What is Further Mathematics?
It’s the last 5 minutes of the final qualifier and Steven Gerrard is about to take a free kick that could take England to the World Cup 2014. The crowd is crying out for him to score. What speed and direction does he need to kick the ball?
To set the World Record, a team set off early one morning at the end of the Piccadily line at Heathrow. They must visit all the tube stations in London in less than 20 hours to claim their prize. What route should they take?
We created negative numbers, fractions and surds to solve equations such as x + 3 = 0, 3x – 2 = 0 and x2 – 3 = 0, but what if you want to solve x2 + 4 = 0? And how are computer animation films made?
Further Maths will allow you to answer these and many other questions!
What Mathematics will I do?
If you are a good Mathematician who is likely to get an A or preferably A* at GCSE plus a range of other good grades, you should consider taking AS Mathematics and AS Further Maths.
The AS Further Maths course is made up of 3 modules: Mechanics 1, Decision 1 and Further Pure 1. You must also study AS Mathematics – see the separate leaflet for more info. If you pass both AS Further Maths and AS Maths (with at least a B grade in both) then in the second year you can study A2 Maths and A2 Further Maths. You will study Core 3, Core 4 and Statistics 2 in A2 Maths; and Mechanics 2 and Further Pure 2, along with a choice of 3rd unit for A2 Further Maths. All modules are equally weighted.
The options that are taught will depend on the preferences of all the students; we intend to run two of the four options. In previous years they have been Mechanics 3 and Further Pure 3. There is also an opportunity for gifted students to extend their mathematics further by studying additional units to gain AS (or A2) Further Maths (Additional) in their second year.
What do the different modules involve?
Mechanics will give you the skills to model the flight path of Steven Gerrard’s free kick. You will be able to model friction to find out whether the tyres on a car involved in a crash were below the required tread depth. You will be able to see why Galileo was correct when he said two balls made of different materials rolling down the same slope will reach the bottom at the same time. You will use Newton’s Laws of Motion to find the driving force a car needs in order to accelerate up a hill at a given acceleration.
Decision will give you the skills to determine the shortest path around all the London underground stations. You will be able to see how computers can sort the results of all Maths exams taken by students at the college, to get a rank of students’ achievement. You will also understand the methods used to schedule complex projects, such as building the Channel Tunnel, in order to complete it in the least time. And you will learn how businesses decide what quantity of two different products to produce in order to maximise their profit.
In Further Pure you will learn how to solve x2 + 4 = 0, using imaginary numbers, which are square roots of negative numbers. Imaginary numbers are used in numerous practical applications, such as electronics, weather prediction, etc. You will also learn about matrices which are used to represent transformations of sets of co-ordinates, such as those representing the position of the arms, legs, head and body of a cartoon character – needed when making computer animation. You will also discover the Maths behind why satellite dishes are parabolic.
Mathematics is highly valued in a very wide range of careers and professions as it provides good evidence of the ability to think clearly and logically. It is accepted almost everywhere as a good entry qualification for practically every subject at degree level. It is often a requirement for anyone interested in scientific, Computing, Economics and Statistics related careers.
By also studying Further Maths, the extra depth and breadth of modules you study will give better preparation for degrees in Mathematics, Engineering or Physics. Studying Further Mathematics is seen as an indication of high academic aptitude which is often essential when making applications to certain courses and universities.
Whilst you must have an average GCSE score of at least 5.5 to do four AS levels, past experience suggests that students with better GCSE grades are more likely to get good results. You can check your likely GCSE point score by going to 'Choosing the Right Course' on the website and entering your predicted grades.
For AS Further Maths you must have at least a grade A in GCSE Maths (at the higher tier). You must also do AS Maths.
All students will be expected to provide their own stationary, textbooks (around £70 for both AS Maths & AS Further Maths) and calculator. All students should have a scientific calculator with natural display. We recommend the Casio FX-991ES PLUS (around £15) which has many features useful for AS Maths and Further Maths. Some students buy a graphics calculator, such as the Casio FX-9700GII (around £55).
If the costs of equipment, materials and trips may cause you financial hardship, you may wish to read through details of our financial support scheme on our website.
- Sixth Form Course: