• 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. 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

• #### Advanced Algebraic Techniques to Graph a Parabola 3 concepts

1. Sketching a perfect square

3. Sketching the quadratic function from the completed square

• #### Parabola and a Line Intersecting 1 concept

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

• #### Introduction to Functions 4 concepts

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

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

3. Finding the output of a piecewise defined function

4. Identify if a set of coordinates is a 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. Find the radius and centre of a circle by completing the square

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

4. Sketching a circle

5. Sketching semi-circles

• #### 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

• #### Sketching Hyperbolic Functions 7 concepts

1. Sketch a hyperbola applying vertical translation of the graph

2. Sketch a hyperbola applying horizontal translation of the graph

3. Sketch a hyperbola with dilation

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

5. Determine the equations of asymptotes

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

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 applying reflection of the graph across the x or y axis

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

3. Sketch a power function with dilation

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

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

### Ready to start this program? Simply pick a time that works for you  We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime