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 generate 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.
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 generate 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.