IB Mathematics Analysis and Approaches (AA) SL Internal Assessment Example

The aim is stated clearly and gives the exploration a focused direction. This works well because the reader immediately understands what is being investigated and what relationship the student intends to model.

The sectioning is clear and easy to follow. Starting with rules before moving into the investigation creates a logical progression that helps the reader understand the game context before the mathematics begins.

The table is effective because it places the round number, expected value, banker offer, and decision in one place. This supports readability and makes the progression of the game easy to track without searching through the prose.

The discussion of the graph is interrupted across pages, which makes the development feel slightly disjointed. The student should make sure each graph is followed immediately by a complete interpretation so that the argument does not appear to pause mid-thought.

The permutation section takes up a relatively large amount of space for a point that could be made more briefly. The student could reduce repetition here by stating the direct probability method and keeping only the essential working, which would improve conciseness.

The banker-rule summary is helpful, but the student could make the section more concise by integrating the rules into the analysis rather than presenting them separately if they are only used once. That would keep the focus on the investigation itself.

Introducing a clearly labeled round structure helps the investigation feel organized and intentional. This is effective presentation because the reader can immediately see where the simulation evidence for each round begins.

The lower-bound calculation is presented clearly, but the working is not fully aligned with the regression equation shown earlier. The student should keep the same model form throughout so the reader can verify that the bound is being calculated from the correct line.

The explanation here would be clearer if the final numerical statement matched the value being discussed. The student should check that the written interpretation and the computed upper bound are consistent, because that helps prevent confusion in the final argument.

The final results and conclusion section gives the exploration a clear endpoint. Ending with a dedicated conclusion helps the reader see that the investigation has been completed and the main claim has been addressed.

The evaluation section would be even stronger if the student used a consistent substructure for strengths and limitations. That would make the final pages easier to scan and would present the evaluation more like a deliberate analysis rather than a list of points.

The notation here is not fully accurate: expected value should be written as a sum such as $E(X)=\sum xP(x)$ rather than $\Sigma \ast P(x)$. The student should use standard mathematical notation consistently so the meaning is immediately clear.

The student correctly writes out the full expected value calculation using the prize distribution. This is strong mathematical communication because it shows the structure of the calculation and makes the result traceable.

The table uses multiple variables in a compact but readable way, and the column labels make the simulation process understandable. This supports the argument because the reader can connect the expected value, offer, and decision for each round.

The permutation notation is introduced clearly, but the communication would be stronger if the student distinguished more carefully between counting arrangements and finding probability. The current wording risks making the two ideas seem interchangeable, which can confuse the mathematical argument.

The scatterplot and displayed $R^2$ value are effective representations because they allow the reader to see the strength of the linear relationship visually and numerically. This is a strong example of combining graph and statistic to communicate a result clearly.

The regression equation is communicated well, but the student should keep variable notation consistent. Using the same symbol form throughout, rather than switching between uppercase and lowercase variables, will reduce ambiguity for the reader.

The bound calculation is not communicated with enough mathematical clarity because the full regression model is not retained in the substitution step. The student should show the actual function being evaluated so the reader can see exactly how the bound was obtained.

The equation is readable, but the variable formatting is inconsistent with earlier sections. The student should keep the same notation for the independent variable and the same algebraic style across rounds so the communication feels disciplined and professional.

Including the calculator output is a useful communication choice because it helps verify the regression result independently. This adds transparency and shows the student is checking the mathematics rather than relying on an unshown calculation.

The phrase ‘high statistical significance’ is not communicated precisely. If the student means the line fits well, that should be stated directly; if statistical significance is intended, the relevant test or p-value must be identified.

The student’s personal motivation is clear and relevant here: linking the investigation to weekly personal training gives the topic an authentic context. This works well because it explains why the show matters to the student, rather than presenting the choice as arbitrary.

The student shows independent mathematical initiative by framing the game as a problem of dependent events. That choice is more sophisticated than a purely formulaic approach and shows the student is actively interpreting the structure of the game, not just applying procedures.

The permutation argument for Eva’s situation is not the most appropriate model for the claim being made. If the aim is to find the chance of ending with the $400,000 box, the student should use a direct probability argument based on the remaining boxes rather than counting permutations, which obscures the reasoning.

The modelling becomes more distinctive when the student moves from raw simulation data to regression-based bounds. To strengthen the personal approach further, the student could briefly explain why this modelling choice was preferred over other possible approaches, such as using average offers only or comparing medians by round.

The student’s round-by-round simulation work shows clear initiative: generating data, plotting it, and extracting a trend line gives the exploration a self-directed modelling direction. This is effective personal engagement because the mathematics is being used to build a model, not just to reproduce known results.

The limitations section is a good start, but the student could push the personal engagement further by explaining how the simulation design could be improved in a way that reflects their own modelling priorities. For example, why was 25 simulations chosen, and how might a larger or more targeted sample change the conclusions?

The simulation table is relevant and well chosen because it captures the relationship the student is trying to model: expected value, banker offer, percentage of EV, and the player’s decision. That is exactly the kind of data needed for the research aim.

The student uses the expected value result to make a meaningful claim about the game, which shows the mathematics is being applied to the investigation rather than left as a standalone calculation. This is a strong connection between method and purpose.

The mathematical tool chosen here is not the most efficient one for the question being asked. Since the student wants the chance of ending with a particular box, a direct probability approach would be clearer and more relevant than a full permutation count.

The regression equation itself is appropriate for SL level work and is used in a relevant way to model the banker’s offer. This shows the student is applying course-level mathematics to a genuine modelling problem.

The substitution step appears to omit the intercept from the regression equation shown earlier. The student should check that the full model is used in the calculation, because omitting the constant term changes the predicted banker offer.

The numerical result here appears inconsistent with the previous expression and with the written interpretation. The student should recheck the arithmetic carefully, because accuracy in the bounds is essential to the credibility of the model.

The round 2 lower-bound calculation should be checked against the regression model because the output depends entirely on accurate substitution. Small arithmetic slips here have a large effect on the model’s final predictions.

The final results table is useful, but the student could strengthen the mathematics further by adding one sentence explaining how each % of EV was obtained from the corresponding regression model. That would make the table easier to audit mathematically.