CIE IGCSE Maths

Revision Notes

1.8.3 Speed, Density & Pressure - Harder

What are speed, density and pressure?

  • Speed, density and pressure are compound measures – they are made from other measures
    • Speed is related to the measures distance and time
    • Density is related to mass and volume
    • Pressure is related to force and area
  • The relationship between each of these sets of measures follows the same pattern – what we refer to as “blue triangles”

SDPHard Notes fig1, downloadable IGCSE & GCSE Maths revision notes

  • If you do not remember the blue triangles – do not worry, these can often be deduced from information given in the question – see the examples below
  • It is important you understand and can do the basic questions with speed, density and pressure

Speed, distance and time harder problems

  • Speed is commonly measured in metres per second (m/s) or
    miles per hour (mph)

    • There are other possibilities such as kilometres per hour (kmph)
    • The units indicate speed is distance per time
      ie speed = distance ÷ time
  • “Speed” (in this formula) means “average speed
  • In harder problems there are often two journeys – or two parts to one longer journey

SDPHard Notes fig2, downloadable IGCSE & GCSE Maths revision notes

Density, mass and volume harder problems

  • Density is usually measured in grams per cubic centimetre (g/cm3)
    or kilograms per cubic metre (kg/m3)

    • The units indicate that density is mass per volume
      ie density = mass ÷ volume
  • In harder problems there are often two metals (alloys), liquids or gases that have been combined rather than working with a single substance

SDPHard Notes fig3, downloadable IGCSE & GCSE Maths revision notes

Pressure, force and area harder problems

  • Pressure is usually measured in Newtons per square metre (N/m2)
    The units of pressure are often called Pascals (Pa) rather than N/m2

    • The units indicate that pressure is force per area
      ie pressure = force ÷ area
  • Remember that weight is a force; it is different to mass

Exam Tip

Do look out for a mixture of units:

  • Time can be given as minutes but common phrases like “half an hour
    (ie 30 minutes) could also be used in the same question.
  • Any mixed units should be those in common use and easy to convert
    g to kg (and vice versa)
    m to km (and vice versa)

Worked Example

SDPHard Example fig1 sol, downloadable IGCSE & GCSE Maths revision notes

SDPHard Example fig2 alt sol, downloadable IGCSE & GCSE Maths revision notes

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