IB Math AI Worksheet SL 5.7 - Optimisation in Context

This IB Maths AI SL 5.7 – Optimisation in Context resource develops students’ ability to apply calculus techniques to real-world optimisation problems. Learners follow a structured toolkit that moves from defining variables and forming an objective function to applying derivatives, testing critical points, and interpreting results with correct units and context. The material emphasises modelling situations mathematically before using calculus to find maximum or minimum values.

Guided examples walk students through classic optimisation scenarios, including maximising the volume of an open-top box, maximising profit using revenue and cost models, and minimising fencing cost under area constraints. Each task reinforces forming equations from context, differentiating, solving first-order conditions, and checking domains or endpoints. Students practise expressing answers in meaningful terms rather than just numerical solutions, strengthening exam-style communication skills.