• Mathematics Advanced
  • Year 10

Non-linear Relationships

approx. 13 hrs

12 topics

49 concepts

Develop essential skills in Non-linear Relationships to enhance your performance in Mathematics.

Available in
ACT NSW NT QLD SA TAS VIC WA

Overview

Students studying Non-Linear Relationships investigate the connection between algebra and geometry for both straight lines and curves, including parabolas, hyperbolas, power functions and circles. In addition, they enhance their ability to sketch curves, including transformations based on the algebraic equation given. This program is aligned to the Australian curriculum.

Topics & Concepts We Cover

This learning program is made up of the following 12 topics, broken down into 49 concepts.

  • Features of a Parabola 5 concepts

    1. Find the vertex of a parabola

    2. Find the axis of symmetry of a parabola

    3. Identify and use features of parabolas and their equations to assist in sketching quadratic relationships

    4. Determine concavity of a parabola

    5. Identify the x and y intercepts of a parabola

  • Transformations of the Parabola 5 concepts

    1. Sketch a parabola applying horizontal translation of the graph

    2. Sketch a parabola applying reflection of the graph across the x or y axis

    3. Sketch a parabola with dilation

    4. Sketch a parabola applying multiple transformations

    5. Sketch a parabola applying vertical translation of the graph

  • Advanced Algebraic Techniques to Graph a Parabola 3 concepts

    1. Sketching a perfect square

    2. Sketching the quadratic function from the completed square

    3. Sketching the quadratic function from the quadratic formula

  • Parabola and a Line Intersecting 1 concept

    1. Finding points of intersection of a line with a parabola

  • Introduction to Functions 4 concepts

    1. Identify if a set of coordinates is a function

    2. Use function notation to find the output of a single function

    3. Use the vertical line test on a graph to decide whether it represents a function

    4. Finding the output of a piecewise defined function

  • Domain and Range of a Single Function 2 concepts

    1. Range of a single function

    2. Domain of a single function

  • Sketching Circles 5 concepts

    1. Find the radius and centre of a circle given the equation or graph

    2. Finding points of intersection of a line with a circle

    3. Find the radius and centre of a circle by completing the square

    4. Sketching semi-circles

    5. Sketching a circle

  • Sketching Exponential Functions 5 concepts

    1. Sketch an exponential function applying reflection of the graph across the x or y axis

    2. Sketch an exponential function applying vertical translation of the graph

    3. Sketch an exponential function applying horizontal translation of the graph

    4. Sketch an exponential function with dilation

    5. Sketching exponentials

  • Sketching Hyperbolic Functions 7 concepts

    1. Finding points of intersection of a line with a hyperbola

    2. Sketch a hyperbola applying horizontal translation of the graph

    3. Determine the equations of asymptotes

    4. Sketch a hyperbola with dilation

    5. Sketch a hyperbola applying vertical translation of the graph

    6. Sketch a hyperbola applying reflection of the graph across the x or y axis

    7. Sketching basic hyperbolas in the from y=a/x where a is a positive integer

  • Sketching Cubic Functions 5 concepts

    1. Sketch a cubic function applying reflection of the graph across the x or y axis

    2. Sketch a cubic function with dilation

    3. Sketch a cubic function applying vertical translation of the graph

    4. Sketch a cubic function applying horizontal translation of the graph

    5. Sketching cubics

  • Sketching Power Functions 5 concepts

    1. Sketch a power function with dilation

    2. Sketch a power function applying horizontal translation of the graph

    3. Sketch a power function applying vertical translation of the graph

    4. Sketch a power function applying reflection of the graph across the x or y axis

    5. Sketching graphs with a higher-order power of four or more

  • Mixed Non-Linear Graphs (including hyperbolas) 2 concepts

    1. Connect the shape of a non-linear graph (including hyperbolas) with the distinguishing features of its equation

    2. Sketch a function applying multiple transformations

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 Non-linear Relationships

Reporting

  • 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

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Access to practice questions

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