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Scale | Mathematics for GCSE/IGCSE - Year 11 PDF Download

What is scale?

  • In mathematics, scale can have various interpretations, but concerning accurate drawings and constructions, scale denotes a ratio.
  • Maps are typically crafted to a specific scale.
  • The selection of the scale relies on the area being charted. For instance:
    • A map of a classroom necessitates a large scale to exhibit intricate details.
    • In contrast, a map of a country or the world utilizes a small scale to represent a broader area with less detail.

How can scale be used to convert lengths?

  • A scale ratio does not include units and is applicable to any unit of length on both sides.
    • For instance, the scale 1:50000 can mean 1 cm = 50000 cm, 1 km = 50000 km, or 1 yard = 50000 yards.
  • When measuring from a map, it is easiest to use centimeters.
  • The scale converts map lengths to real-life lengths.
  • To convert a map length to a real-life length:
    • Step 1: Measure the distance on the map accurately with a ruler, e.g., 5.8 cm from A to B.
    • Step 2: Use the scale to find the actual distance in the same units, typically cm. For a scale of 1:150000, the actual distance is 5.8 cm × 150000.
    • Step 3: Convert the actual distance to a more suitable unit. For instance, 5.8 × 150000 = 870000 cm = 8.7 km.
  • To convert real-life lengths to a map length:
    • Step 1: Convert the scale into a ratio of 1 cm to the actual distance unit. For example, if the scale is 1:500000 and the distance is in km, convert 500000 cm into km. So, 1:500000 becomes 1 cm: 5 km.
    • Step 2: Use this ratio to convert the actual distance to the scale distance. For instance, if the actual distance is 20 km, the scale distance will be 20 ÷ 5 = 4 cm.

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How can scale be used to convert lengths?
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FAQs on Scale - Mathematics for GCSE/IGCSE - Year 11

1. What is scale?
Ans. Scale is a ratio of the length in a drawing or model to the actual length of the object being represented.
2. How can scale be used to convert lengths?
Ans. Scale can be used to convert lengths by simply multiplying or dividing the actual length by the scale factor.
3. What are the different types of scales commonly used in measurements?
Ans. The most common types of scales used in measurements are linear scales, logarithmic scales, and proportional scales.
4. How does scale help in accurately representing objects in drawings and models?
Ans. Scale helps in accurately representing objects in drawings and models by ensuring that the relative sizes and proportions of the objects are maintained.
5. What are some practical applications of scale in real-world scenarios?
Ans. Scale is used in various real-world scenarios such as map making, architectural drawings, engineering designs, and model building to accurately represent objects and structures in a scaled-down form.
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