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 example— Worked 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 example— Worked 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 example— Worked 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 mistakes— Common 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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