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.

 

Audience

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

 

Teaching Standards

2.1.2 Proficient Level - Know the content and how to teach it - Content and teaching strategies of the teaching area:  Apply knowledge of the content and teaching strategies of the teaching area to develop engaging teaching activities,

6.2.2 Proficient Level - Engage in Professional Learning - Engage in professional learning and improve practice:   Participate in learning to update knowledge and practice targeted to professional needs and school and/or system priorities

 

Are you in NSW? If so, this is relevant for you

Completing “Mathematics Extension 1 Year 11: In Depth Part III – Trigonometry & Rates of Change” before 4th February 2022 under NESA’s interim arrangements will contribute 10 hours of NSW Education Standards Authority (NESA) Accredited PD in the priority area of Delivery and assessment of NSW curriculum addressing standard descriptors  2.1.2, 6.2.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.

 

Course curriculum

  • 1

    Introduction

    • Course Administration

    • Introduction to the Mathematics Extension 1 In Depth Year 11 Series

    • Introduction to Part III

  • 2

    Trigonometry

    • Introduction to Trigonometry

  • 3

    Trigonometry 1: Cyclometry

    • Lesson 1 Overview

    • A Deeper Understanding of Trigonometry

    • The Unit Circle and the (simplified) Origins of Trigonometry

    • The Hexagon Mnemonic

    • Examples

    • Trigonometric Ratios and Intervals in the Unit Circle

    • Example

  • 4

    Trigonometry 2: Inverse Trigonometric Functions - Definitions and Sketching

    • 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

    • Examples

  • 5

    Trigonometry 3: Inverse Trigonometric Functions - Further Manipulation

    • Lesson 3 Overview

    • Function of a Function Background Information

    • Trig Function of an Inverse Trig Function

    • Examples

    • Inverse Trig Function of a Trig Function - Restricted Domain

    • Inverse Trig Function of a Trig Function - Full Graphs

    • Examples

    • Properties of inverse trigonometric functions (with Examples)

  • 6

    Trigonometry 4: Compound Angles

    • Lesson 4 Overview

    • Compound Angle Results

    • Examples

    • Alternative Proofs - Sum of Angles

  • 7

    Trigonometry 5: Double Angle Results

    • Lesson 5 Overview

    • Applications of Compound Angles

    • Double Angle Results

    • Examples

  • 8

    Trigonometry 6: 𝑡-formulae

    • Lesson 6 Overview

    • Ratios in terms of the tan of half angles

    • Examples

  • 9

    Trigonometry 7: Product to Sum Identities

    • Lesson 7 Overview

    • Product to Sum Identities

    • Examples

    • Sum to Product Identities

    • Examples

  • 10

    Trigonometry 8 (Optional): Beyond the Syllabus

    • Lesson 8 Overview

    • Graphing Inverse Trig Function of a Trig Function

    • Examples

    • Further Trig and Inverse Trig Identities

    • Trig Functions in Terms of Each of the Other Ratios (with Example)

    • Trig of Inverse Trig Identities (with Example)

  • 11

    Rates of Change

    • Introduction to Rates of Change

  • 12

    Rates of Change 1: Simple Rates of Change

    • Lesson 1 Overview

    • Rates of Change Background Information

    • Graphing a Quantity

    • Graphing the Rate of Change

    • Examples

  • 13

    Rates of Change 2: Motion along a straight line

    • Lesson 2 Overview

    • Motion Along a Straight Line

    • Motion graphs

    • Examples

  • 14

    Rates of Change 3: Simple Exponential Growth and Decay

    • Lesson 3 Overview

    • Simple Exponential Growth and Decay

    • Graphing Simple Exponential Growth and Decay

    • Examples

  • 15

    Rates of Change 4: Modified Exponential Growth and Decay

    • Lesson 4 Overview

    • Modified Exponential Growth Model

    • Graphing Modified Exponential Growth and Decay

    • Newton’s Law Of Cooling

    • Examples

  • 16

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

    • Lesson 5 Overview

    • The Chain Rule and Simplifying Related Rates of Change

    • Examples

  • 17

    Conclusion

    • Conclusion to Part III

  • 18

    Course Feedback

    • Course Feedback

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