IB Mathematics Applications & Interpretation (AI) SL Internal Assessment Example

A clear contents page helps the reader navigate the exploration efficiently. This is a strong structural choice because it signals the main stages of the investigation and makes the progression from introduction to conclusion easier to follow.

The overall aim is interesting, but it shifts between “which football club to support” and later “where a new club should be built.” The student should make the research question more precise and keep the same purpose throughout, otherwise the logical development becomes difficult to evaluate.

The choice of seven relevant stadiums gives the exploration a clear mathematical focus and avoids unnecessary distraction. This works well because it defines a manageable set of sites for the Voronoi model and keeps the investigation tied to the stated aim.

This explanation is difficult to follow and relies heavily on an image rather than a clear method. The student should briefly state the criteria used to choose the map extent and zoom level, so the reader can see why this specific view was mathematically suitable.

Consider summarising the repeated construction steps in a compact table or a brief pattern description. That would preserve the mathematical content while making the section more concise and easier for the reader to scan.

This section is relevant, but it becomes long and partly repetitive. The student should tighten the explanation by keeping only the key interpretive points needed for the conclusion, especially where the text restates what the diagram already shows.

The notation and wording here are not precise enough for mathematical communication. The student should define the term more accurately and use consistent grammar, because unclear definitions weaken confidence in the rest of the explanation.

The student uses appropriate mathematical language such as “sites,” “cells,” “edges,” and “vertices,” which helps connect the real-world context to the Voronoi model. This terminology is essential because it shows the student understands the structure of the construction.

This step introduces the process, but the actual formula is not visible in the transcription and the explanation is incomplete. The student should state the exact formula being used and define each variable so the algebra can be followed unambiguously.

The notation here is inconsistent: the equation and domain restriction are merged in a way that makes the boundary difficult to read. The student should separate the line equation from its domain, since clear notation is essential when multiple edges are being compared.

The student communicates the perpendicular bisector in an explicit equation, which is exactly the kind of notation needed in a coordinate-geometry investigation. Writing the boundary algebraically makes the link between the diagram and the mathematics clear.

A final summary table listing each edge, equation, and restricted domain would improve clarity. It would let the reader see the full Voronoi construction in one place and reduce the need to search across several screenshots.

What assumptions are being made here about what matters most to a new supporter: geography, family ties, team success, or travel convenience? Clarifying that value judgement would make the personal motivation more meaningful and the modelling choices more defensible.

The investigation has a clear personal origin, which gives it authenticity and direction. This is strong personal engagement because the student is not selecting a context at random; the question grows out of a real situation that motivated the modelling.

The student makes independent modelling choices by selecting a specific set of clubs and building a framework around them. This shows initiative because the investigation is not just reproducing a standard textbook example; it is adapted to a personally relevant context.

Extending the investigation to the largest-empty-circle property is a creative step. This adds depth beyond the basic Voronoi construction and shows that the student is trying to extract additional meaning from the model.

This is a promising attempt at validation, but it is too informal to support a mathematical conclusion. The student should define how many people were asked, what exactly was recorded, and how the responses were compared to the diagram if this is to count as evidence.

The student shows genuine reflection by identifying a key limitation of the model: Euclidean distance is not the same as real travel distance. This is an important insight because it shows awareness that the mathematics has boundaries in the real world.

This is a crucial point for reflection because the scale factor is used incorrectly later on. The student should revisit this conversion and check whether graph units should be multiplied or divided by the ratio, since the validity of the final radius values depends on it.

The student notes uncertainty, but the reflection is too brief to test the impact of that uncertainty. A stronger response would estimate how this rounding difference affects the final choice and explain whether the conclusion would still hold if the values were recalculated more carefully.

The student does not stop at calculation; they reflect on how close the top two candidates are and what that means for certainty. That kind of comparison is valuable because it moves the work beyond a single numerical answer and towards interpretation.

Consider turning this visual comparison into a clear decision rule. For example, the student could explain what counts as “more population” or “better access” and then apply the same rule to both candidate locations so the conclusion is evidence-based.

The student is attempting to connect the coordinate model to real-world distance, which is essential in a modelling exploration. This shows the mathematics is being used for a real interpretation rather than remaining purely symbolic.

This is a strong conceptual statement because it explains how the geometry of bisectors becomes the actual Voronoi boundary. The student is using the mathematics in a structurally relevant way, not just calculating isolated lines.

The error estimate is not justified, and the units are not handled carefully. The student should explain how this error was derived and keep graph units separate from kilometres, otherwise the uncertainty claim is not mathematically reliable.

This rounded value is incorrect because it does not match the preceding calculation. The student should check the arithmetic before rounding, since even a small transcription of the wrong digit changes the interpretation of the result.

The scale conversion is applied in the wrong direction. Since the graph distance corresponds to $2.838$ graph units per kilometre, the graph radius should be divided by this factor to obtain kilometres, not multiplied by it. This affects all later real-world radius and area values.

How was the population-density comparison actually measured? If the student cannot quantify the difference, then it may be better treated as a qualitative observation rather than evidence strong enough to choose between the two sites.