• Mathematics Advanced
  • Year 11

Geometrical Applications of Differentiation

approx. 10 hrs

6 topics

19 concepts

Develop proficiency in Geometrical Applications of Differentiation and advance into Year 12 with confidence.

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The Geometrical Applications of Differentiation program covers an essential component of Calculus studied in Year 11 Mathematics Advanced, as specified in the NSW Mathematics syllabus.  We help students studying Geometrical Applications of Differentiation to incorporate deductive and modelling skills to solve a range of questions and problems, including problems of maxima and minima. We explore the relationship between geometrical properties of functions and analytic properties of functions incorporating calculus techniques.

Topics & Concepts We Cover

This learning program is made up of the following 6 topics, broken down into 19 concepts.

  • Curve Sketching using Calculus Techniques 5 concepts

    1. Sketch polynomials using calculus techniques

    2. Sketch rational functions using calculus techniques

    3. Sketch unknown functions using calculus techniques

    4. Sketch the derivative function of a given curve

    5. Sketch the primitive function of a given curve

  • Problems of Maxima and Minima 1 concept

    1. Problems of maxima and minima

  • Primitive Function 1 concept

    1. The primitive function

  • Tangent and Normal 2 concepts

    1. Finding the equation of the tangent

    2. Finding the equation of a normal

  • Application of the First Derivative 4 concepts

    1. Find where a function is increasing or decreasing

    2. Find the coordinates of stationary points

    3. Classify stationary points using the first derivative

    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 absolute minimum or maximum point with domain restrictions

    2. Find horizontal points of inflexion

    3. Find the second derivative of a function

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

    5. Classify stationary points using the second derivative

    6. Find the coordinates of the point of inflexion

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 Geometrical Applications of Differentiation


  • 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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