Use compound measures including speed, density and pressure; rearrange the defining formulae; and convert between units such as m/s and km/h.

What this dot point is asking

OCR references R1 and R11 cover compound measures: quantities built from two others, such as speed (distance per time), density (mass per volume) and pressure (force per area). You must use and rearrange the defining formulae and convert between compound units like m/s and km/h. Compound measures connect ratio to science and to real-life contexts, and they appear on every tier, frequently on the calculator paper, often as multi-step problems that reward AO3.

Speed, distance and time

Speed is the most common compound measure.

The unit of time matters: for km/h, the time must be in hours. A journey of $90$ km in $1$ hour $30$ minutes uses $1.5$ hours, giving $\dfrac{90}{1.5} = 60$ km/h. "Average speed" assumes constant speed over the whole journey, so total distance over total time, even if the actual speed varied. Distance-time graphs link to this directly, where the gradient is the speed.

Density and pressure

Density and pressure follow the same pattern.

So a block of mass $480$ g and volume $60$ cm$^3$ has density $\dfrac{480}{60} = 8$ g/cm$^3$, and a force of $200$ N on an area of $0.5$ m$^2$ gives a pressure of $\dfrac{200}{0.5} = 400$ N/m$^2$. A common link is that the same material has the same density, so finding one block's density lets you find another block's mass or volume.

Pressure questions often involve a shape resting on a surface, where the area is the area of contact. A heavier object spread over a larger area can exert less pressure than a lighter object on a small point, which is why a drawing pin pierces easily (tiny area, high pressure) while a person on snowshoes does not sink (large area, low pressure). Reading the question to identify which quantity is force and which is area, then choosing the right rearrangement of $P = \tfrac{F}{A}$, is the key step that OCR rewards with method marks.

Converting compound units

Converting between m/s and km/h is a classic Higher skill.

The same care applies to density (g/cm$^3$ to kg/m$^3$ multiplies by $1000$) and to areas and volumes, where the conversion factor is squared or cubed. Always write the units alongside the number, because a compound measure without its units is incomplete.

Why compound measures matter

Compound measures are where mathematics meets physics and everyday life: speed limits, fuel economy, material density, tyre pressure. OCR rewards correct units and clear rearrangement, and the formula-triangle approach makes the algebra reliable under exam pressure. Because the questions are usually multi-step (find one quantity, then use it), method marks are available throughout even if the final figure slips.