The Advanced Higher Mathematics course consists of three units – Methods in Algebra and Calculus, Applications of Algebra and Calculus, and Geometry, Proof and Systems of Equations.
Pupils will study towards the units during the course of the school year.
The Advanced Higher Mathematics course has an externally-assessed exam made up of two papers (Non-calculator and calculator).
METHODS IN ALGEBRA AND CALCULUS
The general aim of the Unit is to develop advanced knowledge and skills in algebra and calculus that can be used in practical and abstract situations to manage information in mathematical form. The Outcome covers partial fractions, standard procedures for both differential calculus and integral calculus, as well as methods for solving both first order and second order differential equations. The importance of logical thinking and proof is emphasised throughout.
APPLICATIONS OF ALGEBRA AND CALCULUS
The general aim of the Unit is to develop advanced knowledge and skills that involve the application of algebra and calculus to real life and mathematical situations, including applications to geometry. Learners will acquire skills in interpreting and analysing problem situations where these skills can be used. The Outcome covers the binomial theorem, the algebra of complex numbers, properties of functions, rates of change and volumes of revolution. Aspects of sequences and series are introduced, including summations, proved by induction.
GEOMETRY, PROOF AND SYSTEMS OF EQUATIONS
The general aim of the Unit is to develop advanced knowledge and skills that involve geometry, number and algebra, and to examine the close relationship between them. Learners will develop skills in logical thinking. The Outcome covers matrices, vectors, solving systems of equations, the geometry of complex numbers, as well as processes of rigorous proof.
