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.
Related practice
Practise this topic
Exam-style questions with instant Study Coach feedback.
Flashcards
Quick-fire recall to lock in the key facts.
Worksheets
Printable practice you can work through offline.
Past papers
Full papers with examiner-grade marking.
Study Coach
Ask for a step-by-step explanation any time.
All Mathematics
Every Mathematics topic across every exam board.
Related topics
Key terms explained
Short, exam-ready definitions with a formula, a worked example and an examiner tip.
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.
Create a free account to practise compound measures (speed, density, pressure) with Study Coach feedback
Try 5 questions now, get instant examiner-grade marking and ask the Study Coach to explain anything. Free during our early launch period — no credit card required.
Related on MathsGradeUp
Keep studying
- Mathematics courses & specifications
Every board and level we cover for mathematics.
- Formula sheets
Every GCSE, IGCSE and A Level formula, searchable and explained.
- Maths & science glossary
Plain-English definitions with a formula, worked example and examiner tip.
- Free maths calculators & solvers
Step-by-step solvers for the calculations that come up in every paper.
- Past paper guides
Paper structure, timings and topic weightings board by board.
- Grade boundaries
Historic boundaries and what each grade typically needs.
- Browse subjects
Specification-mapped courses for every board and level.
Practise it
- Predicted papers
GCSE and A Level predicted papers with full mark schemes.
- Question bank
Filter thousands of exam-board questions by topic and difficulty.
- Past papers workspace
Write on real papers and get every line marked.