Edexcel A-Level Maths (9MA0) Pure Topic Checklist

Pure Mathematics makes up two-thirds of the Edexcel A-Level Maths (9MA0) assessment, split across Paper 1 and Paper 2, with Statistics and Mechanics combined into Paper 3. Because Pure carries so much weight and because many Pure techniques are prerequisites for the applied content too, having a genuinely clear picture of which topics are secure and which are not is one of the highest-value things you can do before the exam season. This checklist lays out the full Pure topic list grouped by area, explains a simple self-audit method, and notes which areas tend to carry the most marks based on how the specification is structured.

How to Use This Checklist

Rather than just reading through the list, use it actively. For each topic below, rate yourself:

Green: You can answer a past paper question on this topic correctly and efficiently without needing to check notes first.
Amber: You understand the concept but make occasional errors, need a reminder of the method, or are slow.
Red: You would need to relearn this from scratch or consistently get it wrong.

This is more useful than a simple "have I covered this" tick because A-Level Maths problems very often combine two or three topics in a single question, so partial familiarity is not enough — an amber-rated topic embedded inside a harder question will still cost you marks. Revisit your ratings every few weeks rather than doing this once, since topics you rated green early in the course can slip to amber if unused for months.

Year 1 Pure Topics

Algebra and Functions

Laws of indices and surds
Quadratic equations, including completing the square and the discriminant
Simultaneous equations, including one linear and one quadratic
Inequalities, including quadratic and simultaneous inequalities
Graphs of functions, including transformations (translations, stretches, reflections)
The modulus function
Polynomial division and the factor theorem

Coordinate Geometry

Equations of straight lines, including parallel and perpendicular lines
Equations of circles, including finding centre and radius from general form
Geometric problems involving lines and circles together

Sequences and Series

Arithmetic sequences and series
Geometric sequences and series, including sum to infinity
Binomial expansion for positive integer powers

Trigonometry

Sine and cosine rules, including area of a triangle
Radian measure and arc length/sector area
Trigonometric graphs and their key features
Trigonometric identities, including sin²x + cos²x = 1
Solving trigonometric equations within a given range

Exponentials and Logarithms

Graphs of exponential functions
Logarithm laws and solving exponential equations using logarithms
Natural logarithms and the exponential function e^x

Differentiation

Differentiation from first principles (conceptual understanding)
Differentiating polynomials
Gradients, tangents and normals
Increasing/decreasing functions and stationary points
Second derivatives and identifying maxima/minima

Integration

Integrating polynomials
Finding the constant of integration given a point
Definite integrals and area under a curve

Vectors (2D)

Vector notation and magnitude
Position vectors and vector geometry problems

Year 2 Pure Topics

Algebraic Methods

Algebraic fractions, including simplifying and combining
Partial fractions
Functions, including domain, range, composite and inverse functions
The modulus function applied to more complex graphs and transformations

Sequences and Series (Extended)

Binomial expansion for any rational power, including validity conditions
Sequences defined recursively and by formula, including increasing/decreasing/periodic behaviour

Trigonometry (Extended)

Secant, cosecant and cotangent, and their graphs
Inverse trigonometric functions
Compound angle formulae and double angle formulae
The R sin(x + a) / R cos(x + a) form for solving equations and finding maxima/minima
Proving trigonometric identities

Parametric Equations

Converting between parametric and Cartesian forms
Sketching curves from parametric equations
Differentiating parametric equations to find gradients

Differentiation (Extended)

Differentiating exponential and logarithmic functions
Differentiating trigonometric functions, including chain, product and quotient rules
Implicit differentiation
Connected rates of change problems
Modelling with differential equations conceptually

Numerical Methods

Locating roots by sign change
Iterative methods, including cobweb/staircase diagrams conceptually
Newton-Raphson method
Numerical integration using the trapezium rule

Integration (Extended)

Integrating a wider range of functions, including exponentials, trigonometric functions and 1/x
Integration by substitution
Integration by parts
Integration using partial fractions
Solving differential equations by separation of variables
Finding areas between curves and using integration in modelling contexts

Vectors (3D)

3D vector notation and magnitude
Vector geometry in three dimensions, including finding angles and distances

Proof

Proof by contradiction, including proving the irrationality of root 2 and the infinitude of primes as classic examples

Which Topics Carry the Most Marks

While exact weighting varies between series, some patterns are worth knowing because they reflect how the specification is structured rather than just chance:

Algebra runs through everything. Weak algebraic manipulation does not just cost marks in dedicated algebra questions — it undermines calculus, trigonometry and vectors questions too, since nearly every multi-step problem requires rearrangement, factorising, or handling fractions along the way.
Calculus (differentiation and integration combined) is consistently one of the largest topic groups across both papers, particularly once Year 2 techniques like integration by parts and differential equations are included, so it is rarely worth under-revising.
Trigonometric identities and equations appear repeatedly, often combined with calculus or algebra in longer questions rather than as standalone questions, so fluency with compound and double angle formulae pays off across the whole paper, not just in trigonometry-labelled questions.
Proof and numerical methods carry fewer total marks than algebra or calculus but are frequently under-revised relative to their weighting, partly because they feel unfamiliar compared to GCSE-style content, making them a relatively efficient area to shore up if you are short on time.
Vectors and parametric equations are smaller topic groups individually but often appear combined with coordinate geometry or calculus in longer questions, so treat them as connector topics rather than isolated ones.

Running the Self-Audit Properly

Go through the checklist above topic by topic and mark green, amber or red honestly — the value of this exercise disappears if you rate yourself generously. Once you have a full picture:

Attack red topics first, using resources for topic-specific explanations and worked examples, since these represent the highest-risk gaps.
Convert ambers to greens through targeted past paper practice on that specific topic in isolation, rather than always working through full papers, since full papers can let you avoid a weak topic if it happens not to appear prominently.
Retest greens periodically, particularly topics from early in Year 1 that you have not used recently, since Pure content compounds and small foundational weaknesses resurface in Year 2 questions.
Once individual topics are solid, move to full timed past papers from our past papers library, since this is where you practise identifying which combination of topics a long question is actually drawing on.

Pair this topic-level audit with the broader execution habits — algebraic reliability, mark-scheme literacy, and disciplined timed practice — covered in How to Get an A* in A-Level Maths, since a complete topic checklist without reliable execution still leaves marks on the table.

If you are also taking or considering Further Maths, several of these Pure topics (particularly complex numbers-adjacent algebra, proof, and calculus) form the foundation for Further Maths content, so a strong Pure audit here also makes that transition considerably smoother — see Is A-Level Further Maths Worth It? if you are still deciding.

When to Get Extra Help

If your audit reveals a cluster of reds concentrated in one area — commonly calculus techniques, trigonometric identities, or numerical methods — rather than scattered evenly across the specification, this is often a sign that a specific concept was missed or misunderstood early on and has been compounding since. Targeted, one-to-one input can resolve this far faster than generic revision, since a tutor can diagnose exactly where the misunderstanding originates. A-Level Maths Tutoring offers this kind of focused support if you find particular Pure topic clusters are consistently amber or red despite repeated practice.

Our revision timetable generator can also help turn this checklist into an actual weekly plan, allocating more time to red and amber topics without neglecting green ones entirely, since green topics still need periodic reinforcement to stay reliable under exam conditions.

Takeaway

The Edexcel 9MA0 Pure specification is large, but it is not unstructured — it groups into clear families (algebra, coordinate geometry, sequences and series, trigonometry, exponentials and logarithms, calculus, vectors, proof and numerical methods) that build on each other across Year 1 and Year 2. A honest green/amber/red audit against the full list above, repeated periodically rather than done once, is one of the most efficient ways to direct your remaining revision time, particularly when paired with targeted past paper practice on the specific topics that come out amber or red.

Keeping the Checklist Current

Specifications are occasionally refined, so cross-check this list against the current official Edexcel 9MA0 specification document before relying on it as your sole reference, particularly if you are starting the course some time after this checklist was written. Treat it as a structured starting point for your audit rather than a substitute for the specification itself, and update your green/amber/red ratings as a living document throughout the two years rather than a one-off exercise done at the start of Year 13.