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Using formulae


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We often use formulae without even noticing. For example, we might convert miles to km by multiplying by 1.6, or find the circumference of a circle by multiplying pi by the diameter.

km = 1.6 x miles is an example of a formula.

Using formulae

We have already seen that km = 1.6 x miles and C = π × d are examples of formulae. There are many others that we use regularly in other subjects. Sometimes we have to construct our own formula:



A taxi firm charges £0.50 per mile plus a fixed charge of £2.00. Write down a formula for the cost (C) of hiring this taxi to travel 'n' miles.


  • It costs £2 + £0.50 to travel 1 mile.
  • It costs £2 + 2 x £0.50 to travel 2 miles.
  • It costs £2 + 3 x £0.50 to travel 3 miles.

So travelling for 'n' miles will cost £2 + n x £0.50.

The formula is C = £2 + (n x £0.50).

Note: £0.50 = 50p.


A rectangle has a width of x and a length of 2x.

image: rectangle, top length: 2x, right length: x

Write down a formula for the perimeter (P) in terms of x.

toggle answer


P = 2x + x + 2x + x

Did you remember to include all 4 sides?

So P= 6x


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