Further algebra and functions

This guide builds on introductory algebra to explore the more sophisticated mathematical structures you will encounter in university-level courses. It offers clear explanations of quadratic equations, including factorisation, completing the square and the quadratic formula. The content extends to polynomial manipulation, exponential growth and decay models, and logarithmic functions, providing the rules and worked examples necessary to simplify and solve equations involving these more complex expressions.

A major focus of the guide is the concept of functions themselves. You will develop fluency in function notation, learn to determine domains and ranges, and explore composite and inverse functions in detail. The resource also covers graphical transformations, showing how shifts, reflections and stretches alter the shape and position of curves. These skills are essential for interpreting non-linear relationships in scientific data and financial modelling, equipping you with the analytical versatility needed for advanced study and professional practice.