GCSE Proofs
In these lessons, we will learn various mathematical proofs, suitable for GCSE Maths students.
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More GCSE Maths
Algebraic Proof
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.
Algebraic Proof
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.
Proof using Algebra
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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Penguin Solitaire
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