FURTHER MATHEMATICS (PEARSON)

AS Course Outline

What is Further Mathematics AS?

Further Mathematics AS extends above the standard Mathematics A-level. It strengthens university applications in Mathematics, Sciences and Social Sciences, or it may be studied to take your understanding of Mathematics a few steps deeper and a few topics wider than the standard A-level.

It also gives you the chance to study Applied Mathematics more deeply and increase your knowledge in an area of particular interest, skill or assistance to other studies. You can choose modules in Mechanics (which will compliment studies in Physics), Statistics (to compliment and prepare you for studies in Biology, Economics and the Social Sciences) or in Decision Mathematics (which will enhance your studies of Computer Science, Economics or Business-Studies). In each applied strand the modules build upon previous ones, for example it is very difficult to perform well in Mechanics 2 without already having a good understanding and result in Mechanics 1.

Further Mathematics AS is accessible to students who are doing well in Mathematics A-level, typically those on course for a B grade or higher, extending and broadening your knowledge without the formidable challenge of the full Further Mathematics A-level, which requires a much greater degree of problem solving skills.

What Topics will I study?

In Further Pure Mathematics 1 you will:

• Find out what matrices are and learn to manipulate them to transform data and co-ordinates as used in Economics, Science, Graphic Design and Computer Science.
• Find out how to prove general relationships by inspecting just a few cases; a process analogous to knocking over the first domino pictured above.
• Discover what happens when we imagine the square root of a negative number, an idea which has shed light in, for example, the world of Quantum Physics.
• Learn how to generate approximate numerical answers to problems.

In addition you will take two modules of Applied Mathematics which will build upon those covered in Mathematics A-level. In Statistics you learn how to test ideas and claims using the scientific method, and find out how confident you can be in your answers. Mechanics provides you with skills to model motion, forces and stability. Decision mathematics introduces techniques to plan for optimal efficiency, providing management and leadership skills as well as the logical foundations of computer programming.

FURTHER MATHEMATICS (EDX) AS Specification Each paper has a 1½ hour exam with 75 marks and is equally weighted toward the AS qualification.
Paper 1 Compulsory 50%	Core Pure Mathematics 1: Series, complex numbers, numerical solutions of equations, co-ordinate systems, matrix algebra, proof.
Paper 2 One of the following (7 options not listed) 50%	2A: Further Pure Mathematics 1 & 2 Inequalities, series, first & second order differential equations, further complex numbers, Maclaurin and Taylor Series. 2B: Further Pure Mathematics 1 & Further Statistics 1 Starting from the analysis and representation of data, statistics moves towards testing the truth of claims and quantitatively considering bias and the efficiency of methods. 2C: Further Pure Mathematics 1 & Further Mechanics 1 The study of forces and motion, building up from Newton's laws in one dimension with a constant force to more dimensions, variable forces and composite bodies. 2D: Further Pure Mathematics 1 & Further Decision Mathematics 1 Looks to optimise systems, finding the most efficient and suitable method for completing a variety of tasks.

Structure of the Course
This course will be taught for 5x 1hour lessons per week. Homework is set at the end of each session and deadlines for submissions must be met. A full set of notes and examination questions is provided. The UK Senior Mathematics Challenge is offered as an enrichment activity.

Introductory Reading

Number: A Very Short Introduction by Peter M. Higgins

Core Textbooks
Edexcel AS and A level Further Mathematics Core
Pure Mathematics Book 1/AS Textbook

Recommended Reading
Euler: The Master of Us All    ISBN-13: 978-0883853283 William Dunham
Letters to a Young Mathematician    ISBN-13: 978-0465082322 Ian Stewart