IB Mathematics Analysis and Approaches (AA) SL Internal Assessment Exemplar: How to find the optimal mousepad size based on the DPI and sensitivity settings maximizing the comfort and efficiency in the gameplay

The exploration has a clear research objective and immediately states what is being investigated. This helps the reader understand the purpose from the outset and gives the later modelling a focused direction.

The equation is written ambiguously as $$\text{Distance}=k/D\ast C$$. As written, this can be read as multiplying by $$C$$ rather than dividing by it. The student should use clear parentheses and keep the dependence on sensitivity mathematically consistent, for example $$\text{Distance}=\frac{k}{DC}$$ if that is the intended model.

The variable table is a strong organizational choice because it defines the symbols before they are used in equations. This makes the later mathematical reasoning easier to follow and reduces ambiguity.

This table compresses several variables and values into a single line, which makes the progression of the data difficult to read. The student should separate the columns more clearly so that DPI, sensitivity, distance, angle, and mousepad size can be compared without confusion.

The second method interrupts the coherence of the exploration because the linear regression is introduced without a clear justification for why it is preferable to the inverse model established earlier. The student should explain the purpose of this comparison and how it relates to the original relationship before presenting the calculator output.

The evaluation section would be stronger if the student explicitly linked each implication to the model’s output, such as translating a chosen DPI/sensitivity combination into a concrete mousepad recommendation. That would make the conclusions feel more developed and less general.

The definitions of $$D$$, $$C$$, and the movement distance are helpful because they establish a shared vocabulary for the mathematics. This is good communication practice and supports later formula use.

The raw-data table is hard to interpret because the headings and values run together. The student should format the table so each trial, mean value, and mousepad category is clearly separated; otherwise the calculations are difficult to verify.

The calculation shown here is ambiguous because the multiplication and division are not grouped clearly. The student should write it with parentheses, such as $$\frac{13080}{800\cdot 0.5}=32.7$$, to avoid misreading the result.

The mean calculation is not written in standard mathematical form. The student should show the operation as $$\frac{32.7+32.7+32.7}{3}=32.7$$ so the order of operations is explicit and the work is easier to check.

The regression equation is rounded too early and should ideally retain the calculator’s coefficients if it is going to be used for analysis. Rounding to $$y=-0.01x+36.75$$ can hide the actual fitted relationship and makes later comparisons less precise.

The graph should be interpreted carefully because the plotted linear model does not match the inverse relationship established earlier. The student should explain what the axes represent and why a linear fit is mathematically appropriate before relying on this representation.

The rationale is personally grounded in the student’s own gaming experience, which gives the exploration a genuine purpose. This personal context supports engagement because the mathematical question arises from a real decision the student wants to make.

The student shows initiative by designing and carrying out their own experiment with specific DPI values and a controlled testing setup. This is stronger than using pre-made data because it demonstrates ownership of the investigation.

The personal angle could be made more distinctive by comparing how the recommendation changes for different play styles or comfort preferences. That would turn the exploration into a more individual mathematical investigation rather than a single one-size-fits-all calculation.

Trying an alternative calculator-based method shows curiosity and a willingness to test a second approach. Even though the modelling could be better justified, the attempt itself shows independent effort beyond the first solution path.

The conclusion that the equation is proven is too strong for the evidence shown. The student should reflect on whether one matched example is sufficient, or whether more trials and a comparison with alternative models are needed before claiming the theory is verified.

The evaluation is quite broad and does not critically assess the model choice. A stronger reflection would compare the inverse model and the linear regression, then explain which is more defensible and why.

The limitations section identifies measurement accuracy, but it stays general. The student should explain how those limitations affect the results numerically or conceptually, for example by discussing possible error margins in the measured distances.

The summary would be stronger if it ended with a forward-looking statement about what would be improved next, such as collecting more DPI values or testing additional players. This would show that the student has considered how the investigation could be extended mathematically.

Determining $$k=13080$$ from the data shows effective use of the inverse model and gives the exploration a clear algebraic result. This is a central mathematical achievement because it turns measurements into a usable formula.

The student successfully extends the model to include sensitivity, which makes the mathematics more relevant to the real gaming context. This shows the formula is not just abstract but tied to the variables the investigation set out to study.

The worked example is mathematically inconsistent with the formula as written. If the model is $$\frac{13080}{D\cdot C}$$, the calculation should be shown exactly that way; otherwise the result may be interpreted incorrectly.

The later claim that a 32.7 cm movement means a Large mousepad is suitable is under-justified. The student should define the size boundaries used for each mousepad category, otherwise the conclusion is not mathematically supported.

The calculator regression is not well matched to the original inverse relationship, so the mathematical method is not fully appropriate. The student should justify why a linear regression is being used and explain what information it adds beyond the inverse model.

The graph-based analysis would be more convincing if the student included a brief comparison of predicted versus observed values. A simple residual-style discussion would help show whether the model actually fits the data well.