Scale drawings and maps | AQA GCSE Maths Notes

Visual model

A scale links drawing length to real length

4\text{ cm on map}

1\text{ cm}=2\text{ km}

8\text{ km}

Gold-standard guide

20 mins

What you will learn

Use scales to connect drawings and real measurements.

Use a clear step-by-step method for scale drawings and maps.

Check your answer and avoid the most common exam mistake.

Useful before you start

Core number skillsEarlier ratio, proportion and rates of change skillsShowing clear working

Core knowledge

Know the rule, then use it

These are the short notes. Read each one, then check you can use it in the worked example below.

Method

Scale 1:n means 1 unit on the map represents n units in reality

Step 1

State what 1 cm on the map represents

Scale 1:25,000 means 1 cm represents 25,000 cm = 250 m = 0.25 km

Step 2

Multiply to find the real distance

8.4 cm × 25,000 = 210,000 cm

Step 3

Convert to km

210,000 cm ÷ 100,000 = 2.1 km

Watch out

Students multiply then forget to convert units from cm to km

Scale

$real length = drawing length \times scale factor.$

Units

Convert units after scaling, not halfway through.

Worked example

A map has scale 1:25,000. Two villages are 8.4 cm apart on the map. Find the real distance in km.

State what 1 cm on the map represents: Scale 1:25,000 means 1 cm represents 25,000 cm = 250 m = 0.25 km.

Multiply to find the real distance: 8.4 cm × 25,000 = 210,000 cm.

Convert to km: 210,000 cm ÷ 100,000 = 2.1 km.

Final answer

2.1 km

Question ladder

Build up to the hardest questions

Do them in order. If you miss a step, read the solution, then redo the question without looking.

Workedreasoning

A map has scale 1:25,000. Two villages are 8.4 cm apart on the map. Find the real distance in km.

3 marks4 minsscale-drawings-and-maps-worked

Show solution

Worked solution

1.State what 1 cm on the map represents: Scale 1:25,000 means 1 cm represents 25,000 cm = 250 m = 0.25 km.
2.Multiply to find the real distance: 8.4 cm × 25,000 = 210,000 cm.
3.Convert to km: 210,000 cm ÷ 100,000 = 2.1 km.

Final answer

2.1 km

Mark points

M1: state what 1 cm on the map represents
M1: multiply to find the real distance
M1: convert to km
A1: 2.1 km

Watch out

Students multiply then forget to convert units from cm to km. Always show the full conversion chain explicitly.Also, note that 1 km = 100,000 cm, not 1,000 cm — writing this at the start of a question prevents the error.

Diagnosticrecall

Scale 1:50,000. Distance on map is 3.6 cm. Find real distance in km.

1 mark2 minsscale-drawings-and-maps-q1

Show solution

Worked solution

1.Spot the skill: Scale 1:n means 1 unit on the map represents n units in reality.
2.Use the state what 1 cm on the map represents stage first, then multiply to find the real distance.
3.Keep the final answer visible: 1.8 km.

Final answer

1.8 km

Mark points

M1: use the correct scale 1:n means 1 unit on the map represents n units in reality.multiply map measurement by n to get real measurement. for areas: scale factor for area = (linear scale factor)².
A1: 1.8 km

Watch out

Easyprocedure

Real distance is 5 km. Map uses scale 1:200,000. Find map distance in cm.

2 marks3 minsscale-drawings-and-maps-q2

Show solution

Worked solution

1.Spot the skill: Scale 1:n means 1 unit on the map represents n units in reality.
2.Use the multiply to find the real distance stage first, then convert to km.
3.Keep the final answer visible: 2.5 cm.

Final answer

2.5 cm

Mark points

M1: use the correct scale 1:n means 1 unit on the map represents n units in reality.multiply map measurement by n to get real measurement. for areas: scale factor for area = (linear scale factor)².
A1: 2.5 cm

Watch out

Mediumreasoning

A garden is drawn at scale 1:200. The drawing shows an area of 12 cm². Find the real area in m².

3 marks4 minsscale-drawings-and-maps-q3

Show solution

Worked solution

1.Spot the skill: Scale 1:n means 1 unit on the map represents n units in reality.
2.Use the convert to km stage first, then state what 1 cm on the map represents.
3.Keep the final answer visible: 4.8 m².

Final answer

4.8 m²

Mark points

M1: use the correct scale 1:n means 1 unit on the map represents n units in reality.multiply map measurement by n to get real measurement. for areas: scale factor for area = (linear scale factor)².
A1: 4.8 m²

Watch out

Hardproblem solving

A scale drawing shows a room 6.5 cm long. Scale is 1:40. Find the real length in metres.

3 marks5 minsscale-drawings-and-maps-q4

Show solution

Worked solution

1.Spot the skill: Scale 1:n means 1 unit on the map represents n units in reality.
2.Use the state what 1 cm on the map represents stage first, then multiply to find the real distance.
3.Keep the final answer visible: 2.6 m.

Final answer

2.6 m

Mark points

M1: use the correct scale 1:n means 1 unit on the map represents n units in reality.multiply map measurement by n to get real measurement. for areas: scale factor for area = (linear scale factor)².
A1: 2.6 m

Watch out

Exam-stylemulti-step

On a map scale 1:100,000, two towns are 4.3 cm apart. Find the real distance in km.

4 marks6 minsscale-drawings-and-maps-q5

Show solution

Worked solution

1.Spot the skill: Scale 1:n means 1 unit on the map represents n units in reality.
2.Use the multiply to find the real distance stage first, then convert to km.
3.Keep the final answer visible: 4.3 km.

Final answer

4.3 km

Mark points

M1: use the correct scale 1:n means 1 unit on the map represents n units in reality.multiply map measurement by n to get real measurement. for areas: scale factor for area = (linear scale factor)².
A1: 4.3 km

Watch out

Grade 9 stretchproblem solving

A map has scale 1:25,000. Two points are 6 cm apart on the map. Find the real distance in kilometres.

4 marks7 minsscale-g9

Show solution

Worked solution

1.Multiply by the scale factor.
2.Convert centimetres to kilometres.

Final answer

1.5 km

Mark points

M1: obtain 150,000 cm
A1: 1.5 km

Watch out

Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.

Timed checkpoint

12 mins - 9 marks

Switch between skills

Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.

1Scale drawings and maps - 2 marksScale 1:50,000. Distance on map is 3.6 cm. Find real distance in km.Mark answer

Answer

1.8 km

2Ratio and sharing - 2 marksTwo people share profit in ratio 5:3. Total profit £640. Find each share.Mark answer

Answer

£400 and £240

3Fractions and ratios - 2 marksA map scale is 1:25,000. Express as a fraction.Mark answer

Answer

$\frac{1}{2}5$ ,000

4Direct and inverse proportion - 3 marksy ∝ 1/x². When x = 2, y = 9. Find y when x = 6.Mark answer

Answer

Mastery check

I can explain the method for scale drawings and maps.
I can show clear working without skipping key steps.
I can avoid this mistake: Students multiply then forget to convert units from cm to km.Always show the full conversion chain explicitly.Also, note that 1 km = 100,000 cm, not 1,000 cm — writing this at the start of a question prevents the error.

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