Mathematics

Course summary

Maths at A level deals with abstract and sometimes difficult concepts, but it always examines the knowledge and understanding of these concepts using practical questions. Two-thirds of the A level involves the study of Pure Maths, which greatly extends the Geometry and Trigonometry and particularly the Algebra studied at GCSE or IGCSE, as well as introducing a new topic called Calculus which deals with finding the gradients of curves and areas between curves and lines, and also with solving what are known as differential equations. The other one-third of the A level involves the study of Statistics and Mechanics. Statistics involves studying the idea of sampling, the presentation and interpretation of data, probability, statistical distributions (essentially patterns) and hypothesis testing. The Statistics part of A-level Maths builds on the Handling Data and Probability sections of GCSE or IGCSE Maths. Mechanics involves studying kinematics (including the SUVAT equations), Newton’s laws of motion and forces and moments. The Mechanics part of A-level Maths will be familiar to students who have studied or are studying Physics or the Physics part of Combined Science. Students need to study both Statistics and Mechanics in Maths A level. Much of the first term of the course builds the foundations of the subject, starting with familiar topics from IGCSE such as indices, quadratic functions, trigonometry and coordinate geometry. Later the fundamentals of calculus are introduced together with some of its applications. In the first year, we also look at Mechanics. We examine the concept of a force and the idea of resultant forces, which leads to Newton’s laws of motion. We also look at moments, that anybody who has ever been on a see-saw will know about. Calculus is covered in considerable depth with the emphasis on extended problem-solving which draws on a wide range of mathematical concepts. Various methods of proof are also looked at – we consider why there must be infinitely many prime numbers and why the square root of 2 cannot be equal to any fraction. In the second year, we also look at Statistics. We examine different ways of looking at data and the concept of probability. We move on to look at statistical distributions (essentially patterns) that occur naturally.