Unit 2 – differentiation applications

A 9-lesson unit for Year 12 with resources. These resources represent ‘one way’ of designing teaching and learning experiences.

This program of learning addresses content from the focus area of Applications of calculus.

The lessons and sequences in this program of learning are designed to allow students to explore the concepts of turning points, inflections and curve-sketching, focusing on the analysis of functions through their derivatives.

Additionally, students will learn to classify points using first and second derivatives, apply these concepts to optimisation problems and effectively graph functions by considering their behaviour across various intervals and under different conditions.

Introduction

Differentiation applications (DOCX 8.3 MB)

Lesson 1 – continuity and differentiability

• Continuity and differentiability (DOCX 2.4 MB)
• Continuity and differentiability – slide deck (PPT 2.5 MB)

Lesson 2 – the first derivative and stationary points

• The first derivative and stationary points (DOCX 3.1 MB)
• The first derivative and stationary points – slide deck (PPTX 1.9 MB)

Lesson 3 – introduction to the second derivative

• Introduction to the second derivative (DOCX 4.4 MB)
• Introduction to the second derivative – slide deck (PPTX 4.4 MB)

Lesson 4 – the second derivative and stationary points

• The second derivative and stationary points (DOCX 3.2 MB)
• The second derivative and stationary points – slide deck (PPTX 2 MB)

Lesson 5 – the second derivative and points of inflection

• The second derivative and points of inflection (DOCX 4 MB)
• The second derivative and points of inflection – slide deck (PPTX 3.4 MB)

Lesson 6 – introducing graphing with calculus

• Introducing graphing with calculus (DOCX 2.2 MB)
• Introducing graphing with calculus – slide deck (PPTX 8.6 MB)

Lesson 7 – graphing functions with calculus

• Graphing functions with calculus (DOCX 2.5 MB)
• Graphing functions with calculus – slide deck (PPTX 2.3 MB)

Lesson 8 – global maximum and minimum

• Global maximum and minimum (DOCX 3.9 MB)
• Global maximum and minimum – slide deck (PPTX 2.4 MB)

Lesson 9 – modelling optimisation

• Modelling optimisation (DOCX 2.4 MB)
• Modelling optimisation – slide deck (PPTX 2.5 MB)