How to Write Assumptions in a Maths Methods PSMT

Assumptions are most often one of the sections of the Maths Methods PSMT that senior students struggle with. Most students list five broad statements with no justification and move on, forgetting to link to the context of their assignment and considering how it impacts their solution and mathematical approach.

If you're in Year 10 or a Year 11 Maths Methods student, here's your step-by-step guide explaining what assumptions actually are in mathematical modelling, how to write and justify them properly and how they connect to the rest of your report so that you can obtain full marks.

What Is an Assumption in Mathematical Modelling?

A mathematical model is always a simplified version of reality. No model can account for every variable, every measurement error or every external factor that might affect the situation being investigated. Assumptions are the conditions you choose to accept as true so that your model can function.

💡 Think of it this way: real-world problems are messy. Mathematics requires defined variables, consistent relationships and clear parameters. Assumptions are how you bridge the gap between a complicated real-world scenario and a mathematical model that can actually be solved.

This is why assumptions are not weaknesses or errors in your work. They are a necessary and explicit part of mathematical modelling. The key is being honest about what you have assumed and clear about why each assumption is reasonable given the context.

Here's a clearer example of an PSMT assumption for a given model:

Imagine you are building a mathematical model that shows the speed of a runner in metres per second over time. You might choose to represent this using a linear function, a quadratic or another model type depending on what the data suggests.

But here is the thing: models cannot account for everything that affects a runner's speed in real life.

• What about fatigue setting in after the first 200 metres?

• What about a slight headwind slowing them down?

• What about the fact that the track has a gentle incline at one end? What about the runner's footwear, their hydration level or the temperature on the day?

None of these factors are in your equation. So what do you do with them? You assume they do not exist or that their effect is so small it can be ignored. That is an assumption.

You might write it like this:

• "It is assumed that wind resistance and external environmental factors such as temperature and track gradient have a negligible effect on the runner's speed. This allows the relationship between speed and time to be modelled using a single-variable function without accounting for additional forces."

This is what separates a strong assumption from a weak one. You are not just saying "wind doesn't exist." You are saying why you can reasonably ignore it and what that decision allows you to do mathematically. Every assumption in your PSMT works the same way. You are making a deliberate choice to simplify reality so your model can function, and you are being transparent with the marker about exactly what you have simplified and why.

Assumptions vs Observations: The Important Difference

Before writing your assumptions, make sure you understand the difference between an assumption and an observation. Confusing the two is one of the most common mistakes in the PSMT formulate section.

• 🔎 Observations are facts or pieces of information given to you in the task or collected from your data. You did not decide them as they were already there.

• 🧠 Assumptions are decisions you make that you assume to be true. They are conditions you are choosing to accept because it simplifies the model or makes the mathematics workable.

  
  

For a detailed comparison with examples, see Observations vs Assumptions in a Maths Methods PSMT.

What Makes a Good Mathematical Assumption?

Not every statement qualifies as a useful assumption.

Before including something in your list, check it against these three questions:

• Is it my decision, not something already stated in the task?

• Does it actually affect the mathematics, the model or the data I am using?

• Can I justify it using the context, evidence or mathematical reasoning?

If the answer to any of these is no, the statement probably does not belong in your assumptions section.

Types of assumptions that commonly appear in strong PSMTs:

How to Write a Justified Assumption

There are three levels of quality when it comes to writing assumptions. Most students write at Level 1 or 2. Strong responses operate at Level 3.

✅ Low-level assumption: Statement only (not enough)

• "It is assumed that air resistance is negligible."

• This tells the marker what you have assumed but nothing else. It does not explain why the assumption is reasonable or how it affects the model.

✅✅ Mid-level assumption: Statement with explanation (better but incomplete)

• "It is assumed that air resistance is negligible because the object is small and the distances involved are short."

• This adds a reason but still does not connect the assumption to the mathematics.

✅✅✅ High-level assumption: Statement with justification and impact (what the ISMG rewards)

• "It is assumed that air resistance is negligible because the projectile is small, dense and travelling over a relatively short distance, meaning drag forces are minimal compared to gravitational force. This assumption allows the motion to be modelled using standard quadratic equations rather than requiring complex differential equations, which are beyond the scope of this investigation."

• This version tells the marker what you assumed, why it is reasonable given the context and what mathematical consequence the assumption has. That third part is what most students miss.

Weak vs Strong Assumptions: A Comparison Table

Validity and Reliability: Why These Words Matter in Your Methods PSMT

The QCAA ISMG for the PSMT and IA1 specifically looks for evidence that you understand the validity and reliability of your model. Your assumptions are directly connected to both.

• ☑️ Validity refers to whether your model actually measures or represents what it is supposed to. If you assume a linear relationship when the true relationship is exponential, your model may lack validity because it does not accurately reflect the real-world situation.

• ☑️ Reliability refers to whether your model produces consistent results. If you assume your data is representative of the broader population but your sample is small or biased, the reliability of your conclusions may be affected.

Writing strong assumptions that acknowledge their potential impact on validity and reliability is one of the clearest ways to demonstrate high-level thinking in the formulate section.

Where Do Assumptions Appear in Your PSMT Report?

Assumptions are introduced in the Formulate section of your report, typically in a dedicated subsection after your observations. However, they do not stay there.

They appear in two other places as well:

• ✍️ In the solution section: When you make a mathematical decision that depends on an assumption, reference it. For example: "Using Assumption 2, the domain is restricted to x values between 0 and 12, and the model is therefore solved within this range."

• 📝 In the evaluation section: Each significant assumption should be revisited when you evaluate the reasonableness of your model. Ask whether the assumption held true, whether it affected the accuracy of your results and whether relaxing the assumption would change your conclusion. This is where your assumptions become the basis for your limitations. See How to Write Limitations in a Maths Methods PSMT and How to Evaluate a Maths Methods PSMT Model for guidance on this.

  
  

Numbering or labelling your assumptions, for example Assumption 1, Assumption 2, makes it easy to reference them throughout the report without repeating them in full each time.

How Many Assumptions Do You Need?

There is no fixed number required by the QCAA. The right number depends on your task and your model. However, your school teacher is likely to advise you to include around 3-5 justified assumptions in your report. A response that lists ten vague assumptions earns fewer marks than one that identifies three genuinely important assumptions and justifies each one clearly.

As a general guide, most strong PSMTs include between three and six well-justified assumptions. The emphasis should always be on quality and relevance rather than quantity.

✅ A Quick Checklist for Your PSMT Assumptions

Before submitting your PSMT, check each assumption against the following:

☐ Is this my decision, not something stated in the task?

☐ Does this assumption affect the mathematics, the model or the data?

☐ Have I explained why this assumption is reasonable given the context?

☐ Have I explained what mathematical impact this assumption has?

☐ Could this assumption affect the validity or reliability of my model?

☐ Is this assumption numbered or labelled so I can reference it later?

☐ Have I revisited this assumption in the evaluation section?

Common Assumption Mistakes to Avoid

• Describing observations as assumptions: If the task tells you the starting population is 5,000, that is an observation. Writing it as an assumption suggests you have misunderstood the difference. For a clear explanation of how to separate the two, see Observations vs Assumptions in a Maths Methods PSMT.

• Writing assumptions after the fact: Some students complete their solution and then add assumptions to satisfy the criteria without checking whether they actually affect the model. Markers can usually tell. Assumptions should arise naturally from the decisions you made while building your model.

• Including trivial assumptions: Stating that "numbers will be rounded to two decimal places" is only useful if you also explain how rounding at that precision affects the accuracy of your results. On its own it is unlikely to earn marks.

• Not linking assumptions to limitations: If an assumption is worth making, it is worth evaluating. Every significant assumption should appear again in your evaluation section as a discussion of how it affects the model's validity, reliability or real-world applicability. For guidance on writing strong limitations, see How to Write Limitations in a Maths Methods PSMT.

Getting Maths Methods Tutoring Support For Your PSMT

If you are finding it difficult to identify relevant assumptions for your specific task, or if you have received feedback that your justifications are too vague, working through the formulate section with an in-person or online tutor can make a significant difference. Our online Maths Methods tutors work with Year 11 and Year 12 students through every part of the PSMT and can help you connect your assumptions to the specific context and mathematical decisions of your task. Book a free trial lesson to get started.

Frequently Asked Questions

What is an assumption in a Maths Methods PSMT?

An assumption is a condition you choose to accept as true so your mathematical model can function. Unlike an observation, which is a fact given in the task, an assumption is your decision. Every assumption should be justified by explaining why it is reasonable in context and what effect it has on the mathematics or the model.

How many assumptions do I need in my PSMT?

There is no set number. Most strong PSMTs include between three and six well-justified assumptions. Quality and relevance matter far more than quantity. A single assumption that is clearly connected to your model and thoroughly justified earns more marks than five vague statements with no mathematical impact.

What is the difference between an assumption and an observation in a PSMT?

An observation is a fact or piece of data given to you in the task or collected from your research. An assumption is a decision you make to simplify or enable your model. Confusing the two is one of the most common mistakes in the formulate section. See Observations vs Assumptions in a Maths Methods PSMT for a detailed comparison.

How do assumptions connect to the evaluation section?

Every significant assumption you make in the formulate section should be revisited in the evaluation. You should assess whether the assumption held true, whether it affected the accuracy or reliability of your results and whether relaxing the assumption would change your conclusion. Assumptions that are not evaluated represent a missed opportunity to demonstrate critical mathematical thinking.

What does validity and reliability mean in the context of PSMT assumptions?

Validity refers to whether your model accurately represents the real-world situation it is meant to model. Reliability refers to whether your model produces consistent and trustworthy results. Strong assumptions acknowledge how they might affect both. For example, assuming a linear relationship when the true relationship is non-linear reduces validity. Assuming a small or biased sample is representative of a broader population may reduce reliability.

Other related articles:

• What Is a PSMT in QCE Maths Methods?

• Maths Methods PSMT Structure Explained

• How to Write Limitations in a Maths Methods PSMT

• Maths Methods PSMT Common Mistakes

• How to Evaluate a Maths Methods PSMT Model

• Observations vs Assumptions in a Maths Methods PSMT

• How to Refine a Mathematical Model in a PSMT