Mathematics (Further)

Course summary

Further Mathematics A Level consists of a broad range of topics in Pure Maths, Mechanics, and Statistics. It is taken in addition to Mathematics A Level and only as part of a four A Level study program. The pace is fast, and topics are covered in more depth than in the single Mathematics A Level. Pure Maths is the study of mathematical ideas and methods for their own sake and to give a ‘toolkit’ for solving mathematical problems. All Pure Maths is expressed in terms of algebra. Most of the course is Pure Maths but in addition to this, you will study Statistics and Mechanics. Statistics involves learning how to conclude data. It is very different from Statistics at GCSE and focuses on probability. Mechanics involves using Mathematics to describe the motion of objects and how they respond to forces acting on them – from cars in the street to satellites revolving around a planet. It includes topics such as energy and collisions. The qualification is both deeper and broader than the single, Mathematics A Level, which covers Pure Maths with some Statistics and Mechanics. As well as covering all the material for Mathematics A Level, the Further Mathematics A Level core content introduces additional topics. The additional topics in Pure Maths include: • Imaginary numbers – How negative numbers can have square roots and what the consequences are. This is the basis of chaos theory and is unexpectedly useful in electrical engineering. • Maclaurin’s Series – The Maths behind how values of sin, cos, and tan are found. • Linear Algebra – The Maths behind how a computer can solve 102 simultaneous equations in 102 unknowns as easily as you can solve 2 equations in 2 unknowns. • Second-order differential equations – The Maths behind why bridges can wobble dangerously if people walk across them at a critical speed. The additional topics in Mechanics include: • The mathematics behind bungee jumping. • The mathematics of collisions, such as in snooker. The additional work in Statistics and Probability includes among other things, looking at the Maths behind how casinos ensure they almost always make a profit (and gamblers almost always make a loss!).