Unit 1 –further differentiation, modelling and graphing

An 11-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 areas of further graph transformations and modelling and differential calculus.

The lessons and sequences allow students to explore transformations of trigonometric functions, including reflections, translations, and dilations using graphing applications; modelling and solving practical problems with periodic phenomena and to apply differentiation techniques to exponential, logarithmic and trigonometric functions, using derivatives to analyse tangents and normals of the functions within the scope of the Mathematics Advanced course.

Introduction

Further differentiation, modelling and graphing (DOCX 7.4 MB)

Lesson 1 – reflections and translations of trigonometric functions

• Reflections and translations of trigonometric functions (DOCX 2.2 MB)
• Reflections and translations of trigonometric functions – slide deck (PPT 4.7 MB)

Lesson 2 – dilations of trigonometric functions

• Dilations of trigonometric functions (DOCX 7 MB)
• Dilations of trigonometric functions – slide deck (PPTX 3.4 MB)

Lesson 3 – trigonometric functions and modelling

• Trigonometric functions and modelling (DOCX 2.2 MB)
• Trigonometric functions and modelling – slide deck (PPTX 3.2 MB)

Lesson 4 – logarithmic scales

• Logarithmic scales (DOCX 3.9 MB)
• Logarithmic scales – slide deck (PPTX 2.6 MB)

Lesson 5 – differentiating exponential functions with base e

• Differentiating exponential functions with base e (DOCX 3 MB)
• Differentiating exponential functions with base e – slide deck (PPTX 2.8 MB)

Lesson 6 – differentiating exponential functions with base a

• Differentiating exponential functions with base a (DOCX 3 MB)
• Differentiating exponential functions with base a – slide deck (PPTX 3.2 MB)

Lesson 7 – differentiating natural logarithmic functions

• Differentiating natural logarithmic functions (DOCX 3.9 MB)
• Differentiating natural logarithmic functions – slide deck (PPTX 3.7 MB)

Lesson 8 – differentiating logarithmic functions

• Differentiating logarithmic functions (DOCX 4.1 MB)
• Differentiating logarithmic functions – slide deck (PPTX 3.3 MB)

Lesson 9 – differentiating sine and cosine functions

• Differentiating sine and cosine functions (DOCX 2.3 MB)
• Differentiating sine and cosine functions – slide deck (PPTX 2.7 MB)

Lesson 10 – differentiating tangent functions

• Differentiating tangent functions (DOCX 2.3 MB)
• Differentiating tangent functions – slide deck (PPTX 3 MB)

Lesson 11 – differentiating cosecant, secant and cotangent functions

• Differentiating cosecant, secant and cotangent functions (DOCX 4.1 MB)
• Differentiating cosecant, secant and cotangent functions – slide deck (PPTX 2.3 MB)