# Algebraic Proofs

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Examples, solutions, videos, games, activities and worksheets that are suitable for GCSE Maths to help students learn how to proof algebraically.

GCSE Maths - Algebraic Proof Basics (Not Induction) Algebra Higher A star Edexcel
Examples:

1. Proof that the sum of any three consecutive integers is always a multiple of 3.
2. Prove that, if the difference of two numbers is 4, then the difference of their squares is a multiple of 8.
3. Prove that (3n + 1)2 - (3n - 1)2 is amultiple of 6 for all positive integer values of n.
4. Prove that (n + 1)2 - (n - 1)2 + 4 is always even for all positive integer values of n.
5. Prove that (n + 1)2 - (n - 1)2 + 1 is always odd for all positive integer values of n.
6. Prove algebraically that the sum of the squares of any two consecutive numbers always leaves a remainder of 1 when divided by 4.
7. Prove algebraically that the difference between the squares of any two consecutive numbers is always a multiple of 4.
8. Prove algebraically that the sum of the squares of any three consecutive even numbers is always a multiple of 4.
9. Prove algebraically that the difference between the squares of any two consecutive odd numbers is always a multiple of 8.

GCSE Tutorial Basic Algebraic Proof Higher maths Algebraic Fractions Examples:

1. Prove that half of the sum of any four consecutive integers is odd.
2. Prove that the sum of any three consecutive integers is always a multiple of 3.
3. Prove that, is the difference of two numbers is 4, then the difference of their squares is a multiple of 8.

How to do Algebraic Proof GCSE Maths revision Higher level exam questions (include Algebraic fractions) Examples:

• Prove that the product of two odd numbers is always an odd number.
• Given that n is an integer, prove that (n +3)(2n + 1) + (n - 2)(2n + 1) is not a multiple of 2.

Edexcel GCSE Paper 1 February 2013 - Q21 Algebraic Proof

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