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Tasmanian Certificate of Education · TASC · 2026

TCE Mathematics Specialised (Tasmania): complete 2026 guide to the pre-tertiary Units 3 and 4

Study-note hub for TCE Mathematics Specialised (TASC Level 4 pre-tertiary), covering Unit 3 (complex numbers, 3D vectors, further calculus) and Unit 4 (integration, differential equations, statistical inference) with worked examples and exam tips.

Exam: Mon 9 Nov Browse guides Syllabus dot points (17)ATAR calculator

TCE Mathematics Specialised study hub

Welcome to the study-note hub for TCE Mathematics Specialised (TASC Level 4 pre-tertiary, Tasmania). This course extends the calculus, algebra and trigonometry of Mathematics Methods into more abstract and powerful territory: complex numbers, three-dimensional vectors, advanced calculus and differential equations, plus the foundations of statistical inference.

How the course is structured

The course is built from two units, each split into topics. These dot-point notes follow the TASC topic structure so you can revise one idea at a time and build toward the bigger picture.

Unit 3

Unit 4

Assessment at a glance

TCE Mathematics Specialised is a TASC Level 4 pre-tertiary course. Your final result is made up of two parts:

  1. School-based internal assessment - your teacher rates your performance against the course criteria using class tasks, tests and assignments across the year.
  2. TASC external examination - a single end-of-year written exam set and marked externally.

Because it is a pre-tertiary course, the result counts towards your ATAR. That means steady internal-assessment work and disciplined exam revision both pay off.

How to use these notes

Each dot-point page opens with a quick TL;DR answer, then explains what the syllabus point is really asking, works through a full example, and warns you about a common mistake. Read actively: cover the worked example and try it yourself first, then check each line of your working against ours.

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Common questions

What level is TCE Mathematics Specialised and does it count towards ATAR?
It is a TASC Level 4 pre-tertiary course. Like other Level 3 and 4 pre-tertiary courses it contributes to your ATAR through your study score, so a strong result here carries significant weight.
How is Mathematics Specialised assessed in Tasmania?
Assessment combines school-based internal assessment against the course criteria with a TASC external examination. Both components feed into your final award, so consistent classwork and exam preparation both matter.
What mathematics should I already know before starting this course?
It is designed to be studied alongside or after Mathematics Methods. You should be confident with calculus, trigonometry, algebra and functions, since the Specialised content extends all of these into harder territory.
What topics are in Unit 3 and Unit 4?
Unit 3 covers complex numbers, vectors in three dimensions and further calculus. Unit 4 covers integration techniques and applications, differential equations and statistical inference.
How much working do I need to show in the external exam?
Full method marks require clear, logical working: state results used, show key algebraic steps, and justify reasoning. Correct answers with no working often earn fewer marks than the question is worth.
Is a calculator allowed in the exam?
TASC permits an approved calculator in the external examination, but many questions reward exact and analytic work. Practise both exact methods and efficient calculator use so you can choose the right tool under time pressure.

Sources & how we know this

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Built from the official TASC syllabuses, past papers and marking guides. Not individually reviewed; always check your school's materials and TASC for current rules.

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