is inversely proportional to x

...


Find a formula linking x and y
...
[3]
16 Write

9x7

#

2 x

in the form kxm
...
[4]
© OCR 2024

17
o o
2
17 (a) Without using a calculator, show that 0
...


(b) Explain how

2
oo
11 = 0
...



...


10

11

© OCR 2024

=
...

Not to scale

A
8 cm

B

D

60°

6 cm
20°

55°

C
Angle ABC = 60°, angle ACB = 20° and angle ACD = 55°
...

Calculate length AD
...


AD =
...

The tangent at (12, -5) crosses the x-axis at (p, 0)
...

You must show your working
...
[5]

Turn over for Question 20
© OCR 2024

Turn over

20
20 Write as a single fraction in its simplest form
...


...
OCR qualifications include
AS/A Levels, Diplomas, GCSEs, Cambridge Nationals, Cambridge Technicals, Functional Skills,
Key Skills, Entry Level qualifications, NVQs and vocational qualifications in areas such as IT,
business, languages, teaching/training, administration and secretarial skills
...
OCR is a not-for-profit organisation; any surplus made
is invested back into the establishment to help towards the development of qualifications and
support, which keep pace with the changing needs of today’s society
...
It shows the basis on which marks were awarded by examiners
...

All examiners are instructed that alternative correct answers and unexpected approaches
in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and
skills demonstrated
...

© OCR 2024

Oxford Cambridge and RSA Examinations

J560/06

Mark Scheme

June 2024

PREPARATION FOR MARKING
RM ASSESSOR
1
...


2
...
These are available in
RM Assessor
...


Log-in to RM Assessor then mark and annotate the required number of practice responses (“scripts”) and the required number of
standardisation responses
...


Mark strictly to the mark scheme
...


Marks awarded must relate directly to the marking criteria
...


The schedule of dates is very important
...
If you experience
problems, you must contact your Team Leader (Supervisor) without delay
...


If you are in any doubt about applying the mark scheme, consult your Team Leader via the RM Assessor messaging system
...


Where a candidate has crossed out a response and provided a clear alternative then the crossed out response is not marked
...


6
...


7
...
For additional objects (if present), a
tick must be inserted on each page to confirm that it has been checked
...


Mark Scheme

June 2024

Award No Response (NR) if:
• there is nothing written in the answer space
Award Zero ‘0’ if:
• anything is written in the answer space and is not worthy of credit (this includes text and symbols)
...


The hash key (#) on your keyboard will enter NR
...

9
...
Please refer to these comments when checking your practice responses
...

If you have any questions or comments for your Team Leader, use the RM Assessor messaging system
...
Assistant Examiners should send a brief report on the performance of candidates to their Team Leader (Supervisor) by the end of the
marking period
...
Your report should contain notes on particular strengths displayed as well as common errors or weaknesses
...
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
3

J560/06

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
...


5

J560/06

Mark Scheme

June 2024

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

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
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:
6

J560/06

Mark Scheme

June 2024

(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
...


7

J560/06

Mark Scheme

Question
1

Answer
2
5
1

2
(19)

Two from:
• Horizontal scale uneven
• No vertical scale
• Vertical scale does not start at 0

3
(20)

18 nfww

June 2024

Marks
3

Part marks and guidance
B1 for each

2

B1 for each

18

3

See Appendix
Mark the best part of a statement
if no contradiction
If more than two reasons (often
two in one statement), mark the
worst two
e
...
9911 = 9 and then 2 × 9

B2 for answer 99

or
2×99

M2 for

oe

For B1 accept , 0
...
182 or
18
...
2%

11

or

Condone k as 0
...
5 10) oe
or
M1 for 2
...
5 10 oe
or
M1 for their 750 2
...
g
...
If in doubt, consult TL
...
g
...
75 to h = 8
...
258 to 8
...
26
following M1 but not from area
1

10 ×

×6× ℎ

ℎ oe

Do not award 36 or 54 if
calculated as an area

6

ℎ

ℎ

or tan 54 = 6

ℎ

=

sin 36

M2dep

6

1

M1 for

or

sin36

=

sin 54

×6× ℎ

Accept other notation used for ‘h’
sin54

6

ℎ oe may be implied by

ℎ

Their h dep on previous M2 or M1

2

2

24
...
775

Accept correct use of

1

sin

2

247
...
749
(b)

5
...
449 to 5
...
75 may be their more

450×3

M2 for

ℎ=

247
...
75 = 450 oe

accurate 247
...
749
or 247
...
8 or 247
...
g
...

AND
56, 112, 168, …
...
10 : 14 and
or
20:28 and

eg: b = bananas, a = apples, t =
original total
5

B2 for
or

11

+4=

7

5

B1 for
or for

12

40[+4]

96[+4]

44

and

11( +4)

5 +4

All methods:
If 0 scored
SC1 for answer 44 or 100
-4 and 0

2

B1 for one correct value

13

oe or better
oe or better

25

11

=
14

identified
5 +4

, where k

9

eg

14

19

,
16

28

39

44

,

100

oe, ,
oe
40

12 + 4

88

(a)

oe or better

100

or
B1 for 2 fractions of the form
is a positive integer

8

14

+4=
7

By fractions:
B2 for

11:14
22:28

24

52

oe,

29

34

,
64

76

oe

J560/06
Question
(b)

Mark Scheme
Answer
Correct curve

Marks
3

June 2024

Part marks and guidance
B2FT for 6 or 7 points accurately plotted
Mark curve first
...
4

1FT

Strict FT from graph to 1 d
...


Do not accept answers to more
than 1 d
...
or answers without a
graph
If curve is between two grid lines
accept either value eg if crossing
between 3
...
5 accept 3
...
5
If curve has more than one x value
where y = 5 then they must give
all

14

J560/06
Question
9 (a)

Mark Scheme
Answer
30

× × 122 oe

Marks
M2

June 2024
Part marks and guidance
M2 oe e
...


M1 for × 122 implied by 144π or 452
...
45

360

360

= 12 and

×122

30

12

Condone 3
...
69 to 37
...
5 to 68
...
7
With area of parallelogram as 120 or from an
attempt at 20 × 6:

ℎ

M3 for

(20 × 6) − 37
...
7 may be their more accurate
37
...
704 from (a)
M3 oe e
...
100 –

37
...
7 implied by 82
...
7

or for
[× 100] implied by 31
...
5
or
M1 for 20 × 6 implied by 120
ℎ

(20 × 6)

If correct method for area of parallelogram is
not shown or an incorrect value is used:
If A > 37
...
7

or
SC1 for

15

37
...
g SC2 for

240 − 37
...

Top half:
n + (n + 1) + (n + 2) + (n + 3) = 4n + 6
Bottom half:
(n + 4) + (n + 5) + (n + 6) + (n + 7) = 4n +
22
(4n + 22) – (4n + 6) = 16

5

B2 consistent algebraic terms for
consecutive numbers for the whole grid
or B1 consistent algebraic terms for at least
3 consecutive numbers
AND
M2 for algebraic sums for top half and
bottom half of grid
or M1 for algebraic sum for top half or
bottom half of grid

June 2024
eg
...

Top half: 2n + (2n + 1) + (2n + 2)
+ (2n + 3) = 8n + 6
Bottom half: (2n + 4) + (2n + 5) +
(2n + 6) + (2n + 7) = 8 n + 22
Accept unsimplified or simplified
for M marks

AND
A1dep for sum of bottom half – sum of top
half = 16 shown algebraically or explained
from correct working
...

“difference between n+4 and n is
4”

Must not be the numbers 5 to 12

J560/06
Question
11 (a)

Mark Scheme
Answer

Marks
2

10

28

oe

June 2024
Part marks and guidance
Accept 0
...
36

10

M1 for

with k > 10 or 28 with 0 < m < 28

4+6

or for

13+6+5+4

If 0 scored,
SC1 for answer 10 : 28 or 5 : 14
(b)

Eg
...
55[5…] to 0
...
68 to 0
...
6 and 0
...

Condone wrong labelling for M
marks only
Include working on the diagram

4

6

9

19

0
...
3[1] to 0
...
2 for 0-5 bar soi
Figures may be seen on bars
Could be implied by correct fd
used for bars 2 and 3 or from
M2 for 1
...
4 × 10 may be implied by 14
OR

(b)

Bar for 30-45 drawn with height 3 small
squares

2

For k ≠ 1
M3 for their (16k + 10k + 14k) ÷ k
or
M2 for 16k + 10k + 14k
or
M1 for two from 16k, 10k, 14k

e
...
5
or M2 for 40 + 25 + 35
or M1 two from 40, 25, 35

M1 for 9 ÷ 15 soi by 0
...
5 and 6
...
52 – 122 or better
or M1 for 122 + h2 = 12
...
5

Accept -3
...
5

AND
M1 for 10 + their 3
...
5 or 10 – their
3
...
5
If 0, 1 or 2 scored, instead award
SC3 for both 13
...
5 as answers with
no or insufficient working
If 0 or 1 scored, instead award
SC2 for either 13
...
5 as answer with no
working or insufficient working

Their 3
...
75 = 0
or
M2 for 144 + t2 – 20t +100=
156
...
52
AND
M1 for correct method to solve
their 3-term quadratic

20

J560/06

Mark Scheme

Question

Answer

15
3

Marks

Part marks and guidance

3

6912

=

June 2024

oe

oe soi by

3

M1 for =

4=

123

oe

B1 for [k = ] 6912
16

6x3
...
5

nfww

or
7

If attempting both
and
mark
to candidate’s benefit rather than
√

B2 for

7
...
5 or

from

⬚

√

4
3
...
5
2

choice

4

J560/06
Question
17 (a)

Mark Scheme
Answer
x = 0
...

100x = 18
...
1818 …– 0
...
or
or accept
better
M1 for 100x = 18
...
18 and 100x = 18
...
181…
M2 for “carry-over” of 9 and 2 and
answer to division of 0
...
1…
(b)
̇

1

2

0
...
g
...
18÷2 =

̇
0
...
09× 10

‘divide by 2 and then multiply by
10’
Working may be to min of 4dp but
answer must use recurring
notation
̇

=

1dep

dep on first mark
Answer only scores 0

0
...
5 to 17
...
2 to 20
...
32 + 62 − 2 × ℎ

Their 20
...
3 × 6 × cos55

or
M1 for
ℎ

20
...
3 × 6 × cos55

If 0, 1 or 2 scored, instead award
SC3 for 17
...
6 with no working or
insufficient working
If 0 or 1 scored, instead award
SC2 for 306
...
4 with no working or
insufficient working
If 0 scored, instead award
SC1 for 20
...
3 with no working or
insufficient working

23

J560/06
19

Mark Scheme
169

12

1

̇

June 2024
‘Correct working’ requires

5

evidence of at least M2M1 or
M1M1M1
SC3 applies to all methods

or 1412 or 14
...
g
...
083̇with

12

no or insufficient working

24

12

PTO for alternative methods

J560/06
Question

Mark Scheme
Answer

Marks

June 2024

Part marks and guidance
Alternative method (Pythagoras and trig):
Alternative method (Pythagoras
and equations)
may be
M2 for 132 + (p – 12)2 + 52 = p2 oe
implied by 13 in working or on diagram
or
2
2
M1 for [angle at O] sin θ =
or cos θ =
or M1 for (p – 12) + 5 oe
M1 for [O to (12, -5)]

√122 + 52

5

12

13

may be implied
by 13 in working or on diagram
2

13

or for

tan θ =
angle)

5

12

or better (do not imply from just an

AND

√122

+5

AND
M2 for 338 – 24p = 0 oe

13
M2 for [p =] 12

13

or
M1 for cos theirθ =

or
13

or p =

13

cos ℎ

θ from earlier trig work)

25

(Their

M1 for 169+p2–24p+144+25 = p2
or better

J560/06
Question
20

Mark Scheme
Answer
5 −19

−3

final answer nfww

Marks
5

June 2024
Part marks and guidance

−7

nfww
or
M1 for (x + 7)(x – 7)
M2 for −3

AND
M2 for 4x – 12 + x – 7
or
M1 for 4(x – 3) + x – 7

For M2 and M1 accept written as
separate fractions
4 −12

−7

+
e
...
M2 for

Alternative method:
M2 for 4(x2 + 4x – 21) or better
or
M1 for 4(x + 7)(x – 3)
AND
M2 for (5x – 19)(x + 7)
or
M1 for 5x2 + 16x – 133

26

−3

−3

J560/06

Mark Scheme

June 2024

Appendix
Question 2
Reason

Mark

Reason

It doesn’t have months for each year
...
Statement
doesn't recognise the uneven scale
y axis not referenced

J560/06

Mark Scheme

The graph is on a small scale/ It’s not drawn to scale

June 2024
0

Do not accept reference to “drawn to scale”

Question 4a(ii)
Reason

Mark

Reason

In real life Heidi will not be able to walk in a straight line

1

Implies distance increases

Roads aren’t straight

1

Implies distance increases

She doesn’t consider buildings in the way of the straight line distance

1

The km are estimated as 750 where it is not in real life

0

She may have to go a different route

0

Implies “not a straight line”
Correct but does not reference using a direct
distance
Doesn’t say that the overall distance may be
greater (than calculated)

Do not accept
Average speed is just an estimate

0

Because it’s a decimal so doesn’t give an exact number of days

0

Because it seems unrealistic
She will get tired/slow down/toilet stops

0
0

There is not enough information

0

Rounded down

0

Do not address error in method of using straightline distance

Question 4b
Reason

Mark

Kilometres is not the same as cm

1

Not converting km to cm

1

Not converting to the same units

1

28

Reason
BOD recognises the different units
“Not converting the units” is not enough

J560/06

Mark Scheme

June 2024

The 1 and 150 aren’t both cm

1

BOD implies different units

They are in different measurements

1

He hasn’t used units making it seem 1 cm = 150 cm

1

If it was 1 : 150 then 1 cm would be 1
...

The words before 1 cm
...


5

10 apples :14 bananas also means
C&NC

12

of the fruit are apples

5

1
1

An example with a different number of apples
with some words of explanation

1

Sufficient for first mark
...


5:7=12

5

10:14=

Reason
An example with the same number of apples

0

12

29

J560/06

Mark Scheme

June 2024

C&NC
5

5:7=12
...
3 × 5 = 15 apples and 3 × 7 = 21 bananas still has
the same ratio but different numbers
...

C&NC
...
Middle column of mark scheme
...

10

24 appl es i n the other
...

5

5 : 7 means that there must be 5 apples so the f raction of apples must be 12
...

25

25 apples and 35 bananas is 25 : 35 which is 5 : 7 and the fraction of apples is
C
...

However, if A or B have more fruits than the other, they will have more apples than the
other
...



...
Both bags coul d hav e the s am e num ber of apples but

they could be different as we do not know how much fruit is in each bag
...


30

Not numerical but would be SC if 0 scored
Sufficient
...
So, a = 12
...
So, a : b = 5 : 7 and a = 12

There may be 12 apples in one bag but

Insufficient for second mark
...


1

5

Bag Y must be 5x : 7x as
for the number of apples
...

The number of apples will only be equal if x = 1
...

C&NC
...

Correct statement and tick
...


12 appl es s o bag X is

June 2024
0

5

NR
0

12 appl es
...
Ticked box mark is dependent on at
least one other mark



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