This introduction covers Proving It's ALWAYS True within Proof for GCSE Mathematics. Revise Proof in Algebra for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 1 of 4 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.
Proving It's ALWAYS True
"The sum of two consecutive numbers is always odd." Is this true? You could try 5 + 6 = 11 ✓, or 100 + 101 = 201 ✓. But that doesn't PROVE it's always true. With algebra, n + (n+1) = 2n + 1, which is always odd!
Practice questions for Proof
Which expression represents an even number for all integer values of n?
Prove by exhaustion that when you divide any single-digit positive integer by 4, the remainder is always 0, 1, 2, or 3. Show your working by testing all possible cases.
Quick recall flashcards
What is a counter-example in mathematics?
A single specific example that shows a statement is NOT always true.
One counter-example is enough to disprove a conjecture.
What are the three steps in an algebraic proof?
1. State what your letters represent (e.g. let n be any integer)
2. Manipulate algebraically (expand, simplify, factorise)
3. Show the result matches the required form with a clear conclusion