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

The title is descriptive but somewhat verbose; consider streamlining it to improve clarity and conciseness while retaining key terms.

The table of contents is comprehensive but could be condensed by grouping similar sections to improve overall organization and reader navigation.

The aim effectively frames the mathematical modeling objective and links it to real-world decision making, providing clear direction for the exploration.

Variable formatting (e.g. boldface $v$, $I$) is inconsistent; adopt a single style for all symbols to improve readability.

The heading “Wrong” appears to be a typo in place of “Front”; correct this label to maintain professional presentation.

The conclusions on page 16 repeat earlier observations; consider consolidating to maintain conciseness and avoid redundancy.

The equation containing symbol “β” is unclear and appears incorrect; replace with an explicit relationship in familiar mathematical notation.

References display varied formats for authors and dates; adopt a consistent citation style (e.g. APA or MLA) throughout the list.

The rationale relies heavily on a popular anecdote but lacks deeper physical justification; expand on the mechanics of rain impact and time trade-off to enrich the context.

The travel time formula uses “n” instead of the defined velocity variable “v”; this inconsistency can cause confusion, so align notation throughout.

The conversion of 3.5 mm/h to m/s is clearly shown. To further enhance precision, include units at each step of the calculation.

In the W_front formula, the intensity symbol changes between $I$ and $\rho$; unify notation and specify units to avoid ambiguity.

The expression for W_front introduces $x$ instead of the velocity $v$, breaking notational consistency; align variable names.

Graph 6 is effective but lacks labeled axes and units; adding clear axis titles will greatly enhance interpretability.

Notation “W_{\text{rong}}” appears in the heading, likely intended as “W_{\text{front}}”; standardize labels to avoid misinterpretation.

The insight that a specific speed can avoid both front and back rain entirely is excellent and shows deep understanding of the model’s implications.

Graph 15 would benefit from a legend distinguishing $W_{top},W_{front},$ and $W_{back}$; this will help the reader follow multi-component comparisons.

The choice of rainfall velocity and intensity is grounded in literature and demonstrates initiative in realistic parameter selection.

The exploration draws strong interdisciplinary connections to physics and geography, reflecting genuine personal engagement and broader impact.

The evaluation that W_front contributes minimally under certain conditions demonstrates critical appreciation of each component’s influence on total exposure.

The suggested extensions are thoughtful; prioritizing them or indicating expected impact would enhance the critical evaluation and planning.

Modeling the person as a cuboid is a sound simplification that is later acknowledged in the evaluation, demonstrating thoughtful abstraction in the mathematical model.

The initial form of the W_top equation omits the travel time factor; integrate the $d/v$ term from the start to maintain coherence in the derivation.

The arithmetic simplification to 0.0972 g appears inconsistent with earlier factors; re-calculate the numeric coefficient carefully.

The derivation of the 1000 m world record speed uses an unclear sum for time; provide the precise competition time rather than $60+60+11$ s.

The derivative $\frac{d{w}_{total}}{dv}$ contains sign and factor mistakes; revisit each differentiation step to ensure mathematical correctness.

The claim that the top‐rain correlation remains unchanged at $\theta =45^{\circ }$ would benefit from an algebraic justification rather than a numerical observation.

The derivative in Equation 5 includes both $\sin \theta$ and $\cos \theta$ incorrectly; re-derive to confirm which function is appropriate.

The derivative of W_front in Equation 2 should account for the product with the velocity term; explicitly expand before differentiating for full accuracy.

The third scenario discussion lacks a supporting plot for W_top at $\theta =135^{\circ }$; include the corresponding graph for completeness.

Identifying the velocity threshold where $ucos\theta +v=0$ yields a critical insight into avoiding frontal rain; this is a strong mathematical observation.

Incorporation of W_back rounds out the model effectively by recognizing rearward rain impact, enhancing the comprehensiveness of the study.