Proof
What makes a proof-by-induction answer complete?
A base case, a clear assumption for n = k, a valid step to n = k + 1, and a final conclusion that states what has been proved.
StudyVector is an early-stage exam platform. These pages are written to help students revise better, then move into useful practice without pretending official specifications or past papers do not still matter.
AQA A-Level Further Maths revision for proof-heavy, method-heavy papers
Use this page to choose the next Further Maths repair route: compulsory pure content first, then the optional mechanics, statistics or discrete strand your school teaches.
Supported boards
AQA
Free plan availableNo credit card required
AQA A-Level Further Maths revision needs more than doing harder questions at random. Students need to know whether the issue is proof structure, notation, algebraic execution, calculus method, vectors, polar form, differential equations, or an optional application strand. This page keeps those routes visible and pushes students towards the next useful practice action.
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How to revise AQA Further Maths without drowning in hard questions
Start with one method family at a time. Proof, vectors, complex-number algebra, polar curves, calculus and differential equations each fail for different reasons. A mixed hard set is useful only after the underlying method has been repaired.
For optional applications, follow the option your school entered. Mechanics, statistics and discrete maths are not interchangeable, and the best revision plan keeps that route explicit.
What to log after a Further Maths mistake
Log the first line that failed, not just the topic name. In Further Maths, a mark can disappear because the proof assumption was weak, the exact value was rounded, the vector notation was incomplete, or a result from an earlier part was not used.
That level of error detail gives StudyVector a better next action: a short repair set, a proof walkthrough, or a retry of the same method under a different surface.
Topic list
Further Maths strands to revisit first
Start with the compulsory pure routes that create the biggest knock-on effect, then move into your optional application strand.
Complex NumbersAQAEdexcelOCRWJECEduqasCCEACIESQAIBAPMatricesAQAEdexcelOCRWJECEduqasCCEACIESQAIBAPProof by InductionAQAEdexcelOCRWJECEduqasCCEACIESQAIBAPDifferential EquationsAQAEdexcelOCRWJECEduqasCCEACIESQAIBAPAlgorithms & Graph TheoryAQAEdexcelOCRWJECEduqasCCEACIESQAIBAPChi-Squared TestsAQAEdexcelOCRWJECEduqasCCEACIESQAIBAP
Example questions
Quick checks before full practice
Exact values
Why can premature rounding lose marks in Further Maths?
Many methods depend on exact values or symbolic form. Rounding too early can destroy the structure needed in later parts.
Review
What should a hard-question review record?
The failed move: choice of method, notation, algebra, interpretation, or using an earlier result.
How StudyVector helps you revise smarter
Meaningfully board-specific
This page focuses on how AQA usually assesses Further Maths, not just generic subject advice with a board name pasted on top.
Question style and mark behaviour
Students can see what the board tends to reward, where structure matters most, and how to avoid predictable answer-shape errors.
Links into the next weak topic
Board-specific search traffic converts better when the page sends students into the exact topic or practice route they need next.
Built to support real revision decisions
Use the page to choose between topic repair, formula revision, past-paper work, and a fresh practice set rather than reading and stopping.
Pick your route
Browse subjects
Subject cards show board support and coverage upfront, so you can decide faster instead of clicking through blind.
A-Level
A-Level Further Maths
50 topics5 areas
Core pure, further mechanics, statistics and decision topics in one place.
AQAEdexcelOCRWJEC
Complex NumbersArgand DiagramsSeries
Launch-ready against strict trust/depth gates.
Launch readyOpen subject hub
A-Level
A-Level Maths
22 topics3 areas
Pure maths, statistics and mechanics with topic-by-topic walkthroughs.
AQAEdexcelOCRWJEC
ProofAlgebra & FunctionsCoordinate Geometry
Launch-ready against strict trust/depth gates.
Launch readyOpen subject hub
A-Level
A-Level Physics
31 topics3 areas
Mechanics, waves, electricity, fields and practical problem solving.
AQAEdexcelOCRWJEC
Measurements & Their ErrorsParticles & RadiationElectromagnetic Radiation & Quantum Phenomena
Launch-ready against strict trust/depth gates.
Launch readyOpen subject hub
Frequently asked questions
Is AQA Further Maths the same as A-Level Maths?
No. Further Maths builds on A-Level Maths and includes more advanced pure content plus optional applications. Use both routes, but do not treat them as duplicate pages.
Which AQA Further Maths option should I revise?
Revise the option your school teaches and enters: mechanics, statistics or discrete maths. If unsure, check your teacher or exam entry information.
Can StudyVector guarantee an A* in Further Maths?
No. StudyVector can help structure practice and mistake repair, but no platform can guarantee an exam result.
Ready to practise for your real exam board?
Questions follow AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP spec wording — not generic AI answers. Start free, or try one question first.