**Advanced Higher Mathematics Course**

The Advanced Higher Course extends students’ mathematical knowledge in algebra, geometry and calculus. It includes matrix algebra, complex numbers and vectors and formalises the concept of mathematical proof.

Advanced Higher Mathematics emphasises the need for students to undertake extended thinking and decision making, to solve problems and integrate mathematical knowledge.

This Course is designed to enthuse, motivate, and challenge learners by enabling them to:

select and apply complex mathematical techniques in a variety of mathematical situations, both practical and abstract

extend and apply skills in problem solving and logical thinking

extending skills in interpreting, analysing, communicating and managing information in mathematical form, while exploring more advanced techniques

clarify their thinking through the process of rigorous proof

## The course consists of three units:

**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 Outcomes cover 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 of geometry. Learners will acquire skills in interpreting and analysing problem situations where these skills can be used. The Outcomes cover 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 Outcomes cover matrices, vectors, solving systems of equations, the geometry of complex numbers, as well as processes of rigorous proof.

Students are encouraged to work independently from the start and to develop good study techniques.

## Assessment:

To gain the award of the Course, the learner must pass all of the Units as well as the Course assessment.

The Course assessment will consist of one Component:

Question paper - 3 hours

The purpose of the question paper is to assess mathematical skills. A calculator may be used. The question paper will consist of a series of short and extended response questions (some of which may be set in contexts) that require the application of skills developed in the Course. Learners will be expected to communicate responses clearly and to justify solutions.

The paper will have 100 marks.

**Revision**

Students have access to course notes and revision materials on their UMPC and students also have their own password to access scholar revision materials.