课 13, 主题 4

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Scale Aqa Foundation

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Exam code:8300

Scale

What is a scale?

For accurate drawings and constructions scale refers to a ratio
- This ratio describes the relationship between the drawn size and the real-life size
Maps are usually drawn to a scale
The ratio will work for any unit of length applied to both sides
- For example, the scale 1: 50 000 could mean 1 cm = 50 000 cm, 1 km = 50 000 km or even 1 yard = 50 000 yards
- If you’re measuring the length from a map it will be easiest to measure in cm

Examiner Tips and Tricks

When working with lots of different units and converting between them, make sure to use “common sense” checks
- e.g. When converting 500 km into metres, am I expecting a bigger or smaller number?

Maps

How can I use a scale to find the actual lengths from a map?

A map can be used to calculate the real-life distances between points
STEP 1
Use a ruler to measure the distance accurately on the map
- For example, measuring a length from A to B as 5.8 cm
STEP 2
Use the scale to find the actual distance in the same units
- For example, if the scale is 1 : 150 000 the actual distance = 5.8 cm × 150 000 = 870 000 cm
STEP 3
Convert the actual distance to a more suitable unit
- For example, 870 000 cm = 8 700 m = 8.7 km

Worked Example

A map is drawn where a length of 5 cm is equal to an actual distance of 0.6 km.

(a) Write the scale that is used for the map.

Convert both parts of the scale to the same units
The answer needs to be in the form 1 : n so convert 0.6 km into cm using 1 m = 100 cm and 1 km = 1000 m

0.6 km = 0.6 × 1000 m = 600 m
600 m = 600 × 100 cm = 60 000 cm

Now the ratio has the same units 5 cm : 60 000 cm, you can remove the units

5 : 60 000

Write in the form 1 : n by dividing both sides by 5

1 : 12 000

(b) The width of a park on the map is 17 mm.

Find the actual width of the park, giving your answer in metres.

Convert 17 mm into cm

17 mm = 1.7 cm

Use the scale to find 1.7 cm on the map in real life

1.7 cm × 12 000 = 20 400 cm

Convert to metres

20 400 cm ÷ 100

204 m

Find this distance on the map.

Convert 125 metres to cm

125 m = (125 × 100 cm) = 12 500 cm

Use the scale to find 12500 cm in real life on the map

12 500 cm ÷ 12 000 = 1.0416… cm

1.04 cm

Scale drawings

How can I use a scale to find lengths for an accurate drawing?

A scale can be used to produce an accurate drawing or model of an object
STEP 1
Convert the scale into a ratio where one side is 1 cm and the other side uses the units the real distance is measured in
- For example, if the real distance is in km and the scale is 1 : 500 000,
- 1 : 500 000 = 1 cm : 500 000 cm = 1 cm : 5 000 m = 1 cm : 5 km
- So 1 cm on the map, represents 5 km in real life
STEP 2
Use this ratio to convert the actual distance to the scale distance
- For example, if the actual distance = 20 km, the scale distance will be 20 ÷ 5 = 4 cm

Maths Gcse Aqa Foundation