Mathematics develops an increasingly complex and sophisticated understanding of calculus, statistics, mathematical arguments, and proofs, and using mathematical models. By using functions, their derivatives, and integrals and mathematically modelling physical processes, students develop a deep understanding of the physical world through a sound knowledge of relationships involving rates of change. Students use statistics to describe and analyse phenomena that involve uncertainty and variation.
Stage 1 Mathematics provides the foundation for further study in Stage 2 Mathematical Methods and Stage 2 Specialist Mathematics.
Stage 2 Mathematical Methods can lead to tertiary studies of economics, computer sciences, and the sciences. It prepares students for courses and careers that may involve statistics, such as health or social sciences.
Stage 2 Specialist Mathematics can be a pathway to mathematical sciences, engineering, space science, and laser physics. Specialist Mathematics is designed to be studied in conjunction with Mathematical Methods.
Source – Subject Outline, South Australian Certificate of Education 2023
1.2 Inverse Proportion
1.3 Relations
1.4 Functions
1.5 Quadratic Relationships
1.6 Cubic and quartic Polynomials
2.2 Circular Measure and Radian Measure
2.3 Trigonometric functions
2.4 Counting
2.5 Discrete and continuous Random Data
2.6 Samples and Statistical Measures
2.7 Normal Distributions
3.2 Exponential functions
3.3 Logarithmic Functions
3.4 Rate of Change
3.5 The Concept of a Derivative
3.6 Computations of Derivatives
3.7 Properties of Derivatives
3.8 Applications of Derivatives
4.2 Geometric Sequences and Series
4.3 Circle Properties
4.4 The Nature of Proof
5.2 Component and Unit Vector Forms
5.3 Projections
5.4 Geometric Proofs using Vectors
5.5 Further Trigonometric Functions
5.6 Trigonometric Identities
6.2 Transformations in the Plane
6.3 The Number Line
6.4 Introduction to Mathematical Induction
6.5 complex Numbers
6.6 The complex (Argand) Plane 6.7 Roots of Equations