A-Level Mathematics Revision — Proof
Revise Proof for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP.
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
- Practice is aligned to major specifications (AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP).
- Free plan
- Sign up free to use tutor paths and feedback on your answers. Free access is 7 days uncapped, then 45 min revision/day. Pricing
- What makes it different
- Syllabus-shaped practice and progress tracking—not generic AI answers.
Topic has curated content entry with explanation, mistakes, and worked example. [auto-gate:promote; score=70.6]
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 1: Core method
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.
Worked example 2: Exam variation
Now change one detail in the question and keep the same structure: name the Proof idea being tested, show the method or evidence, then explain why it answers the command word. This helps A-Level Mathematics students avoid memorising one surface pattern.
Worked example 3: Mark-scheme check
Finish by checking the answer against marks: one point for the correct Proof idea, one for accurate working or evidence, and one for a precise final statement. If any step is vague, rewrite it before moving to timed practice.
Mini lesson for Proof
1. Understand the core idea
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.
Can you explain Proof without copying the notes?
2. Turn it into marks
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.
Underline the method, evidence, or command-word move that would earn credit in A-Level Pure Mathematics.
3. Fix the likely mark leak
Watch for this mistake: Assuming what you are trying to prove. For example, when proving an identity, starting with the assumption that the two sides are already equal.
Write one correction rule before doing another practice question.
Practise this topic
Start with low-focus cards for Proof, then move into full exam-style practice when you want the heavier session.
Mini quiz: Proof
Three quick checks for revision practice. They are original StudyVector prompts, not official exam-board questions.
Question 1
In one A-Level sentence, explain what Proof is testing.
Answer: 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.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Proof question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Assuming what you are trying to prove. For example, when proving an identity, starting with the assumption that the two sides are already equal." What should their next repair task be?
Answer: Do one Proof question and review the mistake type.
Mark focus: Error correction and next-step practice.
Proof flashcards
Core idea
What is the main idea in 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...
Common mistake
What mistake should you avoid in Proof?
Assuming what you are trying to prove. For example, when proving an identity, starting with the assumption that the two sides are already equal.
Practice
What is one useful practice task for Proof?
Answer one Proof question and review the mistake type.
Exam board
How should you use board notes for Proof?
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.
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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP specifications.
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 tutorFree full access to Proof
Sign up in 30 seconds to unlock step-by-step explanations, low-focus question cards, instant feedback and Play routes — completely free, no card required.
Try one low-focus question
Unlock Proof low-focus cards
Get instant feedback, step-by-step help and a calmer first run — free, no card needed.
Start free low-focus cardsAlready have an account? Log in
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.