## Formulae

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).

 Example 1 Example 2 is the formula for the area of a trapezium. If a = 5 cm, b = 7 cm and h = 10 cm A = 60 cm2 V = IR is a formula used in physics, where V = voltage, I = current and R = resistance. If I = 10 amps and R = 5 ohms V = 10 × 5 V = 50 volts

### Changing the Subject

The subject of a formula is the variable or letter that stands alone.

e.g.

 A is the subject 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 Example 2 To make b the subject of v2 = u2 − 2fs is a formula used in physics. To make u the subject

### Rearranging Rational Functions

Often rational expressions such as  have to be rearranged to make x the subject.

### Rearranging formulae with Squares and Square roots

To rearrange formulae involving squares the square root often needs taking.

To rearrange formulae involving square roots both sides of the formulae need squaring.

 Example involving square roots Example involving squares