GCSE Maths revision · Ratio and proportion

Scale drawings and maps

Foundation and Higher

The idea

A map scale such as $1 : 25\,000$ means $1\text{ cm}$ on the map is $25\,000\text{ cm}$ in real life, which is $250\text{ m}$ .

Map to real: multiply by the scale.
Real to map: divide by the scale.
Convert units at the end: $100\text{ cm} = 1\text{ m}$ , $1000\text{ m} = 1\text{ km}$ .

Watch out Keep the units the same on both sides of the scale before you convert.

Worked exampleNon-calculator4 marks

A map has a scale of $1 : 50\,000$ .

(a) Two villages are $4$ cm apart on the map. Work out the real distance between them in kilometres.

(b) Two farms are $3.5$ km apart. How far apart are they on the map, in centimetres?

Answer (a) $2$ km; (b) $7$ cm

Question 1Non-calculator3 marks

A plan uses a scale of 1 : 80. A wall is 6.5 cm long on the plan. Work out its actual length in metres.

Question 2Non-calculator4 marks

A scale drawing shows a 5 m wall as 10 cm. A second wall is 7.5 cm on the drawing.

(a) Find the scale in the form 1:n.

(b) Find the actual length of the second wall in metres.

Question 3Non-calculator5 marks

Map A has a scale of $1 : 25\,000$ . Map B has a scale of $1 : 40\,000$ .

(a) A lake is $8$ cm long on map A. How long is the lake on map B?

(b) On map A, the area of the lake is $12\ \text{cm}^2$ . Work out the real area of the lake in $\text{km}^2$ .

86 official questions in 80 papers since 2017. The latest:

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