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Further Mathematics AS/A Level at S. Peter's Collegiate School - A CofE Academy

Course description

This course will build upon GCSE Mathematics knowledge to a greater extent than single Mathematics – extending familiar algebraic, spatial and statistical concepts.  It therefore has to be taken in conjunction with single mathematics at A Level.

  • There is no coursework component in this specification, which allows students more time to concentrate on practising their techniques.
  • All students have to complete three compulsory Further Pure Modules over the two years (one at AS and two at A2)
  • The Advanced (A Level) award comprises six units
  • Students will have the opportunity of completing two Applied Modules in Year 12 (Decision 1 and Statistics 1). In Year 13 the final applied modules will depend on student interest and numbers.
  • Each paper will consist of short (4 or 5 marks) and long questions (up to 18 marks).
  • Students studying Further Mathematics must opt for Mechanics 1 in single Mathematics lessons.
  • All units will be examined in the summer.
  • Candidates for AS are expected to have already obtained (or to be obtaining concurrently) an AS and/or A Level award in Mathematics.

Course content


Unit 1Mathematics Further Pure 1 (Code: FMP1)

  • Algebra and Graphs
  • Complex Numbers
  • Roots and Coefficients of a quadratic equation
  • Series
  • Calculus
  • Numerical Methods
  • Trigonometry
  • Matrices and Transformations

Unit 2 –  Mathematics Decision 1 (Code: MDO1)

  • Simple Ideas of Algorithms
  • Graphs and Networks
  • Spanning Tree Problems
  • Matchings
  • Shortest Paths in Networks
  • Route Inspection Problem
  • Travelling Salesperson Problem
  • Linear Programming
  • Mathematical Modelling

Unit 3 –  Mathematics Statistics 1 (Code: MS1B)

  • Numerical Measures
  • Probability
  • Binomial Distribution
  • Normal Distribution
  • Estimation
  • Correlation and Regression


Unit 4Mathematics Further Pure 3 (Code: MFP3)

  • Series and Limits
  • Polar Coordinates
  • Differential Equations
  • Differential Equations . First Order
  • Differential Equations . Second Order

Unit 5Mathematics Further Pure 4 (Code: MFP4)

  • Vectors and Three-Dimensional Coordinate Geometry
  • Matrix Algebra
  • Solution of Linear Equations
  • Determinants
  • Linear Independence

AS Optional Modules Unit 6 (Choose one unit)

Mathematics Further Pure 2 (Code: MFP2)

  • Roots of Polynomials
  • Complex Numbers
  • De Moivre’s Theorem
  • Proof by Induction
  • Finite Series
  • The Calculus of Inverse Trigonometrical Functions
  • Hyperbolic Functions
  • Arc Length and Area of surface of revolution about the x-axis

Mathematics Decision 2 (Code: MDO2)

  • Critical Path Analysis
  • Allocation
  • Dynamic Programming
  • Network Flows
  • Linear Programming
  • Game Theory for Zero Sum Games
  • Mathematical Modelling

Mathematics Statistics 2 (Code: MS2B)

  • Discrete Random Variables
  • Poisson Distribution
  • Continuous Random Variables
  • Estimation
  • Hypothesis Testing
  • Chi-Square Contingency Table Tests

Mathematics Mechanics 3 (Code: MM03)

  • Relative Motion
  • Dimensional Analysis
  • Collisions in one dimension
  • Collisions in two dimensions
  • Further Projectiles
  • Projectiles on Inclined Planes

Mathematics Mechanics 4 (Code: MM04)

  • Moments
  • Frameworks
  • Vector Product and Moments
  • Centres of mass by Integration for Uniform Bodies
  • Moments of Inertia
  • Motion of a Rigid Body about a Fixed Axis

Mathematics Mechanics 5 (Code: MM05)

  • Simple Harmonic Motion
  • Forced and Damped Harmonic Motion
  • Stability
  • Variable Mass Problems
  • Motion in a Plane using Polar Coordinates

Entry requirements

GCSE Higher Tier – Grade A at Higher Tier

GCSE APS of 43


A written paper for each of the 3 units lasting 1 hour 30 minutes

Maximum Marks available:

Each unit has 75 marks in total which is scaled to a UMS mark of 100.

Information regarding Assessment:

All questions are compulsory.

A scientific or graphics calculator can be used.

Weighted at 16.7% of an A Level.

How to apply

If you want to apply for this course, you will need to contact S. Peter's Collegiate School - A CofE Academy directly.

Last updated date: 04 December 2014
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Key information

  • Start date: Next September
  • Duration: 1-2 years