01Understand the rubric
Four criteria. One connected argument.
The ISMG separates evidence into Formulate, Solve, Evaluate and Communicate, but a high-level report makes them reinforce one another. A strong assumption shapes the method, the method produces a result, and the same assumption later helps you test that result's reasonableness.
At the top band, assumptions and observations must be important and justified, technology must be efficient, results are verified, and mathematical decisions are justified within Communicate.
Formulate
Build a defensible bridge from the real world to mathematics.
- Justified statements of important assumptions
- Justified statements of important observations
- Justified mathematical translation of important aspects of the task
Solve
Use accurate mathematics and technology to finish the whole task.
- Accurate use of mathematical knowledge for important aspects
- Efficient use of technology
- A complete solution
Evaluate
Prove the result is dependable, then define its limits.
- Verified results
- Reasonableness considering assumptions and observations
- Justified strengths and justified limitations of the solution
Communicate
Make the reasoning precise, independent and easy to follow.
- Correct use of appropriate mathematical language
- Logical organisation, readable independently of the task sheet
- Justification of decisions using mathematical reasoning
Small word, large consequence
Look for singulars and plurals.
The 2025 subject report highlights that top-band Formulate normally requires more than one justified important assumption and more than one justified important observation. Top-band Evaluate requires verified results, while the middle band refers to a verified result. Plan repeated, high-quality evidence rather than one isolated example.
Name a relevant feature, choice or result.
Make the relationship or method clear.
Use evidence or reasoning and show the impact on the solution.
02Build the report
Give every section one clear job.
The following structure is not compulsory, but it makes the reasoning easy to follow and supports a report that can be read independently. The word allocations are planning guides from the supplied PSMT resource, not quotas.
Introduction
~200 wordsReconstruct the problem for a new reader, explain why it matters, state the goal and preview the mathematical approach.
Evidence target: Independent context, purpose, scope, mathematical translation and technology plan.Formulating a solution
~400 wordsDefine variables and constraints, then develop your own important observations and assumptions.
Evidence target: Statement + evidence/reason + specific impact on the model or result.Developing a solution
~700 wordsJustify each major decision, execute the mathematics, show efficient technology and reach every required outcome.
Evidence target: Decision -> mathematics -> interpretation or verification, repeated as a clear chain.Evaluating the solution
~600 wordsVerify key results, test sensitivity, judge reasonableness and explain strengths, limitations and useful scope.
Evidence target: Independent checks and quantified impact, not unsupported claims such as 'this seems reasonable'.Conclusion
~100 wordsReturn directly to the original purpose and state the final result or recommendation.
Evidence target: A concise answer with the quantity, units, conditions and model selected where relevant.The independent-reader test
Hide the task sheet. Does the report still make sense?
- Can a reader reconstruct the context and exact objective?
- Are variables, data, units, domains and constraints defined?
- Can the reader follow why each method was chosen?
- Does the conclusion answer the original question directly?
03Master each criterion
Build evidence deliberately, not by accident.
Treat each criterion as a set of decisions the reader must be able to see. The strongest evidence names the feature, gives a valid reason or source, and traces its consequence through the mathematics.
Formulate · 4 marks
Make the model possible.
Observation or assumption?
An observation is factual information or a pattern in data that can be checked. An assumption is a condition accepted as true so the problem can be modelled. Both must matter to the solution, not merely to the topic.
Your own evidence matters
Assumptions and observations already supplied in the task sheet cannot earn Formulate marks. You may consider them later in Evaluate, but Formulate needs evidence you identify or develop yourself.
The importance test
If this statement disappeared, would the mathematics or final result change?
If the answer is no, it is probably background information, not an important observation or assumption. Prioritise statements that determine data treatment, model form, parameters, constraints, domain, accuracy or interpretation.
Observation frame
evidence → mathematical consequence
It was observed that [factual pattern/source]. This is important because it requires [specific change to model, parameter, domain or method].
Assumption frame
condition → simplification → impact
It is assumed that [condition]. This allows [mathematical action], but means the result will [specific effect or scope].
Translation frame
task feature → mathematics → output
Because the task requires [feature], [concept or technique] will be used to [produce the required mathematical result].
Solve · 7 marks
Make every major step reproducible.
Why this model, formula, data treatment, parameter or domain?
Show accurate equations, substitutions, graphs, tables or code outputs.
Interpret, verify or connect the result to the next decision.
Accurate knowledge
Correct where it matters.
- Use valid concepts, rules, definitions and algorithms.
- Keep precision consistent and round only when appropriate.
- Show units, domains and constraints through the working.
- Make transformations and substitutions visible.
Efficient technology
Fast, effective and understood.
- Automate repeated calculations with spreadsheet formulas.
- Fit, compare or graph models with suitable software.
- Show a representative formula, input or setting.
- Explain what the tool did and why it was suitable.
Complete solution
Answer the entire task.
- Map every task requirement to an output in the report.
- Respect all constraints and required comparisons.
- Interpret the final values in the real-world context.
- Give a decision or recommendation when asked.
What counts as evidence?
Show the method, not a gallery of screenshots.
Graph or table + representative formula + explanation of automation
Relevant view + equations/settings + explanation of the analysis
Input and result + enough manual reasoning to show understanding
Purpose, key logic or output + validation of what the code produced
Evaluate · 5 marks
Challenge the solution before the marker does.
Estimation
Simplify the situation and check that the order of magnitude is plausible.
Alternative method
Re-solve an important result using a genuinely different mathematical path.
Technology
Use an independent tool or representation to reproduce a manual result.
Research or data
Compare with a credible external benchmark, known value or held-out data.
Re-entering the same formula into the same spreadsheet does not provide independent evidence. State the method, show the comparison and explain what agreement or disagreement means.
Reasonableness in four moves
Keep the solution at the centre.
- 1State the relevant result or conclusion.
- 2Name the assumption or observation that affects it.
- 3Change or challenge that condition, preferably with mathematics.
- 4Judge whether the solution remains valid, accurate or useful.
Sensitivity example
input ± 5% → result ± 1.8% → decision unchanged
This is stronger than saying the input is realistic. It quantifies the consequence and uses that evidence to judge the solution.
Strengths ask
What makes the solution useful?
- Which real-world features are represented well?
- Where is the model supported by data or verification?
- Can the method adapt to related cases?
- What improves accuracy or decision quality?
Limitations ask
Where does usefulness break down?
- Which factors or relationships are omitted?
- Where is extrapolation or sparse data involved?
- Which assumptions restrict the model's scope?
- What cannot be verified with available evidence?
Communicate · 4 marks
Make correctness easy to recognise.
Terminology
Use precise procedural verbs and subject-specific nouns: determine, verify, derivative, residual, parameter and domain.
Symbols and equations
Define symbols before use, align equations logically, preserve equality and use an equation editor rather than improvised text.
Graphs and tables
Add informative titles, labels, units, sensible scales, legends and readable precision. Refer to each visual in the text.
Organisation
Use a coherent sequence, numbered equations where helpful, descriptive headings and a conclusion that returns to the purpose.
Justifying a decision
04Upgrade the writing
Move from a statement to mark-bearing evidence.
These generic examples show the structure of stronger writing. Adapt the reasoning to your own context, mathematics and data; do not copy a sentence that your solution cannot support.
ObservationIs it factual, important, and tied to a modelling consequence?+
Statement only
The data rises over time.
Evidence + reasoning + impact
The data increases rapidly at first and then levels near an upper bound. This observed behaviour makes an unbounded exponential model unsuitable and supports testing a logistic model.
AssumptionDoes the solution rely on it, and have you explained the impact?+
Statement only
The growth rate is constant.
Evidence + reasoning + impact
It is assumed that the measured conditions remain stable over the prediction interval. This allows one parameter set to be used throughout; if conditions change, the extrapolated values may be systematically over- or underestimated.
Mathematical translationWhy is this mathematics suitable for this feature of the task?+
Statement only
A regression model will be used.
Evidence + reasoning + impact
Because the task requires both prediction and rate of change, a differentiable regression function will model the data and its derivative will quantify the instantaneous rate.
DecisionIs the choice supported by mathematical evidence, not preference?+
Statement only
Model B is the best model.
Evidence + reasoning + impact
Model B is selected because it has the lower RMSE within the observed domain, its residuals show no systematic pattern, and its long-term behaviour is consistent with the contextual upper limit.
VerificationCan the reader see the method, comparison and conclusion?+
Statement only
The result was checked in Desmos.
Evidence + reasoning + impact
Substituting t = 8 into the fitted equation gives 42.61. The spreadsheet output gives 42.61 for the same input, independently confirming the substitution and calculation.
ReasonablenessAre you judging the solution and quantifying the assumption's effect?+
Statement only
The assumption is reasonable.
Evidence + reasoning + impact
The solution remains reasonable under this assumption because increasing the parameter by 5% changes the final prediction by only 1.8%, without changing the recommended option.
StrengthWhy does this feature improve usefulness, validity or accuracy?+
Statement only
The model uses real data.
Evidence + reasoning + impact
A strength is that the model is calibrated with data across the full decision interval. This reduces reliance on extrapolation and makes the comparison within that interval more dependable.
LimitationWhat is limited, why, and what consequence follows?+
Statement only
There are not many data points.
Evidence + reasoning + impact
Only six observations constrain three parameters, so individual measurement errors can noticeably shift the fitted curve. Predictions between the observations are therefore less stable than the reported fit statistic alone suggests.
Common mark leaks
Six habits to remove before submission.
Borrowing the task sheet
Given assumptions and observations do not earn Formulate marks. Develop your own evidence from the data, research or mathematical structure.
Justifying relevance only
Saying an idea is connected to the topic is not enough. Explain why the solution depends on it and what would change without it.
Hiding behind screenshots
A screenshot proves software was open, not that it was used efficiently. Include a representative formula, setting or method and explain its role.
Evaluating the assumption
The required judgment is about the solution's reasonableness when that assumption is considered. Keep the result at the centre of the sentence.
Listing generic limitations
Word count, time pressure and 'human error' rarely evaluate the mathematical solution. Analyse model scope, data quality, parameters and omitted factors.
Sending evidence to the appendix
Appendices are not marked. Keep the equations, outputs and explanations needed for a descriptor in the report body.
05Use the workflow
Write the report in the same order you build the evidence.
Do not leave evaluation until the last night. Verification and sensitivity testing often reveal errors or better modelling decisions, so they belong inside the development process.
Decode
Turn the task into a requirements table: output, constraints, data, subject matter and decisions.
Formulate
Define variables, identify important observations, select assumptions and map real features to mathematics.
Prototype
Test candidate methods quickly. Record why each model, parameter, domain and tool was selected.
Solve
Build the solution in small reproducible steps. Label outputs and interpret each major result in context.
Verify
Check important results as they appear using estimation, technology, research or an alternative method.
Stress-test
Change influential inputs and assumptions. Measure whether the conclusion, recommendation or accuracy changes.
Edit
Audit against each descriptor, remove repetition, fix mathematical language and make the report independent.
A practical drafting order
Formulate → Solve → Evaluate → Introduction → Conclusion
You may understand the introduction better after the model is complete. Drafting it near the conclusion helps keep the stated purpose, actual method and final answer aligned.
06Run the final check
Audit the evidence, one descriptor at a time.
Complete this after the mathematical content is stable. Your selections are saved on this device so you can return to the checklist during revision.
This is an evidence audit, not an automatic mark calculator. Quality, importance and task-specific relevance still determine the teacher's on-balance judgment.
07Sources and scope
Grounded in the supplied guides and current QCAA material.
This guide interprets the supplied source documents into student actions. It does not replace the official syllabus, task-specific ISMG, teacher judgment or school authentication requirements.