Using and rearranging formulae
Word formulae, substitution and changing the subject
A formula is a rule that links quantities, like the cost of a taxi or the area of a rectangle.
Formulae in action
- Word formula: Cost = £3 + £1.50 per mile. In symbols: C = 3 + 1.5m.
- Substitute the values you know to find the one you don’t.
- Change the subject: rearrange to get a different letter on its own, using inverse operations, just like solving equations.
Example: v = u + at. Make t the subject: v − u = at, so t = (v − u)/a.
Worked examples
Example 1. A plumber charges £40 call-out plus £30 per hour: C = 40 + 30h. Find C when h = 3.
Example 2. Use P = 2l + 2w to find P when l = 9 and w = 4.
Example 3. Make x the subject of y = 3x − 6.
Example 4. Convert 20 °C to °F using F = 1.8C + 32.
Top tips and common mistakes
- Write down the formula, then substitute, then work it out: show every step.
- Units matter: if speed is in km/h, time must be in hours.
- When changing the subject, do the same thing to both sides.
We used a formula to work out cooking times for our roast. It really works!
Practise
Answer as many as you like. Every question is new, and you get a “correct” tick for each one you get right first time. Use “Show answer” to see a worked solution.
Quiz: earn your stamp
Printable worksheet
Using and rearranging formulae worksheet. The questions come first and the answers for grown-ups are on the last page, so you can print just the question pages.
Printing is optional. A4 size.