SACE Stage 2 Specialist Mathematics: complete 2026 guide to the six topics

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 (30%). 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 (40%). A folio in which you investigate a mathematical model or situation, apply the course methods, and communicate your reasoning and conclusions. This is the single largest component of the subject.

External Assessment (30%).

• A single 2-hour 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

• Proof by mathematical induction

Topic 2: Complex Numbers

• Complex arithmetic and the Argand plane
• Polar form and de Moivre's theorem
• Roots of complex numbers

Topic 3: Functions and Sketching Graphs

• Rational functions and asymptotes
• Modulus functions
• Composite and inverse functions

Topic 4: Vectors in Three Dimensions

• Vectors and the dot product
• The cross product
• Vector and cartesian equations of lines and planes

Topic 5: Integration Techniques

• Integration by substitution
• Integration by parts
• Partial fractions

Topic 6: Rates of Change and Differential Equations

• Separable differential equations
• Modelling with 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: this folio is worth 40%, so 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 2-hour 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.