Pure Mathematics (AS)
10
specification units
43
named subtopics
Year 12
year groups
Pearson Edexcel AS Level Pure Mathematics (AS) is organised here into 10 specification units covering 43 named subtopics, studied across Year 12. The units are Proof, Algebra & Functions, Coordinate Geometry, Sequences & Series, Trigonometry, Exponentials & Logarithms, Differentiation, Integration, Numerical Methods and Vectors.
Each subtopic is tagged on the question bank, so you can practise one skill at a time, sit a full Edexcel AS past paper, or build a mixed worksheet from several units at once. Answers are checked against the Pearson Edexcel AS Level mark scheme, awarding method, accuracy and final-answer marks separately so you can see exactly where marks were lost.
Algebra & Functions is the widest unit on this specification with 6 subtopics, so it is usually the highest-value place to start revision.
How Pearson Edexcel AS Level Pure Mathematics (AS) is examined
Edexcel AS Pure Mathematics is the algebraic and calculus spine of the AS qualification. Nearly every question builds on manipulation done correctly at the first line, so a single early slip usually costs the whole chain of accuracy marks.
Assessment at a glance
- •Pure content is assessed alongside applied content within the AS papers; the pure material carries the larger share.
- •A calculator is permitted, but proof, exact-value and 'show that' questions are written to defeat calculator-only approaches.
- •Structured questions build across parts — later parts often depend on the earlier answer, so a lost part can cascade.
Where marks are most often lost
- •Differentiation from first principles and 'show that' proofs, where the required argument is not written out.
- •Exact values with surds and logs, where a decimal answer scores nothing.
- •Coordinate geometry of circles: tangents, perpendicular bisectors and completing the square on two variables.
- •Integration with limits where the constant, the limits or the sign is mishandled.
What to revise first: Algebraic manipulation and quadratics first, then differentiation and integration. Trigonometric identities and equations after that — they are the most common source of unforced errors at AS.
Proof
- Proof by deduction
- Proof by exhaustion
- Disproof by counterexample
- Proof by contradiction
Algebra & Functions
- Indices & surds
- Quadratics
- Simultaneous equations & inequalities
- Polynomials
- Functions & transformations
- Partial fractions
Coordinate Geometry
- Straight lines
- Circles
- Parametric equations
Sequences & Series
- Binomial expansion
- Arithmetic series
- Geometric series
- Recurrence relations
Trigonometry
- Trig ratios & graphs
- Identities
- Radians
- Compound & double angles
- Solving equations
Exponentials & Logarithms
- Exponential models
- Logarithms
- Natural log & e
- Modelling with logs
Differentiation
- First principles
- Rules of differentiation
- Stationary points
- Implicit & parametric
- Applications
Integration
- Indefinite & definite
- Areas under curves
- Integration by parts & substitution
- Differential equations
Numerical Methods
- Location of roots
- Iteration
- Newton-Raphson
- Numerical integration
Vectors
- 2D & 3D vectors
- Magnitude & direction
- Position vectors
- Geometric problems
How to revise Edexcel AS Pure Mathematics (AS)
- 1
Diagnose with one mixed set
Start with a mixed set drawn from all 10 units to find where Pure Mathematics (AS) marks are actually being lost, rather than revising what already feels comfortable.
- 2
Drill unit by unit
Work through the subtopics in order, from Proof to Vectors, doing short focused sets rather than long unfocused sessions.
- 3
Sit a full past paper under timing
Once two or three units are solid, sit a complete Edexcel AS Pure Mathematics (AS) paper to timing and mark it against the official mark scheme.
- 4
Re-practise only the dropped marks
Convert every dropped mark into a targeted set on that subtopic, then re-test it a week later to check the fix stuck.
Continue with Pure Mathematics (AS)
Every board and level we cover for this subject
A Level MathematicsSearchable formula sheet with worked micro-examples
Predicted papersPractice papers built from the topics that recur most
Past paper practiceSit whole papers online with examiner-grade marking
Other specifications for this subject
Pure Mathematics (AS) — frequently asked questions
Everything students and parents ask about revising Edexcel AS Pure Mathematics (AS).
The fastest route is past-paper-first revision: practise exam-style questions by topic, mark every answer against the real Pearson Edexcel AS Level mark scheme, then drill the topics where you lose marks. On MathsGradeUp you can do all of this for Pure Mathematics (AS) in one place — topic practice, full past papers and instant examiner-grade feedback.
Pearson Edexcel AS Level Pure Mathematics (AS) is mapped to the official specification and covers 10 units, including Proof, Algebra & Functions, Coordinate Geometry, Sequences & Series, Trigonometry, Exponentials & Logarithms and more. Every unit is broken down into subtopics so you can target exactly what you need to revise.
Yes. You can open full Edexcel AS Pure Mathematics (AS) past papers, write directly on them with pen and maths tools, save your work, export a PDF, and submit for examiner-grade marking against the mark scheme.
Yes — our predicted papers for Pure Mathematics (AS) are assembled from the topics that recur most in Pearson Edexcel AS Level exams and the topics you have practised least. They are a revision aid built from the specification, not leaked content.
Each answer is checked against the real Pearson Edexcel AS Level mark scheme, awarding method, accuracy and final-answer marks the way a real examiner would. You see exactly where marks were earned or dropped, with feedback you can act on.
Pure Mathematics (AS) on the Pearson Edexcel AS Level specification is aimed at Year 12. You can filter practice by year group and topic so the questions always match where you are in the course.
Yes. The Pure Mathematics (AS) content follows the current Pearson Edexcel AS Level specification, including all units and subtopics, so what you practise reflects what you will actually be examined on.
Yes — Pure Mathematics (AS) practice, past papers and marking are free during our early launch period. Subscription plans may be introduced later, but launch users get full access now.
You do not just get an answer to copy. Pure Mathematics (AS) marking guides you with hints, worked steps and mark-scheme-based feedback so you understand the method and pick up the marks yourself next time. Questions are tagged calculator and non-calculator so you can practise exactly the way each paper is sat.
Yes. Parents and tutors can see completed Pure Mathematics (AS) practice, accuracy, weak topics and overall exam readiness, making it easy to support revision and focus on the right areas.
Short, regular sessions beat occasional long ones. Aim for a few focused Pure Mathematics (AS) sessions a week, always finishing by marking your work so each session ends with clear next steps. The progress dashboard shows what to revise next.