R3Ratio & ProportionFoundation & Higher

Compound Measures

Compound measures combine two units, like speed (distance per time) or density (mass per volume). A formula triangle is a handy way to rearrange them quickly.

40 min Video by Maths Genie AQA GCSE Maths

Speed and DensityWatch the walkthrough, then read the notes below.

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What you'll learn

Use the speed–distance–time formula
Use the density–mass–volume formula
Use pressure–force–area
Rearrange with a formula triangle

Speed, distance, time

Speed is distance divided by time. Cover the quantity you want in the triangle (D over S × T) to see how to rearrange it.

speed = \frac{distance}{time}

D = S × T, T = D ÷ S.

1Speed

= \frac{150}{2}

= 75

km/h.

Answer75 km/h

Density and pressure

Density is mass divided by volume; pressure is force divided by area. They work exactly the same way as speed — just different units. Always check your units match.

density = \frac{mass}{volume}, pressure = \frac{force}{area}

Same triangle idea.

Tip — Make sure the units agree (e.g. convert minutes to hours) before substituting.

Remember these

S = \frac{D}{T}

Speed.

D = \frac{M}{V}

Density.

P = \frac{F}{A}

Pressure.

Watch out for these

Mixing units (e.g. distance in km but time in minutes).

Convert so the units match before calculating.

Dividing the wrong way round.

Use the formula triangle to see what divides by what.

Key takeaways

Speed = distance ÷ time.
Density = mass ÷ volume; pressure = force ÷ area.
Use a formula triangle and check units match.

Test yourself

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