• Mathematical Methods
  • Year 12

Further differentiation and applications

approx. 18 hrs

11 topics

28 concepts

Enrol in Further differentation and applications to master calculus techniques to solve problems.

Available in


In this learning program, students will develop proficiency in selecting and applying calculus techniques including chain, product and quotient rules. We will help students understand the application of calculus to curve sketching and explore the impact of stationary points and points of inflection on the concavity of non-linear graphs. Students will investigate rates of change and motion by establishing equations to represent velocity and acceleration and solving practical related problems.

Topics & Concepts We Cover

This learning program is made up of the following 11 topics, broken down into 28 concepts.

  • Derivative of exponential function 2 concepts

    1. Use given information to produce a model for natural growth and decay

    2. Differentiate exponential functions with linear arguments

  • Derivative of logarithmic function 1 concept

    1. Differentiate logarithmic functions with linear arguments

  • Derivative of circular functions 1 concept

    1. Differentiate trigonometric functions with linear arguments

  • Chain rule 1 concept

    1. Chain rule of differentiation

  • Product and Quotient rules 4 concepts

    1. Apply the product rule to logarithmic, exponential and circular functions

    2. Apply the quotient rule to logarithmic, exponential and circular functions

    3. Product rule of differentiation

    4. Quotient rule of differentiation

  • Rates of change 1 concept

    1. Find the average rate of change over a given interval

  • Velocity and acceleration 4 concepts

    1. Solve motion problems involving the acceleration-time equations

    2. Finding the acceleration-time equation using differentiation

    3. Solve motion problems involving the velocity-time equation

    4. Finding the velocity-time equation using differentiation

  • Application of the First Derivative 4 concepts

    1. Classify stationary points using the first derivative

    2. Find where a function is increasing or decreasing

    3. Find the coordinates of stationary points

    4. Understand the relationship between the sign of the derivative and the gradient of the tangent

  • Application of the Second Derivative 6 concepts

    1. Find the coordinates of the point of inflexion

    2. Find the second derivative of a function

    3. Determine the concavity of a curve by investigating the second derivative

    4. Classify stationary points using the second derivative

    5. Find horizontal points of inflexion

    6. Find the absolute minimum or maximum point with domain restrictions

  • Problems of Maxima and Minima 1 concept

    1. Problems of maxima and minima

  • Curve sketching using calculus 3 concepts

    1. Sketch rational functions using calculus techniques

    2. Sketch polynomials using calculus techniques

    3. Sketch unknown functions using calculus techniques

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Further differentiation and applications


  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

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Starting at

$49(inc. GST)

per session

Fully flexible

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Access to practice questions

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