Worksheets · Foundation and Higher

Scale factors, scale drawings and maps

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 4 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. (2)
(b) Two farms are $3.5$ km apart. How far apart are they on the map, in centimetres? (2)
Question 2Non-calculator · 4 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. (2)
(b) Find the actual length of the second wall in metres. (2)
Question 3Non-calculator · 5 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? (2)
(b) On map A, the area of the lake is $12\ \text{cm}^2$ . Work out the real area of the lake in $\text{km}^2$ . (3)

Answers and marks

(a) $2$ km

(b) $7$ cm

(a) $1:50$

(b) $3.75$ m

(a) $5$ cm

(b) $0.75\ \text{km}^2$

P1 Writing 1 cm represents $0.25$ km (or 250 m).
P1 Squaring the length scale: $1\ \text{cm}^2$ represents $0.0625\ \text{km}^2$ (or $62\,500\ \text{m}^2$ ).
A1 $0.75\ \text{km}^2$ .

Scale factors, scale drawings and maps

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