Compound Measures (Cambridge (CIE) IGCSE International Maths)

Compound Measures

What is a compound measure?

• A compound measure is something that is calculated by using more than one measurement

• Compound measures can be used to measure rates

  • This measures how much one quantity changes when the other is increased by 1

  • Examples include:

    • Speed – how much the distance changes for each unit of time

    • Flow rate – how much the volume changes for each unit of time

    • Population density – how many people there are for each unit of area

    • Fuel consumption - volume of  fuel used for each unit of distance travelled

How do I find the units for a compound measure?

• You can use the formula for a compound measure to derive its units

  • Use the units for the quantities in the formula to derive the units of the compound measure

  • Write a division as a/b and pronounce it as “a per b”

• Examples include:

  • 

    • If the distance is measured in km and the time is measured in minutes then the speed is measured in km/min; kilometres per minute

  • 

    • If the volume is measured in m³ and the time is measured in minutes then the flow rate is measured in m³/min; metres cubed per minute

How do I find the formula for a compound measure?

• You can use the units for a compound measure to help remember its formula

  • You just need to remember what each unit measures

  • If the unit is a/b then the formula will be the quantity that a measures divided by the quantity that b measures

• Examples include:

  • Density can be measured in kg/cm³

  • kg is a measure of mass and cm³ is a measure of volume

  • Therefore 

What is a formula triangle?

• A formula triangle shows the relationship between the different measures in a compound formula 

• They can be useful if you are less confident with rearranging formulas

• Three examples are shown below

  • Speed is equal to distance divided by time

  • Density is equal to mass divided by volume

  • Pressure is equal to force divided by area