# Further Mathematics A Level at Truro and Penwith College

## Course description

Further Mathematics provides an excellent preparation for a wide range of university courses as well as being a versatile qualification that is well respected by employers. Further Mathematics is an essential requirement for many degree level Mathematics courses. By studying Further Mathematics you will increase your knowledge and understanding of mathematical techniques and their applications as well as enhancing your study of other subjects, in particular Physics, Chemistry, Biology, Geography, Psychology, Economics, Business Studies and PE.

Further Mathematics is a full AS or A Level qualification that you can take alongside Mathematics. You will need to be studying (or have already achieved) the corresponding level in Mathematics. Taking A Level Mathematics and Further Mathematics will give you two A Levels and will mean that you spend about half your time at college studying on your Mathematics courses, it is also possible to take AS Further Mathematics alongside either AS Mathematics or the second year of A Level Mathematics, which will give you 1½ A Levels.

Further Mathematics is designed to stretch and challenge able young mathematicians by introducing you to new techniques and concepts, such as complex numbers and matrices, as well as studying material from A Level Mathematics in greater depth. You will be taught by highly qualified specialist subject tutors in classes consisting exclusively of Further Mathematics students.

If you are still not convinced then you may be interested to know that Mathematics is the only A Level proven to increase earnings in later life - by an average of 10% - although hopefully your motivation is based on your desire to study a course that is satisfying, interesting, well respected, useful, fun and full of surprises.

## Course content

**3 modules for AS Mathematics and 3 modules for AS Further Mathematics**

**Core Mathematics 1 (exam)**

You will be sent a workbook for the summer break before you start the course. This will help you to be ready for the start of the course and make sure that there are no important topics that you missed out on. You will extend some of the core ideas from GCSE Higher level Mathematics, such as quadratics, lines, indices, graphs, inequalities and sequences, and meet material that may be new to you, such as differentiation and integration.

**Core Mathematics 2 (exam)**

You will explore the topics from Core 1 in greater depth and also study some new topics, such as circle geometry, binomial expansions, logarithms, geometric progressions, functions, polynomials and extend your work in calculus and trigonometry. You will use the core material to solve practical problems and find out about some of the background stories behind the ideas.

**Mechanics 1 (exam)**

In Mechanics 1 you will study why moving objects move in the way they do and why stationary objects remain in static equilibrium. You will learn about modelling forces using vectors, calculate moments and develop equations for simple kinematics in one-dimension. You will learn how to apply Newton’s laws and the Amonton-Coulomb model of friction to predict the motion of simple systems that can be modelled as particles. There is some crossover with AS Physics, but you do not need to be studying Physics to understand Mechanics 1.

**Statistics 1 (exam)**

In Statistics 1 you will extend the quantitative methods and data handling work from GCSE Mathematics. Much of the material will seem familiar, such as probability, measures of location and spread, statistical diagrams and correlation, although obviously you will take the ideas beyond what you did at GCSE. You will learn how to interpret statistical data presented in various forms and use algebra to investigate the effects of coding. You will also learn about regression, discrete random variables and use the normal probability distribution (Gaussian) as a continuous probability model.

**Statistics 2 (exam)**

In Statistics 2 you will extend the work begun in Statistics 1. You will study the binomial distribution, the Poisson distribution and general continuous random variables. You will also learn how to set up, carry out and interpret hypothesis tests in a variety of different practical situations.

**Further Pure 1 (exam)**

In this module you will be introduced to some new, and potentially very useful, areas of Pure Mathematics, such as complex numbers, conic sections, matrix algebra and the method of proof by induction. These ideas will be developed further in the second year of the course.

You will be encouraged to use a graphical calculator in this module, although this is not essential.

**Year 2 **

**3 modules for A2 Mathematics and 3 modules for A2 Further Mathematics**

**Core Mathematics 3 (exam)**

You will be given a workbook for the summer break before you start the second year of the course. This will help you to be ready for the start of the course and make sure that there are no important topics that you have missed out on. You will extend some of the core ideas from AS Mathematics, such as exponential and logarithm functions, transforming graphs, trigonometry and the use of trigonometric identities and extend the types of functions that you can differentiate.

**Core Mathematics 4 (exam)**

You will extend some of the topics from AS Mathematics and also study some new topics, such as partial fractions, the general binomial expansion, parametric equations, differential equations and the use of vectors in geometry. You will also develop integration techniques that will enable you to deal with a wide variety of functions. You will use the core material to solve practical problems and find out about some of the background stories behind the ideas.

**Decision 1 (exam)**

In this module you will study the mathematical principles that underpin decision making in Economics and also some of the algorithmic methods that are used in the design of computer programs. You do not need to understand programming in order to do this module. You will learn how to model various real life problems using networks and then how to use network algorithms to solve the problems. You will also extend your knowledge of linear programming techniques, bipartite graphs and matchings.

**Mechanics 2 (exam)**

Mechanics 2 extends the ideas met in Mechanics 1 but with some of the modelling assumptions relaxed. You will study projectiles, calculate centres of mass and deal with problems involving collisions. You will learn about the work-energy principle and the impulse-momentum principle and use these in problem solving.

**Further Pure 2 (exam)**

In Further Pure 2 you will extend the work begun in Further Pure 1. You will study de Moivre’s theorem to deal with products, quotients and powers of complex numbers. You will deal with transformations from one complex plane to another. You will also learn how to calculate areas and arc lengths in polar form and you will study the solution of first and second order differential equations. You will also learn how to calculate a Taylor series or Maclaurin series and see how these can be used to give a series solution approximation for a differential equation.

**Further Pure 3 (exam)**

You will meet the idea of hyperbolic functions and use these to significantly extend the types of functions that you can integrate. You will also extend your study of conic sections and matrices from the work begun in Further Pure 1. You will learn about eigenvectors and how they can be used to diagonalise a matrix and you will learn how to find the determinant and inverse of a 3x3 matrix. You will also study the vector cross product and use vector methods to solve geometric problems involving distances and angles between lines and planes.

## Entry requirements

The minimum requirement is five GCSEs at good grades in appropriate subjects including grade A or A* in GCSE Mathematics.

## Assessment

Your success in this subject is dependent upon excellent attendance, punctuality and effort. You will complete an AS qualification in Mathematics and an AS qualification in Further Mathematics based on the modules covered in Year 1. You will complete an A Level qualification in Mathematics and an A Level qualification in Further Mathematics based on the modules covered in both years.

- You will have weekly homework assignments. These will be quite substantial and you should expect to spend a couple of hours on each assignment.
- You will have regular tests, carried out in class, generally two for each module.
- You will be encouraged to enhance your study experience by following up the work done in class with further reading, using websites or trying extra questions from the online text books.
- You will have access to exam board past papers, mark schemes and online worked solutions through the college Moodle site.
- You will review your own performance in 1:1 discussions with your tutor.
- You will be given a mock examination in each module.
- You will be formally examined on each unit that you study. The examinations are traditional written exams and are sat at the end each year in May or June.

## Future opportunities

A qualification in Further Mathematics is highly valued by many universities and employers. Further Mathematics is also an excellent subject to complement your other studies. There are obvious links with computing, sciences and finance based courses but Further Mathematics can also be useful for sharpening up your thinking skills, your logical reasoning and your pattern spotting, and as such it is useful for students studying most A Level courses. Most universities require Further Mathematics (at least to AS level) for admission to their Mathematics degree courses, a few universities prefer applicants for their Engineering and Computing courses to have studied Further Mathematics to at least AS level. Further Mathematics is also useful for applicants to Economics and Actuarial Science degrees at some universities.

## Further information

You will be expected to do a significant amount of work outside class. Workshops and drop-in support sessions are available for all Mathematics and Further Mathematics students.

We will encourage you to read widely and conduct your own research into topics that interest you. We will also direct you towards websites that you may find interesting or useful. Through the STEM academy and Maths Academy Moodle site we offer enhancement activities. In the first year this includes interview skills and the presentation of an independent piece of research to an audience of peers. In the second year it includes preparation for university entrance papers and scholarship papers, Advanced Extension Award (AEA) and Sixth Term Entrance Papers (STEP).

We also enter students for the UKMT Senior Maths Challenge and the Senior Team Challenge each year, some of whom progress to the Senior Kangaroo or rounds of the British Maths Olympiad.

## How to apply

If you want to apply for this course, you will need to contact Truro and Penwith College directly.