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

The introduction is overly verbose and contains digressions. Consider streamlining by focusing on key motivations and removing repetitive phrases to enhance clarity and conciseness.

Including full Logger Pro data tables in the main text pads the discussion. Move extensive raw data to the appendix and summarize key values in the body.

Label “Optimization” clearly signals a new stage of the investigation. This structure enhances reader navigation.

References and bibliography are formatted consistently and include pertinent sources, demonstrating good research practice.

In the variables table, $s\_y$ and $s\_x$ definitions are swapped. Ensure $s\_x$ is horizontal displacement and $s\_y$ is vertical displacement.

Notation $V\_\{\backslash gamma\}$ is used instead of $V\_x$. Adopting consistent symbols throughout will avoid confusion in component decomposition.

Lines of gibberish ($\backslash mathcal\{L\}$) appear in the derivation. Remove placeholders and ensure all displayed math is accurate and meaningful.

Phrase “very no variation” in explaining $r^2$ is unclear. Revise to more precise language when describing the coefficient of determination.

Caption for Figure 6 refers to $V\_\{\backslash chi\}$ instead of $V\_x$. Correct notation in captions to maintain mathematical consistency.

Personal interest in basketball is evident, but deeper reflection on how the project influenced your understanding could strengthen personal engagement.

The assumption that air resistance is negligible is stated without discussing its quantitative effect. Reflect more deeply on how drag would alter the trajectory and optimal angle.

Acknowledging loss of precision from rounding to three decimals shows good consideration of error sources.

The unexpected high $V\_y$ value for trial 4 (5.804 m/s) is a clear outlier. Discuss why this anomaly occurred or consider excluding it when averaging.

Averaging $V\_0$ across all trials without addressing the outlier inflates the mean. Consider robust statistics (e.g., median) or justify inclusion.

Choosing the larger root (53.503°) for the optimal angle requires justification. Discuss physical reasoning for preferring the higher-angle solution.

Comparison of model and experimental angles acknowledges a 4.7° discrepancy and links back to initial assumptions, demonstrating thoughtful critical analysis.

Acknowledge how iterative model refinement (e.g., adding drag) could extend the exploration, offering avenues for further investigation.

Conclusion effectively restates the aim and findings, linking to literature value (52°). Consider adding implications for training practice or further research.

The description ‘horizontal component represents how fast the ball moves upward’ is incorrect. Revise to state the horizontal component governs lateral motion.

The integration of gravity term omits a clear discussion of the constant of integration and sign conventions. Clarify how $c$ corresponds to $h\_0$.

The clear derivation $t\; =\; \backslash frac\{s\_x\}\{V\_0\backslash cos\backslash theta\}$ demonstrates correct mathematical thinking in isolating time for substitution.

Substitution in the optimization equation uses $s\_x=3$ despite earlier stating basket is 2 m away. Check consistency of parameter values.

Tabulated optimal angles and their average are clearly presented, reflecting good use of statistics to summarize results.