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Algebraic proof uses algebra to show a statement is always true, for example expressing consecutive or even numbers as 2n and 2n+1 to prove results about their sums or products. It's a core topic in GCSE and iGCSE Maths with Edexcel and the other major boards. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Write the numbers algebraically first: 2n for an even number, 2n plus 1 for odd, and consecutive integers as n, n plus 1 and so on. Expand and simplify, then rearrange into a form that makes the required property obvious.
Before you start
Start once you are confident with algebraic notation and expanding brackets. From here the path runs to higher-tier reasoning questions.
What you learn
To prove a statement is always true, we use algebra rather than examples. We represent numbers with letters — 2n for an even number, 2n + 1 for an odd one, n and n + 1 for consecutive integers — then expand and simplify to reach the result. Many proofs come down to expanding brackets and simplifying. To show an expression is a multiple of a number, factorise it so that number appears outside a bracket. The course works through representing numbers, proof by expanding and proving multiples. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Algebraic Proof is a Algebra topic in the GCSE syllabus, covered here at Higher tier. The course is built from 3 concept sections, 2 worked examples and 3 check points before the exam-style set. It sits alongside Completing the Square, Differentiation, Expanding Brackets and Factorising in the same strand. The Algebra revision engine gives you as many extra questions as you want, tracked on your skill tree.
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