Proof — A-Level Mathematics Revision
Revise Proof for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Algebra & FunctionsWhat is Proof?
Proof in A-Level Mathematics involves using logical deduction to demonstrate the truth of a mathematical statement. This can include proof by deduction, proof by exhaustion, and disproof by counter-example, which are fundamental methods for establishing mathematical certainty.
Board notes: Proof by induction is a key component of the A-Level Further Maths specification for all major exam boards (AQA, Edexcel, OCR), but the fundamental methods of proof are covered in the standard A-Level Maths course.
Step-by-step explanationWorked example
Prove that the sum of two consecutive odd numbers is always a multiple of 4. Let the two consecutive odd numbers be 2n+1 and 2n+3. Their sum is (2n+1) + (2n+3) = 4n+4. This can be factorised as 4(n+1). Since n is an integer, n+1 is also an integer, and therefore 4(n+1) is a multiple of 4.
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Common mistakes
- 1Assuming what you are trying to prove. For example, when proving an identity, starting with the assumption that the two sides are already equal.
- 2Making a leap in logic without justification. Every step in a proof must be a clear consequence of the previous steps or a known mathematical fact.
- 3Using a single example to prove a general statement. A proof must hold for all possible cases, not just a specific one.
Proof exam questions
Exam-style questions for Proof with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Proof
Core concept
Proof in A-Level Mathematics involves using logical deduction to demonstrate the truth of a mathematical statement. This can include proof by deduction, proof by exhaustion, and disproof by counter-ex…
Frequently asked questions
What is the difference between proof by deduction and proof by exhaustion?
Proof by deduction uses a series of logical steps to arrive at a conclusion from a set of premises. Proof by exhaustion involves checking every possible case to show that a statement is true.
How do I disprove a statement?
To disprove a mathematical statement, you only need to find one single case where the statement is false. This is called a counter-example.