Mathematics (Further)

Course summary

The AS Level Further Mathematics content falls under one of three broad areas: ➢ Core Pure - On this side of the course, some pure topics from A Level mathematics are studied in greater depth, while some new topics are introduced. Algebraic work with series is extended and the powerful technique of proof by induction is used in various contexts. Complex numbers are introduced and these lead to solutions of problems in algebra and geometry. Matrices are used to solve systems of equations and to explore transformations. Vector methods are applied to problems involving lines and planes. ➢ Statistics - On the Statistics side of the course, situations are modeled by discrete random variables; this allows inference about a population in the form of hypothesis testing and point and interval estimates of population parameters. The suitability of models is tested and bivariate data are investigated. ➢ Numerical Methods - Much of AS/A Level Mathematics and Further Mathematics is restricted to problems that are amenable to exact solutions. For many real-world problems, no exact methods exist and numerical methods are required to solve them. On this side of the course, you will learn to apply numerical approaches to four topics from mathematics: solution of equations, differentiation, integration, and approximating functions. You will learn how to use a spreadsheet to implement the methods and learn to analyze the errors associated with numerical methods. The A Level Further Mathematics content both extends those techniques covered in year 12 and introduces new methods and concepts: ➢ Core Pure - Complex numbers are revisited with a particular focus on the solution of problems in trigonometry. Calculus techniques are extended, including the use of hyperbolic functions and polar coordinates, and culminate in the solution of differential equations. ➢ Statistics - In year 13, continuous random variables are considered. Simulation of random variables is also introduced - a powerful way of tackling challenging problems.