AS-Level Maths Help — Video Lessons & Practice
Get clear, step-by-step explanations for any AS-Level Maths problem and build exam-ready confidence for your A-Level journey.
Certified-Teacher Concept Videos
Every AS-Level Maths lesson is taught by a certified teacher who shows you the method step by step — so you understand how to solve it, not just what the answer is. That understanding is what carries you through your A-Level exams.
Diagnostic Assessment + Adaptive Practice
A quick diagnostic pinpoints exactly which AS Maths topics need work, so you stop wasting time on what you already know. Practice then adjusts to your level, keeping every session focused and effective.
A-Level Exam-Style Practice Built In
Practice with questions based on real A-Level exam style — covering Pure Maths, Statistics, and Mechanics. Build the exam confidence you need before sitting your AS papers.
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AS-Level Maths Topics
1. Set Theory
2. Number System
3. Surds
4. Laws of Indices
5. Linear Functions
6. Quadratic Functions
7. Quadratic Equations
8. Simultaneous Equations
9. Inequalities
10. Factorisation
11. Operations with Algebraic Fractions
12. Functions
13. Transformations of Functions
14. Algebraic Division
15. Reciprocal Functions
16. Rational Functions
17. Circle Theorems
18. Binomial Expansion
19. Trigonometry
20. Trigonometric Ratios and Angle Measure
21. Sine Rule and Cosine Rule
22. Trigonometric Identities and Equations
23. Graphing Trigonometric Functions
24. Exponentials Functions
25. Logarithms
26. Growth and Decay
27. Differentiation
28. Integration
29. Vectors
30. Statistics
31. Data and Graphs
32. Correlation and Regression
33. Probability
34. Hypothesis Testing
35. Scalars, Vectors, and Motion
37. Forces
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What is AS-Level Maths?
AS-Level Maths is a Year 12 qualification in England, Wales, and Northern Ireland that forms the first half of the A-Level Mathematics programme. It is examined separately by Edexcel, AQA, and OCR and covers Pure Mathematics, Statistics, and Mechanics. Students who complete AS-Level Maths gain a recognised qualification and a strong foundation for A-Level — or for degree courses and apprenticeships requiring quantitative skills.
What topics are covered in AS-Level Maths?
The AS-Level Maths syllabus divides into Pure Mathematics and Applied Mathematics. Pure covers algebra and functions, coordinate geometry, sequences and series, trigonometry, exponentials and logarithms, differentiation, and integration. Applied covers two strands: Statistics (data representation, probability, binomial distribution, hypothesis testing) and Mechanics (kinematics in one and two dimensions, forces, Newton's laws of motion). All three major exam boards — Edexcel, AQA, and OCR — follow the same core content mandated by Ofqual, though question style and mark-scheme wording can differ.
Is AS-Level Maths harder than GCSE?
Yes, notably so. GCSE Maths rewards procedural accuracy; AS-Level Maths demands flexible, connected reasoning. The algebra becomes more abstract, proofs require logical precision, and applied topics like hypothesis testing require students to interpret context rather than just calculate. Students who find the transition tough most often struggle with: constructing algebraic proofs, applying differentiation rules to unfamiliar functions, and interpreting statistical conclusions in plain English. Recognising these sticking points early — ideally through a diagnostic — means you can target exactly the areas that will cost you marks on your AS papers.
How is AS-Level Maths graded and examined?
AS-Level Maths is assessed through two written examinations at the end of Year 12, each lasting 1 hour 30 minutes. Paper 1 covers Pure Mathematics; Paper 2 covers Statistics and Mechanics. Both papers permit scientific calculators. Grades run from A (highest) to E (lowest pass), with U for ungraded. The AS result is a standalone qualification — it does not count toward the A-Level grade. However, practising AS-style exam questions is the most efficient revision strategy, because the reasoning skills tested at AS are exactly those extended at A-Level.
What are the hardest concepts in AS-Level Maths, and how do you approach them?
Three topics generate the most lost marks across Edexcel, AQA, and OCR AS papers:
Differentiation and its applications. First principles, the chain rule, and optimisation problems require students to see differentiation as a tool for reasoning about rates of change — not just a procedure to apply. Work from the definition outward, sketch the function before differentiating, and always check that a stationary point is a maximum or minimum using the second derivative.
Trigonometric identities. Proving and applying identities like sin²θ + cos²θ = 1 and the double-angle formulae requires algebraic fluency. The method is always the same: start from one side, substitute known identities, and simplify. Never try to work from both sides simultaneously in a proof.
Hypothesis testing in Statistics. Students often lose marks by failing to state their hypotheses, critical region, and conclusion clearly and in context. Practise writing conclusions in full sentences that reference both the probability and the real-world scenario in the question.
Why StudyPug for AS-Level Maths?
StudyPug is built around the way exam marks are actually won: by understanding the method behind each problem type, not by memorising worked examples. Every AS-Level Maths lesson is delivered by a certified teacher who walks through the reasoning step by step — so when you see a slightly different question on your Edexcel or AQA paper, you know how to adapt.
The platform starts with a diagnostic assessment that maps your current understanding against the AS syllabus and identifies exactly which topics to prioritise. There is no guesswork and no wasted revision time. From there, adaptive practice adjusts difficulty in real time — harder when you are confident, gentler when a concept needs more work — so every session pushes you forward without overwhelming you.
Lessons are aligned to the UK AS-Level curriculum across Edexcel, AQA, and OCR. Practice questions are based on real A-Level exam style, so revision feels directly relevant to the papers you will sit. You can also use StudyPug's Photo Search feature on any grade and any subject: photograph a problem from your textbook or past paper, and the platform finds the matching lesson instantly.
For students who are also preparing for the A-Level jump, everything in the subscription is included — Year 2 A-Level content, further practice sets, and mock-style tests — at no extra cost.
What you will learn — AS-Level Maths curriculum coverage
StudyPug covers the full AS-Level Maths content specification as set by Ofqual, applicable across Edexcel, AQA, and OCR:
- Pure Mathematics: Algebra and proof; coordinate geometry of straight lines and circles; quadratics and polynomials; binomial expansion; sequences and series; trigonometry including radians and identities; exponential and logarithmic functions; differentiation (including chain, product, and quotient rules); integration including definite integrals and area under curves.
- Statistics: Sampling and data representation; measures of location and spread; probability; statistical distributions including the binomial distribution; statistical hypothesis testing.
- Mechanics: Quantities and units; kinematics in one and two dimensions including constant acceleration equations; forces and Newton's three laws of motion; variable acceleration using calculus.
Because no validated internal topic-page links are available for this page in the current sitemap, the curriculum links above point to the broad topic areas rather than individual pages — your StudyPug dashboard lists every lesson under the correct heading once you log in.
How to use StudyPug for AS-Level Maths revision
Step 1 — Run the diagnostic. Start with the AS-Level Maths diagnostic assessment. It takes around ten minutes and produces a personalised topic priority list. Focus your first week on the two or three topics flagged as weakest — these are most likely to be the difference between a D and a B on your papers.
Step 2 — Watch the concept video, then practise immediately. For each topic, watch the certified-teacher video that explains the method. Pause before each worked step and try it yourself. Then move straight to the practice problems. The research is clear: retrieval practice within minutes of learning dramatically improves long-term retention.
Step 3 — Use exam-style practice tests. Once you have covered a topic, complete an exam-style practice set. Review every question you got wrong using the video solution — not just the mark scheme. Understanding why you were wrong is more valuable than knowing the right answer.
Step 4 — Revisit weak areas with adaptive practice. StudyPug's adaptive practice engine tracks your performance and surfaces the topics that need reinforcement. Return to these regularly, especially in the four weeks before your AS papers.
Step 5 — Use Photo Search for textbook problems. When you get stuck on a textbook or past-paper question, use Photo Search to find the matching StudyPug lesson instantly. It works across all subjects and all grades, making it a fast way to get unstuck without losing momentum.
There is no free trial of the subscription, but StudyPug offers a 30-day money-back guarantee — so you can start, work through your toughest AS Maths topics, and request a full refund within 30 days if it is not the right fit for you.
AS-Level Maths FAQ
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What do you learn in AS-Level Maths, and what topics does it cover?
AS-Level Maths is the first year of A-Level Mathematics in England, Wales, and Northern Ireland. It covers Pure Mathematics — including algebra, coordinate geometry, trigonometry, differentiation, and integration — alongside Applied Mathematics in Statistics (data, probability, statistical distributions, hypothesis testing) and Mechanics (kinematics, forces, Newton's laws). Together these topics build the quantitative reasoning skills needed for further study in science, engineering, economics, and computing.
What is the difference between AS-Level Maths and A-Level Maths?
AS-Level Maths is a standalone qualification covering roughly the first year of content. A-Level Maths extends that foundation with harder Pure topics — such as further calculus, sequences, and differential equations — plus more advanced Statistics and Mechanics. Many students sit AS-Level at the end of Year 12 before deciding whether to continue to A-Level. The AS qualification carries fewer UCAS points than the full A-Level but still demonstrates solid mathematical ability to universities and employers.
Is AS-Level Maths hard, and where do students struggle most?
AS-Level Maths is a significant step up from GCSE. The jump in abstraction catches many students off guard, particularly in algebraic proof, trigonometric identities, and the chain and product rules in differentiation. Statistics — especially hypothesis testing and the binomial distribution — is another common sticking point. Students who struggle often do so because GCSE habits (memorising procedures) break down when problems require flexible reasoning. Building genuine understanding of each method, not just the answer, is the key shift needed.
What should I take before AS-Level Maths, and what comes after it?
You should complete GCSE Maths at Grade 6 or higher before starting AS-Level, with Grade 7+ strongly recommended. A GCSE in Further Maths is helpful but not required. After AS-Level, students can progress to the full A-Level by studying the Year 2 content, which opens doors to university courses in mathematics, physics, engineering, computer science, and economics. AS-Level Maths alone is also respected in applications for numeracy-heavy apprenticeships and vocational programmes.
Is AS-Level Maths on the A-Level exam, and how is it tested?
In England, AS-Level Maths is examined by Edexcel, AQA, and OCR through two written papers at the end of Year 12. Each paper is 1 hour 30 minutes; one covers Pure Maths and the other covers Statistics and Mechanics. Questions are a mix of short answer and extended problem-solving. Calculators are permitted in both papers. The AS grade (A–E or U) is separate from the A-Level grade and does not contribute to the A-Level result — though the skills tested overlap significantly.
What is one of the hardest concepts in AS-Level Maths, and how do you tackle it?
Differentiation from first principles and its application via the chain, product, and quotient rules trips up many Year 12 students. The key is understanding why the rules work before applying them mechanically. Start with simple polynomials and build up: sketch the function, find the gradient of a chord, then shrink the interval to derive the derivative. Once the concept is solid, practise applying the rules to trigonometric and exponential functions. Repeated worked examples — pausing to predict each step before watching the solution — build reliable exam technique.
