Students engage with a variety of linear and quadratic equations, mastering techniques such as factoring, completing the square, and using the quadratic formula. These questions aim to strengthen their algebraic skills by solving for unknowns and interpreting the real-world implications of solutions. Students will explore how these equations can be used to model real-world situations like projectile motion, area optimisation, and financial calculations, fostering a deeper understanding of algebra's utility in diverse scenarios.

In this module, students encounter complex algebraic expressions and polynomials that they must simplify using techniques including combining like terms, utilising the distributive property, and applying the laws of exponents. This practice enhances their analytical thinking and prepares them for more advanced algebraic operations. By tackling these problems, students solidify their foundational algebra skills, essential for success in higher mathematics and practical problem-solving in physics and engineering contexts.

Students delve into the study of different types of functions, including linear, quadratic, exponential, and piecewise functions. They learn to interpret graphs, apply transformations, and utilise these functions to solve real-life problems that model economic, scientific, and statistical data. This section not only boosts their mathematical fluency but also enhances their ability to apply mathematical concepts to analyse and predict patterns and changes in various applied contexts.