AS and A2 level Mathematics

AS and A2 level Mathematics

This course builds on the knowledge and skills that you acquired during your GCSE. It will increase your understanding of familiar ideas and introduce you to new concepts and techniques. You will apply mathematical ideas in a context of your choice - Statistics, Mechanics or Decision Mathematics.

WHAT WILL I BE STUDYING ON THE COURSE?
You will study a combination of Pure and Applied Mathematics. The Pure Mathematics is divided across four core units and you will select two application units to study.

The AS units are:

Pure Core 1 and Pure Core 2 plus one chosen from Mechanics 1 or Statistics 1 or
Decision 1.

·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
-
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.

The A2 units are:


Pure Core 3 and Pure Core 4 plus one more Statistics or Mechanics or Decision Mathematics unit dependent on your choice at AS.

·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.

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 graphics calculators and computer software such as â€OEAutograph†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 in January, Pure Core 2 plus option in June.
A2 - Pure Core 3 in January, Pure Core 4 plus option in June.

WHAT OTHER SUBJECTS COULD I DO WITH MATHS?
Mathematics with Statistics options offers support in the study of subjects such as Accounts, Biology, Business Studies, Economics, Geography, Psychology and Sociology. Mathematics with Mechanics options offers support in the study of Physics and Design Technology. Mathematics with Decision Mathematics options offers support in Business Studies, Economics and Computing. However, students do take Mathematics with a wide range of other subjects including Modern Languages.

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.
To choose to study this course you should have high grades in your GCSEs including an A in Mathematics, and you should really enjoy Mathematics!
The A level Mathematics course you will follow is exactly as described above.
The Further Mathematics A level also consists of six units in total, divided between Pure and Applied Mathematics. There are four compulsory Further Pure units, which extend your knowledge into areas such as complex numbers, differential equations and matrices.
For the Further Mathematics AS in the first year, you take Further Pure 1 plus two option units selected from Mechanics, Statistics, Decision Mathematics.
In the second year, you study three more Further Pure units plus another option unit selected from Mechanics, Statistics, Decision Mathematics.

USE OF MATHEMATICS
This course is designed for students who wish to extend their study of Mathematics beyond GCSE but are more interested in applications than theoretical ideas. From September 2010 it will be possible to continue with this course to a full A2 the following year.

The course is open to all students with a Mathematics GCSE at grade C or above from the higher tier.

The AS units are:

·Algebra
-building on GCSE knowledge of quadratics and trigonometry

·FSMQ Data Analysis
â€" summarising and displaying statistical information

·FSMW Decision Mathematics
â€" you look at problems such as choosing the shortest route for a delivery van using algorithms, graphs and networks


The A2 units are:

·FSMQ Calculus
·Mathematical Applications
- project work done in the classroom

·Mathematical Comprehension

AND AFTER THE COURSE?
Mathematics is highly regarded and provides strong support to any application for employment or further study. The applied units in Mechanics and/or Statistics are necessary for many courses in science and engineering. The Statistics and Decision Mathematics studied at A level 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.