In QCE Mathematical Methods, your three internal assessments (IA1, IA2 and IA3) make up 50% of your final result, the same weighting as the external exam. They are set and marked by your school but quality-checked by the QCAA, and the 2025 subject report shows clearly what high-scoring responses did.
This guide breaks down the internal assessment sections of QCAA's 2025 Mathematical Methods subject report. It covers how students scored on each IA, what QCAA said separated strong responses, and the changes under the revised 2025 syllabus that students starting Units 3 and 4 from 2026 need to know. For the external exam, see our companion 2025 QCE Maths Methods external assessment breakdown.
Key Takeaways
- Internal assessments are worth 50% of your Maths Methods result: IA1 20%, IA2 15%, IA3 15%.
- IA1 (the problem-solving and modelling task) was the highest-scoring assessment: about 30% of students scored a perfect 20/20.
- School marks were very reliable. QCAA agreed with schools' provisional marks 100% of the time for IA2 and IA3 and 95.77% for IA1, so the mark your teacher gives you almost always stands.
- In IA1, Evaluate and verify was the hardest criterion to earn full marks in. Strong responses linked their evaluation back to their assumptions and observations and discussed both strengths and limitations.
- Under the 2025 syllabus, IA1 needs justified assumptions and observations, efficient use of technology and verified results. The IA2 and IA3 exams are now 90 minutes and sample three of the five topics in the unit.
How Internal Assessment Works in QCE Maths Methods
| Assessment | Type | Weighting | Content |
|---|---|---|---|
| IA1 | Problem-solving and modelling task (PSMT) | 20% | Unit 3 (under the 2025 syllabus, Unit 3 or Unit 4) |
| IA2 | Examination | 15% | Unit 3 |
| IA3 | Examination | 15% | Unit 4 |
| External assessment | Two examination papers | 50% | Units 3 and 4 (Units 1 and 2 assumed) |
Your school writes each IA, but before students sit it the QCAA must endorse it, checking that it matches the syllabus and is fair. After marking, the QCAA confirms a sample of student responses to check that your school's marks are accurate.
💡 New to the system? Read our explainer on how QCE internal assessments work.
How Students Scored in 2025
| Assessment | Maximum Mark | Approximate % of Students on Full Marks |
|---|---|---|
| IA1 (PSMT) | 20 | 30% |
| IA2 (Unit 3 exam) | 15 | 12.5% |
| IA3 (Unit 4 exam) | 15 | 14% |
| Total IA | 50 | 7% |
Approximate values read from the mark distribution charts in QCAA's 2025 Mathematical Methods subject report.
A few patterns stand out:
- IA1 marks were high. Almost half the cohort scored 19 or 20 out of 20.
- The two exams were much more spread out. IA2 and IA3 marks were spread fairly evenly from about 7 to 15, so the internal exams separate students far more than the PSMT does.
- The total IA mark peaked at 50/50, but most students finished somewhere between 30 and 49.
In other words, a strong IA1 is expected. The IA2 and IA3 exams are where your internal result is really decided.
How Reliable Were School Marks?
| Assessment | Instruments Endorsed First Time | Samples Reviewed | Agreement With School Marks |
|---|---|---|---|
| IA1 | 83% | 3,238 | 95.77% |
| IA2 | 46% | 3,236 | 100% |
| IA3 | 57% | 3,224 | 100% |
Source: QCAA Mathematical Methods subject report, 2025 cohort.
What this means for students:
- Your IA2 and IA3 marks will not change. The QCAA agreed with every school's exam marks it reviewed in 2025.
- IA1 marks are occasionally adjusted. Where they changed, they were more often lowered than raised, mostly in the Formulate and Evaluate and verify criteria. Make sure your response clearly shows each characteristic in the marking guide.
- Most school exams were revised before students sat them. Only 46% of IA2 papers and 57% of IA3 papers were endorsed the first time, usually because questions did not match the syllabus. This is why the questions in your school's exam are carefully limited to the subject matter in the syllabus.
IA1: Problem-Solving and Modelling Task (20%)
The PSMT asks you to solve a real-world problem using calculus, write it up as a report and evaluate your solution. In 2025, it used subject matter from Unit 3 Topic 2 (Further differentiation and applications 2) and/or Topic 3 (Integrals).
QCAA praised tasks with contexts students could understand without teacher explanation, such as designing a smooth, continuous go-kart track, finding the area of a mini-golf course and designing a rollercoaster. Student samples in the report included a cheeseboard designed using areas between curves and a logistic growth model comparing the spread of a virus in two countries.
How Students Scored on Each Criterion
| Criterion | Marks | Approx. % on Full Marks | What Earned Full Marks |
|---|---|---|---|
| Formulate | 4 | 62% | Clear, documented assumptions and observations, with the problem translated into mathematics |
| Solve | 7 | 51% | Complex procedures in multiple related steps, with technology used to actively solve the problem |
| Evaluate and verify | 5 | 45% | Reasonableness evaluated against the stated assumptions and observations, with strengths and limitations |
| Communicate | 4 | 77% | Precise mathematical language and a coherent report with an introduction, body and conclusion |
Approximate full-mark percentages read from QCAA's 2025 criterion charts.
What Earned the Marks
Formulate: Strong responses listed their assumptions (for example, that a design was symmetrical, or that the model stayed above the x-axis so areas did not need signs considered) and their observations (for example, that functions must be continuous over the interval being integrated). The best responses linked each one to the problem.
Solve: QCAA rewarded responses that used several connected steps of Unit 3 calculus to reach a valid solution. Technology counted when it actively helped solve the problem, not just when it drew a graph. One sample graphed P′(t) to confirm that a logistic model had no stationary points, because the derivative never crossed the x-axis.
Evaluate and verify: This was the hardest criterion for full marks. Strong responses showed clear connections between the reasonableness of their result and the assumptions and observations they had already documented, for example: "the model aligns with assumption 2, as it never has a negative rate". QCAA wants evaluations that include both strengths and limitations, each with a clear justification.
Communicate: Full-mark responses used precise technical vocabulary and had a clear structure: an introduction, a body and a conclusion that answered the task.
Explain vs Justify
QCAA specifically wants students to understand the difference between explaining an assumption and justifying one. Explaining says what the assumption is and how it is used. Justifying gives a mathematical or real-world reason why the assumption is valid. Under the 2025 syllabus, the top marks in Formulate need justified statements, so this difference matters.
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What Changes for IA1 Under the 2025 Syllabus
Students completing Units 3 and 4 under the revised 2025 syllabus will see these changes to the PSMT:
| Area | 2019 Syllabus | 2025 Syllabus |
|---|---|---|
| Subject matter | Unit 3 | At least one topic from Unit 3 or Unit 4 |
| Duration | 4 weeks | Set by your school |
| Formulate (top level) | Appropriate assumptions and relevant observations | Justified statements of important assumptions and observations, which must be essential to solving the problem |
| Solve | Accurate and appropriate use of technology | Efficient use of technology, so the solution is developed quickly, easily and effectively |
| Evaluate criterion | Called "Evaluate and verify" | Renamed "Evaluate", with five descriptors at the top level, including verified results |
| Justifying decisions | Part of Evaluate and verify | Moved to Communicate, with mathematical reasoning |
Two details from the report are worth knowing:
- Plurals matter. The 3–4 mark range in Formulate needs justified statements of important assumptions and observations, so you should typically justify more than one of each. In Evaluate, the 2–3 mark range needs "a verified result" but the 4–5 mark range needs "verified results".
- Each descriptor is now one characteristic. Teachers match the whole descriptor to your work, so a partly met descriptor will not earn the mark.
You do not need to include or refer to the problem-solving and modelling flowchart in your report, but you are still expected to follow its process.
IA2: Unit 3 Examination (15%)
IA2 is a supervised exam on Unit 3 subject matter, which centres on differentiation, integration and their applications. It includes simple familiar, complex familiar and complex unfamiliar questions, and a balance of technology-free and technology-active questions.
What QCAA Said About Marking
Your teacher marks your exam against a marking scheme, then converts your percentage into a mark out of 15 using the marking guide. In one sample, above 93% earned 15 and above 87% earned 14. QCAA's samples show:
- Half marks are used. Teachers can award part marks within a question, for example 3.5 out of 4.
- Follow-through marks are awarded. If you make an early error but use the wrong value correctly in later steps, you can still earn the later marks. One sample lost a mark for substituting x = π/4 into sin(x) instead of sin(2x), but still earned follow-through marks for the rest of the working.
- Clear reasoning is rewarded. QCAA highlighted a response that explained why a tangent point gave a particular gradient before calculating, then set out the integral for the area clearly.
- Alternative correct methods count. Teachers are expected to award marks for valid methods that differ from the marking scheme.
What Changes for IA2 Under the 2025 Syllabus
- Working time is 90 minutes (down from 120 minutes), with 5 minutes of perusal time.
- The exam samples three of the five Unit 3 topics, not all of them. You may also need assumed knowledge from Units 1 and 2.
- Exponential and logarithmic equations in Unit 3 Topic 1 use base e.
- Cubic (and higher-order) equations solved without a calculator will be given in factorised form.
IA3: Unit 4 Examination (15%)
IA3 is a supervised exam on Unit 4, covering further integration, trigonometry, discrete and continuous random variables, and sampling and proportions. Like IA2, it should include a balance of technology-free and technology-active questions and at least one opportunity to evaluate the reasonableness of a solution.
What QCAA's Samples Show
- Justify your reasoning in words. One sample explained that as the sample size increases, the standard deviation of the sample proportion decreases, so the z-value increases and the probability increases. The student then checked the reasoning with technology by recalculating with a larger sample.
- Define your variables and state the distribution. A full-mark binomial response defined X, stated n = 10 and p = 0.4, and identified the distribution before calculating.
- Show the complement step. For P(X ≥ 5), the sample wrote 1 − P(X ≤ 4) before using binomcdf. Marks were awarded for that step, not just the final answer.
Content That Is Not in Maths Methods
QCAA flagged school exams that included content outside the syllabus. You will not be assessed on these in Maths Methods:
- the normal approximation to the binomial distribution
- confidence intervals for sample means, which belong to Specialist Mathematics. Methods covers confidence intervals for proportions.
What Changes for IA3 Under the 2025 Syllabus
- Working time is 90 minutes (down from 120 minutes), with 5 minutes of perusal time.
- The exam samples three of the five Unit 4 topics, plus assumed knowledge from Units 1 and 2.
- The first two dot points of Topic 2: Trigonometry have been removed. Basic trigonometric ratios (such as sin θ = O/H) are no longer Unit 4 subject matter.
How to Improve Your Maths Methods IA Results
- For IA1, justify everything. Give each assumption and observation a reason, and link your evaluation back to them.
- Discuss strengths and limitations of your model, each with a justification. This was the criterion where most marks were lost.
- Use technology to solve and verify, not just to draw graphs. Explain what each tool showed you.
- Use your checkpoint feedback. QCAA expects schools to give feedback on one complete or near-complete draft, so submit a full draft and act on what your teacher says.
- For IA2 and IA3, show every step. Half marks and follow-through marks reward clear working even when the final answer is wrong.
- Explain your reasoning in words whenever a question asks you to justify, evaluate or explain.
- Practise 90-minute papers with a mix of technology-free and technology-active questions.
For more preparation:
- read our 2025 QCE Maths Methods external assessment breakdown
- follow our guide to getting an A in QCE Mathematical Methods
- learn how IA1, IA2 and IA3 work
- understand how the QCE ATAR is calculated.
Need Help With QCE Maths Methods?
Our QCE Mathematical Methods tutors work one-on-one with students to plan and write a high-scoring PSMT, prepare for the IA2 and IA3 exams, and show their working the way markers expect.
Source: Queensland Curriculum & Assessment Authority, Mathematical Methods subject report, 2025 cohort (January 2026).
