DOUBLE MATHEMATICS (MATHEMATICS AND FURTHER MATHEMATICS)
This course enables you to study for a second A level called Further Mathematics, alongside the single Mathematics A level.
In your first year you will study both AS Mathematics and AS Further Mathematics. In the second year you will follow the A2 courses in Mathematics and Further Mathematics, leading to two full A levels.
This course gives you the opportunity to broaden your study of Mathematics to include more Pure Mathematics plus a choice of options. It provides an excellent background for studying Mathematics, Science subjects or Engineering at university.
WHAT WILL I BE STUDYING ON THE COURSE?
You will study a combination of Pure and Applied Mathematics. In AS Mathematics you study Pure Core 1 and Pure Core 2 plus Statistics 1. In AS Further Mathematics you study Mechanics 1, Decision 1 and Further Pure 1.
The AS units are:
- Pure Core 1 - you build on the knowledge of algebra and graphs that you studied at GCSE. You solve quadratic and cubic equations and sketch their graphs.You find the equation of a circle and use its geometric properties to find tangents. Calculus is introduced and you learn to find gradients and areas using
differentiation and integration.
- Pure Core 2 -you build on the work in Pure Core 1 to extend your knowledge of algebra, calculus and trigonometry. Topics include series, indices and logarithms, sine rule and cosine rule, and solving trigonometric equations e.g. sin x = 0.5 in a given interval.
- Statistics 1 - probability theory is used to model data and to enable you to interpret what is really happening and to predict unknown quantities: for example how many people in a large group will be over 180 cm tall? How many people should be surveyed in opinion polls and what is the expected error in the results? Is the UK crime rate related to economic conditions?
- Mechanics 1 - the motion of objects is studied using simple experiments. Theoretical methods are developed to model the movement of an object. What is the best speed and angle to throw a basketball into the basket? What are the safe dimensions for a child’s slide? What happens when pool balls collide?
- Decision 1 - you look at problems such as choosing the shortest route for a delivery van using algorithms, graphs and networks. You look at methods to help simplify complex situations and develop the most efficient solutions.
- Further Pure 1 - introduces you to the ideas that you study in greater depth in Further Pure 2, 3 and 4 in the second year. You will be introduced to complex numbers, matrices, differentiation from first principles and graphs of more complex functions.
In the second year, you complete A level Mathematics by taking Pure Core 3, Pure Core 4 and an application. For A level Further Mathematics you study three more Further Pure units plus another option unit selected from Mechanics, Statistics and Decision Mathematics.
The A2 units are:
- Pure Core 3 and 4 - you extend the ideas of algebra, trigonometry and calculus developed in Pure Core 1 and 2.
- Statistics 2 -you use probability to model more complex situations. You consider how to test if a hypothesis is true; for example, test if there is a link between gender and voting preferences in an election.
- Mechanics 2 - you extend the ideas developed in Mechanics 1 to analyse more complex situations. Techniques used include consideration of the forces, work and energy acting in a situation; for example when is it safe to loop the loop on a rollercoaster?
- Decision 2 - you build on the ideas developed in Decision 1 to enable you to analyse more complex situations, such as maximising factory production with given constraints in raw materials. You also investigate game theory.
- Futher Pure 2 - you study complex numbers and hyperbolic functions
- Futher Pure 3 - you study differential equations
- Futher Pure 4 - you study matrices and vectors
WHAT WILL I BE DOING IN LESSONS?
You will use a variety of methods and techniques to help you develop and understand the concepts and techniques used.
During lessons you will:
- extend your ability to solve equations in more complex situations
- learn more about drawing graphs and be introduced to calculus, which is the foundation stone of much advanced mathematics
- use computer software such as “Autograph” to investigate series, functions and graphs
- investigate practical problems in statistics, mechanics, or decision mathematics and write reports to explain what you have done
- work independently and in groups to tackle problems and then present their solution.
HOW WILL THE COURSE BE ASSESSED?
By unit examinations in January and June.
AS - Pure Core 1 and Mechanics 1 in January, Pure Core 2 , Statistics 1, Decision 1 and Further Pure 1 in June.
A2 - Pure Core 3 and Pure Core 4 in January, Further Pure 2, 3 and 4 plus application in June.
WHAT QUALIFICATIONS DO I NEED TO TAKE THE COURSE?
You should have at least a grade A in Mathematics. You should also really enjoy Mathematics. Experience shows that your chances of success in this subject are greater if you have performed very well at GCSE and have a range of high grades.
WHAT OTHER SUBJECTS COULD I DO WITH MATHEMATICS AND FURTHER MATHEMATICS?
Double Mathematics students take a wide variety of other courses. Many take one or more from the sciences. However, students do take a wide range of other subjects including languages, arts, humanities and music.
AND AFTER THE COURSE?
Mathematics and Further Mathematics are highly regarded and provide strong support to any application for employment or further study. It is important to have studied Further Mathematics for some courses in mathematics, physics and engineering at some universities. The applied units in Mechanics and/or Statistics are necessary for many courses in science and engineering. The Statistics and Decision Mathematics studied is very useful for many courses in the social sciences.
The study of Pure Mathematics develops logical thinking and a systematic approach to problem solving - attributes which are highly valued in the workplace.
