Compound Measures (Speed, Density, Pressure)Cambridge IGCSE Maths: Revision notes

A compound measure combines two other quantities into a single rate, e.g. speed combines distance and time. Common compound measures include hourly pay rates, exchange rates, flow rates, fuel consumption, speed, density and pressure.

Formulas for pressure and density are always given in the question — you don't need to memorise them, but you must know how to rearrange and apply them.

speed $= \dfrac{\text{distance}}{\text{time}}$

This formula can be rearranged (using the 'formula triangle' or algebra) to find distance or time instead:

• distance $= \text{speed} \times \text{time}$
• time $= \text{distance} \div \text{speed}$

Units must match — e.g. speed in km/h requires distance in km and time in hours; mixing units (like minutes with hours) is a common source of error.

These formulas are given in the question, but you must substitute and rearrange correctly:

• Density $= \dfrac{\text{mass}}{\text{volume}}$, typically in g/cm³ or kg/m³
• Pressure $= \dfrac{\text{force}}{\text{area}}$
• Population density $= \dfrac{\text{population}}{\text{area}}$, e.g. people per km²

As with speed, each formula can be rearranged to find any one variable given the other two.

• Hourly pay rate: total pay ÷ hours worked
• Exchange rate: amount in one currency ÷ (or ×) the rate to convert to another currency
• Flow rate: volume of liquid ÷ time, e.g. litres per minute
• Fuel consumption: distance travelled ÷ fuel used, e.g. km per litre, or fuel used ÷ distance for litres per 100 km

All of these follow the same structure as speed: one quantity divided by another to create a rate.

The units of a compound measure always show which quantities were divided:

• Speed in m/s means metres divided by seconds
• Density in g/cm³ means grams divided by cubic centimetres
• Always match your working units to the units required in the final answer, converting where necessary before calculating