Mathematics is the study of order, relation and pattern. From its origins in counting and measuring it has evolved in highly sophisticated and elegant ways to become the language now used to describe much of the modern world. Statistics is concerned with collecting, analysing, modelling and interpreting data in order to investigate and understand real-world phenomena and solve problems in context. Together, mathematics and statistics provide a framework for thinking and a means of communication that is powerful, logical, concise and precise.

The major themes of Specialist Methods are calculus and statistics. They include as necessary prerequisites studies of algebra, functions and their graphs, and probability. They are developed systematically, with increasing levels of sophistication and complexity. Calculus is essential for developing an understanding of the physical world because many of the laws of science are relationships involving rates of change. Statistics is used to describe and analyse phenomena involving uncertainty and variation. The Specialist Methods course extends and develops the Mathematical Methods course with both additional content and greater depth and breadth of treatment. This is provided by more emphasis on structure and proof, by incorporating more challenging and abstract problems and the inclusion of more opportunities to develop their mathematical insight through research and exploration.

For these reasons this subject provides in-depth preparation for further studies in disciplines in which mathematics and statistics have major roles. In summary, the subject Specialist Methods is designed for students whose future pathways involve mathematical and statistical applications in a range of disciplines at the tertiary level. In addition, this course is designed for students who wish to pursue the study of mathematics itself.

For all content areas of Specialist Methods, the proficiency strands of the F-10 curriculum are still applicable and should be inherent in students’ learning of this subject. These strands are Understanding, Fluency, Problem solving and Reasoning, and they are both essential and mutually reinforcing. For all content areas, practice allows students to achieve fluency in skills, such as calculating derivatives and integrals, or solving quadratic equations, and frees up working memory for more complex aspects of problem solving. The ability to transfer skills to solve problems based on a wide range of applications is a vital part of mathematics in this subject. Because both calculus and statistics are widely applicable as models of the world around us, there is ample opportunity for problem solving throughout this subject.

Specialist Methods is structured over four units. The topics in Unit 1 build on students’ mathematical experience. The topics ‘Functions and graphs’, ‘Trigonometric functions’ and ‘Counting and probability’ all follow on from topics in the F-10 curriculum from the strands, Number and Algebra, Measurement and Geometry and Statistics and Probability. In Specialist Methods there is a progression of content and applications in all areas. For example, in Unit 2 differential calculus is introduced, and then further developed in Unit 3 where integral calculus is introduced. Unit 4 looks at topics in probability and statistics, introduces linear regression, and progresses to probability distributions and inferential statistics.

The Specialist Methods course is written under The MATHEMATICS FRAMEWORK 2021: BSSS MATHEMATICS Framework

Achievement Standards for MATHEMATICS courses can be found within the Framework.

Mathematics is a way of thinking in which problems are explored and solved through observation, reflection and logical reasoning. Students identify appropriate mathematical processes, transfer skills between contexts, make informed decisions, make connections and develop mathematical arguments.

Unit 1: Specialist Methods

Topic 1: Functions and graphs

• Functions
• Lines and linear relationships
• Quadratic relationships
• Powers and polynomials
• Inverse proportion
• Graphs of relations

Topic 2: Trigonometric functions

• Cosine and sine rules
• Circular measure and radian measure
• Trigonometric functions

Topic 3: Counting and probability

• Combinations
• Language of events and sets
• Review of the fundamentals of probability
• Conditional probability and independence

Unit 2: Specialist Methods

Topic 1: Exponential functions

• Indices and the index laws
• Exponential functions

Topic 2: Arithmetic and geometric sequences and series

• General sequences and number patterns
• Arithmetic sequences
• Geometric sequences

Topic 3: Introduction to differential calculus

• Rates of change
• The concept of the derivative
• Computation of derivatives
• Properties of derivatives
• Applications of derivatives
• Anti-derivatives

Unit 3: Specialist Methods

Topic 1: The logarithmic function

• Logarithmic functions

Topic 2: Further differentiation and applications

• Differentiation rules
• Exponential functions
• Logarithmic functions
• Trigonometric functions
• Furhter differentiation
• The second derivative and applications of differentiation

Topic 3: Integrals

• Anti-differentiation
• Definite integrals
• Fundamental theorem
• Applications of integration

Unit 4: Specialist Methods

Topic 1: Simple linear regression

Topic 2: Discrete random variables

• General discrete random variables
• Bernoulli distributions
• Binomial distributions

Topic 3: Continuous random variables and the normal distribution

• General continuous random variables
• Normal distributions

Topic 4: Interval estimates for proportions

• Random sampling
• Sample proportions
• Confidence intervals for proportions

Specialist Methods T (788 KB)

Specialist Methods T (323 KB)

The following courses are also available:

• Specialist Mathematics