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GCSE/Mathematics/Edexcel

R11Compound units including speed, density, pressure

Notes

Compound units — speed, density, pressure

Compound units measure one quantity per another. Edexcel tests them on Paper 2 or 3 (calculator papers) at both tiers, with Higher candidates expected to handle unit conversions and rearrangements.

The three core formulas

  • Speed = distance ÷ time. Unit: m/s, km/h, mph.
  • Density = mass ÷ volume. Unit: g/cm³, kg/m³.
  • Pressure = force ÷ area. Unit: N/cm², N/m² (Pa).

The "formula triangle" is a useful memory tool but Edexcel mark schemes accept any correct algebraic rearrangement.

Rearranging

If S = D/T:

  • D = S × T.
  • T = D/S.

Same logic for ρ = M/V and P = F/A.

Unit conversion (the most-tested skill)

  • 1 m/s × 3.6 = 1 km/h. (Multiply by 3.6 for m/s → km/h.)
  • 1 km/h ÷ 3.6 = 1 m/s.
  • 1 g/cm³ = 1000 kg/m³.
  • 1 N/cm² = 10000 N/m² = 10000 Pa.

Worked exampleWorked example — speed change

A car travels at 72 km/h. Convert to m/s.

72 km/h × (1000 m / 1 km) × (1 h / 3600 s) = 72 × 1000/3600 = 20 m/s.

Worked exampleWorked example — density

A metal cube has side 5 cm and mass 750 g. Find its density.

V = 5³ = 125 cm³. ρ = 750 / 125 = 6 g/cm³.

Worked exampleWorked example — pressure

A force of 200 N acts on an area of 0.25 m². Find pressure.

P = 200 / 0.25 = 800 N/m² = 800 Pa.

Edexcel paper alignment

  • Paper 2F/3F (Foundation): plug-in formula questions, single conversion.
  • Paper 2H/3H (Higher): multi-step problems mixing two formulas (e.g. "speed → time → distance" inside a density question).

Common Edexcel exam tip

State the formula explicitly before substituting M1. Then state the units of the final answer, including any conversion. Forgetting units loses A1 even with the right number.

Common mistakesCommon errors

  • Mixing units (km with seconds, g with m³).
  • Inverting the formula (writing S = T/D instead of D/T).
  • Using volume = side instead of side³ when computing a cube's density.

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Practice questions

Try each before peeking at the worked solution.

  1. Question 15 marks

    Average speed — Foundation

    Edexcel Paper 2F (calculator)

    A coach travels 240 km in 3 hours 20 minutes.

    (a) Express 3 hours 20 minutes as hours in decimal form. (1 mark)
    (b) Calculate the average speed in km/h. (2 marks)
    (c) Convert this speed to m/s. (2 marks)

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    AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

  2. Question 25 marks

    Density of a metal block

    Edexcel Paper 2H — Higher

    A block of metal has dimensions 8 cm × 5 cm × 4 cm and mass 1280 g.

    (a) Find its volume. (1 mark)
    (b) Find its density in g/cm³. (2 marks)
    (c) Convert this density to kg/m³. (2 marks)

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  3. Question 37 marks

    Pressure with conversion — Higher

    Edexcel Paper 3H — Higher

    A force of 600 N acts on a square of side 20 cm.

    (a) Find the area in m². (2 marks)
    (b) Calculate the pressure in N/m². (2 marks)
    (c) The force doubles and the side length halves. Find the new pressure. (3 marks)

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Flashcards

R11 — Compound units including speed, density, pressure

7-card SR deck for Edexcel GCSE Mathematics (1MA1) — Leaves Batch 3 topic R11

7 cards · spaced repetition (SM-2)