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 2 syllabus. The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 100 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 covers Further Integration (MEX-C1). 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 100recorded examples, with a 178 page course handout including 99 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.



Mathematics teachers who are preparing to teach the new Extension 2 syllabus. This course is suitable for teachers with any level of previous experience.


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 2: In Depth Part III - Integration” 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


    • Course Administration

    • Introduction to the Mathematics Extension 2 In Depth Series

    • Introduction to Part III

  • 2


    • Introduction to Integration

    • Relevant Parts of the Syllabus

  • 3

    Integration 1 - Standard Integrals & Completing the Square

    • Lesson Overview

    • Integration in Extension 2

    • Standard Integrals

    • Mnemonics for Differentiating and Integrating with Trigonometry

    • Completing the Square in a Denominator

    • Lesson 1 Quiz

  • 4

    Integration 2 - The Reverse Chain Rule and U Substitutions

    • Lesson Overview

    • Background: The Reverse Chain Rule and u-substitutions

    • Reverse Chain Rule

    • Reverse Chain Rule and u-substitution Examples

    • Reverse Chain Rule and Completing the Square

    • Lesson 2 Quiz

  • 5

    Integration 3 - Splitting the Numerator and Partial Fractions by Inspection

    • Lesson Overview

    • Splitting the Numerator

    • Partial Fractions by Inspection

    • Lesson 3 Quiz

  • 6

    Integration 4 - Partial Fractions

    • Lesson Overview

    • Partial Fractions

    • Method 1 - Equating Coefficients

    • Method 2 - Elimination by Substutition

    • Method 3 - Cover Up Method

    • Finding or Evaluating Integrals with Partial Fractions

    • Lesson 4 Quiz

  • 7

    Integration 5 - Other Substitutions

    • Lesson Overview

    • Simplifying Integrands

    • Simplifying Compound Functions

    • Simplifying Other Functions Involving Indices

    • Other Substitutions

    • Lesson 5 Quiz

  • 8

    Integration 6 - Trigonometric Functions I - Powers of Trig Functions and Product to Sum identities

    • Lesson Overview

    • Powers of Trigonometric Functions

    • Powers of Sine and Cosine

    • Powers of Tangent and Secant

    • Powers of Cotangent and Cosecant

    • Mismatched Pairs of Ratios

    • Product to Sum Identities

    • Lesson 6 Quiz

  • 9

    Integration 7 - Trigonometric Functions II - T-results and Trig substitutions

    • Lesson Overview

    • Integrating with t-formulae

    • Trig Substitutions

    • Lesson 7 Quiz

  • 10

    Integration 8 - Integration by Parts

    • Lesson Overview

    • Integration by Parts

    • Integration by Parts Using DETAIL

    • Integration by Parts Using the Reverse Chain Rule

    • Lesson 8 Quiz

  • 11

    Integration 9 - Recurrence Relationships

    • Lesson Overview

    • Recurrence Relationships

    • Integration by Parts or Not?

    • Recurrence Relationship Examples

    • What if the Recurrence Relationship is not Given?

    • Lesson 9 Quiz

  • 12

    Integration 10 - Definite Integrals

    • Lesson Overview

    • Areas Above or Below the x-axis

    • Difference of Two Functions

    • Splitting Integrals

    • Switching Limits

    • Changing Variables

    • Odd and Even Functions

    • Transformations

    • Lesson 10 Quiz

  • 13

    Integration 11 - Beyond the Syllabus: Tabular Integration by Parts

    • Lesson Overview

    • Tabular Integration by Parts

  • 14


    • Highlights of Integration

    • Conclusion to Part III

    • Feedback

Features of TTA Online PD

  • Availability

    Online courses are available 24/7. Designed to be done in your own time at your own pace.

  • Team Online

    All online courses are available for team purchase. Unlimited teachers from the one Campus for any course for $990 + GST

  • Money back Guarantee

    If you complete less than 25% of an online course and aren't completely satisfied, let us know, and we will cancel your enrolment and provide a full refund.