Compound MeasuresEdexcel GCSE Maths: Revision notes
Section 1
What Is a Compound Measure?
A compound measure combines two different units into a single rate, formed by dividing one quantity by another. Speed, density and pressure are the three compound measures you need for GCSE.
| Compound measure | Formula | Common units |
|---|---|---|
| Speed | speed = distance ÷ time | m/s, km/h |
| Density | density = mass ÷ volume | g/cm³, kg/m³ |
| Pressure | pressure = force ÷ area | N/m², Pa |
You also need to be able to change freely between related standard units (length, area, volume, mass, time, money) — both numerically and within algebraic formulae.
The unit of a compound measure tells you the formula: km/h means 'kilometres per hour', i.e. distance ÷ time.
Section 2
Speed, Distance and Time
speed = distance ÷ time, so:
- distance = speed × time
- time = distance ÷ speed
Example: a car travels 150 km in 3 hours. Speed = 150 ÷ 3 = 50 km/h.
Always check the units match before calculating — if distance is in km but time is given in minutes, convert time to hours first (or distance to metres and time to seconds).
Mixing units (e.g. dividing km by minutes) without converting first is one of the most common errors in compound measure questions.
Section 3
Density, Mass and Volume
density = mass ÷ volume, so:
- mass = density × volume
- volume = mass ÷ density
Example: an object has mass 45 g and volume 9 cm³. Density = 45 ÷ 9 = 5 g/cm³.
Density questions often combine with volume formulae for cuboids, cylinders or spheres — work out the volume first, then apply the density formula.
A metal cube has side length 2 cm and density 8 g/cm³. Volume = 2³ = 8 cm³, so mass = 8 × 8 = 64 g.
Section 4
Pressure, Rates and Unit Pricing
pressure = force ÷ area, so:
- force = pressure × area
- area = force ÷ pressure
Compound measures also appear as everyday rates, such as unit pricing (cost per item, price per kilogram) and rates of pay (earnings per hour). These are all calculated the same way — total quantity divided by the other quantity — and are compared by finding a common unit rate.
Example: 5 kg of apples costs £4.50, so the unit price is £4.50 ÷ 5 = £0.90 per kg.
To compare two rates (e.g. two special offers), always convert both to the same unit — such as price per kg or price per item — before comparing.
Must Know
- speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area
- Rearrange each formula to find the other two quantities (e.g. distance = speed × time)
- Always convert units so they match before calculating (e.g. minutes to hours, or cm to m)
- Volume formulae (cuboid, cylinder, sphere) are often needed before applying the density formula
- Unit pricing and rates of pay are compound measures too — divide total cost/earnings by the other quantity
- To compare rates fairly, convert them to the same unit first
That's the notes covered.
Carry on to the next subtopic.