What is a Compound Measure?
A compound measure is a quantity that's calculated by combining two or more different measurements together. Think of it like mixing two ingredients to create something new — the result tells you something meaningful that neither ingredient alone could tell you.
The key thing compound measures do is measure rates — they show you how much one quantity changes when another quantity increases by one unit. This is incredibly useful in real life:
- Speed tells you how far you travel in each hour (or second)
- Density tells you how heavy something is per cubic centimetre
- Pressure tells you how much force is pushing on each square metre
- Flow rate tells you how much liquid flows per minute
Without compound measures, these ideas would be much harder to understand or compare. If someone just told you "a car travelled 480 km", you wouldn't know if that was fast or slow. But if they say "the car travelled at 80 km/h", now you can picture it.
Why Units Matter for Compound Measures
Here's something important: the units of a compound measure tell you the formula. You don't need to memorise every formula if you understand how to read the units.
When you write a compound measure with a "/" or "per" in it, you're showing division:
- km/h means kilometres ÷ hours
- g/cm³ means grams ÷ cubic centimetres
- N/m² means Newtons ÷ square metres
So if you see a unit like kg/m³, you immediately know the formula must be: Mass ÷ Volume = Density. The units tell you what operation to perform and in which order.
Master Formula Triangles
A formula triangle is a visual tool that shows you all the relationships between the quantities in a compound measure formula. It's like a cheat sheet you can draw whenever you forget a rearranged formula.
How Formula Triangles Work
The rule is simple: cover up the quantity you want to find, and the remaining two tell you what operation to do.
- If your unknown is on the top of the triangle → multiply the two at the bottom
- If your unknown is on the bottom of the triangle → divide the top by the other bottom value
Let's see three examples:
Speed, Distance, Time
Distance = Speed × Time
Speed = Distance ÷ Time
Time = Distance ÷ Speed
Density, Mass, Volume
Mass = Density × Volume
Density = Mass ÷ Volume
Volume = Mass ÷ Density
Pressure, Force, Area
Force = Pressure × Area
Pressure = Force ÷ Area
Area = Force ÷ Pressure
Pro tip: Draw these triangles every time! They take 5 seconds and save you from rearranging algebra. Examiners expect to see them in your working.
Speed, Distance & Time
The Core Formula
Understanding Units
Speed is measured in metres per second (m/s) or kilometres per hour (km/h).
- m/s is used in physics problems, science experiments
- km/h is used in real life (car speeds, running speeds)