Mathematics and Further Mathematics

MATHEMATICS and FURTHER MATHEMATICS

WHAT DOES THE COURSE INVOLVE?

Compared with the GCSE course, you will find that a much greater part of lesson time is taken up with discussion of new ideas and techniques, leaving much of your own written practice to be completed privately. As the course progresses, an increasing emphasis is placed on developing your ability to present a reasoned solution to a problem, rather than on simply obtaining an “answer”.

Pure Mathematics (Part of A level Mathematics but extended in the Further Mathematics A level)

It develops the algebraic techniques of simplification and equation solving well beyond the level of GCSE. The two branches of calculus are introduced: “differentiation” deals with the way in which continuously varying quantities change, and “integration” studies the cumulative effect of a continuous vaiable. Other topics include: the study of geometry through graphical representation, further development of algebraic and trigonometric functions, and the introduction of logarithmic and exponential functions.

Mechanics (Part of A level Mathematics but extended in the Further Mathematics A level)

Mechanics is the study of forces and motion. It explores the properties of position, velocity, acceleration, force, momentum, energy, power and work for a moving object, and the relationships between the forces acting on a stationary object.

Statistics (Part of A level Mathematics but extended in the Further Mathematics A level)

Statistics is concerned with the collection, organisation, representation, analysis, and interpretation of data.

Topics covered are:-

– Descriptive statistics.

– Probability.

– Random variables.

– Linear regression.

– Sampling.

– Hypothesis testing.

Discrete Mathematics (Taken as part of the Further Mathematics course)

This covers problem-solving techniques (flow-charts and algorithms), network theory such as the most efficient way to traverse a network (the “travelling salesman problem”) and linear programming (how to maximise profit or efficiency when there are constraints on the quantities available).

WHAT QUALIFICATIONS DO I NEED?

Students wishing to study Mathematics at Advanced Level are recommended to have a grade 9, 8, 7 or 6 at GCSE; and to have been entered for the Higher Tier. Further Mathematics is usually taken by students who have a grade 9 or 8 at GCSE.

Equipment

calculator that can perform calculations with statistical distributions and deal with 3×3 matrices is essential for both Mathematics and Further Mathematics. The recommended calculator is the Casio FX-991 EX, which will be available to purchase through the school. A graphical calculator is not essential but some types are permitted in the examination – students will be made aware of allowed calculators at the commencement of the course.

ASSESSMENT

The course is linear, with three two hour examinations, taken at the end of year 13. Also on offer is Further Mathematics, again examined at the end of year 13 by three two hour examinations. Further Mathematics takes the pure maths to a greater depth, introduces discrete maths and continues the study of statistics and mechanics. Further Mathematics is very much aimed at those students who are thinking of studying maths, or a subject which is maths ‘heavy’, at university. Further Mathematics cannot be taken by a student who is not also studying A level Mathematics. In Further Mathematics there is the option to sit the third examination on a combination of either
Mechanics and Statistics, Mechanics and Discrete or Statistics and Discrete.

FUTURE PROSPECTS

Mathematics qualifications are inevitably highly regarded in many areas of work: computer studies, finance, engineering, logistics, management, science and systems analysis are all areas looking for well qualified mathematicians.