A-Level Maths: A Guide to Core Pure Content
Why Pure Maths Matters
In A-Level Mathematics, Pure content typically makes up around 67% of the overall marks across all exam papers. Getting a firm grip on Pure Maths is therefore the single highest-leverage thing you can do for your overall grade.
The Core Topics
Algebra and Functions
- Laws of indices, surds, and algebraic manipulation
- Partial fractions
- Functions: domain, range, composite, inverse
- Modulus function and inequalities
Coordinate Geometry
- Straight lines (gradient, midpoint, distance, perpendicular)
- Circles (equation, tangent, chord)
Sequences and Series
- Arithmetic and geometric series
- Binomial expansion (for positive integer powers in Year 12; general binomial theorem in Year 13)
Trigonometry
- Radians, arc length, sector area
- Reciprocal trig functions (sec, cosec, cot)
- Trig identities and proof
- Addition formulae, double angle formulae
Exponentials and Logarithms
- Laws of logarithms
- Solving exponential equations
- Natural logarithm and e
Calculus
- Differentiation: product rule, quotient rule, chain rule
- Integration: standard integrals, integration by parts, integration by substitution
- Differential equations (separable variables)
- Parametric differentiation and integration
Proof
- Proof by contradiction, counter-example, and deduction
How to Revise Pure Maths
Pure Maths is not a reading subject. You learn it by doing. Work through problems from each topic until the methods are automatic. When you make a mistake, diagnose whether it is a conceptual misunderstanding or a procedural slip — they require different fixes.
The Mistake to Avoid
Many students revise by working through examples with their notes open. This feels productive but does not train the retrieval skills needed in an exam. Close your notes. Attempt the problem. Then check.