Course Description

This course covers every dot point from ME-T3 Trigonometric Equations, ME-C2 Further Calculus Skills, ME-C3 Applications of Calculus and ME-S1 The Binomial Distribution from the new NSW Mathematics Year 12 Extension 1 syllabus - four topics that bring together skills from the Year 11 and 12 courses.

The course goes into greater detail than the textbooks, so teachers become 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.

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:

  • 140 recorded examples

  • 284 page course handout

  • 140 optional practice questions matching the examples from the course, with fully worked solutions

A suggested scope and sequence for Year 12 Advanced, Extension 1 and Extension 2 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.

The remainder of the Mathematics Extension 1 syllabus, is covered in four other courses:

EXT1#1 of the series covers  ME-A1 Working with Combinatorics and ME-F1 Further Work with Functions (F1.1: Graphical Relationships)

EXT1#2 of the series covers the remainder of ME-F1 Further Work with Functions plus ME-F2 Polynomials.

Ext1#3 covers ME-T1 Inverse Trigonometric Functions, ME-T2 Further Trigonometric Identities and ME-C1 Rates of Change.

Ext1#4  covers ME-P1 Proof by Mathematical Induction and ME-V1 Introduction to Vectors.


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

Do you teach in NSW? If so, this is relevant to you:

Completing Mathematics Extension 1 Year 12: Trigonometry (Year 12), Calculus & Statistics - EXT1#5 will contribute 10 hours of NSW Education Standards Authority (NESA) Accredited PD in the priority area of Delivery and assessment of NSW Curriculum/Early Years Learning Framework addressing standard descriptors 2.1.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.


Course curriculum

  • 1


    • Course Administration

    • Introduction to Mathematics Extension 1 In Depth Year 12 Series

    • Introduction to Part II

  • 2

    Trigonometric Equations

    • Introduction to Trigonometric Equations

  • 3

    Trigonometric Equations 1 - Auxiliary Angle Method

    • Lesson Overview

    • Auxiliary Angle Method

    • Harder Questions

    • Lesson 1 Quiz

  • 4

    Trigonometric Equations 2 - Other Methods

    • Lesson Overview

    • Factorising

    • Double Angle Formula

    • t-formulae

    • Compound Angle Formulae

    • Lesson 2 Quiz

  • 5

    Trigonometric Equations 3 - Other Trigonometric Identities and Equations

    • Lesson Overview

    • Product to Sum Identities

    • Other Trigonometric Identities

    • Lesson 3 Quiz

  • 6

    Further Calculus

    • Introduction to Further Calculus

  • 7

    Calculus 1 - Integration by Substitution

    • Lesson Overview

    • Technology

    • Integration by Substitution and the Reverse Chain Rule

    • Other u Substitutions

    • x=f(u) Substitutions

    • Lesson 1 Quiz

  • 8

    Calculus 2 - Integrating with Sine Squared and Cosine Squared

    • Lesson Overview

    • Trigonometric Identities

    • Integrating Using the Trig Identities

    • Similar Integrands

    • Lesson 2 Quiz

  • 9

    Calculus 3 - Derivatives of Inverse Functions

    • Lesson Overview

    • Derivatives of Inverse Functions

    • Derivatives of Inverse Trigonometric Functions

    • Lesson 3 Quiz

  • 10

    Calculus 4 - Integrating to Inverse Functions

    • Lesson Overview

    • Integrating with Inverse Trig Functions

    • Lesson 4 Quiz

  • 11

    Calculus 5 - Area Between Two Curves

    • Lesson Overview

    • Area Between Two Curves

    • Lesson 5 Quiz

  • 12

    Calculus 6 - Volumes of Solids of Revolution

    • Lesson Overview

    • Sketching Solids of Revolution

    • Calculating the Volume of Solids of Revolution

    • Area of an Annulus

    • Volumes by Cylindrical Shells

    • Lesson 6 Quiz

  • 13

    Calculus 7 - Simple Differential Equations

    • Lesson Overview

    • Differential Equations

    • Testing Given Solutions

    • Solving Differential Equations of the Form dy/dx=f(x)

    • Solving Differential Equations of the Form dy/dx=g(y)

    • Lesson 7 Quiz

  • 14

    Calculus 8 - Harder Differential Equations

    • Lesson Overview

    • Solving Differential Equations of the Form dy/dx=f(x)g(y)

    • Logistic Equation

    • Testing Solutions of Differential Equations of the Form dy/dx=f(x,y)

    • Lesson 8 Quiz

  • 15

    Calculus 9 - Slope Fields

    • Lesson Overview

    • Slope Fields

    • Slope Fields Using Technology

    • Examples

    • Solution Curves

    • Lesson 9 Quiz

  • 16

    The Binomial Distribution

    • Introduction to the Binomial Distribution

  • 17

    Binomial 1 - The Bernoulli Random Variable

    • Lesson Overview

    • Bernoulli Trials

    • Mean and Variance

    • Lesson 1 Quiz

  • 18

    Binomial 2 - The Binomial Random Variable

    • Lesson Overview

    • The Binomial Distribution

    • Mean and Variance

    • Mode

    • Lesson 2 Quiz

  • 19

    Binomial 3 - Normal Approximations

    • Lesson Overview

    • The Shape of the Binomial Distribution

    • The Binomial and Normal Distributions in More Detail

    • The Problem with Discrete Distributions

    • Sample Proportion

    • Understanding the Behaviour of the Sample Proportion

    • Theoretical Sample Proportion Distribution

    • Continuity Correction

    • The Binomial Distribution and the Normal Distribution

    • Lesson 3 Quiz

  • 20


    • Highlights from Trigonometry, Calculus and Statistics

    • Conclusion to Part II

    • Course Feedback


Steve Howard

Steve Howard

Steve Howard has inspired and equipped hundreds of Maths teachers with his In-Depth Senior Mathematics courses, providing all the tips, examples and resources to teach the HSC syllabus with confidence. He loves to discover the most efficient techniques for solving mathematical problems, by analysing other experts' solutions or by developing his own approaches when he finds a better way. As a student, Steve did Unit 4 Mathematics, gaining a mark of 198/200, before training as an actuary. After retraining as a teacher, Steve has taught Maths at Cowra High School, NSW, for 28 years. He has also taught gifted and talented students online through Xsel and Aurora College, and developed all student course material for TTA's Year 12 Extension Maths Portal.

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