# Further Mathematics AS and A level at The Emmbrook School

## Course description

A level Further Mathematics provides students with a deeper understanding of the disciplines included in pure mathematics, mechanics and statistics to meet the needs of university degree courses specialising in Maths, Physics or Engineering. The course requires students to approach problems with enthusiasm and by application of ideas in a thought provoking environment with the support of our equally enthusiastic and highly motivated staff.

## Course content

AS Three modules are required for an AS qualification in Further Maths and a further three modules required for the full A’ level. Further Pure 1- This module covers the basic skills that you will require in Further Maths A’ level and is the only compulsory module in Further Maths AS. In this module you are introduced to complex numbers, matrices, roots of polynomials, rational functions with quadratic denominators, the theory and proof of differentiation, parabolas, ellipses and hyperbolas and the summation of series. As we have a free choice of the other two modules, we try to choose ones that meet the needs of the students both in interest and requirements. Modules studied most recently have been: Decision 1 - covers simple ideas of algorithms, graphs and networks, spanning tree problems, matchings, shortest paths in networks, route inspection problems, travelling salesperson problems, linear programming and mathematical modelling. Decision 2 - covers allocation, critical path analysis, dynamic programming, network flows, linear programming and game theory. Mechanics 1 - covers kinematics in one, two and three dimensions, statics and forces, projectiles, momentum, Newton’s laws of motion, connected particles and mathematical modelling. Mechanics 2 - covers uniform and vertical circular motion, moments and centres of mass, kinematics in three dimensions, work and energy. We try to choose the modules most useful to the needs of each cohort.

A2 Further Pure 3 - In this module we study polar co-ordinates, series and limits and the many methods for solving differential equations of the first and second order. Our choices for the other modules again reflect the requirements of the students in the class. They may include either or both of the two modules not studied at AS or any of the following: Further Pure 2 - The topics studied here are complex numbers, De Moivre’s theorem, hyperbolic functions, proof by induction, arc length and surface area of revolution about the x-axis. Further Pure 4 - The topics studied here are vectors and three-dimensional co-ordinate geometry, matrix algebra, solutions of linear equations, determinants and linear independence. Mechanics 3 - The topics studied here are: - dimensional analysis, relative motion, collisions in one and two dimensions and projectiles on inclined planes. Statistics 2 - This module covers covers discrete and continuous random variables, Poisson distribution, confidence intervals, hypothesis testing and Chi-squared contingency tests.

## Entry requirements

A grade at GCSE

## Financial information

A graphical calculator, Text books.

## Future opportunities

By choosing Further mathematics you provide yourself with the most highly rated A’ level in the country. If you choose to follow a mathematical path then you gain the first step towards higher level mathematics, if you do not then you are still left with a qualification that is admired and respected by both industry and universities. Maths teacher, tax lawyer, operational research, accountant, actuary, computer programmer, software developer, systems analyst, engineer – civil, mechanical, structural electrical, geophysicist. Visit mathscareers.org.uk for more ideas.

## How to apply

If you want to apply for this course, you will need to contact The Emmbrook School directly.