A-Level Mathematics Revision — Proof
Revise Proof for A-Level Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
At a glance
- What StudyVector is
- An exam-practice platform with board-aligned questions, explanations, and adaptive next steps.
- This topic
- Proof in A-Level Mathematics: explanation, examples, and practice links on this page.
- Who it’s for
- Students revising A-Level Mathematics for UK exams.
- Exam boards
- Check your course page and the topic board notes for supported specifications.
- Free plan
- Sign up free to use tutor paths and feedback on your answers. Free access is Free daily revision · No card required. Pricing
- What makes it different
- Syllabus-shaped practice and progress tracking—not generic AI answers.
This page includes a topic explanation and a worked example. Check your course for current practice coverage.
Next in this topic area
Next step: Algebra & Functions
Continue in the same course — structured practice and explanations on StudyVector.
Go to Algebra & FunctionsTopic explanation
What 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 examples
Worked 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.
Practise this topic
Start with low-focus cards for Proof, then move into full exam-style practice when you want the heavier session.
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
Check the available question sets for Proof. Use your course and exam board to confirm which practice is relevant.
Proof exam questionsGet help with Proof
Get a personalised explanation for Proof from the StudyVector tutor. Ask follow-up questions and work through problems with step-by-step support.
Open tutorSave your progress in Proof
Start a free account for low-focus question cards, feedback and Play routes across available topics. Free daily limits apply; no card required.
Continue your revision
A public question for Proof is still being reviewed. Your course page shows the topics currently available for practice.
Continue with Proof
Create a free account to keep your course choice and save your practice progress.
Start free low-focus cardsAlready have an account? Log in
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.