Course Description

The course covers every dot point from MA-F2 Graphing Techniques and MA-T3 Trigonometric Functions and Graphs in the new NSW Year 12 Mathematics Advanced syllabus. 

The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 110 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.

Each lesson includes a section for Extension Students, that covers work that can help them develop skills and techniques that helps prepare them for content they will cover in the Extension 1 or Extension 2 courses.

The course includes:

  • 110 recorded examples

  • 293 page course handout

  • 110 optional practice questions matching the examples from the course

  • 41 mixed questions, all with fully worked solutions


The remainder of the Year 12 Advanced syllabus is covered in four other courses:

ADV#6 Further Differentiation (MA-C2 Differential Calculus and MA-C3 Applications of Differentiation)

ADV#7 Integration (MA-C4 Integral Calculus) 

ADV#9 Statistics (MA-S2 Descriptive Statistics and Bivariate Data Analysis and MA-S3 Random Variables)

ADV#10 Financial Mathematics (MA-M1 Modelling Financial Situations)


Mathematics teachers of any experience level who are preparing to teach the new Advanced 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

This Course:

Integration - ADV#8

  $349 + GST (Teacher)
$1250 + GST (School)

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Complete Subject:

Year 12 Advanced (5 courses)

  $990 + GST (Teacher)
$2990 + GST (School)

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

Completing Year 12 Advanced Mathematics: Functions and Trigonometric Functions - ADV#8 will contribute 10 hours of NSW Education Standards Education 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 Australia Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.


Course curriculum

  • 1


    • Course Administration

    • Introduction to the Mathematics Advanced Year 12 In Depth Series

    • Introduction to In Depth ADV#8

  • 2

    Functions & Trigonometric Functions

    • Introduction to Functions & Trigonometric Functions

    • Relevant Part of the Advanced Syllabus

  • 3

    Lesson 1 Vertical and Horizontal Translations

    • Lesson Overview

    • Introduction to Transformations

    • Using Transformations

    • Transformations in Stage 5 and Stage 6

    • Understanding the Transformation Formula

    • Vertical versus Horizontal Transformations

    • Vertical and Horizontal Translations

    • Extension Students

    • Practice Exercises

    • ADV#8 Lesson 1 Quiz

  • 4

    Lesson 2 Vertical Dilations and Reflections

    • Lesson Overview

    • Vertical Dilations

    • Vertical Reflections

    • Vertical Dilations and Vertical Reflections

    • Extension Students

    • Practice Exercises

    • ADV#8 Lesson 2 Quiz

  • 5

    Lesson 3 Horizontal Dilations and Reflections

    • Lesson Overview

    • Horizontal Dilations and Reflections

    • Horizontal Dilations

    • Horizontal Reflections

    • Horizontal Dilations and Horizontal Reflections

    • Extension Students

    • Practice Exercises

    • ADV#8 Lesson 3 Quiz

  • 6

    Lesson 4 Combining Transformations

    • Lesson Overview

    • Combining Transformations

    • Easy Combinations of Transformations

    • Harder Combinations of Transformations

    • Extension Students

    • Practice Exercises

    • ADV#8 Lesson 4 Quiz

  • 7

    Lesson 5 Choosing Appropriate Methods of Sketching

    • Lesson Overview

    • Review of Graphing Functions in Stage 6

    • Choosing the Most Appropriate Method

    • Extension Students

    • Practice Exercises

    • ADV#8 Lesson 5 Quiz

  • 8

    Lesson 6 Number of Solutions, Equations and Inequalities

    • Lesson Overview

    • Using Graphs to Solve Equations and Inequalities

    • Sketching Graphs to Solve Linear and Quadratic Equations and Inequalities

    • Extension Students

    • Practice Exercises

    • ADV#8 Lesson 6 Quiz

  • 9

    Lesson 7 Transforming Trigonometric Functions

    • Lesson Overview

    • Transforming Trigonometric Functions

    • Terminology for Trigonometric Functions

    • Hints for Sketching Transformed Trigonometric Functions

    • Combining Transformations

    • Extension Students

    • Practice Exercises

    • ADV#8 Lesson 7 Quiz

  • 10

    Lesson 8 Trigonometric Equations and Periodic Phenomena

    • Lesson Overview

    • Trigonometric Equations

    • Modelling Periodic Phenomena

    • Extension Students

    • Practice Exercises

    • ADV#8 Lesson 8 Quiz

  • 11

    Questions from the HSC

    • Advanced Year 12 Functions and Trigonometric Functions in the HSC Exams

  • 12

    Mixed Revision Exercises

    • Mixed Revision

  • 13


    • Highlights of Functions and Trigonometric Functions

    • Conclusion to In Depth ADV#8

  • 14

    Course Feedback

    • Please take a few minutes to give us your 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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