Course Description

This course provides 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 that teachers can become 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.

Ext2#3 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:

  • 100 recorded examples

  • 178 page course handout

  • 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.

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

Completing Mathematics Extension 2: Integration - EXT2#3 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 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


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.

Other Courses by Steve Howard

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