A limitation in a Maths Methods PSMT is a restriction on how accurately or widely your mathematical model can be applied to the real-world situation it is meant to represent. In QCE Mathematical Methods, limitations are assessed as part of the Evaluate criterion and they need to be specific, justified and directly connected to the model you developed.
Unfortunately, simply writing that "the model may not be completely accurate" is not a limitation. It is a vague observation that tells the marker nothing about what you actually understand. Read our guide below to find out what limitations really are, where they come from, how to write them well and how to connect them to the rest of your PSMT.
Cloud Tuition Summary
Cloud Tuition is a Queensland-based online tutoring service offering Year 2-9 English and Maths tutoring, NAPLAN preparation and specialist QCE tutoring in Maths Methods, Biology, Chemistry and other senior subjects.
KEY ARTICLE INSIGHTS:
In Year 10, Year 11 and Year 12 Maths Methods, a limitation is a restriction on how accurately, reliably or widely your model can be applied
Every meaningful limitation should connect back to an assumption you made in the formulate section or an issue that emerged during solving
Generic limitations will not earn marks. Specific, justified limitations that explain the consequence and suggest a realistic improvement will
Strengths and limitations work together in the evaluation section to show the marker you understand what your model can and cannot do
What a Limitation Actually Is
In your Methods PSMT, a limitation is not something you did wrong. It's a boundary on how accurately, reliably or widely your model can be used. All mathematical models simplify reality to some degree. The limitations section is where you acknowledge those simplifications honestly and explain what effect they have on the usefulness of your solution.
The key distinction is between a limitation and an avoidable error. If you made an arithmetic mistake in your Solve section (e.g. the answer was rounded incorrectly or an algebraic substitution went wrong), that is an error. If your model assumes a linear relationship when the true relationship is non-linear, that is a limitation of the modelling approach you chose.
A well-written limitation does three things:
Identifies what the restriction is
Explains what effect it has on the accuracy, reliability or scope of the model
Suggests a realistic way the model could be improved or extended
Where Mathematical Limitations Come From
The most common mistake students make is adding limitations at the end of their PSMT without connecting them to anything earlier in the report. A genuine limitation must trace back to either an assumption you made in the formulate section, an issue with the data or modelling process that emerged during solving, or a genuine constraint on the real-world applicability of the mathematical function you chose.
One of the clearest patterns we see in PSMT drafts during our Maths Methods tutoring sessions is students adding generic limitations in the evaluation that have no connection to their assumptions or their solve section. Limitations need to be specific to your model and traceable back to decisions you made earlier in the report. We recommend going back to your Assumptions section and asking whether these assumptions are realistic or limiting in any way. Is there anything your model doesn't account for or unnaturally assumes?
Types of Maths Method PSMT Limitations With Examples
Limitation Type | What It Means | Example |
📊 Assumption-based | A simplification you made restricts how well the model reflects reality | Assuming a constant growth rate ignores seasonal variation, meaning the model overestimates population during winter months |
📏 Domain restrictions | The function produces mathematically valid but practically impossible values outside the defined range | The quadratic model predicts negative heights for t > 12 seconds, which is physically impossible |
🔢 Sample size | A small or unrepresentative dataset reduces the reliability of any model fitted to it | The model was fitted to data from 15 students, which may not be representative of the broader student population |
📉 Extrapolation | Predictions made beyond the observed data range become increasingly unreliable | Projecting the linear trend beyond 2030 assumes conditions remain constant, which is unlikely given external economic factors |
🌍 Omitted variables | Real-world factors not included in the model may affect the outcome | The model does not account for humidity or temperature variation, both of which affect the dependent variable in practice |
🔣 Function choice | The selected model type may not be the best fit for the underlying relationship | A linear function was fitted to data that shows slight curvature in the residual plot, suggesting a quadratic model may be more appropriate |
📐 Measurement error | Rounding or imprecise measurement introduces inaccuracy into the model | Heights were measured to the nearest centimetre, introducing a possible error of plus or minus 0.5 cm which compounds when the model is used for prediction |
A Detailed Example: Arm Span and Height
To make this concrete, consider a PSMT where you are asked to model the relationship between a student's arm span in centimetres (independent variable) and their height in centimetres (dependent variable). You collect data from 20 Year 11 students and fit a linear regression model.
Here is what a range of limitations might look like for this task:
1️⃣ Limitation 1: Biological differences between male and female students
A weak version: "The model does not account for gender differences."
A strong version: "Male and female students typically have different biological proportions, with research suggesting that female students on average have a slightly shorter arm span relative to height than male students. As the data was collected from a mixed-gender sample without separating the two groups, the linear model represents an average relationship that may not accurately predict height for either group individually. This reduces the validity of individual predictions made using the model. A more refined approach would develop separate regression models for male and female students."
2️⃣ Limitation 2: Small and potentially unrepresentative sample
A weak version: "Only 20 students were measured."
A strong version: "The model was fitted to data from 20 students within a single Year 11 cohort at one school. This sample may not be representative of the broader Australian student population, particularly across different age groups, ethnicities or socioeconomic backgrounds, all of which can influence physical proportions. The limited sample size reduces the reliability of the model when applied beyond this specific group. Collecting a larger and more diverse dataset would improve the generalisability of the model."
3️⃣ Limitation 3: Measurement accuracy
A weak version: "Measurements might not be perfectly accurate."
A strong version: "Arm span and height were measured using a standard measuring tape to the nearest centimetre. This introduces a measurement error of plus or minus 0.5 cm for each variable. Because both variables carry this uncertainty, the combined effect on the regression equation may affect the accuracy of predictions, particularly for values near the boundaries of the observed range. Using a more precise measurement instrument such as a stadiometer would reduce this error."
Weak vs Strong Limitations: A Comparison
Weak Limitation | Why It Falls Short | Strong Limitation |
The model is not completely accurate | Too vague, no explanation of why or what the effect is | The linear model assumes a constant rate of change between variables, but the residual plot shows increasing spread at higher values, suggesting the relationship may be non-linear and that a quadratic model would better capture this pattern |
The data might be wrong | Does not identify the source of the error or its consequence | Measurements were self-reported by participants, which may introduce systematic underreporting of weight values, reducing the reliability of any model fitted to this data |
More data would make the model better | Does not explain why the current data is insufficient | The model was built from 12 data points collected over a single week, which may not capture seasonal variation in the dependent variable. A dataset spanning 12 months would improve the model's ability to account for this variation |
Technology was used | Not a limitation at all | Numerical solving using CAS technology introduced rounding at the fourth decimal place, which may introduce a cumulative error of up to 0.02 units when the model is iterated over 50 time steps |
Looking for a Maths Methods tutor?
Our Year 10-12 QCE Maths Methods tutors personally work through your PSMT evaluation with you, including your limitations and how to connect them back to your assumptions. Your first lesson is completely free.
How to Structure Each Limitation in Your Methods PSMT
A reliable structure for each limitation is:
1) Identify the limitation
State clearly what the limitation is and where it comes from.
"A limitation of this model is that it assumes [condition], as stated in Assumption 2."
2) Explain the effect of the limitation
Describe what consequence this has on the accuracy, reliability or scope of the model.
"This means the model may overestimate / underestimate / fail to account for [specific outcome] when [specific condition]."
3) Suggest an improvement
Propose a realistic refinement, not an impossible one.
"This limitation could be addressed by [specific and feasible change], which would improve the [validity / reliability / scope] of the model."
The improvement does not need to be complex. Collecting more data, separating a dataset into subgroups, using a different function type or extending the domain are all valid suggestions if they are genuinely connected to the limitation you identified.
Limitations vs Recommendations
Students sometimes confuse limitations with recommendations. A limitation explains what the model cannot do and why. A recommendation suggests what could be done next. They are related but distinct.
If your report includes a recommendations section, your limitations should logically lead into it. Each significant limitation suggests a direction for improvement, and your recommendations should follow directly from those limitations rather than appearing unconnected.
How Limitations Connect to Assumptions
This is the most important connection in the evaluation section. Every significant assumption you made in the formulate section has the potential to become a limitation in the evaluate section. When you assumed something was negligible, constant or representative, you were making a decision that simplified your model.
In the evaluation, you revisit those decisions and ask: was that simplification reasonable, and what effect did it have if it was not perfectly true?
For guidance on writing strong assumptions that set up your limitations well, see:
Struggling with your PSMT evaluation section?
Our Maths Methods tutors review your limitations and help you connect them clearly to your assumptions and modelling decisions before you submit. Your first lesson is completely free, no payment details required.
Getting Extra Tutoring Support For Your Maths Methods PSMT
If you are finding it difficult to identify genuine limitations for your specific task, or if your feedback says your evaluation is too vague or too generic, our Maths Methods tutors work with Year 11 and Year 12 students through every part of the PSMT evaluation including limitations, strengths and model refinement. Book a free trial lesson to get started.
Frequently Asked Questions
What are limitations in a Maths Methods PSMT?
Limitations in a Maths Methods PSMT are restrictions on how accurately, reliably or widely your mathematical model can be applied to the real-world situation it represents. They arise from the assumptions you made, the quality of your data, the function you chose or the scope of the model. Each limitation should explain what the restriction is, what effect it has on the result and how the model could realistically be improved.
What are examples of limitations in Maths Methods?
Common examples include assuming a constant rate when the real relationship varies over time, fitting a linear model to data that shows curvature, collecting data from a small or unrepresentative sample, making predictions beyond the observed data range, ignoring real-world variables such as gender differences or environmental factors, and measurement error introduced by rounding or imprecise instruments. Each example should be connected specifically to the model and data used in your investigation.
How do I structure a Maths Methods PSMT?
A Maths Methods PSMT follows the four ISMG criteria: Formulate, Solve, Evaluate and Communicate. Within the evaluate section, you discuss the reasonableness of your solution, then identify and justify specific strengths and limitations of the model, and suggest realistic refinements. Limitations should connect back to assumptions made in the formulate section. For a full breakdown of each section, see Maths Methods PSMT Structure Explained.
How do limitations connect to assumptions in a PSMT?
Every significant assumption you made in the formulate section is a potential limitation in the evaluate section. When you assumed something was negligible, constant or representative, you simplified reality to make the model work. In the evaluation, you revisit those decisions and assess whether the simplification was reasonable and what effect it had if it was not perfectly true. Limitations that cannot be traced back to an assumption or a modelling decision are likely too generic to earn marks.
What is the difference between a limitation and a mistake in a PSMT?
A mistake is an avoidable error in your process, such as an arithmetic error or an incorrect formula. A limitation is an inherent restriction on the accuracy or applicability of the model that arises from the decisions you made in formulating and solving the problem. Limitations are expected in every mathematical model and acknowledging them clearly demonstrates that you understand the boundaries of your solution.
Other related articles:
- 5Page 2
