How do you work with speed?

Speed is distance divided by time, so check units match first. Speed =\dfrac{distance}{time}, so distance = speed × time and time = distance ÷ speed.

How do you work with density?

Density is mass divided by volume, so you often need a volume first. Density =\dfrac{mass}{volume}, so mass = density × volume and volume = mass ÷ density.

Compound Measures Notes

Edexcel GCSE Maths: Revision notes

Key facts

Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area.
The unit tells you the formula: km/h is distance ÷ time.
Rearrange to find the other quantities, e.g. distance = speed × time.
Make units match before calculating: convert minutes to hours, or cm to m.
Unit pricing and pay rates are compound measures: divide total by quantity, then compare.

Three compound measures

A compound measure divides one quantity by another, so its unit combines two units.

Speed, density and pressure are the three you need.

You must also convert between units: $1\text{ m}=100\text{ cm}$ , but $1\text{ m}^2=10\,000\text{ cm}^2$ and $1\text{ m}^3=1\,000\,000\text{ cm}^3$ .

To go from m/s to km/h, multiply by 3.6.

Speed Density Pressure Formula distance \div time mass \div volume force \div area Common units m/s, km/h g/cm³, kg/m³ N/m², Pa

	Speed	Density	Pressure
Formula	distance ÷ time	mass ÷ volume	force ÷ area
Common units	m/s, km/h	g/cm³, kg/m³	N/m², Pa

Speed

Formula:: distance ÷ time
Common units:: m/s, km/h

Density

Formula:: mass ÷ volume
Common units:: g/cm³, kg/m³

Pressure

Formula:: force ÷ area
Common units:: N/m², Pa

Which calculation gives a density in g/cm³?

Speed, distance and time

Speed is distance divided by time, so check units match first.

Speed $=\dfrac{\text{distance}}{\text{time}}$ , so distance = speed × time and time = distance ÷ speed.

If distance is in km but time in minutes, convert the time to hours first (or use metres and seconds).

On a distance-time graph the gradient is the speed.

A car at 50 km/h: the gradient is the speed (150 km in 3 hours).

Speed $\dfrac{\text{distance}}{\text{time}}$

Worked example

A train travels 90 km in 45 minutes. Find its speed in km/h.

1
45 minutes = 0.75 hours.
2
Speed = 90 ÷ 0.75.

Worked example

Convert 20 m/s to km/h.

1
20 m/s = 20 × 3600 = 72 000 m/h.
2
72 000 ÷ 1000 = 72 km/h.

How long does a 60 km journey take at 40 km/h?

Density, mass and volume

Density is mass divided by volume, so you often need a volume first.

Density $=\dfrac{\text{mass}}{\text{volume}}$ , so mass = density × volume and volume = mass ÷ density.

Questions often combine density with the volume of a cuboid, cylinder or sphere. Find the volume first, then use density.

Density $\dfrac{\text{mass}}{\text{volume}}$

Worked example

A metal cube has side 2 cm and density 8 g/cm³. Find its mass.

1
Volume = 2³ = 8 cm³.
2
Mass = density × volume = 8 × 8.

A block has volume 20 cm³ and density 3 g/cm³. What is its mass?

Pressure and rates

Pressure is force divided by area; prices and pay rates are found the same way, then compared in the same unit.

Pressure $=\dfrac{\text{force}}{\text{area}}$ in N/m² (pascals), so force = pressure × area and area = force ÷ pressure.

Rates such as price per kg or pay per hour are total ÷ quantity. To compare deals, convert both to the same unit rate.

Pressure $\dfrac{\text{force}}{\text{area}}$

Worked example

5 kg of apples cost £4.50. Find the price per kg.

1
Unit price = £4.50 ÷ 5.

A force of 200 N acts on 0.5 m². What is the pressure?

Try an exam question

A car travels 90 km in 1 hour 15 minutes. Work out its average speed in km/h.

[3 marks]

That's the notes covered.

Carry on to the next subtopic.