VCE Further Mathematics Units 3 and 4 – Graphs and Relations

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Description

6.1 Straight Lines
6.2 Simultaneous Equations
6.3 Graphs
6.4 Inequalities




Additional information

Outcome

Key knowledge
• intercepts and slope of a straight-line graph and their interpretation in practical situations
• graphical and algebraic solutions of simultaneous linear equations in two unknowns
• intercepts, slope, maximum/minimum points and average rate of change of non-linear graphs and their interpretation in practical situations
• graphical representation of relations of the form \( y = kx^n \) for \( x \ge 0 \), where n ∈ {–2, –1, 1, 2, 3}
• properties of graphs used to model situations involving two independent variables
• linear inequalities in one and two variables and their interpretation in practical situations
• linear programming and its application
• the terms constraint, feasible region and objective function in the context of linear programming
• the sliding-line method and the corner-point principle for identifying the optimal solution of a linear programming problem.

Key skills
• construct and interpret straight-line graphs, line segment graphs and step graphs used to model practical situations
• construct from a table of values and interpret non-linear graphs used to model practical situations
• solve practical problems involving finding the point of intersection of two straight-line graphs
• solve graphically practical problems involving finding the point of intersection of a linear graph with a non-linear graph
• use relations of the form \( y = kx^n \) for x ≥ 0, where n ∈ {–2, –1, 1, 2, 3} to model and analyse practical situations
• interpret graphs used to model situations involving two independent variables
• graph linear inequalities in one or two variables and interpret them when used in practical situations
• formulate a linear programming problem with two decision variables and solve graphically
• extend the linear programming method of solution to include only integer solutions where required.

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