Identities (Edexcel GCSE Maths): Flashcards

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Identities
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Definition of an identity

A mathematical statement that is always true for all variable values

Symbol used to represent an identity

\equiv (not ==)

Key difference: identity vs equation

Identity is true for all values; equation only for specific values

Golden rule when proving an identity

Manipulate each side separately; don't use balance method

Which side to start with when proving an identity

The more complex side (usually the left-hand side)

Algebraic representation of an even number

2n2n

Algebraic representation of an odd number

2n+12n + 1 or 2n12n - 1

Algebraic representation of a multiple of 3

3n3n

Algebraic representation of consecutive numbers

nn, n+1n + 1, n+2n + 2, ...

Algebraic representation of consecutive even numbers

2n2n, 2n+22n + 2, 2n+42n + 4, ...

Algebraic representation of consecutive odd numbers

2n+12n + 1, 2n+32n + 3, 2n+52n + 5, ...

Is 3n3n always a multiple of 3? (where nn is an integer)

Yes, always

Key exam tip when proving identities

Always show every line of your working step by step

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