Notesale: Turn your study into money

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MATHEMATICS

OCR 2024
GCSE Mathematics
J560/02 Paper 2 (Foundation Tier)
With Marking Scheme Merged

Oxford Cambridge and RSA

Monday 3 June 2024 – Morning
GCSE (9–1) Mathematics
J560/02 Paper 2 (Foundation Tier)
Time allowed: 1 hour 30 minutes
You must have:
• the Formulae Sheet for Foundation Tier (inside
this document)

F

You can use:
• geometrical instruments
• tracing paper
Do not use:
• a calculator
*

J

5

6

0

0

2

*

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
...
The question numbers must be clearly shown
...

• Where appropriate, your answer should be supported with working
...

INFORMATION
• The total mark for this paper is 100
...

• This document has 20 pages
...


2
1

Work out
...
3 + 4
...
[1]
(b) £4
...
27

(b) £
...

(a) -7-4

(a)
...
[1]

(c) (-4)2

(c)
...

mirror line

[2]
(b) Rotate the triangle 90° anticlockwise around the point P
...

Find the length of the diameter of the circle
...
cm [1]

© OCR 2024

Turn over

4
5

This probability scale shows the probability of picking a blue counter from a bag of counters
...


(a)
...


6

) the probability of not picking a
[1]

A bathroom shower uses water at a rate of 15 litres per minute
...
litres [2]

7

(a) Write 0
...


(b) Write

© OCR 2024

(a)
...


[1]

17
5 as a mixed number
...


60 mm
...
3
...
17500 m
4

9

[3]

Work out the following, giving each answer as a fraction in its simplest form
...
[2]
(b)

5 5
12 ' 9

(b)
...

(a) 3 y + 6x - y + 5x

(a)
...
[1]
11 The table shows the plan view and front elevation of some 3D solids
...

Plan view

Front elevation

Name of 3D solid


...



...

3 4
(a) 6 #6 =6

[1]

24
(b) _2 i

[1]

=2

13 (a) Work out the next term in this sequence
...


[1]

(b) In the Fibonacci sequence below, the next term is found by adding the two previous
terms
...

Work out the first and fifth terms of the sequence
...


14

7

10

17


...



...

Ivan has a sack containing 50 litres of compost
...

(a) Ivan fills six large pots each holding 7
...

Work out how much compost is left in the sack
...
litres [2]

(b) Ivan uses the remaining compost to fill small pots each holding 400 ml
...


(b)
...


(c)
© OCR 2024


...


Work done on Monday to Friday

£20
...
23 per hour

One week Amaya works for 40 1 hours between Monday and Friday and then for 4 1 hours on
3
4
Saturday
...

By rounding each value to the nearest integer, use estimation to show that Amaya may be
correct
...



...
[1]
© OCR 2024

Turn over

10
17 Work out
...
2 ' 0
...
[2]

18 Kai has these four number cards
...

(a) Complete the table to show all of the possible differences
...


(b)
...
Leave your construction lines visible
...


a

(a) Write vector a as a column vector
...


Write this vector in terms of a
...
[1]

© OCR 2024

13
21 (a) Ryan makes a journey of 200 miles from his home to the coast
...


10

40% of the journey is on roads with a speed limit of 50 miles per hour
...

Find the earliest time that Ryan could arrive at the coast
...


(a)
...


...
[1]

© OCR 2024

Turn over

14
22 The scatter diagram shows the test scores for 20 pupils in Science and Mathematics
...


(a)
...

On the scatter diagram, circle the point that is most likely to represent this pupil
...

(c)
...


...
[1]
© OCR 2024

15
(e) Find the percentage of the 20 pupils who scored less than 30 marks in both Science
and Mathematics
...


© OCR 2024

% [3]

Turn over

16
23 The diagram shows an equilateral triangle and a rectangle
...

Find the value of a
...
[4]
© OCR 2024

17
24 Charlie invests £1200 at a rate of 5% per year compound interest
...


[4]

25 A machine makes bolts that should be 30
...

Jane checks the accuracy of the machine by taking a random sample of 10 of the bolts
...
29
...
1 30
...
0 30
...
0 30
...
0 30
...
0 The machine makes
2000 of these bolts that day
...
That is 60%
...

Give a reason why Jane’s claim may be unreliable
...


...
The Venn diagram shows some of the results
...

One of the 50 people is chosen at random
...

You must show your working
...
[5]
© OCR 2024

19
27 In this question, all lengths are in centimetres
...


(a) Show that x2 + 5x - 84 = 0
...

x2 + 5x - 84 = 0

(b)(i)
(ii)

x =
...
[3]

Find the length of the longer side of the rectangle
...
cm [1]

END OF QUESTION PAPER
© OCR 2024

20
EXTRA ANSWER SPACE
If you need extra space use this lined page
...


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Foundation
GCSE
Mathematics - Paper 2
J560/02: Paper 2 (Foundation 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: RM Assessor Online Training; OCR
Essential Guide to Marking
...


Make sure that you have read and understood the mark scheme and the question paper for this unit
...


3
...


MARKING
1
...


2
...


3
...
It is essential that you meet the RM Assessor 50% and 100% deadlines
...


4
...


5
...
Where no
alternative response has been provided, examiners should give candidates the benefit of the doubt and mark the crossed out response
where legible
...


When a candidate provides contradictory responses, then no mark should be awarded, even if one of the answers is correct
...


On each blank page the annotation BP must be inserted to confirm that the page has been checked
...


2

J560/02
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 RM Assessor comments box is used by the Principal Examiner or your Team Leader to explain the marking of the practice responses
...
Do not use the comments box for any other reason
...

9
...
Please follow the direction of your Team Leader about which questions you should report on and how to submit your
report
...


10
...
These must be used whenever appropriate during your marking
...

For responses that are not awarded either 0 or full marks, you must make it clear how you have arrived at the mark you have awarded and
all responses must have enough annotation for a reviewer to decide if the mark awarded is correct without having to mark it independently
...


4

J560/02

Mark Scheme

June 2024

Subject-Specific Marking Instructions
11
...

A marks are for an accurate answer and depend on preceding M (method) marks
...

B marks are independent of M (method) marks and are for a correct final answer, a partially correct answer, or a correct intermediate
stage
...


12
...

- figs 237, for example, means any answer with only these digits
...
g
...
37, 2
...
00237 would be acceptable but 23070 or 2374 would not
...

- nfww means not from wrong working
...

- rot means rounded or truncated
...

- dep means that the marks are dependent on the marks indicated
...

- with correct working means that full marks must not be awarded without some working
...


13
...


14
...

Do not award the marks if the answer was obtained from an incorrect method, i
...
incorrect working is seen and the correct answer
clearly follows from it
...


Where follow through (FT) is indicated in the mark scheme, marks can be awarded where the candidate’s work follows correctly from a
previous answer whether or not it was correct
...
You may find it easier to mark these questions candidate by candidate rather than question by question
...
g
...
Answers to part questions which are being followed through are indicated
by e
...
FT 3 × their (a)
...


In questions with no final answer line, make no deductions for wrong work after an acceptable answer (i
...
isw) unless the mark
scheme says otherwise, indicated by the instruction ‘mark final answer’
...


In questions with a final answer line and incorrect answer given:
(i) If the correct answer is seen in the body of working and the answer given on the answer line is a clear transcription error allow full marks
unless the mark scheme says ‘mark final answer’
...


(ii) If the correct answer is seen in the body of working but the answer line is blank, allow full marks
...


✓

next to the correct

(iii) If the correct answer is seen in the body of working but a completely different answer is seen on the answer line, then accuracy marks
for the answer are lost
...
Use the M0, M1,
M2 annotations as appropriate and place the annotation next to the wrong answer
...


In questions with a final answer line:
(i) If one answer is provided on the answer line, mark the method that leads to that answer
...

(ii) If more than one answer is provided on the answer line and there is a single method provided, award method marks only
...


19
...

(ii) If more than one response is provided, award marks for the poorer response unless the candidate has clearly indicated which response
is to be marked
...


When the data of a question is consistently misread in such a way as not to alter the nature or difficulty of the question, please follow the
candidate’s work and allow follow through for A and B marks
...
M marks are not deducted for misreads
...


6

J560/02

Mark Scheme

June 2024

21
...
For example, an answer in the mark scheme is 15
...
The
candidate then rounds or truncates this to 15
...
Allow full marks for the 15
...


22
...


23
...
If in doubt, consult your
Team Leader
...


If in any case the mark scheme operates with considerable unfairness consult your Team Leader

7

J560/02

Mark Scheme

1

Question
(a)

11[
...
23

1

2

(a)

2
2

(b)
(c)

3

3

-

11
7

June 2024
Part marks and guidance

Condone [£]4
...

Reflection must be on the grid given
Use overlay as a guide, mark intention,
allow freehand
...

4
5

6
(a)

1

1

1

Maybe seen on the diagram
Accept equivalent fractions

1

Accept any clear intention of identification of

8

5

(b)

7

Arrow at

8
7

8

8

J560/02

Mark Scheme

Question
6

Answer
180

Marks
2
M1 for 15 × 12 oe

Part marks and guidance
Repeated addition, we must see their
method, allow one arithmetic error
...
g
...
g
...
75

1

4

3

If 0 scored, award SC1 for converting the
fractions to a common denominator
2

16
−

5
9

2y + 11x

e
...
g
...
g
...
5 oe

M1 implied by 45
Repeated addition, we must see their
method, allow one arithmetic error
...
g
...
5, 15 then 15×3 [=45]

10

J560/02
Question
(b)

Mark Scheme
Answer
12

Marks
3

June 2024
Part marks and guidance

B2 for 12
...
4

M2 for their (a) × 1000 ÷ 400 or their (a) ÷ [0]
...
2 then all multiples must be
seen

or

M1 for their (a) × 1000 or 400 ÷ 1000
or their (a) ÷ figs 4
(c)

200

2

B2FT for their (a) × 1000 – their (b) × 400
evaluated correctly

their (a) must be > 0
...


or
M1 their (a) × 1000 – their (b) × 400

11

Implied by repeated subtraction or addition
...
00], 30[
...
3, 40
...
15 or 21

16

(b)

4×30

M1

for their 4 x their 30

920 or 800 and 120

A2

A2 dep on B1M1M1
or
A1 dep on B1M1 for 800 or 120

The calculation is an
underestimate

1

1

their 4 can be 4 , 4
...
23 or 31
4

All values were rounded down oe
Mark best response as long as not
contradictory or incorrect
See Appendix 1

17

40

2

M1 for 120 ÷ 3

600

Accept 1200 ÷ 30, 15 ,

120

100

÷

3

100

Do not allow M1 if extra step after 120 ÷ 3
e
...
120 ÷ 3 then divide by 100
18

(a)

2

B1 for 3 or 4 correct entries

12

For 2 marks, ignore entries in shaded
squares if they are 0’s
For B1 ignore shaded squares

J560/02

Mark Scheme

18 (b)

2

6

12

oe nfww

June 2024

If shaded squares are blank or all have zeros
FT their 12 entries for 2 marks

isw conversion/cancelling after their correct
probability
Do not accept ratio or words
If table correct and shaded squares have
zeros allow answer oe for 2 marks
10

16

M1 for all their even numbers and all factors of
10 identified only

M1 may be seen on table by e
...
ringing
values or listing

IF Shaded SQUARES are counted:
FT their 16 entries

We only accept the 16 squares in the Grid,
not the card values

B2FT their table
Or
M1 for all their even numbers and all factors of
10 identified only

Count zero as an even number

6

If 0 scored SC1 for answer

16
19

Correct ruled line with two pairs
of correct arcs

2
B1 for correct ruled line with no or wrong arcs,
or correct intersecting arcs but no line
or correct dashed/dotted line with correct arcs

If table correct apart from all zeros in
shaded squares allow all even numbers and
factors of 10 [0’s in shaded squares]
identified

For SC1 allow answer 3 if 6 seen first
8 16
Use protractor to measure, allow 880-920
Use Ruler to measure, allow 35-39mm from
A or B
Arcs may be two continuous arcs centred at
A and B with two intersections

20 (a)

2

2

2
B1 for answer

k

−3

13

k

2

For B1 allow (

−3

)

or

−3

B0 for incorrect numbers with
vinculum/fraction line
...
5[h], [h] or 30 [mins] nfww
2

1

M1 implied by 20 [miles] nfww

10

AND
Method to find time in 2nd stage
M2 for 0
...
6 [h] isw,
96[mins] or 1[h] 36[min] nfww

or M1 for 0
...
g
...
g
...
g he travels at a constant speed
Mark best response as long as not
contradictory or incorrect
See Appendix 2

22 (a)

Positive

1

Ignore embellishments

22 (b)

Indicates the point (39, 10)

1

22 (c)

Ruled line of best fit

2

Ignore circles around the points ≤ 30 for
both Science and Maths as this working is
for part (e)
Use overlay for LOBF, ruled line needs to
reach both gates set at:
(8,11) and (8,22)
(49,35) and (49,46)
Gates include circles on overlay
Ignore LOBF beyond gates

B1 for ruled line of best fit or answer FT ± 0
...
5 their straight
ruled line at 28 Science marks

15

J560/02
22

(d)

Mark Scheme
Correct explanation
e
...

It is beyond the range of the data
provided on the scatter diagram
...

23

8

4
M2 for a + a + a + 5 + a + 5 = 42 oe
or
M1 for 3 × 14 oe or a + a + a + 5 + a + 5 oe

Allow M2 if correct expression seen first and
then incorrectly simplified before equation =
42
M1 implied by 42 or 4a + 10 oe

AND
M1 for a =

42−10

oe

4

or FT their equation of the form
−

ka + c = d oe to a =

16

oe

FT only from written equation
Where k, c and d are positive integers and
k>1
Allow M1 for one trial into 2(a + 5) + 2a
evaluated correctly

J560/02
24

Mark Scheme
1200 × 1
...
05 oe

M1

1260 or 60 or 1
...
05 oe
or 1260 × 0
...
05 oe or 60 × 0
...
g
...
g
...
05 oe
or their 1260 × 0
...
05 oe
or their 60 × 0
...
052 oe
M1FT implied by 1323 or 63 or 3
For method we do not accept
e
...
105% × 1200 or 5% of 1200

A1 dep M1B1M1

1

She should do the test more than 10 times
She should do the test e
...
100/1000 times
...
g
...


(x - 12)(x + 7) then -12 and 7 scores M1B0
If both correct after x(x + 12) – 7(x + 12)
or x(x – 7) + 12(x – 7) allow M2B1 BOD

J560/02

Mark Scheme

June 2024

APPENDIX
Percentage Methods:
Labels Only
This is when labels such as 10% = are used

If ONLY labels are used, the final answer scores full marks if it correct
...
g
...
5
2% = 7


...
g
...


20

J560/02

Mark Scheme

June 2024

Repeated Addition/Subtraction Methods
This is when division is attempted by listing multiples of a number or by repeated subtraction
...
g
...

We allow ONLY one arithmetic error in this method (unless the mark scheme states otherwise)
Example 1:
400, 800, 1100 (error), 1500, 1900, 2300, 2700, [3100] – one arithmetic error, but correct FT from the error so M1 awarded
...


e
...
400 ÷ 60

-

Repeat Subtraction: 400, 340, 280, 220, 160, 100, 40, [ 20]
When marking this we need to see at least 3 correct subtractions, one of these MUST be the number before reaching 0
...

Example 2:

-

400, 320(error), 260, 210 (error), 150, 90, 30, [ 30] – two arithmetic errors, so M0 awarded
...

If TOTAL is used then this MUST be £920
...
80 (incorrect)

0

9

Because I estimated it meaning she’d probably got more (probably does not mean certain)

0

10

As it has gone over £900 (not describing rounding or underestimate)

0

11

This is correct because she will make 920 (the candidate is not telling us WHY they are certain)

0

12

Because £20
...
23 x4=120
...
92 not including the minimum (All rounded values not used)

0

13

If you added everything without a fraction it adds up to almost £900 (incorrect)

0

14

Because it works out that all of her work will add to over 900 (no reference to underestimate)

0

15

Because it’s over 900 (not enough, need to say WHY it is certainly over £900)

0

16

The estimation is over £900 (not enough, need to say WHY estimation is certainly over £900)

0

17

Because I rounded down (not enough- needs to be e
...
rounded all numbers down)

0

22

1BOD

J560/02

Mark Scheme

June 2024

APPENDIX 2
Question 21(b)
Response

Mark

1

That Ryan does not stop along the way

1

2

He stayed the exact speed limit and was not below the limit

1

3

That he didn’t speed and met the speed limit (travels at speed limit)

1

4

He travels at the speed limit

1

5

Does not have to stop [for fuel, lunch etc]

1

6

Ryan stays at 40 mph and 50mph when on these roads (BOD referencing the roads with the speed limits)

1BOD

7

There was no traffic so Ryan kept on moving (BOD implies that he isn’t stopped/slowed down by traffic)

1BOD

8

That Ryan stayed at a constant speed in each section of the journey

0

9

That he didn’t stop for a brake and drove the same speed (drove same speed is incorrect)

0

10

He makes stops on his journey (He must be travelling at max speed at all times)

0

11

Could not be true due to traffic

0

12

There will not be much traffic

0

13

They are at 50mph and 40mph the whole time (for the third part he doesn’t travel at 50mph or 40mph so this is incorrect)

0

14

He travelled at a constant speed (this is not true)

0

15

The speed limit does not change (this is not true)

0

16

He drove and constant speed and did not stop for lunch (part of statement is incorrect-constant speed)

0

17

There is no traffic (not quite enough – need to say e
...
traffic is not holding them up)

0

23

J560/02

Mark Scheme

June 2024

APPENDIX 3
Question 22(d)

1

Response
It is extrapolated and not in the data provided

Mark
1

2

The diagram has no data above 49 (underlined part gets the mark) (accept range 49 to 59 for this type of statement)

1

3

The graph does not go up to 60 as there is no data above 49 (underlined part gets the mark)

1

4

We do not know that the pattern will continue above 49 (implies trend may not continue)

1

5

The graph does not cover that data range (allow for the underlined part)

1

6

1

7

There are no pupils on the graph with scores above 49 (accept pupils oe for data) (accept range 49 to 59 for this type of
statement)
There are no plots/points/results on the graph above 49 (accept plots/points/results for data) (accept range 49 to 59)

8
9

Most pupils scored between 20 and 50 in Science – we cannot predict accurately for 60 marks
They may be much better at one subject than the other and do not follow the correlation (allow for the underlined part with ‘may’)

1
1

10

There is no data above 50 [for Science] (accept range 49 to 59 for this type of statement)

1

11

It may be an outlier (Implies it may not follow the pattern)

1

12

It is too far away from the last piece of data

1

13

There is insufficient data (implies small sample)

1

14

The graph reaches up to 49 (not referring to data)

0

15

The scatter graph does not go beyond 50 (not referring to data)

0

16

Extrapolated (needs explanation)

0

17

The graph only goes up to 49 (not referring to data)

0

18

The graph does not show information for a score of 60

0

19

There is no data

0

20

They might be better at Maths than Science

0

21

It is an outlier (It is not an outlier – we do not know – needs to be phrased like example 11)

0

22

Because there is no results

0

24

1

J560/02

Mark Scheme

June 2024

APPENDIX 4
Question 25

1

Response
The machine took a random sample so it will not always be 6 bolts out of 10 to the correct length (implies not representative)

2

Janes claim may be unreliable as she only did 1 sample and it might not be 60% all the time (‘only’ implies too small a sample)

1

3

Because she’s only checked 10 out of thousands so she needs to check a higher amount to measure probability

1

4

Because not every 10 bolts will have 6 correct ones

1

5

6/10 of the bolts may not always be 6/10 it could be 4/10 she needs to do the test again

1

6

Only collects 10 bolts (implies small sample)

1

7

It’s a random selection

0

8

Because the more samples you have the more unreliable it is

0

9

Because she hasn’t sampled all 2000 bolts meaning she cannot claim 1200 are of the correct length

0

10

They may not be reliable because her evidence on these lengths are facts its not 60%

0

11

Because they have to be correct to 1 decimal place

0

12

The machine took a random sample so it will not always be 6 bolts to the correct length (not enough)

0

13

Only an estimate

0

14

Because there could be more or less bolts which are longer or shorter

0

15

Might not be accurate, and she is going off the 10 bolts (Not as good as Exemplar 6, ‘only’ needs a reference here)

0

25

Mark
1

J560/02

Mark Scheme

APPENDIX 5
Question 26
Algebraic method
Allow any 2 different letters to represent ‘only car’ and ‘only bike’

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