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
H
You must have:
* 1 3 9 5 1 5 5 9 6 2 *
• the Formulae Sheet for Higher Tier (inside this
document)
You can use:
• a scientific or graphical calculator
• geometrical instruments
• tracing paper
* J 5 6 0 0 6 *
Please write clearly in black ink. Do not write in the barcodes.
Centre number Candidate number
First name(s)
Last name
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided. You can use extra paper if
you need to, but you must clearly show your candidate number, the centre number and
the question numbers.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Use the r button on your calculator or take r to be 3.142 unless the question says
something different.
INFORMATION
• The total mark for this paper is 100.
• The marks for each question are shown in brackets [ ].
• This document has 20 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2024 [601/4606/0] OCR is an exempt Charity
DC (PQ/CT) 337120/3 Turn over
, 2
1 Below are six graphs, numbered 1 to 6, that show different relationships between x and y.
Graph 1 Graph 2 Graph 3
y y y
O x O 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.
x: temperature in °C
y: temperature in °F, where y = 1.8x + 32 . Graph ............................
x: average speed when running 200 m
y: time taken to run 200 m. Graph ............................
x: mass of a solid object made from clay
y: volume of the same solid object. Graph ............................
[3]
© OCR 2024
, 3
2 The graph shows a household’s average daily electricity usage, in kilowatt hours (kWh).
10 kWh
Average
daily
electricity
usage (kWh)
8 kWh
2021 2022 Jan Apr Jul Oct 2024
2023 2023 2023 2023
Give two different reasons why this graph is misleading.
Reason 1: .........................................................................................................................................
..........................................................................................................................................................
Reason 2: .........................................................................................................................................
.................................................................................................................................................... [2]
3 The word MATHEMATICS is spelt using tiles.
M A T H E M A T I C S
The tiles are put into an empty bag.
One at a time, 99 children each take a tile at random from the bag.
They record the letter and then put the tile back in 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.
(a) Below is part of the map showing City A and City B.
Scale: 1 cm represents 150 km
City B
City A
Heidi is planning to walk from City A to City B for charity.
Heidi measures the straight-line distance on the map from City A to City B accurately as 5 cm.
Heidi says she will walk from City A to City B at an average speed of 2.5 km / h for 10 hours
per day.
(i) Use this information to work out how many days Heidi needs to complete the walk from
City A to City B.
(a)(i) .................................................. days [4]
(ii) 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.
...........................................................................................................................................
..................................................................................................................................... [1]
(b) Yoshi writes the scale of the map, 1 cm represents 150 km, as the ratio 1 : 150.
Explain Yoshi’s error and write the scale correctly in the form 1 : n.
Yoshi’s error is ..........................................................................................................................
...................................................................................................................................................
The correct answer is 1 : .......................................................... [2]
© OCR 2024
Monday 10 June 2024 – Morning
GCSE (9–1) Mathematics
J560/06 Paper 6 (Higher Tier)
Time allowed: 1 hour 30 minutes
H
You must have:
* 1 3 9 5 1 5 5 9 6 2 *
• the Formulae Sheet for Higher Tier (inside this
document)
You can use:
• a scientific or graphical calculator
• geometrical instruments
• tracing paper
* J 5 6 0 0 6 *
Please write clearly in black ink. Do not write in the barcodes.
Centre number Candidate number
First name(s)
Last name
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided. You can use extra paper if
you need to, but you must clearly show your candidate number, the centre number and
the question numbers.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Use the r button on your calculator or take r to be 3.142 unless the question says
something different.
INFORMATION
• The total mark for this paper is 100.
• The marks for each question are shown in brackets [ ].
• This document has 20 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2024 [601/4606/0] OCR is an exempt Charity
DC (PQ/CT) 337120/3 Turn over
, 2
1 Below are six graphs, numbered 1 to 6, that show different relationships between x and y.
Graph 1 Graph 2 Graph 3
y y y
O x O 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.
x: temperature in °C
y: temperature in °F, where y = 1.8x + 32 . Graph ............................
x: average speed when running 200 m
y: time taken to run 200 m. Graph ............................
x: mass of a solid object made from clay
y: volume of the same solid object. Graph ............................
[3]
© OCR 2024
, 3
2 The graph shows a household’s average daily electricity usage, in kilowatt hours (kWh).
10 kWh
Average
daily
electricity
usage (kWh)
8 kWh
2021 2022 Jan Apr Jul Oct 2024
2023 2023 2023 2023
Give two different reasons why this graph is misleading.
Reason 1: .........................................................................................................................................
..........................................................................................................................................................
Reason 2: .........................................................................................................................................
.................................................................................................................................................... [2]
3 The word MATHEMATICS is spelt using tiles.
M A T H E M A T I C S
The tiles are put into an empty bag.
One at a time, 99 children each take a tile at random from the bag.
They record the letter and then put the tile back in 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.
(a) Below is part of the map showing City A and City B.
Scale: 1 cm represents 150 km
City B
City A
Heidi is planning to walk from City A to City B for charity.
Heidi measures the straight-line distance on the map from City A to City B accurately as 5 cm.
Heidi says she will walk from City A to City B at an average speed of 2.5 km / h for 10 hours
per day.
(i) Use this information to work out how many days Heidi needs to complete the walk from
City A to City B.
(a)(i) .................................................. days [4]
(ii) 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.
...........................................................................................................................................
..................................................................................................................................... [1]
(b) Yoshi writes the scale of the map, 1 cm represents 150 km, as the ratio 1 : 150.
Explain Yoshi’s error and write the scale correctly in the form 1 : n.
Yoshi’s error is ..........................................................................................................................
...................................................................................................................................................
The correct answer is 1 : .......................................................... [2]
© OCR 2024
