GCSE Maths: Speed, Density and Pressure

Speed, density and pressure are the three compound measures named in the GCSE Mathematics specification, and they share one underlying idea: a quantity defined as one measure divided by another. This quiz practises all three, with the unit conversions that make these questions genuinely testing.

The speed questions cover the full range of formats: a cyclist's average speed when the time is given in minutes (so 45 minutes must become 0.75 hours before dividing), distance from speed and time with a seconds-to-minutes conversion, and the two conversion directions between m/s and km/h — a train's 180 km in 2 hours expressed in metres per second, and a runner's 8 m/s converted to 28.8 km/h. These conversions are exactly where exam marks are won and lost, and the explanations show the factor-of-3.6 reasoning explicitly.

Density questions work in both directions: computing density from mass and volume, and recovering mass from density and volume for a liquid and for water at 1 kg per litre. A reasoning question checks the conceptual layer — what happens to density if the volume doubles at fixed mass. Pressure follows the same pattern with force and area, including a conceptual question about which changes increase pressure.

In line with the real 2025–2027 exams — where a formulae sheet is provided and memorising formulae is explicitly not required — the questions test application and unit discipline rather than formula recall: choosing the right relationship, substituting correctly, and keeping units consistent through multi-step problems. A units question closes the set, checking that kg/m³ and m/s are attached to the right measures. Each answer includes a full worked explanation with the conversion steps spelled out.

• Calculate average speed, distance and time with correct unit handling
• Convert between m/s and km/h in both directions
• Use the density–mass–volume relationship in both directions
• Solve pressure problems from force and area, and reason about what increases pressure
• Keep units consistent through multi-step compound measure problems

Topic scope follows the Ratio, proportion and rates of change strand of the Department for Education's GCSE mathematics subject content: using compound units such as speed, density and pressure. Reflects the 2025–2027 assessment arrangement in which a formulae sheet is provided, so questions test application rather than formula recall.