Course Description

The course covers every dot point from MA-C2 Differential Calculus and MA-C3 Applications of Differentiation 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 135 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:

  • 135 recorded examples

  • 299 page course handout

  • 135 optional practice questions matching the examples from the course 

  • another exercise of 46 mixed questions, all with fully worked solutions.

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

ADV#7 - Integration (MA-C4 Integral Calculus)

ADV#8 - Functions and Trigonometric Functions (MA-F2 Graphing Techniques and MA-T3 Trigonometric Functions and Graphs) 

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.

This Course:

Further Differentiation - ADV#6

  $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 11 Advanced Mathematics: Exponentials Logarithms Probability - ADV#5 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#6

  • 2

    Further Differentiation

    • Introduction to Further Differentiation

    • Relevant Parts of the Syllabus

  • 3

    Lesson 1 Differentiation Review (Polynomials)

    • Lesson Overview

    • Differentiation

    • Differentiating polynomials

    • Tangents and normals

    • Extension Students

    • Practice Exercises

    • Lesson 1 Quiz

  • 4

    Lesson 2 Differentiating Trigonometric Functions

    • Lesson Overview

    • Understanding and Sketching the Gradient Function of Trigonometric Functions

    • The Rules for Differentiating Trigonometric Functions

    • Understanding the Differentiation of Trigonometric Functions using the Unit Circle

    • Mnemonics

    • Examples

    • Motion

    • Extension Students

    • Practice Exercises

    • Lesson 2 Quiz

  • 5

    Lesson 3 Differentiating Exponential Functions

    • Lesson Overview

    • Differentiating exponential functions of base 𝑒

    • Understanding the gradient functions of exponential functions with other bases

    • Differentiating exponential functions of other bases

    • Tangents and normals

    • Extension Students

    • Practice Exercises

    • Lesson 3 Quiz

  • 6

    Lesson 4 Differentiating Logarithmic Functions

    • Lesson Overview

    • Understanding and sketching the gradient functions of the basic natural logarithm

    • Differentiating natural logarithms

    • Understanding and sketching the gradient functions of other logarithmic functions

    • Differentiating logarithmic functions with other bases

    • Extension Students

    • Practice Exercises

    • Lesson 4 Quiz

  • 7

    Lesson 5 Increasing, decreasing and stationary points on a curve

    • Lesson Overview

    • Finding where a curve is Increasing, decreasing and stationary, plus sketch gradient function, from a graph

    • Finding coordinates of stationary points (without determining their nature)

    • Where is a function increasing or decreasing

    • Functions without stationary points

    • Extension Students

    • Practice Exercises

    • Lesson 5 Quiz

  • 8

    Lesson 6 Local and Global Maxima and Minima

    • Lesson Overview

    • Determining the nature of stationary points using the first derivative

    • Local versus Global maxima/minima

    • Extension Students

    • Practice Exercises

    • Lesson 6 Quiz

  • 9

    Lesson 7 Second Derivative and Concavity

    • Lesson Overview

    • The Second Derivative

    • Concavity

    • Gradient and Concavity

    • Stationary Points and Concavity

    • Extension Students

    • Practice Exercises

    • Lesson 7 Quiz

  • 10

    Lesson 8 Second Derivative to Test stationary points and Finding points of inflection

    • Lesson Overview

    • Determining the nature of stationary points using the second derivative

    • Determining whether a point is a point of inflection

    • Extension Students

    • Practice Exercises

    • Lesson 8 Quiz

  • 11

    Lesson 9 Optimisation Problems

    • Lesson Overview

    • Applications of Differentiation

    • Optimisation problems

    • Extension Students

    • Practice Exercises

    • Lesson 9 Quiz

  • 12

    Lesson 10 Sketching Polynomials using Calculus

    • Lesson Overview

    • Curve Sketching Using Calculus

    • Examples

    • Extension Students

    • Practice Exercises

    • Lesson 10 Quiz

  • 13

    Lesson 11 Sketching Unusual Curves using Calculus

    • Lesson Overview

    • Sketching Unusual Functions

    • Extension Students

    • Practice Exercises

    • Lesson 11 Quiz

  • 14

    Questions from the HSC

    • Advanced Year 12 Further Differentiation in the HSC Exams

  • 15

    Appendix 1: Mixed Revision Exercises

    • Mixed Revision

  • 16


    • Highlights of Further Differentiation

    • Conclusion to In Depth ADV#6

  • 17

    Course Feedback

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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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