QCE Specialist Mathematics IA2 and IA3 examinations: how to get top marks

IA2 and IA3 are one instrument sat twice. IA2 draws on any three of the five Unit 3 topics, IA3 on any three of the five Unit 4 topics, and each carries 15% of your Specialist Mathematics result. Your teacher writes the paper, you sit it unseen with 5 minutes perusal and 90 minutes working, and there are no bands to reach: your raw score becomes a percentage and a fixed fifteen-step ladder turns that percentage into your mark. Every step is a strict inequality, which QCAA illustrates with a case of its own: exactly 80% is 12 marks, not 13.

This guide describes the Specialist Mathematics 2025 v1.0 General senior syllabus, which the 2025 subject report calls "first examinable in 2026". The three reports it draws on cover the 2023, 2024 and 2025 cohorts, all of whom sat Units 3 and 4 under the superseded 2019 syllabus, so every figure below is labelled with its cohort year. The fifteen cut-offs came through the version change identical, digit for digit, while the descriptor prose beside them was rewritten.

The specification your teacher writes to

Your school writes the paper and QCAA approves it before you sit it. The specification is a single sentence repeated for each instrument with the unit swapped, and the conditions are identical:

Questions may ask you to interpret unseen stimulus, calculate using algorithms, and draw or label graphs, tables or diagrams. Both papers assess all six assessment objectives and both are marked on one criterion out of 15.

What each paper is allowed to assume you know

This is where Specialist Mathematics differs from the other two QCE maths subjects. The syllabus names Mathematical Methods as assumed knowledge alongside your own earlier units: Methods Units 1 and 2 stand behind IA2, and Methods Units 1, 2 and 3 stand behind IA3.

That gives a Specialist question a much longer reach than its topic label suggests. A Unit 3 vectors question can require Methods differentiation without announcing it, and a Unit 4 statistical inference question can lean on the Methods normal distribution work.

IA2: the Unit 3 examination

IA2 samples any three of these five:

• Further complex numbers
• Mathematical induction and trigonometric proofs
• Vectors in two and three dimensions
• Vector calculus
• Further matrices

Vector calculus was a sub-topic under 2019 and is now a topic in its own right, with its nominal hours nearly doubled. It is the largest single increase in Year 12 and it is now one of the five things IA2 can pick.

You cannot know which three your school will choose, so four of the five is the working minimum. Two topics you revised hard may not appear at all, and the one you skipped may carry a third of the paper.

IA3: the Unit 4 examination

IA3 samples any three of these five:

• Integration techniques
• Applications of integral calculus
• Rates of change and differential equations
• Modelling motion
• Statistical inference

Modelling motion was also promoted from sub-topic to topic for 2025, and a new differential equations sub-topic was carved out of rates of change, which lost most of its hours to it. Both changes push Unit 4 towards calculus applied to a physical situation.

What a pre-2025 revision list gets wrong

Only one piece of subject matter crosses a unit boundary in Year 12, and it leaves. Subsets of the complex plane determined by straight lines and circles moved from Unit 3 down into Unit 2, where the verb also strengthened from identify to identify and sketch. Under 2019 it was directly examinable in IA2. Now it is Year 11 work that IA2 can reach only as assumed knowledge.

Two things moved the other way, up from Unit 2 into Unit 3, so IA2 can now sample them: determinants, inverses and matrix equations for square matrices beyond 2 × 2, all with technology; and the binomial expansion used to prove multi-angle trigonometric identities, which now sits alongside De Moivre's theorem in the induction topic.

The bigger shift is in what you are asked to do with content that stayed put. Of the 41 reworded Year 12 dot points, 31 changed their leading verb:

The four-stage induction requirement is the clearest of these. QCAA has written down the stages it will mark, and the effective-response bullets in the 2024 report reward exactly those four.

Turning your raw score into a mark out of 15

One criterion, Foundational knowledge and problem-solving, worth 15 marks. The instrument-specific marking guide, or ISMG, is the marking guide QCAA prints inside the syllabus for each internal assessment, and this one gives your teacher nothing to match your response against question by question. The sequence is arithmetic:

1. Before you sit the paper, your school builds a marking scheme: a per-question map of where every mark and half mark lives. QCAA treats it as its own artefact, distinct from the ISMG. It is uploaded for the endorsement review before you sit the paper, and it has to be available again at confirmation, the check run on a sample of each school's marking once the papers are marked.
2. Your paper is marked against that scheme, question by question, and the raw marks are totalled.
3. The raw total becomes a percentage of the paper total, computed without significant rounding. QCAA has asked schools to show that calculation in full in each of the last three rounds, and prints worked cases like 40.5/48 = 84.375% and 48.5/60 = 80.833%.
4. The percentage is read off the ladder below.

Eight descriptor blocks stretch across fifteen marks, so the prose can never separate two adjacent marks. Only the percentage can. And the top four marks all require the descriptor's third situation type, which means the complex unfamiliar questions have to be attempted.

Four conversions QCAA has printed from real Specialist papers, which also show how much the paper total varies from school to school:

Nothing fixes the paper total. Only the 60/20/20 split of the marks inside it is specified.

The 60/20/20 blueprint

IA2, IA3 and both external papers are built to one question specification, within ± 2%:

Complex unfamiliar has a definition the syllabus states in full and both versions state identically: all the information needed to solve the problem is not immediately identifiable, the required procedure is not clear from the way the problem is posed, and the context is one you have had limited prior experience of.

Read the cue, then use the method it names

Several Specialist problems have a second solution route that sits outside the syllabus, most often a physics formula for a motion or circular-motion problem. QCAA has told schools in each of the last three rounds to cue the expected approach inside the question, using phrases like "using a vector calculus approach" or "definite integration using technology", and to build the marking scheme around the approach cued.

Take those phrases literally. A correct final answer reached by a route the scheme was not written for has fewer places to attach marks, and on a multi-mark question that is most of the marks.

The same logic runs through the technology split. The syllabus requires each internal paper to provide opportunities for both technology-free and technology-active responses, so one 90-minute paper carries both, and the mode changes where the marks sit. On the technology-free half they are on the algebra. On the technology-active half they are on setting the problem up and interpreting what comes back, so write the expression you evaluated as well as the value it returned. Find out before the day whether your school marks the modes by labelling questions, by cueing them in the wording, or by splitting the paper into sections.

What the marked excerpts reward

There is no prose artefact here to compare against a model answer. The excerpts QCAA reproduces are photographs of handwritten algebra covered in ticks, half marks and marker annotations, and three mechanisms show up in all three years.

All three mechanisms are generous and all three are conditional on the same thing: legible working for the credit to attach to. QCAA even asks schools to annotate a mark awarded for a step you implied and never wrote, which only happens when the lines around it make the step unambiguous.

Where the marks actually went missing

These are the errors QCAA's own markers annotated on Specialist internal papers, quoted from the reports:

Two of the six are three-dimensional vector bookkeeping and one is a boundary convention. None of them is a gap in understanding, and all three cost marks on a paper where 6 to 7 percentage points is a whole ISMG mark.

What happens to your paper before and after you sit it

Two QCAA processes bracket the exam, and they behave very differently in this subject.

Endorsement is the approval QCAA gives your school's paper before anyone sits it. Across the 2023, 2024 and 2025 rounds it was granted at first application to 43%, 50% and 30% of Specialist IA2 papers, and to 47%, 44% and 61% of IA3 papers. The 2025 IA2 figure is the lowest number anywhere in this subject's reporting, and it came with 231 alignment flags against 122 for IA3 in the same round. Alignment to the syllabus specifications is the dominant reason a Specialist internal exam is refused, in every year and on both instruments, and the recurring faults are the ones this guide has already named: items labelled complex unfamiliar that are not, questions resting on assumed knowledge alone, and schemes that do not match the approach the question cued.

Confirmation is the check QCAA runs on a sample of the marking afterwards, and it barely finds anything. Agreement between school and confirmed marks ran 99.01%, 100.00% and 100.00% on IA2 and 99.67%, 100.00% and 100.00% on IA3 across those three cohorts. Two consecutive perfect years on both instruments.

Read together, those two say something practical. Once your raw total is settled the mark out of 15 is close to mechanical, so there is no band judgment to argue with and no descriptor to write towards. The whole contest is over individual raw marks, question by question.

Where our own data lines up with QCAA's advice

QCAA publishes nothing at the level of a single dot point. We do, and two caveats come with it. Our questions are external examination questions, not school-written internal ones, and all of those papers predate the current syllabus. So the figures below say something about the content your paper will sample and nothing about this instrument.

On the Unit 3 side that IA2 draws from, the weakest outcome in our sample is modelling displacement, force, velocity and relative velocity at 30.9% across 427 marked AusGrader attempts, followed by using De Moivre's theorem for integral powers at 47.0% across 546. The first of those corroborates QCAA's 2024 advice about extending vector concepts from two dimensions to three, which is also what one of the marker annotations above is about. Proving complex number identities involving modulus and argument sits at 53.8% across 876 attempts, against QCAA's 2025 advice to practise algebraic manipulation of complex numbers in both forms.

On the Unit 4 side that IA3 draws from, implicit differentiation is one of our two weakest outcomes in the subject at 32.6% across 263 attempts, and motion of a body in non-equilibrium situations under concurrent forces is 39.5% across 409. Statistical inference is the topic that costs the most marks anywhere in the subject, carrying more of the paper than any other topic at an average of 53.9%, which lines up with QCAA naming the comparison of the distributions of $X$ and $\bar{X}$, and the notation for their means and standard deviations, as a practice to strengthen in both 2024 and 2025. The full per-topic and per-outcome picture is on the Specialist Mathematics study guide.

Common mistakes

Preparing for a band instead of for marks. Two students whose papers match the same descriptor word for word can still finish a mark apart. Nothing in the ISMG prose is reachable; only the raw total is.

Solving a cued question your own way. If the wording names an approach, the scheme was written to it.

Treating a three-dimensional problem as flat. Two of the six annotated errors above are exactly this, and both are recoverable in seconds by sketching the axes before starting.

Answering a technology-active question with a bare number. The marks on that half of the paper are for setting up and interpreting, and neither is visible in a result on its own.

Writing a calculator method on the technology-free half. Nothing in the scheme can pay for a route the mode does not allow.

Revising three topics and hoping. The paper samples three of five and you find out which three on the day.

Assuming subsets of the complex plane are still IA2 material. They moved to Unit 2 for 2025, so they now reach your internal exam only as assumed knowledge.

In the room

There is no draft to check in advance, so run this as a per-question routine:

• Has the question named an approach, and am I using the one it named?
• Which technology mode is this, and does my working match it?
• If this is a vector problem, is it two-dimensional or three, and do my unit vectors match the orientation I set up?
• If this is an induction proof, have I written all four stages, including the assumption statement and the conclusion?
• Have I carried every constant through the integration, including the ones outside the integral?
• On an Argand region, have I marked the boundary as included or excluded, by convention or in words?
• If a value two lines up is wrong, is the working after it legible enough for a marker to carry the error through?
• How many marks is this question worth, and has my response given the scheme that many separate things to tick?

Three topics of five is an argument for breadth, and the cheapest way to find the two you are thinnest on is to attempt questions you have not seen from all five, which is what the Specialist Mathematics question bank holds. Read the IA1 problem-solving and modelling task next: it runs on the opposite principle, with four criteria and readable descriptors deciding 20 marks, and it is the only internal assessment you can plan against in advance. The rest of the subject is on the Specialist Mathematics study guide, and the QCE hub has the other subjects.