A formula is a mathematical relationship or rule expressed using symbols.
It shows how one quantity depends on others.
Examples of Common Formulae
|
Quantity |
Formula |
Description |
|
Area of rectangle |
( A = l \times b ) |
A = Area, l = length, b = breadth |
|
Perimeter of rectangle |
( P = 2(l + b) ) | |
|
Area of triangle |
( A = \frac{1}{2}bh ) |
b = base, h = height |
|
Volume of cuboid |
( V = l \times b \times h ) | |
|
Simple Interest |
( I = \frac{P \times R \times T}{100} ) |
P = Principal, R = Rate, T = Time |
|
Speed |
( v = \frac{d}{t} ) |
v = speed, d = distance, t = time |
- Substitution into Formulae
To substitute means to replace letters with the given numbers and then simplify.
Example 1:
If ( A = l \times b ), find A when l = 8 cm and b = 6 cm.
Solution:
( A = 8 \times 6 = 48 \text{ cm}^2 )
Example 2:
Find ( V ) if ( V = l \times b \times h ), and ( l = 10, b = 5, h = 4 ).
Solution:
( V = 10 \times 5 \times 4 = 200 )
- Evaluating Formulae
This means finding the numerical value of an expression after substitution.
Example 3:
Evaluate ( y = 2x + 5 ) when ( x = 7 ).
Solution:
( y = 2(7) + 5 = 19 )
Example 4:
If ( P = 2(l + b) ), find P when ( l = 9, b = 6 ).
Solution:
( P = 2(9 + 6) = 30 )
- Changing the Subject of a Formula
This means rearranging a formula to make another variable the subject.
Example 5:
Given ( v = \frac{d}{t} ), make t the subject.
Multiply both sides by t: ( vt = d ).
Divide both sides by v:
t = \frac{d}{v}
Example 6:
Given ( A = \frac{1}{2}bh ), make h the subject.
Multiply both sides by 2: ( 2A = bh ).
Divide both sides by b:
h = \frac{2A}{b}