Printable · GCSE Foundation · ages 14-16

Scale factors, scale diagrams and maps worksheet — GCSE Foundation

Fifteen questions on "scale factors, scale diagrams and maps" — DfE statement R2. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Scale factors, scale diagrams and maps worksheet — GCSE Foundation

Maths · GCSE Foundation · R2 · Scale factors, scale diagrams and maps · 15 questions

MathsUKwww.geekhero.co.uk

1.A map has a scale of 1 : 25 000. Two towns are 5 km apart in real life. Work out the distance between the towns on the map, in centimetres.
(a)200 cm
(b)2 cm
(c)20 cm
(d)0.2 cm
2.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.
(a)15000 m
(b)1500 m
(c)50000 m
(d)150 m
3.A map has a scale of 1 : 100. A path measures 5 cm on the map. Work out the real length of the path, in metres.
(a)500 m
(b)50 m
(c)5 m
(d)0.05 m
4.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.
(a)3.2 km
(b)20 km
(c)40 km
(d)5 km
5.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.
(a)1:2
(b)1:200000
(c)1:2000
(d)1:20000
6.A plan is drawn to a scale of 1 : 500. Work out how many metres are represented by 1 cm on the plan.
(a)500 m
(b)5 m
(c)50 m
(d)0.5 m
7.A cartographer is choosing a scale for a map to show a small park in as much detail as possible. Which of these scales would show the MOST detail — 1 : 500, 1 : 5000, or 1 : 50 000? Give the correct scale and reason.
(a)1 : 50 000 — covers the largest real area, most detail
(b)1 : 500 — smallest real distance per cm (5 m), most detail
(c)1 : 5000 — the middle value, most balanced
(d)1 : 500 — smallest ratio, covers largest real distance
8.A scale drawing of a car park has a scale of 1 : 300. On the drawing, the car park has an area of 15 cm². Work out the real area of the car park, in square metres.
(a)13,500 m²
(b)0.45 m²
(c)1,350,000 m²
(d)135 m²
9.A furniture designer makes a scale model of a wardrobe using a scale of 1 : 8. The real wardrobe is 2.4 m tall and 1.2 m wide. Work out the perimeter of the front face of the model wardrobe, in centimetres.
(a)510 cm
(b)720 cm
(c)11.25 cm
(d)90 cm
10.A garden plan is enlarged by a scale factor of 3. A flower bed on the original plan is 5 cm long. Work out the length of the flower bed on the enlarged plan, in centimetres.
(a)45 cm
(b)8 cm
(c)1.7 cm
(d)15 cm
11.A plan is drawn to a scale of 1 : 25. A real fence is 10 m long. Work out the length of the fence on the plan, in centimetres.
(a)0.4 cm
(b)4 cm
(c)25000 cm
(d)40 cm
12.A scale drawing states '1 cm represents 25 m'. Which of these is the correct way to write this scale in the form 1 : n?
(a)1 : 25
(b)1 : 2.5
(c)1 : 250
(d)1 : 2500
13.A scale drawing of a playground is drawn to a scale of 1 : 300. A slide measures 4 cm on the drawing. Work out the real length of the slide, in centimetres.
(a)304 cm
(b)600 cm
(c)0.013 cm
(d)1200 cm
14.Map A has a scale of 1 : 25000 and Map B has a scale of 1 : 50000, both showing the same area. A real distance of 10 km is measured on each map. On which map does this distance appear as the longer length, and how long is it on that map, in centimetres?
(a)Map B, where the distance is 20 cm
(b)Map B, where the distance is 40 cm
(c)Map A, where the distance is 40 cm
(d)Map A, where the distance is 20 cm
15.A model railway is built at a scale where the ratio of model length to real length is 1 : 76. Given that a real carriage is 20.6 metres long, work out the length of the model carriage in centimetres, to 1 decimal place.
(a)0.3 cm
(b)271.1 cm
(c)27.1 cm
(d)1565.6 cm

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