This study notes covers Worked Example 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 3 of 4 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 3 of 4
Practice
14 questions
Recall
12 flashcards
Worked Example
Prove that the sum of any two odd numbers is always even.
Solution
Let the two odd numbers be (2a + 1) and (2b + 1)
Sum = (2a + 1) + (2b + 1)
= 2a + 2b + 2
= 2(a + b + 1)
This is 2 × (integer), so it is always even.
Keep building this topic
Read this section alongside the surrounding pages in Proof. That gives you the full topic sequence instead of a single isolated revision point.
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
14 questions on Proof — practise free
Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.
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