Using Formulae

Using Formulae

GCSE(F)

A formula is a rule, that allows the calculation of an answer when other information is known: for example, the area of a rectangle can be calculated when the length and width is known. The formula is shown with letters, numbers and arithmetical operators (signs).

The formula for the area of a triangle is:

A = `frac(1)(2)`bh, where:

A is the area, b is the base and h is the height.

If the base is 15cm and the height is 26cm: replacing (or substituting) b with 15 and h with 26:

A = `frac(1)(2)`bh

A = `frac(1)(2)` x 15 x 26

A = 195 cm2

Check carefully the units involved: if there are different units (e.g. metres, centimetres) involved, make them all the same. Do not, for example, use a mix of centimetres and metres in a formula.

Examples

1. Emma is fund-raising and will be completing a long walk. One of her friends is going to give her £2, and 30p for each kilometre that she completes. Write a formula for the contribution, £C, that will be denoted for each kilometre, k, that she completes.

Answer: C = 2 + 0.3k

There will be a fixed contribution of £2. On top of that, there is £0.30 for each kilometre, remembering to change the 30p to pounds.

2. Emma completes a walk of 12 kilometres. How much did her friend contribute, according to the formula, above?

Answer: £5.60

C = 2 + 0.3k

C = 2 + 0.3 x 12

C = 5.6. Remember to show the amount with two pence digits.