## Proof

The topic Proof involves the communication and justification of an argument for a mathematical statement in a clear, concise and precise manner. Knowledge of proof enables a level of reasoning, justification and communication that is accurate, concise and precise and lays the foundations for understanding the structure of a mathematical argument. The study of proof is important in developing students’ ability to reason, justify, communicate and critique mathematical arguments and statements necessary for problem-solving and generalising patterns.

## Vectors

The topic Vectors involves mathematical representation of a quantity with magnitude and direction and its geometrical depiction. This topic provides a modern language and approach to explore and explain an array of object behaviours in a variety of contexts from theoretical or real-life scenarios. A knowledge of vectors enables the understanding of objects in two and three dimensions and ways in which this behaviour can be expressed, including the consideration of position, location and movement. Vectors are easy to generalise to multiple topics and fields of study, including engineering, structural analysis and navigation.

## Complex Numbers

The topic of Complex Numbers involves investigating and extending understanding of the real number system to include complex numbers. The use of complex numbers is integral to many areas of life and modern-day technology such as electronics. Knowledge of complex numbers enables exploration of the ways different mathematical representations inform each other and the development of understanding of the relationship between algebra, geometry and the extension of the real number system. The study of complex numbers is important in developing students’ understanding of the interconnectedness of mathematics and the real world. It prepares students for further study in mathematics itself and its applications.

## Calculus

The topic of Calculus involves the study of how things change and provides a framework for developing quantitative models of change and deducing their consequences. This topic involves the development of a broader range of techniques and strategies to solve complex problems related to differential equations and integration. The study of calculus is important in developing students’ knowledge, understanding and capacity to operate with and model change situations involving a variety of functions, use algebraic and graphical techniques to describe and solve problems and predict future outcomes with relevance to, for example, Chemistry, Physics and the construction industry.

## Mechanics

The topic of Mechanics involves the study of change in the motion of objects when acted upon by forces. It involves the mathematical representation of quantities with magnitude and direction and their representation graphically and algebraically. Knowledge of mechanics enables understanding of the behaviour of objects according to mathematical law in order to model physical systems and predict the behaviour of objects that are under the influence of forces such as gravity and air resistance. The study of mechanics is important in developing students’ understanding of changes in motion, modelling change situations involving a variety of mathematical techniques and contexts and using algebraic and graphical techniques to describe and solve problems and predict future outcomes with relevance to, for example, physics.

*source – NSW Education Standards Authority*