Calculus
Gr 12

The Grade 12 Calculus module introduces learners to the fundamental principles of differential calculus, providing the tools needed to analyse rates of change, gradients, and the behaviour of functions. This chapter forms one of the core components of senior-phase mathematics and lays the foundation for university-level studies in mathematics, science, engineering, economics, and related fields.

Learners begin by exploring the concept of a derivative as the gradient of a curve, moving from first principles to formal differentiation rules. The lessons cover differentiating basic polynomials, applying the power rule, calculating gradients, determining stationary points, and analysing the shape of graphs using increasing/decreasing intervals and concavity. Students also learn how to use calculus to solve optimisation problems, interpret rates of change in real-life contexts, and sketch functions with greater accuracy.

By the end of this module, learners will be able to differentiate polynomial functions confidently, interpret derivatives both algebraically and graphically, and apply calculus techniques to solve practical and theoretical problems—ensuring a strong foundation for further mathematical study after school.