- 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.
approx. 11 hrs
9 topics
35 concepts
Build advanced skills for Linear and Non-linear Relationships and achieve success in your examinations.
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.
This learning program is made up of the following 9 topics, broken down into 35 concepts.
Find the vertex of a parabola
Find the axis of symmetry of a parabola
Identify and use features of parabolas and their equations to assist in sketching quadratic relationships
Determine concavity of a parabola
Identify the x and y intercepts of a parabola
Sketch a parabola applying horizontal translation of the graph
Sketch a parabola applying reflection of the graph across the x or y axis
Sketch a parabola with dilation
Sketch a parabola applying multiple transformations
Sketch a parabola 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 vertical translation of the graph
Sketch an exponential function applying horizontal translation of the graph
Sketch an exponential function with dilation
Sketching exponentials
Sketch a circle where the centre is the origin
Use Pythagoras' theorem to establish the equation of a circle with centre at the origin
Connect the shape of a non-linear graph with the distinguishing features of its equation
Calculating the 'mean' to find the midpoint, M, of the interval
Using Pythagoras' theorem to calculate distance between two points
Classify the nature of a gradient from a linear function
Find the gradient of a line between two points using rise over run
Form of a horizontal line including the equation of the x-axis
Form of a vertical line including the equation of the y-axis
Finding the x - intercept at y=0
Determine whether a point lies on a line by substitution
Reading the x and y intercept from a graph
Finding the y - intercept at x=0
Sketch a linear relationship from a table of values on a cartesian plane
Convert between general form and gradient-intercept form of a linear equation
Find the equation of a line given the gradient and the y-intercept
Determine the gradient and y-intercept using the gradient-intercept form of a linear relationship
Use the gradient and y-intercept to graph a linear equation
Apply the property that perpendicular lines have gradients that are negative reciprocals of each other
Apply the property that parallel lines have equal gradients
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