Advanced Higher Mathematics
AIMS OF THE COURSE
The aims of the Course are to enable learners 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
- extend 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
ENTRY LEVEL RECOMMENDED
- Pass at Higher Mathematics
COURSE CONTENT
This Course will develop, deepen and extend the mathematical skills necessary at this level and beyond. Learners will acquire and apply operational skills necessary for exploring more complex mathematical ideas. In addition, learners will develop mathematical reasoning skills and will gain experience in logical thinking and methods of proof.
Units are statements of standards for assessment and not programmes of learning and teaching.
They can be delivered in a number of ways.
Mathematics: Methods in Algebra and Calculus (Advanced Higher)
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.
Mathematics: Applications of Algebra and Calculus (Advanced Higher)
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.
Mathematics: Geometry, Proof and Systems of Equations (Advanced Higher)
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.
SKILLS
This Course will develop learners’ ability to:
- Have the ability to use mathematical reasoning skills to think logically, provide justification
and solve problems
- Have a knowledge and understanding of a range of complex concepts
- Have the ability to select and apply complex operational skills
- Have the ability to use reasoning skills to interpret information and to use complex
mathematical models
- Have the ability to effectively communicate solutions in a variety of contexts
- Have the ability to explain and justify concepts through the idea of rigorous proof
- Have the ability to think creatively
ASSESSMENT
To gain the award of the Course, the learner must pass all of the Units as well as the Course assessment.
Course assessment will provide the basis for grading attainment in the Course award.
Unit assessment
- All Units are internally assessed against the requirements shown in the Unit Specification.
- They can be assessed on a Unit-by-Unit basis or by combined assessment.
- They will be assessed on a pass/fail basis within centres.
- The assessment of the Units in this Course will be as follows.
Mathematics: Methods in Algebra and Calculus (Advanced Higher)
Learners who complete the Unit will be able to:
- use mathematical operational skills linked to methods in algebra and calculus
Mathematics: Applications of Algebra and Calculus (Advanced Higher)
Learners who complete the Unit will be able to:
- use mathematical operational and reasoning skills relevant to applications of
algebra and calculus
Mathematics: Geometry, Proof and Systems of Equations (Advanced Higher)
Learners who complete the Unit will be able to:
- use mathematical operational and reasoning skills relevant to geometry and
systems of equations