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IB Mathematics Analysis and Approaches (AA) SL Internal Assessment Exemplar: Predicting future Olympic 100m sprint records: A comparative analysis of linear regression, cubic functions and exponential models based on historical Olympic data.
Predicting future Olympic 100m sprint records: A comparative analysis of linear regression, cubic functions and exponential models based on historical Olympic data.
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5
Official IB Result
13/20
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Criteria A: Presentation
3/4
0
2
4
Criteria Strands
Good
Coherence and logical development
Good
Organization and structure
Good
Conciseness and relevance
Criteria Feedback
Clear sequence and logical development (introduction, modelling, comparison, evaluation, conclusion).
Well‐organized with headings, numbered tables/figures and a recognizable structure.
Majority of content is relevant and supports the research question.
Occasional grammatical slips and digressions interrupt polish.
Some captions are vague and figure referencing is inconsistent.
Minor repetition and tangential historical material reduce conciseness.
1.1·Suggestion
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The title slide effectively states the subject but could be more specific by including the research question, immediately orienting the reader to the investigation’s focus.
1.2·Suggestion
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The abstract is comprehensive but repeats background details. Consider tightening this section to focus strictly on the scope, variables, and intended models for prediction.
1.3·Suggestion
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Model justifications are clear, but the paragraph mixes historical context and technical reasoning. Separate background from model selection to improve logical flow.
1.4·Weakness
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The introduction includes a lengthy history of the modern Games from 1896 and mention of women’s events, which distracts from the research focus. Trim to maintain relevance.
1.5·Weakness
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Table 1 lacks units in the header row and appears misaligned. Label columns with “Year (YYYY)” and “Time (s)” consistently for clarity.
1.6·Suggestion
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The summary table of model comparisons is informative but has uneven column widths and minimal spacing. Reformat for readability and ensure headings stand out.
1.7·Weakness
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Punctuation and sentence structure in the evaluation section are uneven (e.g., fragmented sentence after a period). Proofread to improve coherence and flow.
1.8·Suggestion
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Reference entries use mixed citation formats (APA and URLs inline). Adopt a consistent style (e.g., APA) and format all web sources uniformly.
Criteria B: Mathematical Communication
3/4
0
2
4
Criteria Strands
Good
Mathematical language and notation
Good
Multiple representations
Good
Logical structure and clarity
Criteria Feedback
Mostly consistent use of correct notation (e.g. regression equations, R²).
Effective use of tables, scatter plots, fitted curves and residual plots to compare models.
Good logical flow from graphs to equations to residual analysis.
Inconsistent variable naming (switching between y, v, γ) and some empty equation blocks.
Missing labels and captions (axes unlabeled or small, one residual table misaligned).
Occasional formatting errors and redundant narrative blur clarity.
2.1·Suggestion
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The description of R² as “closest to 1” could be more precise by discussing how it quantifies explained variance and its limitations in non-linear contexts.
2.2·Weakness
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Figure 1’s axes lack units and have small labels, making it hard to interpret scale. Increase font size and include “Time (s)” and “Year (YYYY)” on the axes.
2.3·Suggestion
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The text refers to time as γ, an uncommon symbol here. Stick to y (time) and x (year) consistently to avoid confusion in mathematical communication.
2.4·Suggestion
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The linear regression equation is given without defining the intercept and slope in context. Include brief definitions (e.g. slope as rate of change in seconds per year).
2.5·Weakness
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Table 5 lists only the header for ŷ but lacks an accompanying description. Provide a caption or footnote clarifying that ŷ represents the predicted time from the regression model.
2.6·Weakness
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An empty equation block precedes the definition of e. Remove placeholders or ensure each equation environment contains content to avoid reader confusion.
2.7·Suggestion
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The text mentions a residual graph but fails to label axes or reference figure numbers. Ensure each graph is explicitly cited and fully labeled in the body of the text.
2.8·Weakness
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The exponential model uses v instead of y for time, breaking earlier notation. Standardize variable names across all models for consistency.
2.9·Suggestion
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Figure 7’s caption is generic. Highlight key residual features or anomalies to guide the reader’s interpretation, rather than restating the figure’s title.
Criteria C: Personal Engagement
2/3
0
2
3
Criteria Strands
Good
Independent thinking
Good
Personal approach
Good
Creativity and initiative
Criteria Feedback
Significant independent thinking in selecting and comparing three distinct models.
Personal interest in sprinting topic evident in commentary and model choices.
Demonstration of initiative in computing and interpreting residual statistics.
Approach relies on standard syllabus methods and software outputs rather than novel mathematical techniques.
Limited extension beyond basic model comparison (no multivariate or deeper statistical exploration).
Creativity and initiative are moderate rather than exceptional.
Criteria D: Reflection
2/3
0
2
3
Criteria Strands
Good
Depth of reflection
Good
Critical analysis
Good
Evaluation of outcomes
Criteria Feedback
Meaningful reflection on model suitability, biological limits, and residual signs.
Thoughtful comparison of R² values and discussion of over/underestimation patterns.
Clear evaluation identifying the best model and suggesting additional variables for future work.
Reflection is mostly descriptive rather than deeply critical.
Lacks citation of specific residual examples and parameter uncertainty.
Limited exploration of practical implications and deeper statistical justification.
3.1·Suggestion
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The statement that software was used to find R² lacks detail. Reflect on the choice of tool, its settings, and any checks performed to ensure correct implementation.
3.2·Suggestion
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Interpreting the mean residual of –0.057 s as a slight overestimate is correct but should be linked to model selection in the conclusion for a stronger evaluative reflection.
3.3·Weakness
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The residual discussion refers generally to patterns but lacks citation of specific years or residual values. Quote examples to support analysis and deepen reflection.
3.4·Weakness
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The evaluation paragraph acknowledges limitations but could expand on how residual analysis influenced model preference, deepening critical reflection on outcomes.
Mathematics is commensurate with SL course level and applied correctly.
Good understanding is demonstrated with mostly correct calculations and conceptual explanations.
Minor numerical inaccuracies (e.g. mis-typed predictions, inconsistent residual signs).
Omission of some calculation steps and lack of explanation for coefficient derivation.
No extension beyond SL level or deeper discussion of over-fitting and model complexity.
4.1·Suggestion
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Interpreting R² solely as “accounts for 82.6% of variation” omits discussion of residual patterns and potential bias. Acknowledge that a high R² does not guarantee model adequacy.
4.2·Suggestion
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The cubic function coefficients appear without explanation of how they were derived. Summarize the fitting method or software output to demonstrate understanding of the process.
4.3·Suggestion
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The cubic model’s prediction process is shown but omits the computed value in the first block. Include the intermediate f(x) expression to demonstrate each calculation step.
4.4·Question
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Stating R² = 0.895 implies a good fit but omits discussion of potential over-fitting due to the cubic’s flexibility. Reflect on the balance between fit quality and model complexity.
4.5·Suggestion
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The description of the exponential equation omits units on the exponent’s x-term. Clarify that x is measured in years and discuss any transformations applied.
4.6·Weakness
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The conclusion erroneously mentions predictions for 2080 rather than 2028, conflicting with earlier calculations. Verify dates to maintain accuracy.
Mathematics Analysis and Approaches (AA) IA Exemplar: Olympic 100m… | RevisionDojo
