A-Level Further Mathematics Revision — Proof by Induction
Revise Proof by Induction for A-Level Further 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.
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- Proof by Induction in A-Level Further Mathematics: explanation, examples, and practice links on this page.
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- Students revising A-Level Further Mathematics for UK exams.
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- Practice is aligned to major specifications (AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP).
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What is Proof by Induction?
Proof by Induction belongs to Core Pure in A-Level Further Mathematics. The reliable way to revise it is to learn the trigger condition, write the first method line clearly, and practise enough variations that you can spot when the standard method needs adapting. For Further Maths, pay special attention to proof, notation, and whether a result follows from earlier parts of the question.
Board notes: AQA, Edexcel and OCR differ in wording and calculator/non-calculator balance. Use this as a method lesson, then check your board specification and past-paper style for exact demand.
Step-by-step explanationWorked examples
Worked example 1: Core method
For a Proof by Induction question, first classify the problem: what information is given, what form should the answer take, and which rule from Core Pure applies? Write the method line, carry out each transformation cleanly, then substitute or check the result against the original condition. This creates a mark-scheme-friendly answer even when the arithmetic is demanding.
Worked example 2: Exam variation
Now change one detail in the question and keep the same structure: name the Proof by Induction idea being tested, show the method or evidence, then explain why it answers the command word. This helps A-Level Further 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 by Induction 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 by Induction
1. Understand the core idea
Proof by Induction belongs to Core Pure in A-Level Further Mathematics. The reliable way to revise it is to learn the trigger condition, write the first method line clearly, and practise enough variations that you can spot when the standard method needs adapting.
Can you explain Proof by Induction without copying the notes?
2. Turn it into marks
For a Proof by Induction question, first classify the problem: what information is given, what form should the answer take, and which rule from Core Pure applies? Write the method line, carry out each transformation cleanly, then substitute or check the result against the original condition.
Underline the method, evidence, or command-word move that would earn credit in A-Level Core Pure.
3. Fix the likely mark leak
Watch for this mistake: Starting calculations before identifying the exact form of the question.
Write one correction rule before doing another practice question.
Practise this topic
Start with low-focus cards for Proof by Induction, then move into full exam-style practice when you want the heavier session.
Mini quiz: Proof by Induction
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 by Induction is testing.
Answer: Proof by Induction belongs to Core Pure in A-Level Further Mathematics. The reliable way to revise it is to learn the trigger condition, write the first method line clearly, and practise enough variations that you can spot when the standard method needs adapting.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Proof by Induction 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: "Starting calculations before identifying the exact form of the question." What should their next repair task be?
Answer: Attempt one standard Proof by Induction problem and annotate every theorem, identity, or earlier result you use.
Mark focus: Error correction and next-step practice.
Targeted practice plan
- 1Attempt one standard Proof by Induction problem and annotate every theorem, identity, or earlier result you use.
- 2Attempt one harder Core Pure problem where the first method is not obvious; write two possible routes before solving.
- 3After marking, rewrite the solution in the fewest rigorous steps that still justify every transition.
Proof by Induction flashcards
Core idea
What is the main idea in Proof by Induction?
Proof by Induction belongs to Core Pure in A-Level Further Mathematics. The reliable way to revise it is to learn the trigger condition, write the first method line clearly, and practise enough variations that you can...
Common mistake
What mistake should you avoid in Proof by Induction?
Starting calculations before identifying the exact form of the question.
Practice
What is one useful practice task for Proof by Induction?
Attempt one standard Proof by Induction problem and annotate every theorem, identity, or earlier result you use.
Exam board
How should you use board notes for Proof by Induction?
AQA, Edexcel and OCR differ in wording and calculator/non-calculator balance. Use this as a method lesson, then check your board specification and past-paper style for exact demand.
Common mistakes
- 1Starting calculations before identifying the exact form of the question.
- 2Skipping algebraic or numerical working that the mark scheme would credit.
- 3Not checking whether the final answer needs units, exact form, a diagram interpretation, or a stated conclusion.
Proof by Induction exam questions
Exam-style questions for Proof by Induction 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.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Proof by Induction
Core concept
Proof by Induction belongs to Core Pure in A-Level Further Mathematics. The reliable way to revise it is to learn the trigger condition, write the first method line clearly, and practise enough variat…
Frequently asked questions
How do I get better at Proof by Induction?
Practise in short sets: one easy recognition question, one standard method question, and one mixed question. After each attempt, mark the first line and the final check separately.
What loses marks in Proof by Induction?
Most lost marks come from wrong method selection, missing intermediate steps, or an answer that is mathematically correct but not in the requested form.