- Mathematics General
- Year 12
Algebra and Modelling
approx. 19 hrs
4 topics
40 concepts
Develop an aptitude for Algebra and Modelling and select and apply algebraic techniques for exam success.
approx. 19 hrs
4 topics
40 concepts
Develop an aptitude for Algebra and Modelling and select and apply algebraic techniques for exam success.
The Year 12 Algebra and Modelling program is aligned with the content contained in the NSW General Mathematics syllabus. We show students how to apply algebraic skills and techniques to interpret and use linear and non-linear mathematical models in a range of contexts.
This learning program is made up of the following 4 topics, broken down into 40 concepts.
The zero index
Apply index laws for dividing
Apply index laws for multiplying
Add or subtract algebraic fractions with binomial numerators or denominators
Simplifying algebraic fractions multiplication/ division with a numerical denominator or single algebraic term
Simplify algebraic expressions by adding or subtracting like terms
Identify like terms
Substitute positive or negative values into an algebraic expression and evaluate the result
Solve linear equations involving more than three steps
Solve three-step equations
Solve two-step equations
Solve one-step equations
Rearrange a formula to change the subject of the equation
Substitute positive or negative integers into a given formula
Solve linear simultaneous equations using elimination method where one or both of the equations need to be modified
Solve linear simultaneous equations using substitution method
Solve linear simultaneous equations using elimination method
Classify the nature of a gradient from a linear function
Use the gradient and y-intercept to graph a linear equation
Reading the x and y intercept from a graph
Sketch a linear relationship from a table of values on a cartesian plane
Finding the y - intercept at x=0
Find the gradient of a line between two points using rise over run
Determine the gradient and y-intercept using the gradient-intercept form of a linear relationship
Identify independent and dependent variables in a practical context
Solving practical problems with linear relationships
Graph two intersecting lines on the same set of axes and read off the point of intersection
Interpolation and Extrapolation
Analyse step graphs
Establish meaning for the gradient and intercepts in a practical context
Apply break-even analysis to linear models
Sketch hyperbola graphs - positive quadrant
Sketch cubic graphs - positive quadrant
Develop non-linear equations where one variable varies directly as a power of another
Sketch parabolic graphs - positive quadrant
Sketch exponential graphs - positive quadrant
Recognise the limitations of non-linear modelling - interpolating and extrapolating
Solve contextual problems - including determining minimum and maximum values
Develop linear equations from practical contexts where one variable directly varies with another
Solve inverse variation problems
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