# SACE Stage 1 Mathematics – Functions, Graphs and Polynomials

1.1 Lines and Linear Relationships

1.2 Inverse Proportion

1.3 Relations

1.4 Functions

1.5 Quadratic Relationships

1.6 Cubic and quartic Polynomials

## Functions and Graphs

A key aspect of mathematics is to model real-world situations. To do this effectively, skills enabling students to work algebraically with functions and relations are essential. Using a system of coordinates allows numerical descriptions of different situations to be described using a function or a relation.

Linear functions are suitable for exploring relationships between variables that show a constant rate of change, such as simple interest and power usage. Inverse relationships are used to study contexts in which one variable increases as another variable decreases, such as the effect of increasing the number of workers on the completion time of a building job. Circular relationships can be used to model, for example, the locations of earthquakes and the coverage from mobile phone towers.

In combination with Polynomials, the concepts and techniques covered in this topic develop the understanding of functions and relations and algebraic skills leading to the study of calculus.

The emphasis of this topic is on describing, sketching, interpreting, and discussing the behaviour of graphs that arise from everyday situations. Students focus on describing and explaining the characteristics and behaviour of a graph about the situation being modelled.

The investigation of links between the algebraic and graphical representations of functions relies on using technology to produce graphs of mathematical functions. Students test their conjectures using many examples without plotting graphs themselves.

## Polynomials

Building on the skills and understanding students have developed in Topic 1: Functions and graphs, this topic involves further modelling real-world situations. Polynomial functions are used to explore more complex relationships than linear models.

As students gain a sound understanding of the graphical behaviour of these functions, they develop their skills in the algebraic manipulation of polynomials. The links between these two concepts are strengthened by electronic technology.

*Source – Subject Outline, South Australian Certificate of Education 2023*

SACE Stage 1 Mathematics Courses

SACE Stage 1 Mathematics Syllabus

## Course Content

### Coordinate Geometry

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