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

Your IA1 is worth 20% of General Mathematics, marked out of 20 across four criteria with deliberately unequal marks: Formulate 4, Solve 7, Evaluate 5 and Communicate 4. Formulate and Communicate have only two scoring bands each, so on those there is no middle to land on and a response either carries the top-band adjective or drops straight to the bottom one. The single most reliable way to lose marks is stating an assumption or an observation without justifying it.

This guide describes the General Mathematics 2025 v1.0 General senior syllabus, current for Year 12 from 2026. The four subject reports published so far (2022 to 2025 cohorts) all describe students marked against the superseded 2019 v1.2 criteria, so the criterion-level statistics below use the old criterion names and are labelled with their cohort year. The student excerpts still show what the 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 lets data go either way: it "may be provided or collected individually or collected in groups". In practice most tasks arrive with the data attached, because QCAA has told schools in all four reports from 2022 to 2025 to supply the stimulus and the data. Hunting for sources is not what this task measures.

The appendix rule catches people every year. QCAA names it in the 2022, 2023 and 2024 reports: if your only evidence of technology use is a spreadsheet screenshot in the appendix, the marker cannot credit it under Solve. Move a figure into the body and reference it in your prose.

You are expected to work through QCAA's problem-solving and modelling approach, the four-stage cycle with feedback loops that gives the criteria their names. You do not have to reproduce the flowchart. The 2025 report says so directly: "it is not necessary to include or refer to this flow chart in the task."

The four criteria

Communicate is a marked criterion here, carrying 4 marks of your 20, the same as Formulate. Look for it explicitly: how you write the report is assessed separately from the mathematics in it.

Solve is the only criterion with four scoring bands, which makes it the one place a partially successful attempt lands somewhere sensible. Evaluate has three. Formulate and Communicate have two scoring bands and a zero, so on those there is nothing between the top band and the bottom 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 lower band drops every qualifier: statement of a relevant assumption; statement of a relevant observation; mathematical translation of an aspect of the task.

So the whole criterion turns on the word "justified", and QCAA defines what it wants. For an observation, justification means "citing a source to explain where the observation came from to support the reliability of the observation or an explanation of its relevance and importance in solving the task". For an assumption, it means "explaining why the assumptions are fundamental to mathematising the problem … or the impact on the problem of not making those assumptions".

Number your assumptions and observations (A1, A2, O1, O2) and refer back to them later. The Formulate and Evaluate excerpts QCAA reproduces both do this, and it is what makes the Evaluate criterion possible to satisfy at all.

On mathematical translation, the 2024 report is specific: it wants "accurate translation of all aspects of the problem by identifying relevant mathematical concepts and techniques that are specific to the problem, rather than a list of general definitions". Naming least-squares regression and defining it will not clear the bar. Say why a least-squares line is the right tool for this dataset.

Solve, 7 marks

Top band: accurate use of mathematical knowledge for important aspects of the task; efficient use of technology; a complete solution. One band down: use of mathematical knowledge for an important aspect of the task; use of technology; substantial progress towards a solution.

Three things separate the bands: accuracy, efficiency of technology, and completeness. The 2019 descriptor asked for "complex procedures" and "discerning application"; the current one does not, so choosing a harder technique to look impressive buys you nothing if the solution is incomplete.

"Efficient use of technology" needs to be visible in the body. One strong 2025 excerpt makes it explicit: "All calculations have been finalised on excel using the formulas present in Figures 7 and 8. This program has been used to speed up the calculation process and to create accurate and informative scatter plots." It names what the technology did and why it was the efficient choice.

Evaluate, 5 marks

The top band has five descriptors, up from three under 2019, 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 list as a checklist. Verification is separate from reasonableness. Reasonableness against assumptions is separate from reasonableness against observations. Strengths and limitations are two items, and QCAA has named responses addressing only one of the pair as a problem in every report from 2022 to 2025.

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.

Communicate, 4 marks

Top band: 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.

One of those three is new to this criterion in 2025. Justification of decisions moved here from Evaluate and verify, so every method choice you made, which model, which technique, which sample, needs a reason attached to it somewhere in the report. The other two descriptors were already in the 2019 Communicate band, in different words.

"Can be read independently of the task sheet" is a testable condition. Hand your draft to someone who has not seen the task sheet. If they cannot work out what problem you were solving, your introduction is doing too little: restate the scenario, define every variable with its units, and name the techniques you will use.

Where marks actually get pulled down

QCAA checks a sample of every school's marking, a process called confirmation. Across the 2022 to 2025 cohorts, agreement between school marks and confirmed marks on IA1 ran 75.61%, 84.19%, 76.74% and 82.23%.

Broken down by criterion, using the 2019 names those cohorts were marked against:

Formulate and Evaluate and verify are the two least-agreed criteria in every one of the four years, and Communicate the most-agreed in every one. The disagreement runs almost entirely one way: on Formulate, marks were confirmed lower than the school's provisional mark 12.86%, 8.24%, 10.68% and 8.14% of the time across those four cohorts, against higher at 1.11%, 1.11%, 1.09% and 0.64%.

Schools mark Formulate and Evaluate and verify generously and QCAA pulls them back down. Those are also the two criteria whose descriptors turn entirely on the word "justified", and they are exactly what the reports' advice sections name every year. Treat a top-band mark on either as provisional until confirmation is done.

Common mistakes

Stating assumptions instead of justifying them. Named as a weakness in all four reports from 2022 to 2025. A statement says what you assumed. A justification says why the problem cannot be mathematised without it, or what happens if it is wrong.

Addressing only strengths, or only limitations. The Evaluate top band lists both, so covering one caps you at the middle band however thorough it is.

Putting marked content in the appendix. Raw data, repeated calculations and your notes belong there. Anything you want credit for does not.

Reaching for a harder technique. The current Solve descriptors reward accuracy, efficient technology use and a complete solution. An ambitious model that runs out of pages before the solution is complete scores below a straightforward one that finishes.

Writing an introduction that assumes the marker has the task sheet. Communicate at 3-4 explicitly requires a response that "can be read independently of the task sheet".

Skipping verification. "Verified results" is the first of five descriptors in the Evaluate top band and is separate from any statement about reasonableness. Check a result a second way, by estimation or by substituting back, and say in the report that you did.

Weak versus strong

QCAA reproduces marked excerpts in its subject reports. These are the pairs that separate the bands.

Before you submit

Run these against your own draft:

• Have I justified at least two assumptions and at least two observations, not one of each?
• Is every assumption and observation numbered and referred back to later in the report?
• Does my mathematical translation name techniques specific to this problem, not general definitions?
• Is my evidence of technology use in the body, with a sentence saying what it did?
• Is my solution complete, or does the report stop partway with progress towards one?
• Have I verified a result independently, and said so?
• Have I written about reasonableness against my assumptions and against my observations?
• Have I written both a strength and a limitation, each with evidence behind it?
• Is every decision I made, about model, technique or sample, given a mathematical reason somewhere?
• Could someone who has never seen the task sheet read this and know what problem I solved?
• Am I inside 10 A4 pages and 2000 words, with the appendix carrying only unmarked material?

Ready to work on the content? Practise the Unit 3 and Unit 4 techniques your task will draw on with the General Mathematics question bank, starting with time series analysis or loans, investments and annuities, see how IA1 fits alongside everything else on the QCE General Mathematics study guide, or read how the IA2 and IA3 examinations are marked, where there are no band descriptors to reach at all and a single percentage decides the mark. Other subjects are on the QCE hub.