GCSE Maths Compound Measures (Speed, Density, Pressure) Notes
Compound measures combine two units, such as speed (distance and time). Each has a triangle formula linking the three quantities.
Key concepts
- Speed
- Distance travelled per unit time, e.g. metres per second (m/s) or kilometres per hour (km/h).
- Density
- Mass per unit volume, e.g. grams per cubic centimetre (g/cm³).
- Pressure
- Force per unit area, e.g. newtons per square metre (N/m²).
- Formula triangles
- Cover the quantity you want to find to see whether to multiply or divide.
Key formulas
Speed
speed = distance ÷ time
Density
density = mass ÷ volume
Pressure
pressure = force ÷ area
Worked example
A car travels 150 km in 2 hours. Find its average speed.
- 1Use speed = distance ÷ time.
- 2Substitute: speed = 150 ÷ 2.
- 3Work it out: 75.
- 4Include the units: km/h.
Answer: 75 km/h
Common mistakes
✗ Mixing units, e.g. minutes with km/h.
✓ Convert time to hours (or distance to matching units) before dividing.
✗ Forgetting units in the final answer.
✓ Always state the compound unit, e.g. m/s or g/cm³.
✗ Dividing the wrong way round.
✓ Use the formula triangle to check whether to multiply or divide.
Quick check
Try these, then reveal the answers.
Speed for 60 m in 12 s?Reveal answer
5 m/s
Density of 30 g in 6 cm³?Reveal answer
5 g/cm³
Distance for 40 km/h over 3 hours?Reveal answer
120 km
Exam tips
- Write the formula first, then substitute — it secures a method mark.
- Check units match before calculating; convert if they do not.
- For average speed, use total distance divided by total time.
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Frequently asked questions
What is a compound measure?+
A measure made from two other units, such as speed (distance per time) or density (mass per volume).
How do I convert m/s to km/h?+
Multiply by 3.6 — there are 3600 seconds in an hour and 1000 metres in a kilometre.
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