What is R2: Scale diagrams and maps?

A scale written 1:n compares a diagram length with the corresponding real length in the same units. Multiply a diagram length by n to obtain the real length, or divide the real length by n to obtain the diagram length.

How many marks are R2 questions worth?

In verified past-paper appearances, R2 questions on Edexcel GCSE Maths 1MA1 have been worth 2–5 marks.

Which past exam papers has R2 appeared in?

R2 has appeared in 16 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Use scale factors, scale diagrams and maps

Scale diagrams and maps

Worked answers, methods and verified real exam appearances for R2 on Edexcel GCSE Maths 1MA1.

Explanation

A scale written $1:n$ compares a diagram length with the corresponding real length in the same units. Multiply a diagram length by $n$ to obtain the real length, or divide the real length by $n$ to obtain the diagram length.
Convert units only after establishing which direction the scale factor acts.
For areas, square the linear scale factor; for volumes, cube it.
On a map, measure between the stated points accurately and use any given scale bar or numerical scale.
Examiners award method for applying the scale in the correct direction and then converting units correctly.

A scale of

1:n

multiplies every diagram length by

n

to give the corresponding real length.

Worked example

A map has scale $1:25\,000$ . A route measures $6.4\,\text{cm}$ on the map. Find the real distance in kilometres.

1.Real distance $=6.4\times25\,000=160\,000\,\text{cm}$ .
2. $160\,000\,\text{cm}=1600\,\text{m}$ .
3. $1600\,\text{m}=1.6\,\text{km}$ .

Answer: $1.6\,\text{km}$ .

Common mistakes

Don't divide by the scale factor when converting a diagram length to a real length.
Don't mix centimetres and metres inside the ratio before making the units consistent.
Don't use $n$ rather than $n^2$ when a scale-diagram question asks for area.

Exam tip

Write what $1\,\text{cm}$ represents before scaling, because this makes the direction of the conversion clear.

Worked practice

Tier 1 · Easy

A ranger's sketch uses scale

1:25\,000

. A footpath trace measures

6.4\,\text{cm}

. Find the real distance in kilometres.

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$1.6\,\text{km}$	2	$6.4\times25\,000=160\,000\,\text{cm}=1600\,\text{m}=1.6\,\text{km}$ .

Tier 2 · Standard

A model theatre uses scale

1:40

. A real doorway is

2.04\,\text{m}

high. Work out the model doorway height in centimetres.

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$5.1\,\text{cm}$	2	The real height is $204\,\text{cm}$ . Divide by $40$ : $204/40=5.1\,\text{cm}$ .

Tier 3 · Hard

A site plan has scale

1:2500

. A garden occupies

96\,\text{cm}^2

on the plan. Calculate its real area in hectares. Use

1

hectare

=10\,000\,\text{m}^2

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$6$ hectares	4	At this scale, $1\,\text{cm}$ represents $25\,\text{m}$ , so $1\,\text{cm}^2$ represents $25^2=625\,\text{m}^2$ . The real area is $96\times625=60\,000\,\text{m}^2=6$ hectares.

Tier 1 · Easy

A shape is enlarged so that a side of length

8\,\text{cm}

becomes

14\,\text{cm}

. Work out the scale factor.

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$1.75$	1	The scale factor is $14\div8=1.75$ .

Tier 2 · Standard

A real wall is

18\,\text{m}

long and is drawn as

7.2\,\text{cm}

. Write the scale of the drawing in the form

1:n

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$1 : 250$	2	$18\,\text{m}=1800\,\text{cm}$ . The scale is $7.2:1800=1:250$ .

Tier 3 · Hard

A road is

9.6\,\text{cm}

long on a map with scale

1:12\,500

. Work out its length on a second map with scale

1:30\,000

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$4\,\text{cm}$	3	The real road length is $9.6\times12\,500=120\,000\,\text{cm}$ . On the second map its length is $120\,000\div30\,000=4\,\text{cm}$ .

Tier 2 · Standard

A floor plan uses scale

1 : 75

. A rectangular storage bay measures

6.4\,\text{cm}

3.6\,\text{cm}

on the plan. Work out its real perimeter in metres.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$15\,\text{m}$	3	The real dimensions are $6.4\times75=480\,\text{cm}=4.8\,\text{m}$ and $3.6\times75=270\,\text{cm}=2.7\,\text{m}$ . The perimeter is $2(4.8+2.7)=15\,\text{m}$ .

Tier 3 · Hard

A rectangular terrace measures

9.6\,\text{cm}

6.4\,\text{cm}

on a plan with scale

1 : 125

. The terrace will be covered with square paving slabs of side

40\,\text{cm}

. Work out the number of slabs needed. Assume that no slabs are wasted.

(5)

(Total for Question 8 is 5 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$600$ slabs	5	The real dimensions are $9.6\times125=1200\,\text{cm}=12\,\text{m}$ and $6.4\times125=800\,\text{cm}=8\,\text{m}$ , so the terrace area is $96\,\text{m}^2$ . Each slab has area $0.4^2=0.16\,\text{m}^2$ . The number needed is $96\div0.16=600$ .

Tier 3 · Hard

A model storage tank is made to scale

1 : 40

. The model has volume

54\,\text{cm}^3

. Work out the volume of the real tank in litres.

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$3456$ litres	4	The volume scale factor is $40^3=64\,000$ . The real volume is $54\times64\,000=3\,456\,000\,\text{cm}^3$ . Since $1000\,\text{cm}^3=1$ litre, this is $3456$ litres.

Q10

Tier 3 · Hard

A lake covers

28.8\,\text{cm}^2

on an aerial photograph with scale

1 : 8000

. Work out the area it would cover on a plan with scale

1 : 12\,000

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$12.8\,\text{cm}^2$	4	Lengths on the second plan are $8000\div12\,000=\dfrac{2}{3}$ of those on the photograph. Areas are therefore multiplied by $\left(\dfrac{2}{3}\right)^2=\dfrac{4}{9}$ . The area is $28.8\times\dfrac{4}{9}=12.8\,\text{cm}^2$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2019-06	2F	Q19	4	Allowed	Foundation	QP MS
2021-11	2F	Q5	2	Allowed	Foundation	QP MS
2019-11	2F	Q15	3	Allowed	Foundation	QP MS
2019-06	3F	Q17	2	Allowed	Foundation	QP MS
2021-11	3F	Q12	4	Allowed	Foundation	QP MS
2019-11	1F	Q27	5	Non-calculator	Foundation	QP MS
2019-11	1H	Q8	5	Non-calculator	Higher	QP MS
2024-06	2H	Q8	3	Allowed	Higher	QP MS
2022-11	1F	Q14	5	Non-calculator	Foundation	QP MS
2023-06	2F	Q8	3	Allowed	Foundation	QP MS
2024-11	2F	Q15	3	Allowed	Foundation	QP MS
2022-06	3F	Q13	4	Allowed	Foundation	QP MS
2022-06	2F	Q16	3	Allowed	Foundation	QP MS
2024-06	3F	Q6	4	Allowed	Foundation	QP MS
2023-11	3H	Q11	3	Allowed	Higher	QP MS
2023-11	1F	Q7	2	Non-calculator	Foundation	QP MS

Other points in R Ratio, proportion and rates of change

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