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

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Motions in Straight Lines

Kinematics
Reciprocal Model
Locus
Parameters
Functions
Trigonometry
Trigonometric Graphs
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Course Includes

  • 38 Lessons
  • 205 Topics
  • 32 Quizzes