Notesale: Turn your study into money

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MATHEMATICS

OCR 2024
GCSE Mathematics
J560/03 Paper 3 (Foundation Tier)
With Marking Scheme Merged

Oxford Cambridge and RSA

Monday 10 June 2024 – Morning
GCSE (9–1) Mathematics
J560/03 Paper 3 (Foundation Tier)
Time allowed: 1 hour 30 minutes
You must have:
• the Formulae Sheet for Foundation Tier (inside
this document)

F

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

*

J

5

6

0

0

3

*

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
...

• Use the r button on your calculator or take r to be 3
...

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

• This document has 20 pages
...


2
1

(a) Write down the mathematical name of this solid
...

cone

cube

cylinder

prism

sphere

(a)
...


[1]

(b) The diagram shows a cuboid
...
Work out the volume of the cuboid
...

© OCR 2024

3
cm [2]

3
2

This table shows the weight of each ingredient used to make 5
...

Complete this table to show the weight of each ingredient used to make 44 kg of the
same concrete
...
5

Total weight

5
...

(i)

(ii)

4
6

(a)(i)
...


[1]

529

(b) Complete this statement to make it correct
...

3


...
50
...
83
...


$
...


Give your answer correct to 1 decimal place
...


[3]

(b)
...

Give your answer in its simplest form
...

(a) Write down the letter of the correct calculation to work out Gabi’s share
...


[1]

(b) Work out Finley’s share
...
[2]
© OCR 2024

5
7

A circle has radius 8 cm
...



...

Each keyring costs £1
...

Kai pays with a £20 note and buys the largest number of keyrings
possible
...
p [4]

© OCR 2024

Turn over

6
9

When Layla walks to school she always takes 28 minutes
...

(a) One day Layla leaves home at 08 20 and cycles to
school
...


(a)
...

She walks the rest of the way at her normal walking speed
...


(b)

© OCR 2024


...

h# h# h# h

(a)
...


[2]

(b) Factorise fully
...

Equation

Expression

Formula

Identity

Inequality

Term

(a) x2 + 3x + 2

(a)
...


[1]

© OCR 2024

Turn over

8
12 At an adventure park, all children participate in three activities, choosing exactly one activity
from each of three options
...

The frequency tree shows the number of children choosing some of the activities
...


Swimming

11

3

Bowling
Tennis


...


Swimming

Tennis

12

5

6

100
Rafting
35

Golf

Swimming

5

5

Bowling
Tennis

25


...


4

9
(a) Complete the frequency tree
...



...


...
[3]
(c) One of the 100 children is picked at random
...


(c)
...

What assumption has Alex made?

...
[1]

© OCR 2024

Turn over

10
13 Jane and Kofi both have the same number of newspapers to
deliver
...


(a) Who has delivered the greater proportion of their
newspapers? Show how you decide
...
because
...
[3]
(b) Work out the smallest possible number of newspapers that Jane must deliver
...


[2]

14 A number, n, is given as 2
...

Complete the error interval for n using a number and a symbol
...
G n
...
7 [2]
© OCR 2024

11
15 In this question all measurements are in centimetres
...


g

k

2k
The width of the rectangle is k
...

Each side of the square is g
...


...
Give your answer in its simplest form
...


[2]

(c) (i) Find an expression for the perimeter of the shaded shape
...


(c)(i)
...
4
...

© OCR 2024

[3]

Turn over

[2]

12
2
16 Here is a table of values for y = 2x - 3x
...

y
16
14
12
10
8
6
4
2

-2

-1

0

1

2

3

x

-2
-4
[3]
(b) Use your graph to find the x-coordinates of the points where the graph of y = 2x2 - 3x
crosses the line y = 6
...
and x =
...
After 5 years the total interest that Riley’s investment has earned is £360
...
You must show your working
...
[5]

© OCR 2024

Turn over

14
18 The diagram shows two straight lines AB and DC that intersect at
P
...

A

C

P
D

B
Complete these statements to show that triangle PAD is similar to triangle PBC
...


ADP

= angle
...


alternate

angles

APD

Angle
...
because they are
...
= angle
...
angles
Triangle PAD is similar to triangle PBC because
...


© OCR 2024

[4]

15
19 The graph shows a household’s average daily electricity usage, in kilowatt hours (kWh)
...

Reason 1:
...

Reason 2:
...
[2]

20 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

16
21 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

17
22 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]

18
23 (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 =
...
The question
number(s) must be clearly shown in the margin(s)
...


...


...


...


...


...


...


...


...


...


...


...


...

© OCR 2024

20

...


...


...


...


...


...


...


...


...


...


...


...


...


...


...


...


...


...


...



...


...


...


Foundation
GCSE
Mathematics - Paper 3
J560/03: Paper 3 (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
...


8
...

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
...

Note: Award 0 marks for an attempt that earns no credit (including copying out the question)
...


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

J560/03

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
...


6

J560/03

Mark Scheme

June 2024

(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
...


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
...
g
“triangular prism”

(b)

(i)

12

1

(b)

(ii)

350

2

M1 for 7 × 10 × 5 oe

Accept e
...
70 5

24 [kg]
12 [kg]

2

B1 for each

Accept working in g but final
answer must be correct

2

or
M1 for 44 ÷ 5
...
5
or 36 1
...
5

B

3
2

(a)

(i)

1296

1

(a)

(ii)

23

1

1728

2

M1 for 12 × 12 × 12 oe

1
...
5 ÷ 0
...
83,
1
...
49,… but must reach 207
...
g
...
g
...
7

June 2024

Marks
Part marks and guidance
3
B2 for answer 68
...
65 to 68
...
] or
•

68
...
3[3…]
soi 206

2
103 implies M1
3
2
but not
of 103
3

...
66 to 0
...
6 for

1
5

3

B2 for

400
oe
2000

or
B1 for 2000 [m] or [0]
...
5[0]

2

M1 for

1
14 oe
4

Conversion must be correct
If nothing on answer line look
for clear indication in list
3
Allow 14 on answer line
4
e
...
0
...
5=14

etc but not

1

4

3
14
4
May be seen as 14 – 10
...
0619
...
142 gives 201
...
1 or 201
...
09

2

M1 for π × 82 oe

allowing

9

3

2
seen = a decimal < 1 allow
3
the decimal 103 to imply M1
0
...
2 or 20% for B2
2
If

(b)

2

22
7

or 3
...
142

of 14

J560/03
Question
8

Mark Scheme
Answer
96

Marks
4

June 2024

Part marks and guidance
B3 for 19
...
96
Condone £0
...
19 their k

or

Their k must be:
• from figs 2[0] ÷ figs 119
and
• 15 their k integer 17

M1 for figs 2[0] ÷ figs 119
20 ÷ 1
...
19

10

J560/03
9

Question
(a)

(b)

Mark Scheme
Answer
[0]8 34 oe

21

Marks
2
B1 for 14 [minutes]

3

June 2024
Part marks and guidance
Accept any recognisable time
format e
...
full stop, colon, gap
and inclusion of am but not pm

FT their time added to 8
...
16 is answer in (a)
working does not need to be seen
to FT
Example
Their time in (a) is 56 then
[cycling =] (56 2 =) 28 for B1
[walking =] (28 2 =) 14
M1 for 28 + 14
3 marks for answer 42 (check (a)
= 9
...
g
...
g
...
g
...

The values will be:
[R=] 11 + 12 + 5 + 9 or 37
[S=]3+5+5
or 13
[T=]6+25+4
or 35
and the answer R[afting] and the
sums or totals seen

J560/03
Question
(c)

Mark Scheme
Answer
57
100

oe

June 2024

Marks
Part marks and guidance
FT their 22 or 11 + 3 + their 8
2
Ignore attempts to change form
Accept fraction, decimal (e
...
0
...
g
...
62 and 0
...
5[%] to
Method 1
make comparison
5
128
125
B2 for 64% and correct in a common form e
...

and
or 0
...
625
Condone bad form
or
12
...
5
e
...
5
20
20
or 6
...
25
125
128
B1 for one correct conversion
e
...
0
...
5
200
200
Method 2
Candidate chooses an integer amount of
newspapers
B2 for 64% and 5 of their amount correct
8
or
5
64% or
B1 for
of their amount correct
8

(b)

14

200

If 0 scored, SC1 for correct judgement for
their incorrect conversion(s)
B1 for answer 100
or answer 200n with n integer > 1

2

2
...
g
...
8
5
= 43
...

Do not accept other figures or
symbols on line with correct
answer
Accept trailing zeros

J560/03

Mark Scheme

Question
15 (a)

Answer
The length is twice the width oe
or
The width is half the length

2k2 – g2

(b)

(c)

(i)

(ii)

6k

10
...
g
...
g
...
4 scores M1
but does not score the second
mark as from wrong working

M1 for their part (i) = 62
...
4
6

J560/03
Question
16 (a)

(b)

Mark Scheme
Answer
Correct curve through given points

their –1
...
6

June 2024

Marks
Part marks and guidance
3
B2 for 6 points correctly plotted
Half square accuracy
...

B1 for each
or
ruled y = 6 cutting their curve twice
or
points indicated on their curve where y =
6

16

Must have graph to score
Do not accept coordinates
Half square accuracy or better
For thick lines mark centre of line
Ruled line within half square of y =
6 throughout
Their curve may be a polygon or
straight line
If intersection at mid-point of small
square e
...
–1
...
2 or –1
...
04 or 4 / 100)
oe may be implied by
1800 or
× 100 or N/C e
...

4% = 72, 1% = 18, 100% = 1800 or
20% = 360, 10% = 180, 100% = 1800 or
20% = 360, 360 5 = 1800 or
or 1 year = 90, 1% = 18, 100% = 1800
NB 360 5 = 1800 alone scores M0
360
360
May be implied by 9000 or 18 or N/C e
...

45
4% = 72, 1% = 18 or
oe or
4 or
20% = 360, 10% = 180

5 × 0
...
04

360

5

or

5

or 360
4
×4×5

= 360 oe
100

AND
M1dep for their 1800 + 360
OR

Method 2 Trials

May be implied by 72 or 90 or N/C e
...

4% = 72 or 20% = 360
“May be implied” tells you to look for the
correct working associated with these
values
Their 1800 dependent on M3 and not
spoiled

M2 for two complete trials bracketing 360
and resulting in 360 10
or

Trials must show substitution and
evaluation e
...

1850 0
...
04 5 oe = 350

M1 for one complete trial 360

e
...
500 0
...
64]

17

J560/03
Question
18

Mark Scheme
BPC or CPB

Answer
and [vertically] opposite

DAP or PAD

CBP or PBC alternate

AAA oe

19

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

Marks
B2
B1 for BPC or CPB

B1

June 2024
Part marks and guidance
Must use 3-letter notation

Must have angle and reason

B1dep Dependent on previous B2 and B1

2

B1 for each

18

Condone
• A and B if clear for
e
...
A for PAD and B for CBP
• Changed order
e
...
CBP and PAD
• Use of B or C for P
e
...
DAB for DAP
For reason, condone poor spelling
(alternative) and
accept “third angle in triangle” oe
Accept completely correct
statements e
...
“All corresponding
angles equal”
but not “All angles equal” or “They
have the same angles”
See Appendix
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

J560/03
Question
20

Mark Scheme
Answer
18 nfww

Marks
3

June 2024
Part marks and guidance
18

B2 for answer 99

or
M2 for

2×99

oe

11

e
...


99
11 = 9 and then 2

9

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

B1 for
or
M1 for [k ×]

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
There must be evidence of angle or trig work to score any marks
e
...
working back from 247
...
258…is likely to score 0 or B1

[angle =] 36 or 54
6

[ℎ =]

tan 36

B1
6

or 6 × tan 54 or

54

in correct place if only shown on diagram

M2

6

M1 for tan 36 =

36

ℎ

or

6

10 ×

1

×6× ℎ

ℎ oe

2

sin 36

M2dep

ℎ

or tan 54 =

or

ℎ

=

may be implied by 8
...
259 or 8
...
774 to 24
...
748 to 247
...
45 or 5
...
450 nfww

A1
3

450×3

M2 for
or

ℎ=
247
...
75 = 450 oe
3

oe

247
...
748 to 247
...
7 247
...
74 from (a)
Use of incorrect formula is not MR

J560/03
Question
23 (a)

Mark Scheme
Answer
1176

Marks
2

June 2024
Part marks and guidance
e
...
2 2 2 3 7 7

M1 for 23 × 3 × 72 oe

or for

A

B
3

2

2

7

7

2

Accept no box but need to see A
and B

or for listing at least 3 correct in each list
294, 588, 882,
...

(b)

13 nfww

2

M1 for [26 =] 2 [×]

22

13 oe

For M1 accept 2, 13 or similar
possibly seen in a factor tree,
diagram etc

J560/03

Mark Scheme

June 2024

APPENDIX
Non Calculator methods for percentages
...


If only labels are used the final answer scores full marks if it is correct
...

If there is an error in the values and so the final answer is incorrect this cannot score method
marks
e
...
Find 65% of 80

Method scoring M1A1
10% = 8
5%=4
50% = 40
✓
65% = 52 M1A1

10% = 8



condone this slip as answer correct
50% = 40
✓
M1A1
65% = 52
5%=5

Method scoring M0A0
10%=8
5% = 6



Do not condone this slip as answer incorrect

50% = 40

 M0

65%=54

Build up method
This is where the candidate finds the percentages to build up to the required value but shows the operations used
...
g
...
Does not say “in the same way as the 100”
but indicates representative sample
Representative sample

Because 45 is 45% of every 100 children that come to the park
45%/0
...

360 1
...
04
are good indicators of error
...
40 and then 14
...

In the examples below, the M marks are earned by the
statement Not just for the statement
...


Note: the scheme say “May be
implied by 72” but, as shown in
the example above, 72 can
come from wrong method
...


J560/03

Mark Scheme

June 2024

Question 18

Reason

Mark

Reason

Corresponding [pairs of] angles are equal

1

Matching angles in the triangles are equal

1

They have the same angles

0

Not specific enough

All angles equal

0

Not true

26

J560/03

Mark Scheme

June 2024

Question 19
Reason

Mark

Reason

It doesn’t have months for each year
...
Statement
doesn't recognise the uneven scale
...
5 metres

1

There are 1000 cm in 1 km so he didn’t convert

1

You can’t have two different measurements in the same ratio

1

BOD condone “measurements” oe for “units”
BOD the missed out “the same” as explained by
the example
...
are not enough
Shows statement is incorrect
Incorrect factor but recognises no conversion and
does link cm and km implying “between them”
(The incorrect factor penalised by
wrong 15 000 000)
BOD condone “measurements” oe for “units”

It needs to be in cm

1

BOD “The ratio” needs to be “all” in cm

He did not convert the km to cm correctly

1

BOD references km and cm and conversion

He did not use scale correctly and so has made 150 cm and not 150 km

1

BOD Implies not in same units

He wrote it as 1 cm to 150 cm not km

1

BOD Implies not in same units

Because cm and km are / are not the same scale

0

Incorrect use of scale and the meaning is unclear

He did not convert the units

0

Needs to say “to the same units”

He undervalues the 150 km in the ratio

0

Doesn’t explain how or why

It doesn’t show the units so it would be inaccurate

0

Doesn’t recognise different units

29

BOD recognises the different units



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