Mathematics

Course summary

The subject breaks down into pure mathematics and mathematical applications (mechanics and statistics). In the pure section, which covers two-thirds of the course, students are introduced to methods of proof, algebraic functions, coordinate geometry, sequences, series, trigonometry, exponentials, logarithms, differentiation, integration and numerical methods. The mechanics section introduces units, quantities, kinematics, forces, Newton’s Laws and moments. The statistics section involves sampling, data presentation, data analysis and interpretation, probability, statistical distributions and hypothesis testing. There is also the new big data set to get grips with. In further mathematics, the key themes are developed in much more detail in both the pure and applied sections and weightier topics introduced like proof by induction, complex numbers, polar coordinates and second-order differential equations. You will have an interest in the subject, a fine grounding in algebra and a first-class work ethic. On top of this, a willingness to ask questions, research independently and grapple for answers would be beneficial. You will have much practice via homework assignments and classwork but to get the most out of the course you must be responsible to some extent for your learning and keep going over the material in a structured way and regularly. To help facilitate this, students will be expected to produce a folder of independent work based on the course content. Pure mathematics concepts include algebra, quadratic equations and inequalities, straight lines and circles, trigonometry, binomial expansions, vectors, differentiation, integration, exponentials, logarithms, functions, graphs, sequences, series, radians, parameters and numerical methods. In statistics collecting data, measures of location and spread, correlation, probability, key distributions and hypothesis tests are studied and one has to get familiar with the large data set. In mechanics one studies forces, constant and variable acceleration, statics, kinematics, moments, projectile motion, and connected particles amongst other things. Further mathematics takes all these concepts and develops them further whilst introducing new topics like complex numbers and second-order differential equations.