Advanced Higher Mathematics

Course Overview

The Advanced Higher Mathematics course provides a strong base for those students who either are progressing to university level studies in Mathematics or Engineering as well as providing academic challenge for those students who want to develop their Higher Maths skills further.

Students need to think logically, provide justification, and solve problems in a range of complex concepts. Reasoning skills are vital to success as is effectively communicating solutions. Students algebra skills built up over the previous 5 years of academic study are vital to the success in this course.

Course Assessment

Assessment for this course consists of two external exams during the SQA exam diet.

Question paper 1 (non-calculator) worth 35 marks and lasting 1 hour.
Question paper 2 worth 80 marks and lasting 2 hour and 30 minutes.

Entry Expectations

The Advanced Higher Mathematics course builds upon knowledge previously obtained throughout a pupil's time at school. Any pupil wishing to undertake the course should have already achieved their Higher Mathematics qualification. It is not possible to advance to Advanced Higher Maths from Higher Applications of Maths.

While there is no entry requirement, it is strongly recommended that a good Higher exam score is achieved.

Course Content

The Higher Mathematics course consists of four overarching topics:

Calculus
Algebra, Proof and Number Theory
Matrices, Vectors and Complex Numbers

Pupils will study the following within these topics:

Calculus

Differentiation of logs and exponentials
Differentiation using chain rule
Differentiation using product and quotient rule
Differentiation of logs and exponentials
Differentiation of inverse trigonometric functions
Implicit differentiation
Parametric differentiation
Differentiating problems in context
Integrating standard integrals
Integrating by substitution
Integration by parts
First and Second Order differential equations

Algebra, Proof and Number Theory

Partial Fractions
Investigating functions of graphs
Binomial Theorem
Arithmetic and Geometric Sequence and Series
Maclaurin Expansion
Different methods of proof
Euclid's Algorithm

Matrices, Vectors and Complex Numbers

Gaussian Elimination to solve 3x3 matrices
Matrix Algebra
Determinant and Inverse of matrices
Matrix transformations
Vector Products
Working with lines and planes
Algebraic and Geometric operations of complex numbers

Home Learning

Homework is set fortnightly to allow students to recap key ideas in class. This is set online on Google Classroom. There are other useful resources on Google Classroom.

Independent Practise is vital to achieving success in this course. At least an hour of independent work is expected each week using either online resources or textbooks uploaded onto Google Classroom below.