AQA · Mathematics · 8300
GCSE Maths: Scales and maps
Ratio & Proportion · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Scales and maps (Corbettmaths Video 283), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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On a map with scale 1cm : 3 miles, the map distance between two towns is 7cm. What is the actual distance?
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21 miles. Multiply the map distance by the scale factor: 7 × 3 = 21 miles.
On a map with scale 1cm : 4km, the actual distance between two cities is 52km. What is the map distance?
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13cm. Divide the actual distance by the scale factor: 52 ÷ 4 = 13cm.
What is the formula for finding actual distance when you know map distance and scale?
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Actual distance = map distance × scale factor. For example, if 1cm represents 5km and the map shows 3cm, the actual distance is 3 × 5 = 15km.
What is the formula for finding map distance when you know actual distance and scale?
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Map distance = actual distance ÷ scale factor. For example, if 1cm represents 5km and the actual distance is 20km, the map distance is 20 ÷ 5 = 4cm.
On a map with scale 1:4000, the map distance between two houses is 9cm. What is the actual distance in metres?
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360m. Actual distance in cm: 9 × 4000 = 36000cm. Convert to metres: 36000 ÷ 100 = 360m.
On a map with scale 1:75000, the distance between two towns is 8cm. What is the actual distance in kilometres?
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6km. Actual distance in cm: 8 × 75000 = 600000cm. Convert to km: 600000 ÷ 100000 = 6km.
In real life a boat is 150m long. On a scale drawing with scale 1:20, what is the length on the drawing in centimetres?
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750cm. Convert to cm: 150m = 15000cm. Drawing length: 15000 ÷ 20 = 750cm.
How do you convert a map scale from 'cm represents km' format to a ratio?
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Convert both measurements to the same unit (usually cm), then write as a ratio. Example: 1cm represents 2km → 1cm represents 200000cm → 1:200000.
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