GCSE Mathematics covers many basic skills that will be needed in a variety of ways throughout life, and because of this it is a compulsory subject for all students up to GCSE. In common with many other schools, we at Hurstpierpoint College have decided that we will not enter our top set for GCSE at the end of the Remove (Year 10); however, this policy is under constant review and it is possible that in the future the top set may take GCSE Mathematics in November of the Fifth Form (or even earlier). Pupils in the top set should expect to be stretched throughout the Remove and Fifth Form, often studying topics that are beyond the syllabus. In this way they will be ready to tackle Mathematics in the Sixth Form and, should they choose, Further Mathematics also. Since Summer 2006 the top set has taken the GCSE in Statistics in addition to Mathematics. This policy is under review and it is possible that in the future the top set will be entered for the “Free-Standing Mathematics Qualification” in Additional Mathematics.
The work is a natural progression from studies in the Shell (Year 9) and earlier years. GCSE Mathematics covers a wide range of basic mathematical knowledge and skills. There is no coursework in GCSE Mathematics and there are two written papers at the end of the course, each work 50% of the final assessment.
There are two tiers of assessment at GCSE: the highest grade available on the Foundation Tier is grade C and therefore most, if not all, Hurst pupils will sit the Higher Tier. In the past our weaker pupils have followed a shorter syllabus and it is anticipated that this will continue to be the case: weaker students will not be expected to tackle every topic of Higher Tier, concentrating instead on those topics which are within their ambit. Our aim will always be to get the very best possible grade for each individual student. Some or all of the weakest set may sit the Foundation Tier papers; decisions about which students sit which tier may be made as late as the term before the examinations.
Those embarking on Mathematics at AS level should have studied Higher Level Mathematics at GCSE. Grade B should be considered as the minimum requirement for study to AS Level, whilst a grade A is desirable if study is to continue to A2. Those who are predicted A* at GCSE (or who will come close) should also consider studying Further Mathematics. The top universities are increasingly interested in students who studied mathematics beyond the single A Level.
There are four areas of Mathematics which may be studied as part of a Sixth Form course: Pure Mathematics is mandatory in all courses and provides the methods which are required to solve problems considered from a practical context. Concepts and methods in Algebra and Trigonometry are developed further while Calculus and Coordinate Geometry are introduced. Techniques from Pure Mathematics apply not only to other areas of Mathematics but in certain other A level subjects such as Physics and Chemistry. Mechanics is a development of ideas familiar from Physics. The mathematical modelling of physical situations is considered with a view to solving the problems they pose. Newton's laws of motion are the central theme of an introductory course. Statistics reviews various methods for the collection of data and considers how data may be summarised and represented graphically. Probability laws and the concept of a random variable are introduced. Decision Mathematics considers applications of discrete mathematics to problems in a highly technological world and is closely related to some aspects of Computing. Concepts from the GCSE Mathematics course are developed and a number of different algorithms are studied.
The Pure Mathematics makes up the core of the AS and A Level programme of study and these units are designated C1-C4. An AS in Mathematics will be made up from C1, C2 and a single applications module. The full A Level will comprise C1-C4 and two applications modules. We aim to cover the mechanics module with those students who are studying Physics, and the statistics module with those who are not. However, this is partly dependent on other subjects chosen. In the Upper Sixth the students will usually study a module in Decision Mathematics, D1. Since all units at the “1” level, plus C2 are AS modules, the astute reader will have seen that it is possible to gain an A Level in Mathematics by taking four AS modules and only two A2 modules. Mathematics is unique in this respect.
Summary:
AS Mathematics: C1, C2 plus M1 or S1
A2 Mathematics: C3, C4 plus D1 (other options may be offered)
Degree courses in Engineering, Design, Computer Science, Medicine and the Physical Sciences follow naturally from a GCE qualification in Mathematics and develop many of the concepts and ideas introduced in the Sixth Form. Careers in Architecture and Accountancy (amongst others) will also benefit from a good qualification in Mathematics as this indicates both the abilities to think logically and to explain clearly, required in the course, in addition to an appreciation of mathematical rigour.
This course, as its name implies, goes beyond the requirements of the Mathematics A level, both in depth and breadth; many of the branches of the Mathematics A level are studied more fully and new topics such as complex numbers are introduced. This is a demanding course, suitable only for the more able mathematicians who have a natural flair and enthusiasm for the subject. Further Mathematics is studied in addition to Mathematics A level and provides an excellent foundation for those intending to pursue their Mathematics further, whether in its own right or as part of an Engineering, Finance or Computing degree. In particular, those considering courses at Oxford or Cambridge (or other top universities) which require a mathematical background would benefit from studying at least some of the Further Mathematics course.
For Further Mathematics, students should have at least a good grade A in GCSE Mathematics, preferably A*. In addition, some study of Mathematics beyond GCSE would be beneficial, but is not essential. Success in the Mathematical Challenges – particularly a Gold Certificate – is another indication of suitability for the course. The Further Mathematics course for the Lower Sixth is the same for both AS and A levels and extends the work in Pure Mathematics and a second applications module is studied. In the Upper Sixth a decision can be taken about whether to continue to study for the full A level (12 modules in total), or stop at AS level (9 modules).
The full A level in Further Mathematics, completed in the Upper Sixth, considers concepts such as group theory and vector algebra in Pure Mathematics. The nature and different types of proof within Mathematics are vital to the course and permeate each of the topics covered. Further modules in Mechanics and/or Statistics are also studied. There may be the opportunity for suitably motivated candidates to study for some modules on their own. Students who have done this in recent years have achieved considerable success.
The approach for Further Mathematics is very similar to that for Mathematics with written work assessed regularly. The emphasis on mathematical rigour is even more important to gain a full appreciation of the subject.
Six Mathematics modules are taken at the end of the Lower Sixth. Remaining modules are taken in January or June of the Upper Sixth: nine in total for A Level Mathematics and AS Level Further Mathematics and twelve for two full A Levels. Further Mathematics may be studied as either a fourth or fifth subject in the Lower Sixth and usually as a fourth subject in the Upper Sixth. A student who is unsure about their ability to cope with Further Mathemtics can start it as a fifth subject; should the burden prove too great, the student could drop to just Mathematics and still obtain four AS grades at the end of the Lower Sixth. Further Mathematics gets a lesson allocation of five hours per fortnight, half that of other subjects, so the extra burden for a good mathematician is small. Study of Further Mathematics provides a much fuller understanding and appreciation of the subject and can lead to careers such as a Scientific Researcher or an Actuary. Further Mathematics provides a very useful foundation for some degree courses in Engineering which have an emphasis on theory.
Summary:
AS Further Mathematics: C1, C2, C3, FP1, M1 and one more applications module in the Lower Sixth C4 plus two applications modules in the Upper Sixth
A2 Further Mathematics: C1, C2, C3, FP1, M1 and one more applications module in the Lower Sixth C4, FP2, plus 4 from M2, M3, M4, S1, S2, D1, D2 in the Upper Sixth
For the student who has enjoyed and thrived on the challenges in the double Mathematics A level courses, the possibility of a degree devoted to mathematics, specialising in areas of particular interest, is an enticing prospect. Confidence and competence with algebraic techniques are vital for success in Further Mathematics.
10 September 2010