Formulae

Area_Formula.jpgA 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 rectangle
l = length of rectangle
w = width of rectangle
Cost of plumber
C = 55x + m +1.5k

C = total cost of plumber ($)
x = number of hours worked
m = cost of materials
k = kilometres travelled
Volume of a packing boxes
V = l w h

V = volume of box
l = length of box
w = width of box
h = height of box
Area of a circular design
A = π r2
 A = area of circle
r = radius of circle
π = 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 × 52 cm2

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 :

Y9_Formulae_01.gif

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