- Mathematics General
- Year 12
Algebra and Modelling
approx. 19 hrs
5 topics
52 concepts
Develop an aptitude for Algebra and Modelling and select and apply algebraic techniques with confidence.
approx. 19 hrs
5 topics
52 concepts
Develop an aptitude for Algebra and Modelling and select and apply algebraic techniques with confidence.
The Year 12 Algebra and Modelling program is aligned with the content outlined in the Australian curriculum for General Mathematics. Students studying Algebra and Modelling apply algebraic skills and techniques to enhance their ability to interpret and use linear and non-linear mathematical models in a range of contexts.
This learning program is made up of the following 5 topics, broken down into 52 concepts.
Classify the nature of a gradient from a linear function
Sketch a linear relationship from a table of values on a cartesian plane
Determine the gradient and y-intercept using the gradient-intercept form of a linear relationship
Find the gradient of a line between two points using rise over run
Reading the x and y intercept from a graph
Finding the y - intercept at x=0
Use the gradient and y-intercept to graph a linear equation
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
Use a piecewise linear function to model and solve practical situations
establish meaning for the gradient and intercepts in a practical context
apply break-even analysis to linear models
Determine the maximum value of an objective function for a given feasible region
Determine the minimum value of an objective function for a given feasible region
Set up a basic linear programming problem
Solve basic linear programming problems
Sketch a region defined by a linear inequality
Solve a linear inequation using graphs
Double inequalities
Solve linear inequalities, recognising that there are infinite solutions
Solve linear inequalities by reversing the direction of the inequality sign when multiplying or dividing by a negative number
Represent linear inequalities on the number line
Apply index laws for multiplying
Apply index laws for dividing
The zero index
Add or subtract algebraic fractions with binomial numerators or denominators
Expanding algebraic expressions involving terms with indices and/or negative coefficients
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 one-step equations
Solve two-step equations
Solve three-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
Sketch parabolic graphs - positive quadrant
Sketch cubic graphs - positive quadrant
Sketch hyperbola graphs - positive quadrant
Sketch exponential graphs - positive quadrant
solve contextual problems - including determining minimum and maximum values
develop non-linear equations where one variable varies directly as a power of another
recognise the limitations of non-linear modelling - interpolating and extrapolating
develop linear equations from practical contexts where one variable directly varies with another
Solve inverse variation problems
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