Students are introduced to polynomial functions and their key characteristics. They learn to classify polynomials by degree, interpret graphs, predict end behaviour, analyse zeros and multiplicities, apply transformations, and model real-world situations using polynomial functions. This unit establishes the graphical and conceptual foundation for the remainder of the course.
This unit develops the algebraic skills required to manipulate polynomial expressions efficiently. Students practise adding, subtracting, multiplying, factoring, and dividing polynomials while exploring important results such as the Remainder Theorem and Factor Theorem. These techniques become essential tools for solving equations and analysing functions.
Students learn a variety of methods for solving polynomial equations of increasing complexity. They investigate higher-degree equations, explore the Fundamental Theorem of Algebra, analyse polynomial graphs, and apply these techniques to practical modelling situations. Connections between algebraic solutions and graphical representations are emphasised throughout the unit.
Students extend their understanding of functions by studying rational expressions and rational functions. They simplify rational expressions, perform algebraic operations, solve rational equations, and investigate the unique graphical behaviour of rational functions, including vertical, horizontal, and oblique asymptotes. Careful attention is given to domain restrictions and excluded values.
The final unit brings together the concepts developed throughout the course. Students compare polynomial and rational functions, analyse important graphical features, apply transformations, create mathematical models, and solve complex, multi-step problems. The emphasis shifts toward selecting appropriate mathematical tools and interpreting solutions within real-world contexts.
By the end of this course, students will be able to analyse, manipulate, graph, and solve polynomial and rational functions with confidence. They will understand how algebraic and graphical representations are connected, apply multiple solution strategies to both theoretical and practical problems, and possess a strong foundation for future study in calculus, advanced algebra, and other STEM fields.