Further Mathematics A Level

The Further Maths specification is OCR B (MEI). The teaching programme for this course is designed to run in parallel with the A-level maths course and stretches and enhances the students’ learning in A-level Maths in each of the topic areas.

The topics in Further Maths course follow a similar order to the Mathematics Course, with the exception that the level of complexity of the mathematical processes is greater, for example, 2nd order differential equations are considered; complex numbers are introduced and used in a range of contexts.

At CAST the course is taught by 2 teachers who follow their own strands of the specification but do so in a manner that supports the teaching and learning in the other strand.

Year 12 begins with basic algebra and functions and then develops into using these skills to produce mathematical proofs. Co-ordinate geometry, straight lines and circles are considered which introduces the students to polynomial functions and graphs. From this students are able to consider some basic kinematics, including the use of vectors and the equations of motion (the starting point for a study of mechanics). The first term concludes with a consideration of probability and the binomial expansion as well as the principles of differentiation and their application to the graphical representation of functions (gradients and stationary points).

In Term 2 the students revisit statistics and consider the presentation of data and hypothesis testing as well as building upon the kinematics studied in term one to progress to the more complicated situations involving forces and the application of Newton’s Laws.

In term 3 the students study more complex algebra and functions that leads to a study of numerical methods including the Newton-Raphson method. They also continue building more complex mechanics situations and consider motion in a circle and moments about a point. Year 12 concludes with an introduction to Differential Equations and methods for solving them.

In Year 13 the students begin the year by continuing their study of calculus and now consider integral calculus. They also revisit the proof and vector topics from Year 12 to include proof by contradiction and 3D vectors. Having considered vectors in 3D the students are better placed to analyse more complicated mechanics situations including forces in equilibrium and resultant forces in kinematics. Having covered both differentiation and how to solve differential equations, integration and how to solve a range of integral problems, vectors and trigonometry the students combine these in their final term of study to progress to trigonometrical calculus.

Throughout the course the emphasis is to build the students’ confidence in each area and then to revisit it and add additional layers of complexity. This requires to use progressively more complicated mathematical processes.

All exams are at the end of Year 13

Paper 1 2 hours 40 minutes Pure Mathematics

Paper 2 1 hour and 30 minutes Major optional module (usually Mechanics to Statistics)

Paper 3 1 hour 15 minutes Minor Optional Module (Modelling With Algorithms)

Minimum entry requirements for A level courses: 7 GCSEs at grade 9-4 (including English grade 4) with double or triple science (grade 6/6) and Maths (grade 8).

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