- 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.
approx. 13 hrs
12 topics
49 concepts
Develop essential skills in Non-linear Relationships to enhance your performance in Mathematics.
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.
This learning program is made up of the following 12 topics, broken down into 49 concepts.
Identify and use features of parabolas and their equations to assist in sketching quadratic relationships
Find the vertex of a parabola
Determine concavity of a parabola
Find the axis of symmetry of a parabola
Identify the x and y intercepts of a parabola
Sketch a parabola with dilation
Sketch a parabola applying reflection of the graph across the x or y axis
Sketch a parabola applying horizontal translation of the graph
Sketch a parabola applying multiple transformations
Sketch a parabola applying vertical translation of the graph
Sketching a perfect square
Sketching the quadratic function from the quadratic formula
Sketching the quadratic function from the completed square
Finding points of intersection of a line with a parabola
Use function notation to find the output of a single function
Use the vertical line test on a graph to decide whether it represents a function
Finding the output of a piecewise defined function
Identify if a set of coordinates is a function
Range of a single function
Domain of a single function
Find the radius and centre of a circle given the equation or graph
Find the radius and centre of a circle by completing the square
Finding points of intersection of a line with a circle
Sketching a circle
Sketching semi-circles
Sketch an exponential function applying vertical translation of the graph
Sketch an exponential function applying reflection of the graph across the x or y axis
Sketch an exponential function applying horizontal translation of the graph
Sketch an exponential function with dilation
Sketching exponentials
Sketch a hyperbola applying vertical translation of the graph
Sketch a hyperbola applying horizontal translation of the graph
Sketch a hyperbola with dilation
Sketch a hyperbola applying reflection of the graph across the x or y axis
Determine the equations of asymptotes
Finding points of intersection of a line with a hyperbola
Sketching basic hyperbolas in the from y=a/x where a is a positive integer
Sketch a cubic function applying reflection of the graph across the x or y axis
Sketch a cubic function with dilation
Sketch a cubic function applying vertical translation of the graph
Sketch a cubic function applying horizontal translation of the graph
Sketching cubics
Sketch a power function applying reflection of the graph across the x or y axis
Sketch a power function applying horizontal translation of the graph
Sketch a power function with dilation
Sketch a power function applying vertical translation of the graph
Sketching graphs with a higher-order power of four or more
Connect the shape of a non-linear graph (including hyperbolas) with the distinguishing features of its equation
Sketch a function applying multiple transformations
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