Proof questions are often the most feared part of A-Level Mathematics, but with the right approach, they become much more manageable.
Understanding Proof by Deduction
Deductive proof starts from known facts and uses logical steps to reach a conclusion. Each step must follow logically from the previous one.
Proof by Exhaustion
Sometimes the best approach is to consider all possible cases. This works well when there are a limited number of scenarios to check.
Proof by Contradiction
Assume the opposite of what you want to prove, then show this leads to a contradiction. This technique is particularly useful for proving statements about irrational numbers.
Common Structures to Recognise
- Proving divisibility often involves factoring expressions
- Proving inequalities may require completing the square
- Proving identities usually involves manipulating one side to match the other
Tips for Success
- Read the question carefully and identify what type of proof is required
- Write out what you know and what you need to prove
- Be explicit about each logical step
- Practice regularly with past paper questions
Remember, proof questions reward clear, logical thinking. Take your time and show all your working.
