Differentiation
Differentiate y = 3x^4 - 5x^2 + 7 and state the gradient when x = 2.
A strong answer shows dy/dx = 12x^3 - 10x, then substitutes x = 2 to get 96 - 20 = 76. The common lost mark is substituting before differentiating.
For official specifications and assessment wording, cross-check AQA, Pearson Edexcel and OCR alongside this guide.
What is A-Level Maths revision on StudyVector?
StudyVector's A-Level Maths hub is an independent, board-aligned revision route covering pure maths, mechanics and statistics for AQA, Edexcel and OCR. Practise exam-style questions, find weak topics, review mistakes in an Error Log and get AI-supported worked solutions. It is free to start, is not affiliated with any exam board, and is not a guarantee of grade outcomes.
A-Level Maths Revision Made Simple
Step-by-step explanations for core A-Level Maths topics — from differentiation to statistics. Know what to work on next.
Supported boards
AQAEdexcelOCRWJECEduqasCCEACIEPearson IntlOxfordAQASQAIBAP
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Cross-check official specifications and past papers with AQA, Pearson Edexcel and OCR. StudyVector is independent and not exam-board affiliated.
A-Level Mathematics is one of the most challenging and rewarding subjects you can study. Whether you're working through pure maths topics like calculus and trigonometry, or applied topics like statistics and mechanics, StudyVector breaks concepts into clear, manageable steps. The revision coach explains topics patiently, clearly, with worked examples that actually make sense, and now with curated launch guides for the highest-friction routes. We support AQA, Edexcel, OCR, Cambridge International A-Level, IB Mathematics AA and AI, and AP Calculus where coverage is live.
JC
A-Level and Further Maths explanations reviewed
by James Chen, Cambridge Mathematics offer holder.
Start light first
Start with low-focus cards, drill by topic, or see summer 2026 predicted angles — then set your course and exam board when you want the full loop.
Start low-focus cards · Exam questions by topic · Predicted topics 2026 · All subjects
How to structure A-Level Maths revision
Split each week across pure, statistics and mechanics instead of only revising the topic you prefer. Pure topics such as differentiation, integration, proof, trigonometry, sequences and vectors often carry connected method marks, while statistics and mechanics punish weak setup and interpretation.
A useful session should include one worked method, a short set of exam-style questions, and one correction. If you miss a mark because of notation, units, calculator setup or a missing conclusion, record that mistake and retry later rather than moving straight to a new topic.
Board-specific checks for AQA, Edexcel and OCR
StudyVector organises A-Level Maths around board-aware routes where coverage is live, but students should still check their school specification and official exam-board materials. The safest revision path is to use official specifications and past papers for source truth, then use StudyVector for practice, explanation and weak-topic repair.
If you are using predicted topics, treat them as prioritisation. They can help you choose what to practise first, but they should not replace pure, statistics and mechanics coverage across the full course.
Topic list
Core A-Level Maths topics
Start with the strand that is costing you marks, then move into full practice once the method is secure. Topic depth varies by board, so check your exact specification alongside these launch guides.
Example questions
Quick checks before full practice
Statistics
A random variable follows X ~ B(20, 0.3). What does P(X <= 4) mean in context?
It means the probability of four or fewer successes in 20 independent trials, each with success probability 0.3. State the context before using calculator probabilities.
Mechanics
A particle starts from rest and accelerates uniformly at 2.5 m s^-2 for 8 seconds. Find its speed.
Use v = u + at with u = 0, a = 2.5 and t = 8, so v = 20 m s^-1. Include units because mechanics marks often reward correct physical interpretation.
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Related guides
2026 predicted papersAQA A-Level Maths revisionAQA A-Level Further Maths revisionA-Level Maths past papersAQA A-Level Maths predicted paperEdexcel A-Level Maths predicted paperGCSE and A-Level grade predictorHow to get an A* in A-Level MathsA-Level revision hubCambridge International A-Level MathsEdexcel International A-Level MathsSQA Advanced Higher Maths
Frequently asked questions
Is StudyVector free for A-Level Maths?
Yes. A-Level Maths students can start on the free Starter tier (7 days uncapped, then 45 min revision/day) with explanations and practice questions where coverage is live.
Which exam boards does StudyVector cover?
StudyVector supports major A-Level Maths routes where coverage is live, including AQA, Edexcel and OCR. International and AP-style routes are labelled separately as coverage expands.
Can StudyVector help me aim for an A* in A-Level Maths?
StudyVector identifies weak areas, provides targeted practice, and tracks progress. It supports high-grade revision, but outcomes still depend on consistent work, teaching, and exam performance.
How is this different from watching YouTube videos?
StudyVector is interactive. You don't just watch — you practise, get instant feedback, and follow personalised study plans. It adapts to your specific weaknesses.
Ready to practise for your real exam board?
Questions follow AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP spec wording — not generic AI answers. Start light, then save progress when you want the full loop.
Frequently asked questions
Which A-level Maths exam boards does StudyVector cover?
AQA, Pearson Edexcel, and OCR (A and B). Practice questions and worked solutions tag the relevant specification reference so you can revise against the exact paper you sit.
What topics are included in A-level Maths revision?
Pure Maths (algebra, functions, calculus, trigonometry, vectors, proof, series), Statistics (data, distributions, hypothesis testing), and Mechanics (kinematics, forces, moments). Each topic has explanation pages, worked examples, and exam-style questions.
Does StudyVector use real A-level past paper questions?
We use exam-style questions written against published mark schemes, plus links to official board past papers. The Error Log treats mistakes the way a marker would — by lost marks, command words, and topic, not just right or wrong.
Is A-level Maths revision on StudyVector free?
Yes — core topic pages, worked examples, and a low-focus card path are open without an account. Premium unlocks unlimited revision time, the Error Log, exam-mode mock papers, and revision coach support.
How long should I revise A-level Maths for each day?
Most students get the best gain from 30 to 60 minutes of focused practice plus 10 minutes of error-log review, four to five days a week. StudyVector's revision planner sequences this around the topics you're losing marks on.
A-Level Maths glossary terms
- Chain ruleThe chain rule differentiates composite functions: if y = f(g(x)) then dy/dx = f'(g(x)) · g'(x). It appears across A-Level Maths and Further Maths whenever an outer function wraps an inner function — common examples are sin(2x), e^(3x²) and (1+x²)⁵. Without the chain rule, every composite differentiation drops marks; with it, the standard trick is to spot the inner function first.
- Integration by partsIntegration by parts is the integral analogue of the product rule: ∫ u dv/dx dx = uv − ∫ v du/dx dx. Use it whenever the integrand is a product of two functions where one becomes simpler under differentiation (typically polynomial × exponential, polynomial × trig, or x × log x). The LIATE rule helps pick u: Logarithm, Inverse trig, Algebraic, Trig, Exponential.
- Binomial expansionBinomial expansion expands (a + b)^n using (a + b)^n = Σ (n choose k) a^(n−k) b^k for positive integer n. For rational/negative n the expansion is an infinite series, valid only for |b/a| < 1. A-Level Maths examines both forms; Further Maths extends to approximations. Sloppy work with the validity condition is a high-frequency lost mark.
- Implicit differentiationImplicit differentiation differentiates equations where y is not isolated, e.g. x² + y² = 25. Treat y as a function of x and apply the chain rule whenever you differentiate a y term — d(y²)/dx becomes 2y · dy/dx. Used heavily for circles, ellipses and tangent/normal problems where rearranging to y = f(x) is impractical.
- Differential equationsA differential equation relates a function to its derivatives. A-Level Maths examines first-order separable equations (dy/dx = f(x)·g(y)), solved by separating variables and integrating both sides. Applications include exponential growth/decay (dN/dt = kN), Newton's law of cooling and rate-of-reaction models. Further Maths extends to second-order equations and integrating factors.
- Parametric equationsParametric equations express x and y separately as functions of a parameter t, e.g. x = cos(t), y = sin(t). They model curves that aren't conveniently expressed as y = f(x) — including circles, ellipses, and projectile paths. A-Level Maths uses the chain rule dy/dx = (dy/dt) / (dx/dt) to find gradients, and substitution to eliminate the parameter and recover the Cartesian equation.
- Vectors in 3DA-Level Maths extends vectors from 2D to 3D using the unit vectors i, j and k. Examinable skills: magnitude (|v| = √(x² + y² + z²)), addition/subtraction, scalar multiplication, the equation of a line r = a + λd, scalar (dot) product, and using the dot product to test perpendicularity (v · w = 0) or find angles between vectors.
- P-valueA p-value is the probability of observing test statistics at least as extreme as the one obtained, assuming the null hypothesis is true. A small p-value (typically below 0.05) is evidence against the null hypothesis. A-Level Maths examines p-values for binomial hypothesis tests and normal hypothesis tests. A p-value alone is not a probability that the null is true — that's a common interpretation slip examiners penalise.