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

The Eduqas ratio content asks you to calculate with compound measures, the quantities built from two others, chiefly speed (distance and time), density (mass and volume) and pressure (force and area). You must use each defining formula, rearrange it to find any of the three quantities, and convert between units such as metres per second and kilometres per hour. Compound measures combine arithmetic with careful unit handling, and Eduqas tests them on the calculator Component 2 with real contexts, making unit conversion the most marks-sensitive skill.

Speed, distance and time

Speed is the rate at which distance is covered, found by dividing distance by time.

The most common error is the time conversion. To find speed in km/h, convert the time to hours as a decimal: $1$ hour $45$ minutes is $1\tfrac{45}{60} = 1.75$ hours, not $1.45$. So a journey of $84$ km in $1$ hour $45$ minutes is $\dfrac{84}{1.75} = 48$ km/h.

Density, mass and volume

Density measures how much mass is packed into a given volume.

So a piece of wood with mass $300$ g and volume $400$ cm cubed has density $\dfrac{300}{400} = 0.75$ g/cm cubed. Because density is constant for a material, you can find the mass of any volume of the same substance by multiplying: $0.75 \times 200 = 150$ g for a $200$ cm cubed piece.

Pressure, force and area

Pressure is force spread over an area.

A force of $200$ N on an area of $4$ m squared gives a pressure of $\dfrac{200}{4} = 50$ N/m squared. The same force on a smaller area gives a higher pressure, which is why a sharp blade (small area) cuts more easily than a blunt one.

Converting compound units

Converting between compound units is where careful method pays off.

To convert the other way, from km/h to m/s, divide by $3.6$. The shortcut ($\times 3.6$ or $\div 3.6$) is worth memorising because speed conversions appear often.

The formula triangle

A formula triangle is a quick aid for rearranging. For speed, write distance on top with speed and time below it: covering the quantity you want reveals the calculation, so covering distance leaves speed times time, covering speed leaves distance over time, and covering time leaves distance over speed. The same triangle pattern works for density (mass over density and volume) and pressure (force over pressure and area). The triangle is only a memory aid for a rearrangement you could also do by algebra, but it reliably prevents the upside-down error of dividing when you should multiply.

Why compound measures matter

Compound measures connect mathematics to the physical world, which is why they appear so often in context on Component 2. Speed underlies every journey problem and feeds the speed-time graphs in the growth and rates work; density explains why materials feel heavy or light for their size; pressure explains everything from why snowshoes work to how hydraulic systems lift loads. Because the arithmetic is straightforward but the units are not, Eduqas uses these questions to reward careful, methodical working, so always write the formula, substitute with units, and convert deliberately rather than rushing to a number.