Algebraic Proof (Edexcel IGCSE Maths A)

Algebraic proof is the process of showing something is true in every possible case, using algebra.

True.

Typical algebra skills for algebraic proof include expanding brackets and collecting like terms.

An integer is a whole number.

Consecutive means 'following one after the other in order'.

For example:

• 3, 4 and 5 are consecutive integers

• 3, 5 and 7 are consecutive odd integers

• 2, 4 and 6 are consecutive even integers

In algebraic proof, is the integer immediately after . I.e., and are consecutive integers.

In algebraic proofs, can be used to represent 'any even integer'.

( here is assumed to be an integer.)

In algebraic proofs, can be used to represent 'any odd integer'.

Note that can also be used in this way.

( here is assumed to be an integer.)

An equation is only true for certain values of the variable(s) in it, while an identity is true for all values.

True.

To prove something is even, show that the algebraic result can be written as where is an integer.

(To prove that something is odd, prove that it is one more or one less than an even number.)

To prove a result about odd and even numbers means to show it is true in every possible case, using algebra.