Bury Grammar Schools

Further Maths

Students choose to study Further Mathematics for many of the same reasons that they would choose to study Mathematics.
However, the breadth and depth of their mathematical experience will be significantly greater and will give them a significant advantage when tackling various degree courses, such as Engineering, and of course Mathematics itself. Furthermore, you encounter some of the more fascinating aspects of the subject when you study Further Maths.
Students who choose to study for a Further Mathematics A Level to also have chosen to study Mathematics A Level.

Subject Curriculum

A Level

The A Level will require students to sit four, ninety minute papers at the end of Upper Sixth. These will consist of Further Pure Mathematics 1, Further Pure Mathematics 2, Further Mathematic Option 1, Further Mathematics Option 2.
Further Mathematics Option 1 will require students to choose one of the following options:
  • Further Pure Mathematics 3
  • Further Statistics 1
  • Further Mechanics 1
  • Decision Mathematics 1
Further Mathematics Option 2 will require students to choose one of the following options:
  • Further Pure Mathematics 4
  • Further Statistics 1
  • Further Statistics 2
  • Further Mechanics 1
  • Further Mechanics 2
  • Decision Mathematics 1
  • Decision Mathematics 2
As well as presuming knowledge of the topics taught in A Level Mathematics, A Level Further Mathematics will cover the following extra topics:

Further Pure Mathematics 1 and 2

  • Complex Numbers
  • Matrices
  • Further Algebra and Functions
  • Further Calculus
  • Further Vectors
  • Polar Coordinates
  • Hyperbolic Functions
  • Differential Equations

Further Mathematics 3 and 4

  • Coordinate Systems, Further Vectors
  • Further Numerical Methods
  • Inequalities, Groups
  • Further Matrix Algebra
  • Further Complex
  • Numbers
  • Number Theory
  • Further Sequences and Series

Further Statistics 1 and 2

  • Linear regression
  • Statistical distributions (discrete)
  • Statistical distributions (continuous)
  • Correlation
  • Hypothesis testing
  • Chi squared tests
  • Probability distributions
  • Combinations of random variables
  • Estimation
  • Confidence intervals and tests using a normal distribution
  • Other hypothesis tests and confidence intervals
  • Other hypothesis tests and confidence intervals
  • Probability generating functions
  • Quality of tests and estimators

Further Mechanics 1 and 2

  • Momentum and impulse
  • Collisions
  • Centres of mass
  • Work and energy
  • Elastic strings and springs
  • Further kinematics
  • Further dynamics
  • Motion in a circle
  • Statics of rigid bodies
  • Elastic collisions in two dimensions

Decision Mathematics 1 and 2

  • Algorithms and graph theory
  • Algorithms on graphs
  • Algorithms on graphs II
  • Critical path analysis
  • Linear programming
  • Transportation problems
  • Allocation (assignment) problems
  • Flows in networks
  • Dynamic programming
  • Game theory
  • Recurrence relations
  • Decision analysis