## Formulae formula is a rule or equation used to calculate the value of a quantity.

The plural of formula is formulae or formulas.

There are all types of formulae for calculating various quantities in many areas of life.

### Examples of Formulae

 Quantity being found Formula Variables Perimeter of a rectangle P = 2l + 2w P = perimeter of rectanglel = length of rectanglew = width of rectangle Cost of plumber C = 55x + m +1.5k C = total cost of plumber (\$)x = number of hours workedm = cost of materialsk = kilometres travelled Volume of a packing boxes V = l w h V = volume of boxl = length of boxw = width of boxh = height of box Area of a circular design A = π r2 A = area of circler = radius of circleπ = pi ( 3.14 to 3 sig.fig.)

### Substitution into a Formula

To find the value of a quantity in a formula we put given values into a formula in place of the variables (written as letters).

e.g. Find the area of a 5 m discus circle at an athletics track

A = π r2 is the formula for finding the area of a circle

If      r = 5 m and π = 3.14

A = 3.14 × 5cm2

A = 78.5 cm2

### Constructing a Formula

Sometimes formulae have to be constructed from information given.

e.g. Construct a formula for the perimeter and the area of the rectangle below : Perimeter formula

P = 2x + 4y + 2x + 4y

P = 4x + 8y

P = 4(x + 2y)

Area formula

A = 2x . 4y

A = 8xy

The perimeter and area can now be found if values of x and y are given.

### Sequences and Formulae

In mathematics, numbers are often arranged in a sequence. These sequences can be shown be a formula or function.

Often a sequence follows a rule or pattern.

Easy Sequence
Some sequences are obvious: 1, 3, 5, 7, 9...
This is the sequence of ODD numbers.

The formula for this sequence is 2n − 1 where n stands for a counting number.

To find the next number in this sequence, calculate 2 × 6 − 1 = 11

Harder Sequence
The sequence 1, 8, 27, 64, ... is the sequence of cube numbers.
Comparing this sequence to the set of counting numbers {1, 2, 3, 4...}
 1 2 3 4 ... 1 8 27 64 ...
The formula for this sequence is n3.
The next number in this sequence is 53 = 125