Algebraic Proofs

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.
   • Show Video

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

• Show Video

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.