Contents
01 Foundations
- Algebra FoundationsBuild the symbolic foundations needed for every later topic: variables, expressions, equations, signs, brackets, and fractions.
- Exponents and LogarithmsUnderstand powers, roots, exponent rules, logarithms, and natural logarithms.
- Equations and InequalitiesDevelop reliable methods for solving linear equations, inequalities, compound statements, and absolute-value relationships.
- FunctionsLearn function notation, inputs and outputs, domain and range, and the behaviour of linear functions.
- Function Composition and Inverse FunctionsUnderstand how functions can be combined, how composition order works, and when a function has an inverse.
- Quadratic Functions and EquationsStudy parabolas, roots, factorisation, completing the square, the quadratic formula, and the discriminant.
- Polynomial FunctionsExplore polynomial structure, operations, roots, division, graph behaviour, symmetry, and machine-learning applications.
- Rational FunctionsStudy ratios of polynomials, domain restrictions, asymptotes, holes, intercepts and the behaviour of rational graphs.
- Exponential FunctionsUnderstand exponential growth and decay, the constant e, graph behaviour, transformations and applications.
- Trigonometry FoundationsBuild the foundations of angles, radians, right-triangle ratios, the unit circle, identities and trigonometric functions.
- Sequences and SeriesUnderstand sequences, arithmetic and geometric patterns, summation notation, finite series and convergence.