At a glance
A high-level maths course for students who love maths and want an extra challenge. Students explore topics such as vectors, complex numbers, matrices, advanced calculus and statistical inference.
Important: Specialist Mathematics can only be studied with Specialist Methods. Students take these together as a Major–Minor or a Double Major.
Recommended background: High achievement in Australian Curriculum 10A is needed, plus consistently strong A grades in Year 10 maths.
This course is a good choice for students who:
- enjoy challenging maths and solving complex problems
- are interested in pathways like engineering, physics, maths, statistics or economics
- want to build advanced reasoning and proof skills
About this course
Specialist Mathematics extends the ideas in Specialist Methods and focuses on rigorous reasoning, problem solving and proof. Students use mathematical models, digital tools and precise language to solve complex problems.
Pathways
This course can support pathways into areas such as:
- engineering and physics
- mathematics, statistics and data-heavy university courses
- economics and other quantitative (maths-based) fields
Units in this course
Students complete 2 units for a Minor or 4 units for a Major.
Unit 1: Specialist Mathematics
This unit introduces combinatorics, vectors in the plane, and geometry, with a strong focus on reasoning and proof.
Students will:
- solve problems using combinatorics and vectors, and explain their reasoning clearly
- develop mathematical arguments and proofs (especially in geometry)
Unit 2: Specialist Mathematics
This unit develops trigonometry, matrices, and real/complex numbers, including proof methods such as mathematical induction.
Students will:
- use trigonometric identities, matrices and complex numbers to solve problems
- build and communicate proofs, including induction (a structured proof method)
Unit 3: Specialist Mathematics
This unit extends vectors into three dimensions, develops complex numbers further, and applies calculus ideas to functions and graphing.
Students will:
- model and solve problems in 3D space using vector equations (including motion)
- apply advanced function and calculus techniques to analyse and solve problems
Unit 4: Specialist Mathematics
This unit focuses on advanced integration, differential equations, and statistical inference, using maths to model real situations.
Students will:
- solve problems using advanced calculus (including differential equations)
- use statistical inference (like sample means and confidence intervals) to draw conclusions from data