In these lessons, we will learn various mathematical proofs, suitable for GCSE Maths students.

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More GCSE Maths

How to attempt typical GCSE Algebraic Proof questions?

Examples:

- Prove (x + 10)
^{2}- (x + 2)^{2}is divisible by 16, where x is a positive integer. - Prove the sum of three consecutive even integers is divisible by 6.
- Prove that the product of two odd numbers is always odd.
- Prove that when two consecutive integers are squared, that the difference is equal to the sum of the two consecutive integers.

GCSE Maths revision tutorial video.

Examples:

- Prove algebraically that the sum of two consecutive odd numbers is always a multiple of 4.
- Prove algebraically that the product of two even numbers is always a multiple of 4.

Examples:

- Prove that (5n + 1)
^{2}- (5n - 1)^{2}is a multiple of 5, for all positive integer values of n. - Prove that (n + 2)
^{2}- (n - 12)^{2}is even, for all positive integer values of n. - Prove that the sum of any two consecutive odd numbers is always even.
- Prove that the sum of the squares of any two consecutive numbers is always an odd number.

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