QCE Mathematical Methods IA1 problem-solving and modelling task: how to get top marks

Your IA1 is worth 20% of Mathematical Methods and is marked out of 20 on four criteria carrying unequal marks: Formulate 4, Solve 7, Evaluate 5 and Communicate 4. Solve alone is more than a third of the task, and Formulate and Communicate each offer only a top band and a bottom band, with nothing in between to land on. Almost every mark lost on this task goes the same way: an assumption or an observation stated without a justification attached to it.

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 The three subject reports published so far (2023, 2024 and 2025 cohorts) all describe students marked against the superseded 2019 syllabus criteria, so the criterion-level statistics below use the old criterion names and carry their cohort year. The student excerpts still show what a marker rewards, because the descriptor changes were narrow.

What the task actually is

QCAA's description, verbatim:

Students provide a written response to a specific mathematical investigative scenario or context using subject matter from at least one of the topics in Unit 3 or Unit 4. While students may undertake some research, it is not the focus of this task.

The syllabus permits research and rules it out as the focus in the same sentence. On data it leaves your school the choice: it "may be provided or collected individually or collected in groups".

The appendix rule catches people every year. If your only evidence of technology use is a screenshot sitting behind the reference list, the marker cannot credit it under Solve. Move the figure into the body and refer to it in your prose.

You are expected to work through QCAA's problem-solving and mathematical modelling approach, the iterative cycle whose four stages give the criteria their names. Both "Is it solved?" and "Is the solution verified?" can send you back to Formulate, which is the point of drawing it as a loop. You do not have to reproduce the diagram: the 2025 report says "it is not necessary to include or refer to this flowchart in the task."

The four criteria

Communicate carries its own 4 marks, as many as Formulate. The quality of the report is judged separately from the quality of the mathematics inside it, so a correct investigation written badly loses marks that have nothing to do with the mathematics.

Two objective mappings changed in 2025. Objective 5, justifying procedures and decisions, was added to Communicate, which is why every method choice now needs a reason attached to it somewhere in the report. Objective 2 also moved from Formulate to Solve, though that one is a smaller change than it looks: the slot moved and its wording changed with it, from the 2019 "comprehend mathematical concepts and techniques" to the 2025 "Use mathematical knowledge".

The number of bands varies, and it decides how much a partial attempt is worth. Solve has four scoring bands, so an attempt that goes wrong still lands somewhere sensible. Evaluate has three. Formulate and Communicate have two, a top band and a bottom band with nothing between them, so missing one descriptor on either drops you the whole way. The instrument-specific marking guide, or ISMG, is the marking guide printed inside the syllabus for each internal assessment; this one names no performance levels, listing only characteristics with a mark range beside them.

The six word swaps that separate the bands

The descriptors at each level are close to the same sentences with different qualifiers. These are the qualifiers.

QCAA glosses two of those itself in the 2025 report. Important means "essential for the problem to be mathematised and the solution to be reached". Efficient use of technology means "the technology selected allows the solution to be developed quickly, easily and effectively", which replaced 2019's "accurate and appropriate use". A spreadsheet you used accurately but that saved you nothing is a 2019 top-band answer and a 2025 middle-band one.

Formulate, 4 marks

The top band, verbatim: justified statements of important assumptions; justified statements of important observations; justified mathematical translation of important aspects of the task. The band below drops every qualifier: statement of a relevant assumption; statement of a relevant observation; mathematical translation of an aspect of the task.

So the criterion turns on the word "justified", and the 2023 report unpacks what the behaviour looks like. Its wording describes the 2019 verb "documentation", which 2025 renames, but the behaviour it asks for is exactly what the current top band rewards. For an assumption: "link each assumption to the task and/or model/solution and explain the necessity of making the assumption, or a possible effect of not making it". For an observation: "support each observation with evidence ... explaining where the observations come from, the reliability of the observations, or features of the observations relevant to the model/solution".

Number your assumptions and observations and refer back to them. That numbering is what makes the Evaluate criterion satisfiable at all, because its top band asks you to consider each one again.

Solve, 7 marks

At 6-7 the descriptor reads accurate use of mathematical knowledge for important aspects of the task; efficient use of technology; a complete solution. At 4-5 it reads use of mathematical knowledge for an important aspect of the task; use of technology; substantial progress towards a solution. At 2-3 the knowledge and the technology both become "simplistic".

Three things separate 6-7 from 4-5: whether the mathematics is accurate, whether the technology was efficient, and whether the solution is finished. QCAA has told schools in the 2024 and 2025 reports alike that technology has to be doing real work. The 2025 wording is the sharper of the two, praising "technology that actively facilitated problem-solving, extending beyond basic functions such as graphing". A graph produced and pasted in, with nothing said about what it settled, is the case that wording is written against.

Completeness is where ambitious models come unstuck. Seven marks is more than a third of the task, and an elegant approach that runs out of pages before the solution is finished scores below a plainer one that reaches the end.

Evaluate, 5 marks

The top band has five descriptors and each is a separate thing to do: 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 a checklist of five, not one idea in five phrasings. Verifying a result is a different act from arguing it is reasonable. Reasonableness against your assumptions is separate from reasonableness against your observations. Strengths and limitations are two items.

The middle band is a bare singular of each: 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. Both of those "or"s are what caps a response at 2-3.

The 2023 report is specific about what a justified strength or limitation contains: "the strength of a model that encompasses all data points provided could be how it can effectively be used to interpolate to reach conclusions. Conversely, a limitation may be explained by identifying how a model is only effective within the given domain and extrapolation beyond this domain would yield unreliable results."

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 of those is new to this criterion in 2025, having moved across from Evaluate and verify. So every method choice you made, which model, which technique, which sample, needs a mathematical reason attached somewhere in the report. The 2024 report puts the bar at showing "use of mathematical reasoning ... to support why decisions are right or reasonable", which is more than naming the choice.

"Can be read independently of the task sheet" is the one descriptor in the whole ISMG you can test empirically before you submit. Give the draft to someone in another subject. If they cannot tell you what problem you set out to solve, the introduction is under-built: it needs the scenario restated, every variable defined with its units, and the techniques named up front.

Where marks actually get pulled down

QCAA checks a sample of every school's marking, a process called confirmation. Across the 2023 to 2025 cohorts, agreement between school marks and confirmed marks on IA1 as a whole ran 85.68%, 90.61% and 95.77%, the weakest of the three internal assessments in all three years and rising steadily.

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

Communicate is the most-agreed criterion in all three years and Formulate the least in two of them. The disagreement runs almost entirely one way on both of the weaker criteria. On Formulate, marks were confirmed lower than the school's provisional mark 6.31%, 6.12% and 1.88% of the time, against higher at 0.24%, 0.94% and 0.00%. On Evaluate and verify the split is 5.10%, 3.06% and 1.41% lower against 1.21%, 0.24% and 0.70% higher.

So schools over-award those two and QCAA pulls them back. Both are criteria whose descriptors turn on the word "justified", which is also where the reports' advice sections concentrate year after year. Until confirmation is finished, a top-band mark on either is provisional.

Common mistakes

Assumptions and observations that restate the task. The 2024 report asks for evidence that is "relevant to the solving of the problem and go beyond restating task specifications". Copying a constraint out of the task sheet is not an assumption you made.

Explaining an assumption instead of justifying it. QCAA names this in 2025, asking schools to make sure students "understand the distinction between the cognitions 'explain' and 'justify', so that students do not confuse explaining an assumption with providing 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, or names what breaks if it turns out to be false.

Evaluating reasonableness against the results only. Named in all three reports. The 2024 wording is that judgments "need to consider more than the results"; the 2023 wording is that they "must include consideration of results, observations and assumptions". This is the single most repeated IA1 finding in the subject.

Giving a strength or a limitation, but not both. The Evaluate top band lists both, and QCAA asked schools in 2025 to ensure evaluations "include both strengths and limitations, with clear justification for each".

Stating a decision without the reasoning. Justification of decisions now sits in Communicate, so a report full of correct choices and no reasons loses marks on a criterion that has nothing to do with the mathematics being right.

Using technology only to graph or to type. The condition is that technology goes beyond simple computation or word processing, and the descriptor above the middle band asks for it to be efficient.

Putting marked content in the appendix. The appendix exists for raw data, repeated calculations, authentication evidence and notes, and a marker awards it nothing. A spreadsheet that proves efficient use of technology earns Solve marks in the body and none behind the reference list.

Weak versus strong

The right-hand column below is student work reproduced in a QCAA subject report and marked under the 2019 ISMG. The left-hand column describes the weaker form each one could have taken, and is our characterisation, not quoted student writing. Across all six the difference is the same: a sentence that states a fact scores in the lower band, and the same sentence with a "because", a consequence for the model, or a source attached scores in the upper one.

Before you submit

Answer each of these against your own draft before you hand it in:

• How many assumptions carry a justification, and how many observations? Both counts need to be at least two.
• Would the model still stand without each one? If it would, that assumption is not "important" in QCAA's sense.
• Are they numbered, and does the evaluation section come back to each number by name?
• Did I say why my mathematical translation is the right one for this problem, or only carry it out?
• What did the technology do that I could not have done as quickly by hand, and is that said in the body?
• Does the report reach a complete solution, or does it stop at substantial progress towards one?
• How many results have I verified, and did I verify each by a route independent of how I found it?
• Is reasonableness argued against my assumptions and separately against my observations?
• Is there a strength and a limitation, each with a justification rather than a bare claim?
• Does every choice of model, technique or sample have a mathematical reason attached somewhere?
• Would a reader with no task sheet know what problem this report solves?
• Is it inside 10 A4 pages and 2000 words, with only unmarked material in the appendix?

The mathematics inside your task still has to be right, and a modelling task most often draws on the calculus and distribution work in further applications of differentiation and continuous random variables and the normal distribution. Both have unseen questions on the Mathematical Methods question bank. Read IA2 and IA3 next, because they work on the opposite principle: no band descriptors to write towards at all, and a single percentage deciding all 15 marks. The Mathematical Methods study guide covers the rest of the subject, and the QCE hub covers the rest.