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

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

In this area study, students cover continuous models involving linear and non-linear relations and their graphs, linear inequalities and programming, and variation.

Linear graphs and models

This topic includes:

• review of linear functions and graphs
• the concept of a linear model and its specification
• the construction of a linear model to represent a practical situation including domain of application
• the interpretation of the parameters of a linear model and its use to make predictions, including the issues of interpolation and extrapolation
• fitting a linear model to data by using the equation of a line fitted by eye
• use of piecewise linear (line segment) graphs to model and analyse practical situations.

Inequalities and linear programming

This topic includes:

• linear inequalities in one and two variables and their graphical representation
• the linear programming problem and its purpose
• the concepts of the feasible region, constraint and objective function in the context of solving a linear programming problem
• use of the corner-point principle to determine the optimal solution/s of a linear programming problem
• formulation and graphical solution of linear programming problems involving two variables.

Variation

This topic includes:

• numerical, graphical and algebraic approaches to direct, inverse and joint variation
• transformation of data to linearity to establish relationships between variables, for example $y$ and $x^2$, or $y$ and $\displaystyle \frac{1}{2}$
• modelling of given non-linear data using the relationships $y = kx^2 + c$ and $y = kx + c$ where $k > 0$
• modelling of data using the logarithmic function $y = a \log_{10}(x) + c$ where $a > 0$ .

source – VCE Mathematics Study Design

VCE General Mathematics Units 1 and 2 Courses

VCE General Mathematics Units 1 and 2 Syllabus

Course Content

Motions in Straight Lines

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Kinematics
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Reciprocal Model
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Locus
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Parameters
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Functions
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Trigonometry
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Trigonometric Graphs
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• 38 Lessons
• 205 Topics
• 32 Quizzes