Mathematics Extension 1 Year 11: In Depth Part III – Trigonometry & Rates of Change

Steve Howard
Passionate about Mathematics
A comprehensive guide to the knowledge & techniques needed to teach Trigonometric Functions & Rates of Change from the new Maths Extension 1 Year 11 syllabus.
Target Audience
Mathematics teachers of any experience level who are preparing to teach the new Extension 1 syllabus.

Learning Areas

Teaching Standards

General Description

I created this course to provide teachers with a comprehensive guide to the knowledge and techniques required to teach the new NSW Mathematics Extension I Year 11 syllabus. The course covers every dot point from the new NSW Year 11 Mathematics Extension 1 syllabus, both old and new content. Please note that only Extension 1 content is covered, not Mathematics Advanced.

The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 106 proofs and examples have been recorded, so that you can watch an experienced maths teacher talk through the examples and any important points to note.

Part III of the series covers ME-T1 Inverse Trigonometric Functions, ME-T2 Further Trigonometric Identities and ME-C1 Rates of Change. These topics have Functions and Calculus from Advanced as prerequisites.

New and existing content is explored in detail, including interesting and more efficient techniques that experienced teachers may not have seen before. Important points to be covered with students are noted, and the limits of the syllabus are discussed. As more detail on the syllabus is released by NESA any changes required will be made. Also included are related skills that are beyond the syllabus that you can use to extend more capable students.

The course includes a 175 page course handout, including an additional 106 practice questions matching the examples from the course, with fully worked solutions. A suggested scope and sequence for Year 11 Advanced and Extension 1 for combined classes is provided, plus a lesson by lesson breakdown of the Advanced, Extension 1 and Extension 2 courses for Year 11 and 12 to help you create your own scope and sequences.

Part I of the series covers ME-A1 Working with Combinatorics and ME-F1 Further Work with Functions (Part A) F1.1: Graphical relationships.

Part II of the series covers ME-F1 Further Work with Functions (Part B) and ME-F2 Polynomials.


Mathematics teachers of any experience level who are preparing to teach the new Extension 1 syllabus.

Available Delivery Formats

Format Description

Course Access - This course is available 24/7. Begin the course when it suits you. After completing the course you will still have ongoing access to review content.

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Teaching Standards
2.1.2 Proficient Level – Content and teaching strategies of the teaching area
6.2.2 Proficient Level – Engage in professional learning and improve practice

Are you in NSW? If so, this is relevant for you Accreditation Completing this course will contribute 10 hours of NESA Registered PD addressing 2.1.2 & 6.2.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.

This course contributes to 10.0 professional development hours.


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10 minutes

Course Administration
Introduction to the Mathematics Extension 1 In Depth Year 11 Series
Introduction to Part III

Introduction to Trigonometry

5 minutes

Introduction to Trigonometry

Trigonometry 1: Cyclometry

50 minutes

Lesson 1 Overview
A Deeper Understanding of Trigonometry
The Unit Circle and the (simplified) Origins of Trigonometry
The Hexagon Mnemonic
Trigonometric Ratios and Intervals in the Unit Circle

Trigonometry 2: Inverse Trigonometric Functions - Definitions and Sketching

40 minutes

Lesson 2 Overview
Angle Size and Arc Length
Inverse Sine and Arc Sine
Inverse Trig Functions
Inverse Sine Function
Inverse Cosine Function
Inverse Tangent Function
Inverse Trigonometric Ratios for all Intervals

Trigonometry 3: Inverse Trigonometric Functions - Further Manipulation

50 minutes

Lesson 3 Overview
Function of a Function Background Information
Trig Function of an Inverse Trig Function
Inverse Trig Function of a Trig Function – Restricted Domain
Inverse Trig Function of a Trig Function – Full Domain
Properties of inverse trigonometric functions

Trigonometry 4: Compound Angles

40 minutes

Lesson 4 Overview
Compound Angle Results
Alternative Proofs – Sum of Angles

Trigonometry 5: Double Angle Results

35 minutes

Lesson 5 Overview
Applications of Compound Angles
Double Angle Results

Trigonometry 6: t-formulae

40 minutes

Lesson 6 Overview
Ratios in terms of the tan of half angles

Trigonometry 7: Product to Sum Identities

50 minutes

Lesson 7 Overview
Product to Sum Identities
Sum to Product Identities

Trigonometry 8 (Optional): Beyond the Syllabus

1 hour

Lesson 8 Overview
Graphing Inverse Trig Function of a Trig Function
Further Trig and Inverse Trig Identities
Trig Functions in Terms of Each of the Other Ratios (with Example)
Trig of Inverse Trig Identities

Introduction to Rates of Change

5 minutes

Introduction to Rates of Change

Rates of Change 1: Simple Rates of Change

45 minutes

Lesson 1 Overview
Rates of Change Background Information
Graphing a Quantity
Graphing the Rate of Change

Rates of Change 2: Motion along a straight line

45 minutes

Lesson 2 Overview
Motion Along a Straight Line
Motion graphs

Rates of Change 3: Simple Exponential Growth and Decay

45 minutes

Lesson 3 Overview
Simple Exponential Growth and Decay
Graphing Simple Exponential Growth and Decay

Rates of Change 4: Modified Exponential Growth and Decay

45 minutes

Lesson 4 Overview
Modified Exponential Growth Model
Graphing Modified Exponential Growth and Decay
Newton’s Law Of Cooling

Rates of Change 5: Rates of Change Involving Two or More Variables

45 minutes

Lesson 5 Overview
The Chain Rule and Simplifying Related Rates of Change


1 minute

Conclusion to Part III

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About the team

Steve Howard


Steve is a Mathematics Teacher at Cowra High School, a medium sized rural high school in Central West NSW, where he has taught for 25 years. He has also taught gifted and talented students online through xsel and Aurora College. He has a particular love and passion for Mathematics Extension 2, writing his own textbook and study resources for the old syllabus, to be updated for the new syllabus. He also creates study resources for Mathematics and Extension 1. He loves finding more efficient techniques for solving mathematical questions, by trawling through other teachers' solutions or making up his own approaches when there must be a better way. Steve did 4 Unit Mathematics as a student, gaining a mark of 198/200 and training as an actuary. Working in an office in the city wasn’t for him, so he went back to uni to retrain as a teacher then headed to the country, where he lives in an owner built mud house, with chickens, goats and rescued native birds (which you will sometimes hear in his recordings)!!