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GCSE Maths / Edexcel

Speed, density and pressure

Choose and rearrange the correct compound-measure formula, use consistent units, and show method clearly.

Ratio, Proportion and RatesFoundation and HigherGrades 4 to 6Skill

Curriculum path: GCSE Maths > Edexcel > Ratio, Proportion and Rates > Speed, density and pressure

Pearson Edexcel GCSE Maths ratio R11: use compound measures such as speed, density and pressure.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

A compound measure combines two units, such as miles per hour, grams per cm^3 or newtons per m^2.

Speed = distance / time. The units depend on the units of distance and time.

Density = mass / volume. If mass is in grams and volume is in cm^3, density is g/cm^3.

Pressure = force / area. If force is in newtons and area is in m^2, pressure is N/m^2.

Before calculating, check whether units need converting. Many Edexcel marks are lost through mixed units, not the formula itself.

Key ruleSpeed = distance / time, density = mass / volume, pressure = force / area.

Worked examples

Speed

A car travels 150 miles in 3 hours. Find its speed.

  1. Speed = distance / time.
  2. 150 / 3 = 50.

Answer: 50 mph

Density

A block has mass 240 g and volume 80 cm^3. Find its density.

  1. Density = mass / volume.
  2. 240 / 80 = 3.

Answer: 3 g/cm^3

Pressure

A force of 300 N acts on an area of 6 m^2. Find the pressure.

  1. Pressure = force / area.
  2. 300 / 6 = 50.

Answer: 50 N/m^2

Common mistakes

  • Using the formula upside down.
  • Mixing minutes with hours or metres with kilometres without converting.
  • Leaving out compound units in the final answer.
  • Rounding too early in multi-step compound-measure questions.

Quick exercise

Try these before moving to the exam-style questions.

  1. Find the speed for 120 km in 2 hours.
  2. Find the time for 150 miles at 50 mph.
  3. Find density when mass is 500 g and volume is 250 cm^3.
  4. Find mass when density is 4 g/cm^3 and volume is 20 cm^3.
  5. Find pressure when force is 180 N and area is 9 m^2.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationCalculator2 marks

A cyclist travels 36 km in 2 hours. Work out the cyclist's average speed.

speedcompound measuresfoundation ratio
Standard exam styleFoundation and HigherCalculator3 marks

A metal cube has mass 540 g and volume 200 cm^3. Work out its density.

densitymassvolumeunits
ChallengeFoundation and HigherCalculator5 marks

A train travels 84 km in 1 hour 24 minutes. Work out its average speed in km/h.

speedtime conversioncompound measuresexam reasoning