SACE Stage 2 Specialist Mathematics: complete 2026 guide to the six topics
A complete 2026 guide to SACE Stage 2 Specialist Mathematics: the six topics from mathematical induction to differential equations, how the 70% school and 30% external assessment combine, and links to every dot-point answer we have written.
SACE Stage 2 Specialist Mathematics is the most advanced Year 12 mathematics course in South Australia, developing rigorous proof, complex numbers, three-dimensional vectors and advanced calculus. It is a 20-credit subject studied alongside Mathematical Methods and assessed 70% through school-based work and 30% through a single external examination.
This page is the index. Below you will find the structure of the six topics, how the assessment marks combine, and links to every dot-point answer we have written for SACE Stage 2 Specialist Mathematics.
How the subject is assessed in 2026
Specialist Mathematics uses a 70% school assessment and 30% external assessment split.
School Assessment (70%).
- Assessment Type 1 - Skills and Applications Tasks (50%). Five or six tasks spread across the year, completed mostly under supervised conditions. They test your fluency with the concepts and techniques of each topic - induction proofs, complex arithmetic, vectors, integration techniques and differential equations - through short and extended questions.
- Assessment Type 2 - Mathematical Investigation (20%). One investigation in which you investigate a mathematical model or situation, apply the course methods, and communicate your reasoning and conclusions.
External Assessment (30%).
- A single 130-minute written examination covering all six topics cumulatively, sat at the end of the year. A SACE-approved graphics or CAS calculator is permitted.
The six topics
The course moves from the logical foundation of proof, through complex numbers and graph analysis, into vector geometry and advanced calculus.
- Topic 1: Mathematical Induction
- The principle of induction and rigorous proofs for sums, divisibility and inequalities over the positive integers.
- Topic 2: Complex Numbers
- Cartesian and polar form, the Argand plane, de Moivre's theorem and the roots of complex numbers.
- Topic 3: Functions and Sketching Graphs
- Rational functions and asymptotes, the modulus function, and composite and inverse functions.
- Topic 4: Vectors in Three Dimensions
- The dot and cross products, and vector and cartesian equations of lines and planes.
- Topic 5: Integration Techniques
- Substitution, integration by parts, and partial fractions.
- Topic 6: Rates of Change and Differential Equations
- Separable differential equations and modelling real situations such as growth, cooling and limited growth.
Our 2026 SACE Specialist Mathematics dot-point answers
Every link below is a focused answer to one syllabus concept. Each page identifies the concept, gives the worked answer with full mathematical working, includes worked examples and common-mistake warnings, and cross-links to related dot points.
Topic 1: Mathematical Induction
Topic 2: Complex Numbers
Topic 3: Functions and Sketching Graphs
Topic 4: Vectors in Three Dimensions
Topic 5: Integration Techniques
Topic 6: Rates of Change and Differential Equations
How to use this hub
If you are starting the year: work through the topics in order, since each assumes the last. The induction of Topic 1 underpins proofs throughout, and the polar form of Topic 2 reappears in the roots work.
If you have a Skills and Applications Task coming up: identify which topic it covers, read every dot point in that topic, and drill the worked examples under timed conditions. The task questions closely mirror the technique-and-application style of our worked examples.
If you are planning your Mathematical Investigation (20%): choose a context where you can genuinely apply the methods - a complex-number geometry problem, a vector model, an integration application, or a differential-equation model of growth or cooling. Read modelling with differential equations for the modelling structures examiners reward.
If you are revising for the external exam: the 130-minute paper is cumulative, so revise all six topics. Prioritise the high-frequency techniques - induction proofs, de Moivre's theorem and roots, the cross product and plane equations, integration by parts and partial fractions, and separable differential equations - then complete past SACE examination papers under timed conditions.
The system around SACE Stage 2 Specialist Mathematics
For the official subject outline, performance standards and past examination papers, refer to the SACE Board at sace.sa.edu.au. University prerequisites are listed by SATAC at satac.edu.au.
Every guide on this hub was written by ExamExplained, an initiative focused on clear, syllabus-aligned study notes for Australian senior secondary students.