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CCEA A-Level Further Mathematics: complete guide to the AS and A2 units, the exams and how to study each module

A complete guide to CCEA A-Level Further Mathematics (specification 2018). Covers the AS 1 and A2 1 Pure Mathematics units, the AS 2 and A2 2 Applied Mathematics units with their mechanics, statistics and discrete sections, how the AS and A2 exams are structured and marked, and how to study each unit for top grades.

Browse guides →Syllabus dot points (21)

CCEA A-Level Further Mathematics (specification first taught 2018) is a two-year course split into AS and A2, set and marked by CCEA in Northern Ireland and taken alongside A-Level Mathematics. This page is the index: below is a map of the four examined units, the optional applied sections, the assessment structure, and how to study each unit.

The CCEA Further Mathematics units

The specification has four examined units: two Pure and two Applied, studied across the AS and A2 years.

AS 1 Pure Mathematics
The AS algebraic foundation. It covers complex numbers (arithmetic, the conjugate, the Argand diagram and modulus-argument form), matrices and plane transformations, the roots of polynomial equations, summation of series, mathematical induction, and curve sketching of rational functions. The unifying idea is structure: how algebraic objects behave and how results are proved.
AS 2 Applied Mathematics
The AS applied unit, combining mechanics and statistics. The mechanics covers kinematics with the suvat equations and motion graphs, and forces with Newton's laws, friction and connected particles. The statistics covers sampling and data, and probability with discrete random variables and the binomial distribution.
A2 1 Pure Mathematics
The A2 pure unit, building on AS 1. It covers de Moivre's theorem and complex roots, eigenvalues and eigenvectors, hyperbolic functions, further calculus (Maclaurin series, improper integrals, arc length and surfaces of revolution), polar coordinates, and differential equations.
A2 2 Applied Mathematics
The A2 applied unit, offered as four optional sections: Mechanics 1 (further kinematics and projectiles), Mechanics 2 (momentum and collisions, circular motion and simple harmonic motion), Statistics (the Poisson and normal distributions, the Central Limit Theorem and hypothesis testing), and Discrete and Decision Mathematics (graphs, networks and algorithms). Students answer two sections in permitted combinations.

The optional applied sections

The Applied units present the subject's applied strands as sections. In A2 2 there are four sections - Mechanics 1, Mechanics 2, Statistics, and Discrete and Decision Mathematics - and students answer two of them in permitted combinations (A and B, A and C, A and D, or C and D), each worth 50 percent of the unit. Centres usually teach only the two sections their students will sit, so confirm your school's combination before revising.

Assessment structure

CCEA A-Level Further Mathematics is split between AS (40 percent) and A2 (60 percent), assessed entirely by written examination with no coursework. A formula and statistical tables booklet is provided in every paper.

  • AS 1 Pure Mathematics - a written paper on complex numbers, matrices, series, induction and curve sketching.
  • AS 2 Applied Mathematics - a written paper on mechanics and statistics.
  • A2 1 Pure Mathematics - a written paper on de Moivre, eigentheory, hyperbolic functions, further calculus, polar coordinates and differential equations.
  • A2 2 Applied Mathematics - a written paper with Mechanics 1, Mechanics 2, Statistics and Discrete and Decision sections, of which students answer two.

How to study CCEA Further Mathematics

Further Mathematics rewards fluent technique, full simplification and clear, structured solutions.

  1. Work from the specification statements. Each numbered point is a checklist; questions are written from them.
  2. Secure the AS Pure before the A2 Pure. Complex numbers, matrices and calculus from AS 1 feed directly into A2 1.
  3. Make the standard methods automatic. De Moivre, the matrix inverse and eigentheory, summation and induction, hyperbolic calculus and differential equations should be second nature.
  4. Revise only your chosen applied sections. Focus on the two A2 2 sections your centre teaches, and drill their methods thoroughly.
  5. Drill full past-paper questions. Work under timed conditions and check against CCEA mark schemes, since method marks reward clear structure.

The modules, dot point by dot point

Each unit has a specification-level overview with worked questions and cross-links, plus dot-point pages and a quiz. Browse the full set at /ccea-a-level/further-mathematics/syllabus.

For the official specification

CCEA publishes the full specification, past papers and mark schemes at ccea.org.uk. Always revise from the current CCEA specification and CCEA's own past papers, because question style and section options are board-specific.

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Common questions about Further Maths

How is CCEA A-Level Further Mathematics structured?
CCEA A-Level Further Mathematics is a two-year course split into AS and A2, with four examined units. AS has AS 1 Pure Mathematics and AS 2 Applied Mathematics, each a written examination of 1 hour 30 minutes worth 100 raw marks and 50 percent of the AS; the AS counts for 40 percent of the full A-Level. A2 has A2 1 Pure Mathematics and A2 2 Applied Mathematics, each a written examination of 2 hours 15 minutes worth 150 raw marks and 30 percent of the A-Level. The course assumes the student is also studying or has studied GCE Mathematics.
What are the CCEA A-Level Further Mathematics exam papers?
There are four written papers and no coursework. AS 1 and A2 1 are Pure Mathematics papers. AS 2 and A2 2 are Applied Mathematics papers offering sections in mechanics, statistics and discrete and decision mathematics; in A2 2 the four sections are Mechanics 1, Mechanics 2, Statistics and Discrete and Decision Mathematics, and students answer two of them in permitted combinations. A formula and statistical tables booklet is provided in every paper.
What topics are in CCEA A-Level Further Mathematics?
AS 1 Pure covers complex numbers, matrices and transformations, roots of polynomial equations, summation of series, mathematical induction and curve sketching of rational functions. A2 1 Pure covers de Moivre's theorem, eigenvalues and eigenvectors, hyperbolic functions, further calculus, polar coordinates and differential equations. AS 2 Applied covers kinematics, forces and Newton's laws, sampling and data, and probability with the binomial distribution. A2 2 Applied covers further kinematics and projectiles, momentum and collisions, circular motion and simple harmonic motion, hypothesis testing with the Poisson, normal and Central Limit Theorem, and discrete and decision mathematics.
How do the optional sections in the Applied units work?
The Applied units offer the subject's applied strands as sections. In A2 2 Applied there are four sections, Mechanics 1, Mechanics 2, Statistics and Discrete and Decision Mathematics, and students answer questions from two of them in permitted combinations (A and B, A and C, A and D, or C and D), with each chosen section worth 50 percent of the unit. Centres usually teach only the two sections their students will sit, so confirm which combination your school has chosen before revising.
How hard is CCEA A-Level Further Mathematics, and who should take it?
Further Mathematics is an additional A-Level taken alongside A-Level Mathematics, designed for confident mathematicians, often those intending to study mathematics, physics, engineering or computing at university. It goes well beyond A-Level Mathematics into complex numbers, matrices, hyperbolic functions, differential equations and the chosen applied options. It is demanding but rewarding, and strong fluency in the core A-Level Mathematics content is the best preparation.
How should I revise CCEA A-Level Further Mathematics?
Work unit by unit against the specification statements, because questions are written from them. Secure the AS Pure content before the A2 Pure, since the A2 unit builds on it. Drill the standard methods until they are automatic: complex-number arithmetic and de Moivre, the determinant, inverse and eigentheory of matrices, summation and induction, the calculus of hyperbolic functions and differential equations, and your chosen applied sections. Practise full past-paper questions under timed conditions and check every answer against CCEA mark schemes, since method marks reward clear structure.