Geneva English School

Further Mathematics

Further Mathematics

To study Further Mathematics you really have to love mathematics, and be really good at it! 

Further Mathematics builds on the material in mathematics A Level.

You’ll learn about more abstract concepts and apply them to many more real-life situations. If you aim to study Mathematics, Physics, Computer Science, Engineering or Economics at a top university like Cambridge, Harvard or the Sorbonne, then studying Further Mathematics A Level is almost essential.


Course Content

What number has the property that its square is negative? The answer to this question is found in the Further Mathematics course, and it also poses new and interesting scenarios in which geometrical skills can be applied to shed light on algebraic problems. 

You’ll learn to use matrices both to solve simultaneous equations and to explore transformations of points and shapes on the plane, and much more about using vectors to describe objects in three dimensions. The calculus which you encounter in your A Level Mathematics course is extended and developed so you’ll be able to solve a much greater number of problems, including finding solutions to equations which involve rates of change. 

You’ll learn how to describe space using not only (x, y) Cartesian coordinates but also with polar coordinates, and through doing so you’ll find some interesting new graphs. The applied lessons will build on the statistics and mechanics encountered in the Mathematics course. You will learn to use certain statistical models (Poisson, exponential, rectangular) to make predictions and test hypotheses, and make sensible assertions about how confident you are in your decisions. You’ll be able to model collisions between particles, use your trigonometric understanding to describe circular motion and employ calculus to Newtonian models to make them more realistic and predictions more accurate.


Inspirational starting point

The Map of Mathematics – Video


Course preparation

You should use (see Mathematics A Level) to keep improving your fluency with the topics you have studied so far, especially algebra, rules of indices and graphs. If you are not already at GES, you can sign up with us in order to see our year 11 scheme of work – it would be useful for you to practice questions from this.

You might also read some general interest maths books such as Chaos by James Gleick or Fermat’s Last Theorem by Simon Singh.


Future pathways

Those who want to study mathematics, physics or computer science at university will benefit greatly from successfully completing the A Level in Further Mathematics. The course challenges students to reason carefully and critically in ways which are beneficial to many other possible study and career paths, and as such a highly regarded qualification it can add weight to applications for all sorts of jobs or university courses.

  • Entrance Criteria
  • Exam board & Specification
  • Assessment

Entrance Criteria

Exam board & Specification