For centuries, it was believed that the only numbers that existed were whole numbers and fractions. It was only discovered in Ancient Greece that numbers such as the square root of two do not fit these descriptions and so are known as irrational. All was well in Mathematics until 1000 years later with the discovery of complex numbers, which introduced the square roots of negative numbers, extending beyond the real number line. Today, animators at companies such as Pixar use these mysterious complex numbers frequently to describe and implement 2D computer animations, a feat perhaps not considered at the time of their discovery.

At its core, Further Mathematics explores the ways in which inquisitive minds from antiquity have given rise to our modern technological society. For example, in the Further Core module, you will learn how differential equations have been used to model the oscillation of an engine, or could track the leaking of oil in the Gulf of Mexico in 2010. Similarly, by studying the methods of Newton and Leibniz, you can see how calculus can be used in manufacturing to determine the volumes of curved shapes.

Algorithms describe the mathematical processes which govern our daily lives. For instance, the use of a simple algorithm which finds the highest common factor of two integers can be used to help secure sensitive online information, or allow government operatives to send encrypted messages without enemy interception. Similarly, Sat-Navs use Djikstra’s algorithm to find the shortest path between two locations. Algorithms such as these are studied in the Decision Mathematics module of the course. Finally, the Further Mechanics module, which studies the motion and energy present in systems of objects, will further interest scientifically-minded individuals.

Our Further Mathematics course is ideal for students wishing to pursue Mathematics or a related subject at Higher Education, as it is the perfect introduction to undergraduate material and is a qualification highly regarded by universities.

## COURSE CONTENT AND AIMS

This is a challenging qualification, which both extends and deepens your knowledge and understanding beyond the standard A level Mathematics. For someone who enjoys mathematics, it provides a challenge and a chance to explore new and/or more sophisticated mathematical concepts. As well as learning new areas of pure mathematics you will study further applications of mathematics in mechanics, statistics and decision mathematics.

Students who take Further Mathematics find that the additional time spent studying mathematics boosts their marks in single A level Mathematics.

This course builds on all that is covered in A level Mathematics and provides the opportunity to work on decision mathematics or more advanced statistics and mechanics.

## PROGRESSION

A level Mathematics makes the transition from sixth form to university courses that are mathematically rich much easier. If you are planning to take a degree such as Engineering, Sciences, Computing, Finance/Economics, etc. or perhaps Mathematics itself, you will benefit enormously from taking Further Mathematics, at least to AS Level. AS Further Mathematics introduces new topics such as matrices and complex numbers that are vital in many STEM degrees. Further Mathematics qualifications are highly regarded and are warmly welcomed by universities. Some prestigious university courses require you to have a Further Mathematics qualification and others may adjust their grade requirements more favourably to students with Further Mathematics.

## ASSESSMENT

This course will be assessed over four papers, each representing one quarter of the overall grade, all of which have to be sat in the same academic year. Papers 1 and 2 (Further Pure Mathematics 1 and 2) will assess Proof, Complex numbers, Matrices, Further algebra and functions, Further calculus, Further vectors, Polar coordinates, Hyperbolic Functions and Differential equations. Unlike the Mathematics A level pupils can choose what further areas they wish to study by choosing two papers from the following list. Further Pure Mathematics 3 (Further calculus, Further differential equations, Coordinate systems, Further vectors, Further numerical methods, Inequalities), Further Pure Mathematics 4 (Groups, Further calculus, Further matrix algebra, Further complex numbers, Number theory, Further sequences and series), Further Statistics 1 (Linear regression, Statistical distributions (discrete), Statistical distributions (continuous), Correlation, Hypothesis testing, Chi squared tests), Further Statistics 2 (Probability distributions, Combinations of random variables, Estimation, Confidence intervals and tests using a normal distribution, Other hypothesis tests and confidence intervals, Probability generating functions, Quality of tests and estimators),

Further Mechanics 1 (Momentum and impulse, Collisions, Centres of mass, Work and energy, Elastic strings and springs),

Further Mechanics 2 (Further kinematics, Further dynamics, Motion in a circle, Statics of rigid bodies, Elastic collisions in two dimensions), Decision Mathematics 1 (Algorithms and graph theory, Algorithms on graphs, Algorithms on graphs II, Critical path analysis, Linear programming) or Decision Mathematics 2 (Transportation problems, Allocation (assignment) problems, Flows in networks, Dynamic programming, Game theory, Recurrence relations, Decision analysis)

## ENTRY REQUIREMENTS

For admission to A level Further Mathematics, our usual minimum requirements are:

- Students wishing to study Science or Maths at A level will need to achieve a grade 7.