A formula is a general rule or relation, written as an algebraic equation. There are all types of formulae for calculating various quantities in many subject areas.
Substitution
Substitution involves putting given values into a formula in place of the variables (written as letters).
e.g.
is the formula for the area of a trapezium.
If a = 5 cm, b = 7 cm and h = 10 cm
A = 60 cm2
Changing the Subject
The subject of a formula is the variable or letter that stands alone.
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e.g. |
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A is the subject |
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x + y + z = V |
V is the subject |
To make a different variable the subject of a formula, the usual algebraic techniques can be used.
Example 1
To make b the subject of
Example 2
To make x the subject of A = x2
Take the square root of both sides
x = ±√A
Checking your answers
When you have solved an equation, you can always check your answers by substituting the values back into the equation.
(a) Solve x2 − 4x − 5 = 0
Factorise to (x − 5)(x + 1) = 0
Either: x − 5 = 0 or x + 1 = 0
x = 5 or x = -1
To check:
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x2 − 4x − 5 = 0 52 − 4.5 − 5 = 0 25 − 20 − 5 = 0 0 = 0 (This shows the solution x = 5 is correct.) |
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x2 − 4x − 5 = 0 (-1)2 − 4.(-1) − 5 = 0 1 + 4 − 5 = 0 0 = 0 (This shows the solution x = -1 is correct.) |
