VCE General Mathematics Units 1 and 2 – Graphs of Linear and Non-Linear Relations

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Description

5.1 Motions in Straight Lines
5.2 Kinematics
5.3 Reciprocal Model
5.4 Locus
5.5 parameters
5.6 Functions




Additional information

Outcome

Linear graphs and models
Key knowledge
• the properties of linear functions and their graphs
• the concept of a linear model and its properties
• the concepts of interpolation and extrapolation
• situations that can be modelled by piecewise linear (line-segment) graphs.
Key skills
• develop a linear model to represent and analyse a practical situation and specify its domain of application
• interpret the slope and the intercept of a straight-line graph in terms of its context and use the equation to make predictions with consideration of the limitations of extrapolation
• fit a linear model to data by finding a line fitted by the eye and using piecewise linear (line-segment) graphs to model and analyse practical situations.

Inequalities and linear programming
Key knowledge
• the concept of linear inequality and its graphical representation
• the linear programming problem and its purpose
• the concepts of the feasible region, constraint, the objective function and the corner-point principle defined in the context of solving a linear programming problem
• linear inequalities and their use in specifying the constraints and defining the feasible region of a linear programming problem.
Key skills
• graph linear inequalities in one and two variables and use to solve practical problems
• construct the constraints of a linear programming problem (with two decision variables) as a set of linear inequalities
• construct the feasible region of a linear programming problem by graphing its constraints
• determine the optimum value of the objective function using the corner-point principle.

Variation
Key knowledge
• the concepts of direct, inverse and joint variation
• the methods of transforming data
• the use of log (base 10) and other scales.
Key skills
• solve problems which involve the use of direct, inverse or joint variation
• model non-linear data by using suitable transformations
• apply log (base 10) and other scales to solve variation problems.

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