Course Description

This course covers every dot point from MA-C1 Introduction to Differentiation in the new NSW Year 11 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 118 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:

  • 118 recorded examples
  • 300 page course handout
  • 130 optional practice questions matching the examples from the course
  • 73 mixed questions, all with fully worked solutions.

The remainder of the Year 11 Advanced syllabus is covered in four other courses:

ADV#1 and ADV#2 cover MA-F1 Working with Functions.

ADV#3 covers MA-T1 Trigonometry and Measure of Angles and MA-T2 Trigonometric Functions and Identities 

ADV#5 will cover MA-E1 Logarithms and Exponentials and MA-S1 Probability and Discrete Probability Distributions.


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

This Course:

Introduction to Differentiation - ADV#4

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

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Complete Subject:

Year 11 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 11 Advanced Mathematics: Introduction to Differentiation - ADV#4 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 11 In Depth Series

    • Introduction to In Depth ADV#4

  • 2

    Introduction to Differentiation

    • Introduction to Differentiation

    • Relevant Parts of the Syllabus

  • 3

    Lesson 1

    • Lesson Overview

    • Differentiable Functions

    • Extension Students

    • Practice Exercises

    • Lesson 1 Quiz

  • 4

    Lesson 2

    • Lesson Overview

    • Understanding the Gradient of a Function

    • Describing the Gradient of a Function

    • Gradient and the angle with the 𝑥-axis

    • Estimating the Gradient of a Tangent

    • Extension Students

    • Practice Exercises

    • Lesson 2 Quiz

  • 5

    Lesson 3

    • Lesson Overview

    • Notation for the Gradient of a Function

    • Sketching the Gradient Function

    • Extension Students

    • Practice Exercises

    • Lesson 3 Quiz

  • 6

    Lesson 4

    • Lesson Overview

    • Calculating the Gradient of Secants and Tangents

    • The Gradient of a Secant, the Difference Quotient and the Average Rate of Change

    • Differentiation from First Principles

    • Extension Students

    • Practice Exercises

    • Lesson 4 Quiz

  • 7

    Lesson 5

    • Lesson Overview

    • Techniques for Differentiation

    • Short Methods of Differentiation

    • Extension Students

    • Practice Exercises

    • Lesson 5 Quiz

  • 8

    Lesson 6

    • Lesson Overview

    • Tangents and Normals

    • Extension Students

    • Practice Exercises

    • Lesson 6 Quiz

  • 9

    Lesson 7

    • Lesson Overview

    • Differentiating with Negative and Fractional Indices

    • Extension Students

    • Practice Exercises

    • Lesson 7 Quiz

  • 10

    Lesson 8

    • Lesson Overview

    • Product Rule, Quotient Rule and Chain Rule

    • Product Rule

    • Extension Students

    • Practice Exercises

    • Lesson 8 Quiz

  • 11

    Lesson 9

    • Lesson Overview

    • The Quotient Rule

    • Extension Students

    • Practice Exercises

    • Lesson 9 Quiz

  • 12

    Lesson 10

    • Lesson Overview

    • The Chain Rule

    • Extension Students

    • Practice Students

    • Lesson 10 Quiz

  • 13

    Lesson 11

    • Lesson Overview

    • Applications of Differentiation

    • Understanding Quantities and Rates of Change

    • Extension Students

    • Practice Exercises

    • Lesson 11 Quiz

  • 14

    Lesson 12

    • Lesson Overview

    • Motion in a Straight Line

    • Understanding Displacement, Velocity and Acceleration

    • Motion Graphs

    • Extension Students

    • Practice Exercises

    • Lesson 12 Quiz

  • 15

    Questions from the HSC

    • Advanced Introduction to Differentiation in the HSC Exams

  • 16

    Appendix 1: Mixed Revision Exercises

    • Mixed Revision

  • 17


    • Highlights of Introduction to Differentiation

    • Conclusion to Introduction to Differentiation (ADV#4)

  • 18

    Course Feedback

    • 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.

Other Courses by Steve Howard

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