Quick Links

Quick Links

Aquinas Diocesan Grammar School

  • SearchSearch Site
  • Translate Translate Page
  • Twitter Twitter
  • Facebook Facebook
  • iPayimpact iPayimpact

Further Mathematics







The Key Stage 4 Further Mathematics curriculum is based on the CCEA GCSE Further Mathematics course.

Aims and Key Features

This specification aims to encourage students to:

develop further their mathematical knowledge, skills and understanding;

select and apply mathematical techniques and methods to mathematical, everyday and real-world situations;

reason mathematically, interpret and communicate mathematical information, make deductions and inferences, and draw conclusions;

extend their base in mathematics from which they can progress to:

o higher studies in mathematics;

o studies such as science, geography, technology or business, which contain a significant requirement in mathematics beyond Higher Tier GCSE Mathematics;

design and develop mathematical models that allow them to use problem-solving strategies and apply a broader range of mathematics to a variety of situations.

The following are important features of this specification.

It is designed to broaden the experience of students whose mathematical ability is above average and who would like to:

o study mathematical courses at AS/A level;

o study other courses at AS/A level that require mathematics beyond GCSE Higher Tier;

o extend their knowledge of mathematics.

It gives students the appropriate mathematical skills, knowledge and understanding to help them progress to further academic and vocational study and to employment.

Course Structure

This specification comprises three units. All units are assessed through an external written examination in the form of a single question-and-answer booklet that includes a formula sheet.

Unit 1 Pure Mathematics - 50% - 2 hours

Unit 2 Mechanics - 25% - 1 hour

Unit 3 Statistics - 25% - 1 hour

The units address the three assessment objectives for this specification:

AO1: Use and apply standard techniques;

AO2: Reason, interpret and communicate mathematically;

AO3: Solve problems in mathematics and other contexts

Subject Content

Some of the content associated with each unit appears below.

Unit 1 Pure Mathematics

Algebraic Fractions, Algebraic Manipulation, Completing the Square, Simultaneous Equations, Quadratic Inequalities, Trigonometric Equations, Differentiation, Integration, Logarithms, Matrices

Unit 2 Mechanics

Kinematics, Vectors, Forces, Newton’s Laws of Motion, Moments

Unit 3 Statistics

Central Tendency and Dispersion, Probability, Binomial Distribution, Normal Distribution, Bivariate Analysis



The Key Stage 5 Further Mathematics curriculum is based on the CCEA GCE Advanced Subsidiary (AS) and Advanced (A level) GCE courses in Further Mathematics.


This specification aims to encourage students to:

understand mathematics and mathematical processes in a way that promotes confidence, fosters enjoyment and provides a strong foundation for progress to further study;

extend their range of mathematical skills and techniques;

understand coherence and progression in mathematics and how different areas of mathematics are connected;

apply mathematics in other fields of study and be aware of the relevance of mathematics to the world of work and to situations in society in general;

use their mathematical knowledge to make logical and reasoned decisions in solving problems both within pure mathematics and in a variety of contexts, and communicate the mathematical rationale for these decisions clearly;

reason logically and recognise incorrect reasoning;

generalise mathematically;

construct mathematical proofs;

use their mathematical skills and techniques to solve challenging problems that require them to decide on the solution strategy;

recognise when they can use mathematics to analyse and solve a problem in context;

represent situations mathematically and understand the relationship between problems in context and mathematical models that they may apply to solve these;

draw diagrams and sketch graphs to help explore mathematical situations and interpret solutions;

make deductions and inferences and draw conclusions by using mathematical reasoning; 

interpret solutions and communicate their interpretation effectively in the context of the problem;

read and comprehend mathematical arguments, including justifications of methods and formulae, and communicate their understanding;

read and comprehend articles concerning applications of mathematics and communicate their understanding;

use technology such as calculators and computers effectively, and recognise when such use may be inappropriate;

take increasing responsibility for their own learning and the evaluation of their own mathematical development.

Course Structure 

The course has been divided into four units: two units at AS and two units at A2. All units are assessed through external written examinations

AS 1: Pure Mathematics - 1hr 30mins - 50% of AS (20% of A level)

AS 2: Applied Mathematics - 1hr 30mins - 50% of AS (20% of A level)

A2 1: Pure Mathematics - 2hrs 15mins - 30% of A level

A2 2: Applied Mathematics – 2hrs 15mins - 30% of A level


This section sets out the content and some of the learning outcomes for each unit.

Year 13

Unit AS 1 Pure Mathematics

Algebra and Functions - Roots of Quadratic Equations

Complex Numbers - Cartesian and Modulus-Argument Forms, Argand Diagrams, Solving Quadratic, Cubic, Quartic Equations

Matrices - Linear Transformations, Systems of Simultaneous Linear Equations

Vectors - Equation of Line, Scalar and Vector Products, Equation of Plane, Area and Volum

Unit AS 2 Applied Mathematics Section A: Mechanics 1

Hooke’s Law - Elastic Strings and Springs

Work and Energy - Work Done by Force, Principle of Conservation of Mechanical Energy, Work-Energy Principle

Power - Vehicles in Motion, Pumps

Circular Motion - Motion in Horizontal Circle, Conical Pendulum, Banked Corners

Unit AS 2 Applied Mathematics Section C: Statistics

Sampling - Simple Random, Stratified, Quota, Cluster, Opportunity

Probability - Permutations and Combinations

Statistical Distributions - Geometric Distribution, Poisson Distribution, Discrete and Continuous Probability Distributions, Coding

Bivariate Distributions - Product Moment Correlation Coefficient, Least Squares Regression Analysis

Year 14

Unit A2 1 Pure Mathematics

Proof - Mathematical Induction

Further Algebra and Functions - Partial Fractions, Summation of Series, Maclaurin Series

Complex Numbers - De Moivre’s Theorem, Complex Roots of Unity

Further Calculus - Improper Integrals, Integration using Partial Fractions, Repeated Integration by Parts, Simple Reduction Formulae

Polar Coordinates - Curve Sketching, Area Enclosed by Polar Curve

Hyperbolic Functions - Differentiation and Integration of, Logarithmic Forms of Inverse Hyperbolic Functions

Differential Equations - Integrating Factor Method, First and Second Order Differential Equations

Unit A2 2 Applied Mathematics Section A: Mechanics 1

Simple Harmonic Motion - Simple Pendulum, Elastic Strings and Springs

Damped Oscillations - Model using Second Order Differential Equations

Centre of Mass - Systems of Particles and Rods, Laminae

Frameworks - Problems involving Tension and Thrust

Further Circular Motion - Banked Corners including Sliding and Overturning

Unit A2 2 Applied Mathematics Section B: Mechanics 2

Further Kinematics - Kinematics in 3D, Variable Acceleration

Further Centre of Mass - Laminae and Solids, Suspended Bodies, Sliding/Toppling Problems

Force Systems - System of Coplanar Forces, Couples

Restitution - Elastic Collisions

The A2 assessment units include some synoptic assessment, which encourages candidates to develop their understanding of the subject as a whole.

The A2 assessment units provide opportunities to demonstrate higher order thinking skills by incorporating:

more demanding unstructured questions;

questions that require candidates to make more connections between sections of the specification.