# VCE General Mathematics Units 1 and 2 – Discrete Mathematics

3.1 Matrices

3.2 Understanding Networks

3.3 Number Sequences

In this area of study, students cover matrices, graphs and networks, and number patterns and recursion, and their use to model practical situations and solve a range of related problems.

## Matrices

This topic includes:

- use of matrices to store and display information that can be presented in a rectangular array of rows and columns such as databases and links in social and road networks
- types of matrices (row, column, square, zero and identity) and the order of a matrix
- matrix addition, subtraction, multiplication by a scalar, and matrix multiplication including determining the power of a square matrix using technology as applicable
- use of matrices, including matrix products and powers of matrices, to model and solve problems, for example costing or pricing problems, and squaring a matrix to determine the number of ways pairs of people in a network can communicate with each other via a third person
- inverse matrices and their applications including solving a system of simultaneous linear equations.

## Graphs and networks

This topic includes:

- introduction to the notations, conventions and representations of types and properties of graphs, including edge, loop, vertex, the degree of a vertex, isomorphic and connected graphs and the adjacency matrix
- description of graphs in terms of faces (regions), vertices and edges and the application of Euler’s formula for planar graphs
- connected graphs: walks, trails, paths, cycles and circuits with practical applications
- weighted graphs and networks, and an introduction to the shortest path problem (solution by inspection only) and its practical application
- trees and minimum spanning trees, Prim’s algorithm, and their use to solve practical problems.

## Number patterns and recursion

This topic includes:

Number patterns and sequences

- the concept of a sequence as a function
- use of a first-order linear recurrence relation to generating the terms of a number sequence
- tabular and graphical display of sequences.

The arithmetic sequence

- generation of an arithmetic sequence using a recurrence relation, tabular and graphical display; and the rule for the nth term of an arithmetic sequence and its evaluation
- use of a recurrence relation to model and analyse practical situations involving discrete linear growth or decay such as a simple interest loan or investment, the depreciating value of an asset using the unit cost method; and the rule for the value of a quantity after n periods of linear growth or decay and its use.

The geometric sequence

- generation of a geometric sequence using a recurrence relation and its tabular or graphical display; and the rule for the nth term and its evaluation
- use of a recurrence relation to model and analyse practical situations involving geometric growth or decay such as the growth of a compound interest loan, the reducing height of a bouncing ball, reducing balance depreciation; and the rule for the value of a quantity after n periods of geometric growth or decay and its use.

The Fibonacci sequence

- generation of the Fibonacci and similar sequences using a recurrence relation, tabular and graphical display
- use of Fibonacci and similar sequences to model and analyse practical situations.

*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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### Matrices

Matrix Structure
1 Topic

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Matrix Algebra
5 Topics

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Identity Matrix
4 Topics

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Determinants
3 Topics

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Inverse of a Matrix
5 Topics

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Matrix Equation
4 Topics

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Understanding Networks

Network Diagrams
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Weighted Edges
5 Topics

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Networks and Tables
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Number Sequences

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#### Course Includes

- 23 Lessons
- 141 Topics
- 21 Quizzes

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