What is the difference between IA2 and IA3 in QCE Mathematical Methods?

The unit, and how much assumed knowledge sits behind it. IA2 samples any three of the five Unit 3 topics and may draw on Units 1 and 2; IA3 samples any three of the five Unit 4 topics and may draw on Units 1, 2 and 3, so it has a year more material behind it. Nothing else differs: the conditions, the timing, the mark allocation and the instrument-specific marking guide are word for word the same, and each is worth 15%.

How long is the QCE Mathematical Methods IA2 exam?

Five minutes perusal and 90 minutes working time. The 2019 syllabus allowed 120 minutes working, so anything quoting two hours describes the superseded rules. A school is permitted to run the paper over two consecutive sessions, on the condition that no student has seen the questions in either session and that no teaching or feedback happens in the gap.

How is the Mathematical Methods IA2 mark out of 15 actually worked out?

Your teacher marks the paper against a school-written marking scheme, converts your raw total to a percentage without rounding, then reads that percentage off a fixed 15-step ladder. Every cut-off is strictly greater than, so 36 out of 60 is exactly 60% and earns 9, not 10.

Is the Mathematical Methods IA2 technology-free?

Partly. The syllabus requires each internal examination to provide opportunities for both technology-free and technology-active responses, so one paper carries both. Schools do this by labelling questions, by cueing inside the question wording, or by splitting the paper into separate sections.

Which topics can the Mathematical Methods IA3 cover in 2026?

Any three of the five Unit 4 topics: further integration, trigonometry, continuous random variables and the normal distribution, sampling and proportions, and interval estimates for proportions. The second derivative moved into Unit 3 under the 2025 syllabus, so IA3 can no longer sample it, and integration beyond anti-differentiation moved into Unit 4, so IA3 now can.

QCE Mathematical Methods IA2 and IA3 examinations: how to get top marks

IA2 and IA3 are the same examination sat on different units: IA2 samples Unit 3, IA3 samples Unit 4, and each is worth 15% of your Mathematical Methods result. Both are unseen short-response papers, 5 minutes perusal and 90 minutes working, both carry technology-free and technology-active questions, and both are marked on a single criterion out of 15 by turning your raw score into a percentage and reading it off a fixed ladder. Each rung of that ladder is 6 to 7 percentage points wide, so half a mark on one question can move your criterion mark by a whole point.

This guide describes the Mathematical Methods 2025 v1.2 General senior syllabus, current for Year 12 from 2026. The three subject reports published so far (2023, 2024 and 2025 cohorts) all describe students assessed under the superseded 2019 syllabus, so every statistic below carries its cohort year and none of them describes marking under the current guide. The cut-off ladder itself is unchanged: the thresholds are identical at all fifteen levels in both versions.

What both examinations are

QCAA's specification is the same sentence for each, with two substitutions for IA3, marked in brackets below. Your teacher writes an examination that:

asks students to respond to a number of unseen short response questions; representatively samples subject matter from any three of the five topics in Unit 3 [Unit 4 for IA3]; provides opportunities for both technology-free and technology-active responses; may ask students to respond using single words, sentences or paragraphs; may ask students to: interpret unseen stimulus; calculate using algorithms; draw or label graphs, tables or diagrams; use assumed knowledge from Units 1 and 2 [Units 1, 2 and 3 for IA3]

Conditions, identical for both:


Time	5 minutes perusal, 90 minutes working
Supervision	individual, supervised
Provided	the QCAA Mathematical Methods formula book, which your teacher must supply
Technology	required, with both technology-free and technology-active questions in the paper
Notes	none permitted
Split sittings	allowed across two consecutive sessions only if each session's questions are unseen and no teaching or feedback happens between them

Both papers assess all six assessment objectives, from recalling mathematical knowledge through to solving mathematical problems, and both are marked on one criterion worth 15 marks. Neither paper contains multiple choice. Multiple choice appears only in the external examination specification, in both syllabus versions, so an internal paper that opens with a multiple-choice section is not built to spec.

Technology-free and technology-active, in one paper

The syllabus requires each internal examination to "provide opportunities for both technology-free and technology-active responses", so a single 90-minute paper has to do both. Specialist Mathematics sets the same requirement; General Mathematics does not, which is why advice written across the three maths subjects tends to skip this entirely. The 2025 report lists the three mechanisms schools use: labelling each question with its mode, cueing inside the question wording ("using technology", "use algebraic techniques"), or splitting the paper into separate sections.

Find out which of the three your school uses before the day. If it is the cueing mechanism, the instruction lives inside the question text and is easy to read past.

The General Mathematics syllabus asks only that students use technology in its internal examinations and never sets a technology-free component, so a General Mathematics revision plan has no equivalent of the algebra-only half of your paper.

IA2: the Unit 3 examination

IA2 samples any three of the five Unit 3 topics:

Units 1 and 2 are assumed knowledge, so surds, index and logarithm laws, function transformations and the first-derivative test are all fair game inside a Unit 3 question.

You cannot know which three topics your school will pick, which makes revising four of the five the only strategy the specification leaves you. Under 2019 every topic had to appear, so the paper was more predictable and each topic thinner.

IA3: the Unit 4 examination

IA3 samples any three of the five Unit 4 topics:

IA3 assumes Units 1, 2 and 3, a wider base than IA2 gets. A Unit 4 integration question can legitimately require a differentiation rule you last used in an IA2 paper, and a normal-distribution question can lean on the discrete random variable work from Unit 3.

The content moved between units, and old advice inverts

The 2025 syllabus did not just rename topics. It relocated a large amount of Year 12 subject matter between Unit 3 and Unit 4, and because IA2 samples Unit 3 and IA3 samples Unit 4, every one of those moves changes which internal exam can ask you about it.

Content	Moved	What it means for your internal exams
The second derivative and its applications	Unit 4 to Unit 3	now sampleable by IA2, no longer by IA3
Bernoulli and binomial distributions	Unit 4 to Unit 3	now sampleable by IA2, no longer by IA3
The fundamental theorem of calculus, definite integrals and applications of integration	Unit 3 to Unit 4	now sampleable by IA3, no longer by IA2
General discrete random variables	Unit 2 to Unit 3	summatively assessed for the first time, having been Year 11 formative content
Optimisation modelling	Unit 2 to Unit 3	summatively assessed for the first time, and broadened: the degree-4-polynomial and finite-interval restriction is gone, second derivatives are in play, and you may have to develop the function yourself
The whole logarithm strand	Unit 3 to Unit 2	leaves Year 12 entirely
Arithmetic and geometric sequences and series	appear nowhere in the 2025 Units 3 and 4 topics	on our reading they leave the subject, taking compound interest, annuities, simple interest and the sum to infinity with them. Confirm against the current topic list before you drop them from a revision plan

Published QCAA advice that now says the opposite

Three unit attributions in the reports invert under the 2025 syllabus. The 2023 report tells IA3 writers that "calculating $\frac{d^2y}{dx^2}$ is part of Unit 4"; the 2024 report tells IA2 writers that "expecting students to use acceleration as the second derivative of displacement is not reasonable in a question ... as this is Unit 4 subject matter", and warns IA3 writers off "finding the displacement function from a given acceleration function [which] is Unit 3 subject matter". Under the 2025 syllabus the second derivative is Unit 3 and the integration content is Unit 4, so all three are now backwards. They stay accurate as commentary on the 2019 cohorts.

A fourth attribution from 2023 has not changed: verifying turning points with the first derivative test alone "is using subject matter assessed in Unit 2", and the first-derivative stationary-point test is still an explicit Unit 2 dot point in 2025.

Any revision list or tutor sheet written before 2025 carries the old mapping.

How the mark is actually worked out

There is 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. This one has no named performance levels and gives your teacher nothing to match question by question. Instead:

Your school writes a marking scheme, its own per-question breakdown of where each mark sits. This is a separate document from the ISMG and goes to QCAA at confirmation, the check QCAA runs on a sample of every school's marking after the papers are sat.
Your teacher marks your paper against that scheme and totals your raw marks.
Your raw total becomes a percentage of the paper total, computed on precise values without rounding, which the 2023 report directs schools to do explicitly.
That percentage is matched against a fixed ladder to give your mark out of 15.

The paper total is a school decision. Only the percentage split has to match the specification, which is why the reports show conversions out of 55, 56, 60 and 75.

Your percentage	Criterion mark	What the descriptor says at this level
> 93%	15	consistently correct recall and use; authoritative and accurate communication; astute evaluation of reasonableness; reasoning used to correctly justify procedures and decisions; fluent application across a comprehensive range of simple familiar, complex familiar and complex unfamiliar situations
> 87%	14	(same descriptor)
> 80%	13	correct recall and use; clear communication; considered evaluation; reasoning used to justify; proficient application across all three situation types
> 73%	12	(same descriptor)
> 67%	11	thorough recall and use; communication; evaluation of reasonableness; reasoning used to justify; application in simple familiar and complex familiar situations only
> 60%	10	(same descriptor)
> 53%	9	recall and use; communication; evaluation of the reasonableness of some solutions; some reasoning; some application to make progress towards solving problems in simple familiar situations
> 47%	8	(same descriptor)
> 40%	7	some recall and use; basic communication. Evaluation, justification and application drop out of the descriptor entirely
> 33%	6	(same descriptor)
> 27%	5	infrequent recall and use; basic communication of some mathematical knowledge
> 20%	4	(same descriptor)
> 13%	3	isolated recall and use; partial communication of rudimentary knowledge
> 7%	2	(same descriptor)
> 0%	1	isolated and inaccurate recall and use; disjointed and unclear communication

Eight descriptor blocks cover fifteen marks, so the prose never decides your mark on its own. Two adjacent marks share a descriptor word for word and are separated by the percentage alone.

Two adjective ladders run down the criterion. On recall and use: isolated and inaccurate, isolated, infrequent, some, plain recall and use, thorough, correct, consistently correct. On evaluation: nothing at all, then the reasonableness of some solutions, then the reasonableness of solutions, then considered, then astute. At 7 and below the 2025 ladder drops evaluation and application entirely and asks only about recall and communication. That is a change from 2019, whose 7/6 band still carried "inconsistent evaluation of the reasonableness of solutions".

The conversions QCAA prints across the three reports show the arithmetic on real papers:

Raw score	Percentage	Criterion mark	Where
36/60	60.00%	9	2023 IA3
40/60	66.67%	10	2024 IA2
40.5/55	73.64%	12	2025 IA3
44.5/60	74.2%	12	2025 IA2, a real student script marked B
42.5/56	75.89%	12	2025 IA2
70/75	93.33%	15	2025 IA2

Each rung covers roughly 6 to 7 percentage points. On a 60-mark paper that is about four marks, so one question where you never wrote the conclusion and two where the working was too thin to follow is the difference between a 13 and a 12.

The 60/20/20 blueprint

Every IA2, every IA3 and both external papers are built to the same question specification, within ± 2%:

Degree of difficulty	Share of marks	What you are being asked to do
Simple familiar	60%	relationships and interactions are obvious and have few elements, and all the information you need is identifiable. Either the procedure is clear from the way the question is posed, or the context has been a focus of prior learning
Complex familiar	20%	there are a number of elements, connecting subject matter within or across the domains of mathematics, and all the information you need is still identifiable
Complex unfamiliar	20%	a number of elements as above, and the information you need is not immediately identifiable: the procedure is not clear from the way the problem is posed, and you have had limited prior experience of the context

The syllabus maps the three tiers to objectives, and the mapping tells you what the complex unfamiliar 20% is actually testing. Simple familiar is typically objectives 1, 2 and 3, which are recall, use and communication. Complex unfamiliar is typically objectives 4, 5 and 6: evaluate the reasonableness of solutions, justify procedures and decisions, solve mathematical problems. The descriptor at 12 and above names all three situation types, so those four criterion marks need the complex unfamiliar questions answered.

What a complete response contains

There is no essay to compare, so the excerpts QCAA reproduces are photographs of handwritten working carrying ticks, half marks and follow-through annotations. Five habits earn the marks across all of them.

Write the reasoning that selects the method, before the method. A 2025 IA2 excerpt opens: "when $y_3' = 1$ , it is the point where $y_1$ and $y_2$ are tangents. This is because the gradient for $y_1$ and $y_2$ are $-1$ and $1$ respectively. Because $y_3$ is a parabola symmetrical over the $y$ -axis ..." Nothing has been calculated yet. QCAA's caption on it is "the use of clear mathematical reasoning to justify procedures and decisions", which is assessment objective 5 and carries marks in the scheme.

Declare what the technology did. On a technology-active question, write the call you made, not only the number it returned. The same 2025 excerpt carries the marker's note "used calc for integrals"; a 2025 IA3 excerpt writes 1 - binomcdf(10, 0.4, 4) beside its answer, and a 2024 IA3 excerpt writes Pr(X ≥ 12) = 1 - BinomCdf(20, 0.7, 11) ≈ 0.8867. The 2024 report calls this "clear communication of reasoning when technology has been used to solve a multi-mark question". Both of those sat in IA3 under the old unit mapping; the binomial distribution has since moved to Unit 3, so the same habit now belongs in your IA2.

Check the reasonableness of the answer, because objective 4 carries marks. All three reports tell schools to allocate marks for it in the scheme. A 2023 IA2 excerpt carries the teacher annotation "Reasonableness?" with a cross against a solution that was otherwise correct.

Verify with different numbers where you can. A 2025 IA3 excerpt argues the direction of an effect qualitatively and then closes: "To check: input $n = 300$ , s.d. $= 0.008083$ , $P(X \le 0.03) = 0.892$ ."

Your method does not have to be the marking scheme's method. QCAA's 2025 IA3 advice is that where a student "responded in an alternate way to that expected in the marking scheme, the solution is annotated to show how marks had been awarded based on the merit of the response". The 2024 report shows a worked case: the school's scheme expected a second-derivative test for maximum speed, the student used graph magnitudes and absolute values, and the marks were awarded.

What your paper cannot ask you

Schools do get this wrong, and QCAA names specific rulings you can hold your revision to. From the 2025 report on IA3: confidence intervals of sample means are Specialist Mathematics content and not Methods, and the normal approximation to the binomial distribution is not in the Methods syllabus at all. The 2023 report adds that volumes of revolution "should not be a required procedure in a Mathematical Methods assessment instrument", because Specialist students would gain an unfair advantage. That last one was written about IA1, and its wording covers any instrument.

Alignment to the syllabus specifications was the dominant reason QCAA refused to endorse a Methods examination in each of the 2023, 2024 and 2025 rounds, which is why a school paper has often been through a rewrite before anyone sits it.

How reliably these papers get marked

Confirmation agreement between school marks and QCAA-confirmed marks ran 98.78%, 100.00% and 100.00% on IA2 across the 2023 to 2025 cohorts, and the same three figures on IA3. Those cohorts sat the 2019 syllabus, but the arithmetic that produces them has not changed: a single-criterion percentage instrument leaves a confirmer very little to disagree with. The IA1 modelling task ran 85.68%, 90.61% and 95.77% over the same years.

Getting the paper approved is the hard part. Endorsement, the approval QCAA gives a school's instrument before anyone sits it, was granted at first application to 26%, 34% and 46% of IA2 papers and 39%, 40% and 57% of IA3 papers across those three cohorts, against 61%, 74% and 83% for IA1. IA2 is the least-endorsed instrument in the subject in every one of the three years, and even in the best of them fewer than half of school IA2 papers passed at first application. All three trends are rising.

Where our data lines up with QCAA's advice

QCAA does not publish a score per cognitive verb or per dot point. Our own figures do, with two caveats: they come from external examination questions and not from school-written internal papers, and those papers were all sat under the superseded 2019 syllabus. So treat them as evidence about the content your school paper will sample, and not about this instrument.

QCAA has named evaluating the reasonableness of solutions in the advice sections of all three reports. Across 68 marked AusGrader attempts on evaluate questions and 61 on justify questions, those are the two weakest cognitive verbs in our sample, at 46.7% and 50.7%. They are assessment objectives 4 and 5, and the 60/20/20 table maps them to the complex unfamiliar 20%.

The second derivative is the strongest content finding in the subject, named by QCAA in all three reports and now sitting in Unit 3 where IA2 can sample it. Across 1,511 marked attempts, optimisation using first and second derivatives averages 47.3% for us, and the second derivative test on its own averages 43.2% across 293 attempts. On the IA3 side, calculating the area enclosed by a curve and the $x$ -axis over a given domain averages 39.2% across 261 attempts, our weakest integration outcome, while applied definite-integral problems average 88.2% across 1,265. The full picture across every topic and verb is on the Mathematical Methods study guide.

Common mistakes

Hunting for band descriptors to write towards. The ISMG offers nothing to aim at. Two students sitting on the same descriptor can still finish a mark apart, because the percentage is what separates them, so every individual mark across the paper is the only lever you have.

Answering a technology-active question with the number only. A calculator output with nothing around it evidences one mark-allocation statement at best. Write the expression you evaluated.

Answering a technology-free question with a calculator method written out. The marks there are for the algebra, and the scheme has nothing to award a route the mode does not permit.

Stopping when the value is found. Objective 4 is assessed in every paper. If the question has a context, say whether the answer is sensible in it.

Revising to the old unit mapping. Second-derivative work is Unit 3 now, so it sits in IA2. Integration beyond anti-differentiation is Unit 4, so it sits in IA3. Material written before 2025 has these the other way round.

Assuming the paper covers the whole unit. Three topics of five means two topics you revised hard may never appear, and the fifth you skipped may carry a third of the paper.

In the room

Nothing here is a draft you can check in advance, so make it a routine you run on each question:

Which mode is this question, and have I answered in it?
How many marks is it worth, and how many separate points does the scheme therefore need to see?
If I used technology, have I written the expression I evaluated as well as the result?
Have I written down why this method is the right one, on anything that is not a bare procedure?
Does the question have a context, and have I said whether my answer is reasonable in it?
If something went wrong two lines up, can a marker still follow the rest well enough to carry the error through?
Is there a second route to this answer I could run in the time left, by substituting back or by changing one value?

Two places to go next. The Mathematical Methods question bank has unseen questions on every Unit 3 and Unit 4 topic, which is the only way to find out which of the five your revision is thinnest on. And the IA1 problem-solving and modelling task is marked on a completely different principle: four criteria, band descriptors you can read in advance, and 20 marks that reward planning rather than speed. Everything else in the subject sits on the Mathematical Methods study guide, and other subjects are on the QCE hub.

Syllabus and assessment material referenced in this guide is © State of Queensland (Queensland Curriculum and Assessment Authority), licensed under CC BY 4.0. See our QCAA licensing notice. AusGrader is an independent study tool and is not affiliated with, endorsed by, or operated by the QCAA.