Calculus: Application
Gr 12

The Grade 12 Calculus: Application module extends learners’ understanding of differentiation by focusing on how derivatives are used to analyse and solve real-world and mathematical problems. This chapter helps students move beyond basic rules and develop the ability to interpret results meaningfully, making calculus a powerful tool for problem-solving.

Learners apply first-derivative techniques to determine stationary points, classify them as local maxima or minima, and analyse the overall shape of graphs. The lessons cover identifying points of inflection, sketching functions using derivative information, and understanding how changes in gradient reflect changes in behaviour. Students also explore optimisation problems—such as maximising profit, minimising cost, or determining optimal dimensions—using calculus to model, analyse, and solve practical scenarios.

By the end of this module, learners will be able to interpret derivatives in context, analyse and sketch functions using critical points, and apply optimisation methods confidently. These skills form a crucial part of the Grade 12 curriculum and provide a strong foundation for university-level mathematics, commerce, engineering, and the physical sciences.