Mathematics and Further Mathematics KS5

What will I learn on this Advanced GCE course?

Mathematics at AS and Advanced GCE is a course worth studying not only as a supporting subject for the physical and social sciences, but in its own right. It is challenging but interesting. It builds on work you will have met at GCSE, but also involves new ideas upon which some of the greatest minds of the last millennium have focused. It serves as a very useful support for many other qualifications as well as being a sought-after qualification for the workplace and courses in higher education courses.

While studying mathematics you will be expected to:

  • use mathematical skills and knowledge to solve problems
  • solve increasingly complex problems by using mathematical arguments and logic. You will also have to understand and demonstrate what is meant by proof in mathematics
  • use the mathematics that you learn to solve problems that are given to you in a real-life context, simplifying and modeling to show what is happening and what might happen in different circumstances
  • use technology and other resources (such as formulae booklets or statistical tables) effectively and appropriately; understand calculator limitations and when it is inappropriate to use such technology.

Mathematics at AS and Advanced GCE is divided into four branches:

Pure Mathematics

When studying pure mathematics at AS and A-level you will be extending your knowledge of such topics as algebra and trigonometry as well as learning some brand new ideas such as calculus developed by Newton and Leibnitz in the 17th century. This topic forms a central core to many areas of study including graphs, areas, optimization and motion. If you enjoyed the challenge of problem solving at GCSE, then you should find the prospect of this course very appealing. Although all of the ideas you will meet in pure mathematics are interesting in their own right, they also serve as an important foundation for other branches of mathematics, especially mechanics and statistics.


When you study mechanics you will learn how to describe mathematically the motion of objects and how they respond to forces acting upon them, from cars in the street to satellites revolving around a planet. You will learn the technique of mathematical modelling; that is, of turning a complicated physical problem into a simpler one that can be analysed and solved using mathematical methods. Many of the ideas you will meet in the course form an almost essential introduction to such important modern fields of study as cybernetics, robotics, biomechanics and sports science, as well as the more traditional areas of engineering and physics.

Probability and Statistics

When you study probability and statistics you will learn how to analyse and summarise numerical data in order to arrive at conclusions about it. You will extend the range of probability problems that you started for GCSE by using the new mathematical techniques studied on the pure mathematics course. Many of the ideas you will meet in this course have applications in a wide range of other fields – from assessing what your car insurance is going to cost to how likely the earth is going to be hit by a comet in the next few years.

Decision Mathematics (Further Mathematics)

When you study decision mathematics you will learn how to solve problems involving networks (for example, the quickest way to salt the most important icy roads in winter or how to travel the London Underground arriving at each station once only!). You will study a range of methods, or algorithms, which enable such problems to be tackled. Many of these problems and their algorithms are of recent origin (late 20th century). Ideas on this course have many important applications in business and industry such as the design of circuits on microchips to the scheduling of tasks required to build a new sports stadium.

The Units.

AS Mathematics comprises the study of three units (including C1 and C2). For A-level Mathematics three more units (including C3 and C4) are studied. The units available are shown below.

Pure Mathematics                   Options C1, C2, C3, C4, FP1, FP2, FP3.
Mechanics                              Options M1, M2, M3, M4.
Probability and Statistics         Options S1, S2, S3.
Decision Mathematics             Options D1, D2.

At St Michael’s we wish to ensure that all students are fully prepared for university courses involving a mathematical element. Therefore during Year 12, units C1, C2 and S1 are studied, this forms the AS Mathematics qualification, and in Year 13 you will go on to study C3, C4 and M1.

The examination board used is OCR. Each unit is examined by a 1½ hour examination. All examinations are taken either at the end of Year 12 or at the end of Year 13. There is no coursework.

Each unit has an associated text book, which all students must purchase. For Year 12 the text books are Core 1 and 2 for OCR (isbn 0 521 54896 9) and Statistics 1 for OCR (isbn 0 521 54893 4).

AS Further Mathematics (3 additional units) can also be studied. As can A-level Further Mathematics, which involves the study of six additional units (that is, twelve in total, over two years). These qualifications are highly prestigious and are essential for any student thinking of studying Mathematics at University. It has also proved very useful to students preparing for University courses with a sizeable mathematics input, including sciences at Oxford and Cambridge.

The additional units studied will include further pure mathematics units as well as applied units, although these will vary according to demand.

Again, each further mathematics unit has an associated text book, which all students must purchase. For Year 12 the text books are Further Pure 1 for OCR (isbn 0 521 54898 5), Decision 1 for OCR (isbn 0 521 61914 9) and Decision 2 for OCR (isbn 0 521 61915 7).

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