Algebraic proof
- Represent numbers algebraically.
- Manipulate the expression.
- Conclude using factors or definitions.
Answer: Odd + odd = (2a+1)+(2b+1)=2(a+b+1)
𝑥 Algebra
Algebraic proof
Learn algebraic proof with a GCSE-style explanation, help guide, worked example, practice question and flashcards.
Global XP
Level 10 / 100 XP
1. Explanation
Key idea
- Algebraic proof is part of advanced topics and appears often in KS3–GCSE maths.
- Algebraic proof uses letters to show something is always true.
- Use the worked model, help guide, interactive question and flashcards to practise algebraic proof until the steps feel automatic.
Real-life examples
- Shopping, sport, travel, science, design and everyday decisions all use this skill.
2. Visual
Algebraic proof learning map
Understand the key idea → follow the help guide → practise a question → check your method → build speed with flashcards.
3. Help guide
How to tackle Algebraic proof
- Learn the rule: Algebraic proof uses letters to show something is always true.
- Worked model: Represent numbers algebraically. Manipulate the expression. Conclude using factors or definitions.
- Try the interactive question without looking at the answer first.
- Use the flashcards to test the rule, the method and a common check.
4. Worked examples
Step-by-step working
5. Interactive questions
Try it yourself
Show the sum of two even numbers is even: write 2a + 2b as a factorised expression.
6. Flashcards
Master quick recall
Flip each card, then choose whether you know it or need more practice.
0 mastered
FrontRule for Algebraic proof
BackAlgebraic proof uses letters to show something is always true.
FrontExample answer: Show the sum of two even numbers is even: write 2a + 2b as a factorised expression.
Back2a + 2b = 2(a + b), which is a multiple of 2, so it is even.
FrontCommon check for Algebraic proof
BackCheck units/notation, compare with an estimate, and make sure the answer matches the question.
7. Finish
Complete this topic
When you have read the examples, tried the question and reviewed flashcards, claim your topic completion XP.