QCE Specialist Mathematics IA1 problem-solving and modelling task: how to get top marks

The IA1 carries 20% of your Specialist Mathematics result. Twenty marks are split unevenly across four criteria, Formulate 4, Solve 7, Evaluate 5 and Communicate 4, so Solve alone decides more than a third of the task. Evaluate is the one QCAA rebuilt hardest for 2025, splitting two descriptors into five separate things you have to do. Every top band adds a qualifier the band below it drops, and on three of the four criteria that qualifier is the same word: justified. Solve is the exception, where the qualifiers are accuracy, efficiency and completeness.

This guide describes the Specialist Mathematics 2025 v1.0 General senior syllabus, first examinable in 2026. Its evidence comes from the 2023, 2024 and 2025 subject reports, whose cohorts were all marked under the superseded 2019 criteria, so every criterion-level figure below uses the old criterion names and carries its cohort year. The marked student work in those reports is still the best picture of what earns a mark, and QCAA sets out the descriptor changes itself in the 2025 report.

What the task actually is

A written response to a mathematical investigative scenario or context, produced individually. The conditions:

The appendix rule costs marks quietly. Solve rewards efficient use of technology, and a marker can only credit technology they can see doing something in the body of the report. A spreadsheet or a computer-algebra screenshot filed behind the reference list evidences nothing.

You are expected to work through QCAA's problem-solving and mathematical modelling approach, whose four stages are where the criteria get their names, and which loops back on itself when a solution does not work or does not verify. Reproducing the flowchart earns nothing: QCAA's 2025 report says "it is not necessary to include or refer to this flowchart in the task."

Ten topics, where there used to be two

This is the single largest change to the Specialist IA1, and it sits outside the ISMG entirely.

Under the 2019 syllabus the task had to use subject matter from Unit 3 Topic 2 (Vectors and matrices) or Topic 3 (Complex numbers 2), or both. Under 2025 it requires subject matter from at least one of the topics in Unit 3 or Unit 4, which is ten topics, and Unit 4 has never been in scope before. Integration techniques, differential equations, modelling motion and statistical inference can all now be the mathematical core of a Specialist modelling task.

Two consequences. Any older guidance that tells you what a Specialist IA1 is "usually about" was written against a two-topic rule and no longer bounds anything. And a statistics-based or a motion-based task is now as legitimate as a vectors one, so the technique list you prepare cannot be narrowed by guessing.

The four criteria

The band counts matter as much as the marks. Solve gives you four scoring bands to land in, so an investigation that goes partly wrong still scores. Evaluate gives three. Formulate and Communicate give two, so on those criteria you either satisfy the whole top descriptor set or you fall to the bottom one, with nothing in the middle to catch you. The instrument-specific marking guide, or ISMG, is the marking guide QCAA prints inside the syllabus; each performance level in it is a set of characteristics against a mark range, so what you are matched to is a descriptor set and not a number.

Two objective mappings moved for 2025. Objective 5, justify procedures and decisions, arrived in Communicate, so a method chosen without a stated reason now costs marks on the writing criterion. Objective 2 left Formulate for Solve, changing its wording on the way, from "comprehend mathematical concepts and techniques" to "Use mathematical knowledge".

Formulate, 4 marks

The top band: justified statements of important assumptions; justified statements of important observations; justified mathematical translation of important aspects of the task. The band below is the same three items with every qualifier stripped out: statement of a relevant assumption; statement of a relevant observation; mathematical translation of an aspect of the task.

So two words carry the criterion, and QCAA defines one of them. Important, in its 2025 wording, means that "the assumptions and observations are required for the problem to be mathematised". Apply that as a test on each item you have written: if the model would still work without it, it is a relevant assumption and not an important one, however well argued.

Number your assumptions and observations. The Evaluate criterion asks you to come back to them individually, and numbering is what makes that possible to write and to mark.

Solve, 7 marks

At 6-7: accurate use of mathematical knowledge for important aspects of the task; efficient use of technology; a complete solution. At 4-5 the mathematics covers "an important aspect", the technology is plain "use of technology", and the solution is "substantial progress". At 2-3 both the knowledge and the technology become "simplistic".

Efficient replaced 2019's "accurate and appropriate", and QCAA glosses it: efficient technology is evident "when the technology selected allows the solution to be developed quickly, easily and effectively". Accuracy is no longer enough on its own. A tool you used correctly that saved you nothing scored at the top under the old wording and sits below it under the new one.

Completeness is the other half of the gap, and it is where an ambitious model loses. Seven marks is more than a third of the task, and a plain approach carried through to a finished solution outscores an elegant one that runs out of pages.

Evaluate, 5 marks

The top band is five separate descriptors, and the 2019 version covered the same ground in two:

verified results; justified statements about the reasonableness of the solution by considering the assumptions; justified statements about the reasonableness of the solution by considering the observations; justified statements of relevant strengths of the solution; justified statements of relevant limitations of the solution.

Read that as five items to satisfy. Verification and reasonableness are different acts, and the descriptor asks for both. Reasonableness comes up twice, once against the assumptions and once against the observations, and satisfying it once does not cover the other. Strengths and limitations are two items, not one phrase.

The middle band is the singular of each, with two "or"s doing the capping: a verified result; statement about the reasonableness of the solution by considering an assumption or observation; statement of a relevant strength or relevant limitation of the solution.

QCAA also states what the verification half requires: responses at the highest performance level "must include verification of the results of calculations through the solution development process". Checking at the end is not the same as verifying as you go.

Communicate, 4 marks

Three descriptors at 3-4: correct use of appropriate mathematical language; logical organisation of the response, which can be read independently of the task sheet; justification of decisions using mathematical reasoning.

The third arrived here in 2025 from the old Evaluate and verify criterion. Anywhere you picked one model, one technique or one parameter over another, a mathematical reason has to sit beside the choice.

The first has more in it than it looks. The descriptor itself asks only for "correct use of appropriate mathematical language", but the 2025 subject report spells that out as covering "terminology, symbols, conventions and representations", and the 2023 report names the presentation habits QCAA rewarded in this criterion: labelling tables, figures, graphs and their axes; aligning equations at the equals sign down the centre of the page; and using syllabus notation for matrices, trigonometric functions and summation. In a subject running vector, matrix and complex notation side by side, that last one is a real source of lost marks.

The middle descriptor is the only line in the whole ISMG you can test before you submit. Hand the draft to someone who does not take the subject. If they cannot say what problem you set out to solve, the introduction has not restated the scenario, defined the variables with their units, and named the techniques.

Weak versus strong

Everything on the right is drawn from a QCAA subject report and describes work marked under the 2019 ISMG. The first four rows quote reproduced student writing; the last describes the presentation QCAA named as effective practice. Everything on the left is the thinner version of the same move, built from the lower-band wording of the ISMG and from the practices QCAA asks schools to strengthen. The left column is our characterisation and not quoted student writing.

Marker annotations transcribed beside the 2025 assumptions and observations run "Good idea", "well explained", "very appropriate", "Excellent assumption" and "Well considered & explained".

Common mistakes

Explaining an assumption instead of justifying it. QCAA asked schools in 2025 to ensure students "understand the difference between the cognitions of explain and justify, so that students don't confuse explaining an assumption with a justification of an assumption". An explanation restates the assumption in other words. A justification gives the reason the problem cannot be mathematised without it.

Evaluating the results only. Named in the practices-to-strengthen section in 2023 and 2024, and turning up in 2025 from the other side, as the effective practice QCAA credits: the highest Evaluate mark "was only awarded when there was evidence of consideration of results, observations and assumptions". The 2023 wording asks for "the relevance of the observations and the implications of the assumptions"; the 2024 wording asks that evaluation target the observations and assumptions "considered during formulation".

Treating reasonableness and strengths as the same argument. The 2024 report separates them explicitly: documenting strengths and limitations means giving "evidence about why decisions and refinements contributed to its success or otherwise", and "this was different from considering the reasonableness of the result". Under 2025 they are separate descriptors inside one criterion, so a response doing one and calling it both loses the other.

Justifying the strengths and asserting the limitations. Or the reverse. Both appear as their own descriptor and both need a justification, which QCAA repeated in 2025.

Headings that do not match what sits under them. The 2024 report asks that "care is taken with identifying documentation as student-provided headings do not always align with student-provided statements". A section labelled Assumptions containing observations gets read as neither.

Leaving the decisions unexplained. Justification of decisions is now a Communicate descriptor, so it is marked whether or not your mathematics is right.

Putting the evidence in the appendix. Raw data, repeated calculations, authentication evidence and notes belong there and are not marked. Anything you want credit for goes in the body.

What confirmation does to your mark

QCAA checks a sample of every school's marking after the task is submitted, a process called confirmation. Across the 2023, 2024 and 2025 cohorts, agreement between school marks and confirmed marks on the IA1 as a whole ran 92.46%, 95.02% and 97.42%, the weakest of the three internal assessments in every one of those years.

Per criterion, under the 2019 names those cohorts were marked against:

Agreement on the IA1 overall climbed every year, and three of the four criteria rose in 2025. Evaluate and verify is the only criterion that went backwards that year, and it finished as the least-agreed of the four, with 1.61% of sampled marks confirmed below the school's provisional mark against 0.32% above. On Formulate and Evaluate, and on the criteria taken together, the disagreement runs the same direction in all three years: schools award above the confirmed mark more often than below it. Communicate is the one that runs the other way.

That is the criterion QCAA then rebuilt into five descriptors. Until confirmation finishes, a top-band Evaluate mark on a Specialist IA1 is the least settled number on your result.

What your teacher had to get past QCAA first

Before you sit down to any of this, your school's task went to QCAA for endorsement, the approval given to an instrument before students start it. Of the roughly 310 Specialist IA1 instruments submitted each year, first-application endorsement ran 72%, 74% and 80% across the 2023 to 2025 rounds, the highest of the three internal assessments in every year and rising.

The reasons instruments were flagged, by validity priority:

Four of the five are down on 2023, with alignment spiking in 2024 before falling back. Authentication is the one moving the wrong way. Every one of these is a finding about how the task was built, not about you, but this row is the one with a student-side consequence: the instrument has to specify how your work will be authenticated as yours. Keep your drafts, your class-time work and your checkpoint submissions, and hand them over when asked.

The recurring design faults tell you what a well-built task looks like. QCAA named excessive scaffolding that directs the solution in all three years, and reusing QCAA sample tasks or public examples in 2023 and 2025, because a task that has circulated cannot produce unique responses. The 2025 report adds one specific to this subject: if dominance matrices are used, the task must allow for opportunities that go beyond simple win-loss data.

Before you submit

Take your draft and answer these on it:

• Count the justified assumptions, then count the justified observations. Two of each is the floor the plural descriptors set.
• Strike out any one of them and ask whether the problem could still be turned into mathematics. If it could, that item is relevant and not important.
• Is each one numbered, and does the evaluation cite those numbers when it returns to them?
• Is there a stated reason for the mathematical translation you chose, or only the translation?
• What did the technology do quickly, easily and effectively that you could not have done otherwise, and can a marker see it in the body?
• Did the report finish, or did it stop at substantial progress?
• Were results verified as the solution developed, or only checked at the end?
• Is reasonableness argued twice, once against the assumptions and once against the observations?
• Are there strengths and limitations, both plural, each with its own justification?
• Does every model, technique and parameter choice carry a mathematical reason?
• Does the notation match the syllabus for matrices, trigonometric functions and summation, and is every axis, table and figure labelled?
• Could someone reading it with no task sheet in front of them state the problem you solved?
• Are you under both limits, 10 A4 pages and 2000 words, and is the appendix free of anything you want credited?

A modelling task now has ten topics to draw from, and the ones with the most modelling in them are modelling motion, rates of change and differential equations and statistical inference, all three of which were out of scope before 2025. Unseen questions on each are on the Specialist Mathematics question bank. Read IA2 and IA3 next: they print band descriptors too, but nothing in that prose decides your mark, because one percentage settles all 15. That is as far from this task as the subject gets. The Specialist Mathematics study guide covers everything else, and the QCE hub covers the other subjects.