In Advanced Higher Maths, there are 3 main units.

The calculus involves differentiating exponetial and natural logarithimic functions, the chain rule and the form of a product and quotent, differentiating inverse trigometric functions, finding the derivative, applying differentiation to problems in context and more.

The algebra, proof and number theory involves decomposing a rational function, finding the asymptotes to the graphs of rational functions, investigating ans sketching features of graphs, using the Maclaurin expansion to find specified terms, using indirect or direct proof in straightforward examples, using proof by induction and more.

The matrices, vectors and complex numbers involves using Gaussian elimination to solve linear equations, understanding and using matrix algebra, working with planes, working with lines in three dimensions and performing algebraic operations on complex numbers.

Pupils will sit an SQA exam in order to achieve this qualification. 

For more information: SQA Advanced Higher Maths Website