QCE Specialist Mathematics study guide

Your Specialist Mathematics result out of 100 comes from four instruments sat across Units 3 and 4: a 20% problem-solving and modelling task, two 15% internal examinations written by your school, and a 50% external examination in two papers, the first of which you sit with nothing on the desk but a formula book. The three internal instruments are approved by QCAA before you sit them and rechecked afterwards on a sample. Units 1 and 2 carry no weighting, and neither does Mathematical Methods, which the syllabus names as assumed knowledge behind all three examinations.

This guide describes the Specialist Mathematics 2025 v1.0 General senior syllabus, which the 2025 subject report calls "first examinable in 2026". Three reports are on hand, on the 2023, 2024 and 2025 cohorts, and all three describe students who sat Units 3 and 4 under the superseded 2019 syllabus. Every figure below is labelled with the cohort it came from for that reason.

How the marks add up

The internal half splits 20/15/15, so the modelling task outweighs either internal exam on its own. Those weightings are unchanged from the 2019 syllabus.

One question specification governs the three examinations, within ± 2%: 60% simple familiar, 20% complex familiar, 20% complex unfamiliar. Three fifths of every exam you sit is therefore the straightforward tier, and the syllabus ties the hardest fifth to the evaluate, justify and solve objectives while the easiest three fifths sit on recall, use and communication. The modelling task is the exception: it carries no difficulty tiers at all and is marked on four criteria instead.

The external examination is half your result

All three reports describe the same shape as sat, in identical wording: each paper carried a multiple-choice section worth 10 marks and a short-response section worth 50. Three consecutive years is good evidence about what to expect and it is not a rule, because the syllabus sets no count and no mark total. It also prints no marking guide for the exam. That document is the External Assessment Marking Guide, published separately each year, and it is where the per-question mark allocations live.

The 2025 syllabus loosened Paper 2 slightly. Under 2019 a QCAA-approved graphics calculator was required and a scientific calculator could also be used; under 2025 you may bring either or both.

The pattern that has held for three years

The complex unfamiliar short-response question on Paper 2 has been a statistical inference question in all three of the cohorts covered by the reports we hold. In 2023 it asked students to compare recalculated confidence intervals at an unknown confidence level across two equal-sized samples. In 2024 it moved between a normal $X$ and the sampling distribution $\bar{X}$, requiring simultaneous equations. In 2025 it asked for the probability that a confidence interval built from a second, smaller sample overlaps the first, and QCAA's effective-response bullets single out "recognition that the sample size must be an integer".

Two weaker patterns sit beside it. Mathematical induction was a Paper 1 proof item in 2023 and 2024, on a geometric sum and then on divisibility by 7. A vector calculus motion item appeared in Paper 2 in both of those years, and in 2024 the question specified the approach, with QCAA rewarding students who developed the relationship between speed and angular velocity instead of quoting a formula that sits outside the Specialist syllabus.

What QCAA keeps saying

Read the "practices to strengthen" and "additional advice" sections of the three reports side by side and the same items come back. Ranked by how many cohorts named each one.

The reports also record what the cohort did well. Matrix work is a strength in all three years: matrix algebra inside a matrix equation in 2023, inverses and multiplication of dimension-3 matrices using technology in 2024, and solving a system by Gaussian elimination in 2025. Simple familiar questions on both papers are named in 2023 and 2025, and multiple choice in 2024 and 2025.

Multiple choice, and the two items the cohort got backwards

QCAA prints the full per-option response percentage table for both papers. In the 2023 Paper 1 table, two items had a distractor beat the correct answer outright:

Two more in the same paper were close: Q10 went 37.63% for the correct B against 33.53% for A, and Q8 went 42.34% for the correct A against 33.35% for C. QCAA prints these tables without commentary on any individual item, so none of the four has a published explanation and the reading above is ours.

Which dot points the marks come off

No QCAA publication descends to the level of a single dot point. Our own figures do, and they carry an obvious bias: they describe people who signed up to a practice platform and worked on it when the mood took them, which is nobody's idea of a representative sample. Take them as extra resolution on the board's findings and never as a substitute for them.

Across 14,641 marked attempts on Specialist Mathematics questions on AusGrader, these are the weakest outcomes with a publishable sample.

Unit 3

Unit 4

Two of those twelve are the sampling distribution and the mean, which is the content behind QCAA's repeated advice on comparing $X$ and $\bar{X}$. The weakest Unit 3 row corroborates the board's 2024 advice on extending vector concepts from two dimensions into three, and puts a number on it that QCAA does not publish.

At topic level, as printed in our data: modelling motion is our weakest topic in Unit 4 at 52.1%, with statistical inference just above it at 53.9%, and further complex numbers is our weakest in Unit 3 at 56.9%. Nothing in the subject averages above 65.0%, which is where integration techniques sits.

The strongest individual outcomes in our sample sit above 70%: matrix algebra on matrices beyond dimension 2 at 78.1% across 62 attempts, modelling with a provided differential equation at 74.3% across 253, and the complex conjugate root theorem at 71.3% across 493. The first of those agrees with the board naming matrix work as a strength in all three years, though note that the applied end of the same topic, dominance and Leslie matrices, is one of our weakest Unit 3 rows above.

By the verb the question uses

The subject reports never break performance down this way. Our labels come from our own question tagging and are not QCAA's cognitive verb framework. Averages across 50 or more attempts, weakest first:

Evaluate is the weakest verb in the set by nearly 18 points, on the one cognition QCAA has asked this subject to strengthen in every report. The other judgment verbs, justify, explain and model, sit under 50 attempts, so we have not published a number for them. By question format the two are level, 58.3% across 13,269 multiple-choice attempts against 58.2% across 1,372 short-answer attempts, so the format itself separates nothing here.

Paper 1 sits above Paper 2, in five years out of six

QCAA publishes no mean per paper. Ours, from practice attempts on past papers rather than sittings, all of them 2019-syllabus papers:

Attempt counts in brackets. The 2020 papers run the other way and the two 2023 papers are effectively level, so treat the pattern as five years of one direction with a counter-example, and not as a rule about the papers. The no-calculator paper being the easier one is at least a useful corrective to a revision plan that treats Paper 1 as the frightening one.

The A boundary is not a number you can aim at

QCAA sets the cut-offs against the reporting standards after the cohort has been assessed, so they move.

The A cut rose a mark between 2023 and 2024 and held. The C boundary sat at exactly 49 in all three years, so the pass line is the most stable number here. In the 2025 cohort, 314 schools offered the subject, 95.68% of students earned a C or higher, and the distribution ran 39.56% at A, 35.68% at B, 20.44% at C, 4.30% at D and 0.02% at E. Enrolment rose 16.47% on 2024.

Nearly two in five students finish at A, which is the highest A share of the three QCE mathematics subjects and reflects who chooses to take Specialist.

Where to start

The two internal examinations are the most predictable marks in the course, because once the paper is marked the criterion mark is arithmetic. Read how IA2 and IA3 are marked before your first one, particularly the strictly-greater-than rule on the cut-off ladder and the part about cued approaches.

The IA1 problem-solving and modelling task carries 20% and is the one instrument whose full marking guide you can read before you write a word of it. It is also the least settled mark on your result. Agreement between school marks and QCAA-confirmed marks ran 92.46%, 95.02% and 97.42% on IA1 across the 2023 to 2025 cohorts, against 99.01% on IA2 and 99.67% on IA3 in 2023, then 100.00% on both in 2024 and 2025.

For content, work from the outcomes tables above. Statistical inference and modelling motion carry most of our weakest Unit 4 outcomes, and further complex numbers and vectors in two and three dimensions most of the weakest in Unit 3. Unseen questions on all of them are on the Specialist Mathematics question bank, and the QCE hub has the other subjects.