International AS and A-level Further Mathematics (9665)

Further Mathematics

Challenge your most able mathematicians in preparation for university.

This Further Mathematics qualification is a rigorous second AS/A-level in maths. It provides challenge for the most able mathematicians who are intending to study a maths-related degree.

International AS/A-level Further Mathematics (9665)

Unit FP1: Pure maths (AS)

Unit FPSM1: Pure maths, statistics and mechanics (AS)

Unit FP2: Pure maths (A2)

Unit FS2: Statistics OR Unit FM2: Mechanics (A2)

Pure Maths (AS and A-level)
  • Algebra and graphs
  • Coordinate geometry
  • Complex numbers
  • Roots and coefficients of a quadratic equation
  • Differentiation
  • Trigonometry
  • Calculus
Pure, Statistics and Mechanics (AS and A-level)
  • Matrices and transformations
  • Linear graphs
  • Numerical methods
  • Bayes’ Theorem
  • Uniform distribution
  • Geometric distribution
  • Probability generating functions
  • Linear combinations of discrete random variables
  • Constant velocity in two dimensions
  • Dimensional analysis
  • Collisions in one dimension
Pure Maths (A-level only)
  • Roots and polynomials
  • De Moivre’s Theorem
  • Polar coordinates
  • Proof by induction
  • Finite series
  • Series and limits
  • The calculus of inverse trigonometrical functions
  • Arc length and area of surface of revolution about the x-axis
  • Hyperbolic functions
  • Differential equations – first order
  • Differential equations– second order
  • Vectors and three-dimensional coordinate geometry
  • Matrix algebra
  • Solution of linear equations
Statistics and Mechanics (A-level only)
  • Moment generating functions
  • Estimators
  • Estimation
  • Further hypothesis testing
  • Vertical circular motion
  • Projectiles launched onto inclined planes
  • Elastic strings and springs
  • Collisions in two dimensions
  • Application of differential equations
  • Simple harmonic motion

The exams will measure how students have achieved the following assessment objectives:
• AO1: Recall and select knowledge of mathematical facts, concepts, models and techniques required to solve problems in a variety of contexts.
• AO2: Construct rigorous mathematical arguments and proofs through use of precise statements, mathematical manipulation, logical deduction, modelling assumptions and justifications to solve structured and unstructured problems, and to deduce, interpret and communicate results.


  • Candidates may re-sit a unit any number of times.
  • The best result for each unit will count towards the final qualification.
  • Candidates who wish to repeat a qualification may do so by re-sitting one or more units.

Find all the resources you need to teach Further Mathematics in our resources for teachers pages.

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