• Mathematics
  • Year 10

Linear and Non-linear Relationships

approx. 11 hrs

9 topics

35 concepts

Build advanced skills for Linear and Non-linear Relationships and achieve success in your examinations.

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The Year 10 Linear and Non-Linear Relationships program is aligned to the Australian curriculum. Students studying Linear and Non-Linear Relationships in Year 10 investigate the connection between algebra and geometry for both straight lines and curves. They also identify key features of an algebraic equation to help sketch the relationship on the coordinate plane and develop the ability to apply rules to solve a range of coordinate geometry problems.

Topics & Concepts We Cover

This learning program is made up of the following 9 topics, broken down into 35 concepts.

  • Features of a Parabola 5 concepts

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

    2. Find the vertex of a parabola

    3. Determine concavity of a parabola

    4. Find the axis of symmetry of a parabola

    5. Identify the x and y intercepts of a parabola

  • Transformations of the Parabola 5 concepts

    1. Sketch a parabola with dilation

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

    3. Sketch a parabola applying horizontal translation of the graph

    4. Sketch a parabola applying multiple transformations

    5. Sketch a parabola applying vertical translation of the graph

  • Sketching Exponential Functions 5 concepts

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

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

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

    4. Sketch an exponential function with dilation

    5. Sketching exponentials

  • Sketch a Circle centred at the Origin 2 concepts

    1. Sketch a circle where the centre is the origin

    2. Use Pythagoras' theorem to establish the equation of a circle with centre at the origin

  • Mixed Non-Linear Graphs 1 concept

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

  • Midpoint, Gradient and Distance 4 concepts

    1. Calculating the 'mean' to find the midpoint, M, of the interval

    2. Using Pythagoras' theorem to calculate distance between two points

    3. Classify the nature of a gradient from a linear function

    4. Find the gradient of a line between two points using rise over run

  • Sketch Linear Relationships 7 concepts

    1. Form of a vertical line including the equation of the y-axis

    2. Form of a horizontal line including the equation of the x-axis

    3. Finding the x - intercept at y=0

    4. Determine whether a point lies on a line by substitution

    5. Reading the x and y intercept from a graph

    6. Sketch a linear relationship from a table of values on a cartesian plane

    7. Finding the y - intercept at x=0

  • Gradient-Intercept Form 4 concepts

    1. Convert between general form and gradient-intercept form of a linear equation

    2. Find the equation of a line given the gradient and the y-intercept

    3. Determine the gradient and y-intercept using the gradient-intercept form of a linear relationship

    4. Use the gradient and y-intercept to graph a linear equation

  • Parallel and Perpendicular Lines 2 concepts

    1. Apply the property that perpendicular lines have gradients that are negative reciprocals of each other

    2. Apply the property that parallel lines have equal gradients

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 Linear and Non-linear Relationships


  • 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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