1.2 Divisibility Proofs by Mathematical Induction
2.2 Vector Operations
2.3 Projectile Motion
3.2 Trigonometric Double Angle Formula
3.3 Trigonometric Identities
4.2 Differentiation of Inverse Trigonometric Functions
4.3 Integration of Inverse Trigonometric Functions
4.4 Applications of Integration
4.5 Differential Equations
5.2 Normal Approximation
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. 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 a range of object behaviours in a variety of contexts from theoretical or real-life scenarios. A knowledge of vectors enables the understanding of the behaviour of objects in two dimensions and ways in which this behaviour can be expressed, including the consideration of position, displacement and movement. The study of vectors is important in developing students’ understanding of an object’s representation and behaviour in two dimensions using a variety of notations, and how to use these notations effectively to explore the geometry of a situation. Vectors are used in many fields of study, including engineering, structural analysis and navigation.
Trigonometric Functions
The topic of Trigonometric Functions involves the study of periodic functions in geometric, algebraic, numerical and graphical representations. It extends to include the exploration of both algebraic and geometric methods to solve trigonometric problems. A knowledge of trigonometric functions enables students to manipulate trigonometric expressions to prove identities and solve equations. The study of trigonometric functions is important in developing students’ understanding of the connections between algebraic and graphical representations and how this can be applied to solve problems from theoretical or real-life scenarios, for example involving waves and signals.
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. It involves the development of analytic and numeric integration techniques and the use of these techniques in solving problems. The study of calculus is important in developing students’ knowledge, understanding and capacity to operate with and model situations involving change, and to use algebraic and graphical techniques to describe and solve problems and predict future outcomes with relevance to, for example, science, engineering, finance, economics and the construction industry.
Statistical Analysis
The topic of Statistical Analysis involves the exploration, display and interpretation of data via modelling to identify and communicate key information. Knowledge of statistical analysis enables careful interpretation of situations and awareness of the contributing factors when presented with information by third parties, including its possible misrepresentation. The study of statistical analysis is important in developing students’ ability to consider the level of reliability that can be applied to the analysis of current situations and to predict future outcomes. It supports the development of understanding of how conclusions drawn from data can be used to inform decisions made by groups such as scientific investigators, business people and policy-makers
source – NSW Education Standards Authority