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Scales and Maps

FoundationChallengeAQAEdexcelOCR

Scales and Maps is a key geometry topic at GCSE Maths. This Foundation worksheet gives you exam-style questions on using scales and maps, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. A scale of 1:50000 means 1 cm on the map is 50000 cm in real life.

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Topic overview

A scale tells you how a distance on a map or drawing relates to the real distance. It is usually written as a ratio, such as \(1 : 50\,000\).

That ratio means one unit on the map represents \(50\,000\) of the same units in reality. So \(1\)cm on the map is \(50\,000\)cm, which is \(500\)m or \(0.5\)km.

Converting the units is where most marks are lost. Work in the map's units first, multiply by the scale, then convert to something sensible at the end. Doing it in that order keeps the arithmetic simple.

Revision notes

Using a scale ratio

Multiply the map distance by the scale to find the real distance, and divide to go the other way.

With a scale of \(1 : 25\,000\), a map distance of \(4\)cm represents \(100\,000\)cm, which is \(1\)km.

Converting units

Convert only after multiplying, and remember \(100\)cm in a metre and \(1000\)m in a kilometre.

So \(100\,000\)cm becomes \(1000\)m, which becomes \(1\)km.

Scales written with units

Some scales are written as \(1\)cm represents \(2\)km, which removes the conversion step.

Multiply the map distance by \(2\) to get kilometres directly. Read carefully which form the question uses.

Key points

  • A scale relates map distance to real distance.
  • \(1 : 50\,000\) means 1 unit represents 50 000 of the same units.
  • Multiply to go from map to real.
  • Divide to go from real to map.
  • Convert units only after multiplying.
  • Some scales are given with units, such as 1cm to 2km.

Worked examples

Example 1

A map has scale \(1 : 20\,000\). A distance of \(3\)cm on the map is how far in reality?

Working

\[3 \times 20\,000 = 60\,000\text{cm}\]multiply by the scale
\[60\,000 \div 100 = 600\text{m}\]convert to metres
\[= 0.6\text{km}\]convert to kilometres

Example 2

On a map where \(1\)cm represents \(5\)km, how far apart are two towns \(7\)cm apart?

Working

\[7 \times 5\]multiply the map distance by the scale
\[= 35\text{km}\]state the real distance

Example 3

Two places are \(12\)km apart. On a map where \(1\)cm is \(4\)km, how far apart are they on the map?

Working

\[12 \div 4\]divide to go from real to map
\[= 3\text{cm}\]state the map distance

Common mistakes

  • Forgetting to convert units.

    60 000cm is 600m, not 600cm. Convert after multiplying.

  • Dividing when you should multiply.

    Map to real multiplies; real to map divides.

  • Misreading the scale direction.

    1 : 20 000 means the real distance is 20 000 times larger.

  • Mixing up cm and km in the same calculation.

    Work in one unit throughout, then convert at the end.

Exam tips

  • Write down the scale and what it means before calculating.
  • Multiply first, convert units afterwards.
  • Sense-check that real distances are much larger than map distances.
  • Include units in every answer.

Key terms

Scale
The ratio between a drawing and the real object.
Ratio
A comparison written in the form 1 : n.
Convert
To change between units.
Map distance
The measurement taken on the map.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.