TCE Mathematics Specialised: sequences, matrices, integration and complex numbers

The criteria

Notice that Specialised is organised by technique, with one exam section for each. The course has no probability, vectors or mechanics criterion, which matters if you are comparing it with other states' Specialist courses.

The exam

The specification gives a three-hour written exam, with 15 minutes of preparation time for note-taking. There are five sections, each with five to seven questions, printed in a single question booklet. You can answer them in any order at any time, and you write your answers in five separate lined response booklets. Calculators are allowed in all sections unless a question says otherwise, and you can use the Mathematics Specialised Information Sheet.

Each criterion is marked out of 36, using the same working rules as other TASC mathematics courses: full marks for correct answers with relevant working, and partial marks for correct working with a wrong answer.

Worked examples

An infinite geometric series (Criterion 4)

For 8 + 4 + 2 + 1 + …, the first term is a = 8 and the common ratio is r = ½. Since |r| < 1, the series converges:

State the condition |r| < 1. It is a separate mark.

Division of complex numbers (Criterion 8)

Multiply the top and bottom by the conjugate of the denominator:

A 2 by 2 matrix (Criterion 5)

Take A with rows (3, 2) and (4, 3). Its determinant is 3 × 3 − 2 × 4 = 1, so A is invertible, and its inverse has rows (3, −2) and (−4, 3). A determinant of 1 means the inverse needs no division, which makes it a good check on your arithmetic.

Complex-number questions can be explored in our Complex Number Calculator, and the Calculus course covers integration techniques.

Awards and ratings

TASC decides the award from 13 ratings: 8 internal and 5 external.

The ATAR uses your best Level 3 and Level 4 results across two years, and eligibility needs the TCE and at least Satisfactory Achievement in four TASC Level 3 or 4 courses. Results are released on Wednesday 16 December 2026.

Dates

Use the daily papers as practice

Your provider sets its own trial. Uni-Sine's free daily papers can work as short timed practice of 8 questions worth 25 to 35 marks, marked as you go. They are not TASC exams.

• Maths Extension 2 and Specialist Maths fits on days about complex numbers, series, matrices, second-order differential equations and volumes of revolution. It also covers proof by induction, hyperbolic functions and polar coordinates, which are not named in the course criteria.
• Specialist Maths: Mechanics is not part of this course. Use it only as extension reading, with our Specialist Maths Mechanics guide.

Exam answers

Answers and a worked mark scheme arrive with each daily paper once it is marked. They are Uni-Sine's own, not TASC solutions.

Mistakes in TCE Specialised

• Forgetting the convergence condition before using the infinite sum formula.
• Multiplying the numerator by the conjugate but not the denominator.
• Writing a matrix inverse without checking that the determinant is non-zero.
• Treating the five response booklets as interchangeable and putting an answer in the wrong one.

Read next

Australia · TCETCE Maths Specialised formula sheet: the TASC sheetThe TASC Mathematics Specialised external exam information sheet for the TCE: every section, what is missing, and worked series and calculus examples.