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GCSE Maths / Edexcel

Scale drawings and maps

Convert between drawing lengths and real distances using map scales, scale bars and ratio-style scale factors.

Geometry and MeasuresFoundation and HigherGrades 3 to 6Skill

Curriculum path: GCSE Maths > Edexcel > Geometry and Measures > Scale drawings and maps

Pearson Edexcel GCSE Maths geometry G14 and G15: use scale drawings, maps, scale factors and measured lengths.

Practise this topicUpload your answerAsk AI to explain thisTry exam-style questions
Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

A scale drawing is an accurate drawing where every length has been enlarged or reduced by the same scale.

A map scale tells you how a distance on the map compares with a real distance.

For example, 1 cm represents 2 km means every 1 cm on the map is 2 km in real life.

To find a real distance, multiply the map distance by the scale.

To find a map distance, divide the real distance by the scale.

A ratio scale such as 1 : 50 means 1 unit on the drawing represents 50 of the same unit in real life.

Always check units. If the scale mixes cm and km, keep the meaning clear rather than treating the numbers as the same unit.

Scale drawings often combine with bearings: draw the direction accurately, then use the scale for distance.

Key ruleReal distance = drawing distance x scale value. Drawing distance = real distance ÷ scale value.

Diagram guide

schoolparkmap scale: 1 cm represents 2 km5 cm on map = 10 km in real lifescale bar
Map scaleUse the scale to convert a measured map length into a real distance.
NAB060 degrees5 km on scaledraw bearing first, then measure the scaled distance
Scale drawing with directionWhen direction matters, combine scale distance with an accurate bearing or angle.

Worked examples

Map distance to real distance

A map scale is 1 cm represents 2 km. Two places are 5 cm apart on the map. Find the real distance.

schoolparkmap scale: 1 cm represents 2 km5 cm on map = 10 km in real lifescale bar
Example: map to real distanceEach centimetre on the map represents 2 km.
  1. Real distance = map distance x 2 km.
  2. 5 x 2 = 10.

Answer: 10 km

Real distance to map distance

A map scale is 1 cm represents 4 km. A real distance is 28 km. Find the map distance.

schoolparkmap scale: 1 cm represents 2 km5 cm on map = 10 km in real lifescale bar
Example: real distance to map distanceDivide by the real distance represented by 1 cm.
  1. Map distance = real distance / 4.
  2. 28 / 4 = 7.

Answer: 7 cm

Ratio scale

A model has scale 1 : 50. A length on the model is 6 cm. Find the real length.

4 cm4 cm8 cm8 cmsmallsimilar shapescale factor = 8 ÷ 4 = 2same angles, corresponding sides in the same ratio
Example: ratio scaleA 1 : 50 scale means multiply model lengths by 50.
  1. Real length = 6 x 50 = 300 cm.
  2. 300 cm = 3 m.

Answer: 3 m

Scale drawing with bearing

A point B is 12 km from A on a bearing of 070 degrees. Use a scale of 1 cm represents 3 km.

NAB060 degrees5 km on scaledraw bearing first, then measure the scaled distance
Example: bearing with map scaleConvert distance to 4 cm, then draw it on the bearing.
  1. Map distance = 12 / 3 = 4 cm.
  2. Draw a north line at A.
  3. Draw a bearing of 070 degrees.
  4. Mark B 4 cm along the bearing line.

Answer: B is 4 cm from A on a bearing of 070 degrees.

Common mistakes

  • Multiplying when the question asks for drawing distance.
  • Dividing when the question asks for real distance.
  • Ignoring units in ratio scales.
  • Using a scale bar inaccurately because the ruler starts at the wrong point.
  • Drawing the scale distance before the direction in bearing questions.

Quick exercise

Try these before moving to the exam-style questions.

  1. Scale: 1 cm represents 5 km. A map length is 3 cm. Find the real distance.
    schoolparkmap scale: 1 cm represents 2 km5 cm on map = 10 km in real lifescale bar
    Quick check: map to realMultiply by 5 km for each centimetre.
  2. Scale: 1 cm represents 2 km. A real distance is 18 km. Find the map distance.
    schoolparkmap scale: 1 cm represents 2 km5 cm on map = 10 km in real lifescale bar
    Quick check: real to mapDivide by 2 km for each centimetre.
  3. Scale 1 : 100. A drawing length is 4 cm. Find the real length in metres.
    4 cm4 cm8 cm8 cmsmallsimilar shapescale factor = 8 ÷ 4 = 2same angles, corresponding sides in the same ratio
    Quick check: ratio scaleMultiply by 100, then convert cm to m.
  4. Scale: 1 cm represents 3 km. What map length represents 24 km?
    schoolparkmap scale: 1 cm represents 2 km5 cm on map = 10 km in real lifescale bar
    Quick check: divide by scaleMap distance = real distance divided by 3.
  5. Why should all lengths in a scale drawing use the same scale?
    schoolparkmap scale: 1 cm represents 2 km5 cm on map = 10 km in real lifescale bar
    Quick check: same scaleA scale drawing keeps all lengths in proportion.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

A map scale is 1 cm represents 4 km. The distance on the map is 6 cm. Find the real distance.

schoolparkmap scale: 1 cm represents 2 km5 cm on map = 10 km in real lifescale bar
Question diagram: map scaleEach centimetre represents 4 km.
scale drawingmap scalefoundation geometry
Standard exam styleFoundation and HigherCalculator3 marks

A plan uses a scale of 1 : 200. A wall is 7.5 cm long on the plan. Find the real length of the wall in metres.

4 cm4 cm8 cm8 cmsmallsimilar shapescale factor = 8 ÷ 4 = 2same angles, corresponding sides in the same ratio
Question diagram: ratio scaleA 1 : 200 plan means multiply plan lengths by 200.
scale factorratio scaleunit conversion
ChallengeFoundation and HigherNon-calculator4 marks

Point B is 15 km from A on a bearing of 080 degrees. A map scale is 1 cm represents 5 km. Describe how to draw B on the map.

NAB060 degrees5 km on scaledraw bearing first, then measure the scaled distance
Question diagram: bearing and scale drawingUse both the bearing and the scale distance.
scale drawingbearingsmap distance