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IB Mathematics Analysis and Approaches (AA) SL Internal Assessment Exemplar: Exploring the 2D Area of the FIFA World Cup Trophy
Exploring the 2D Area of the FIFA World Cup Trophy
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4
Official IB Result
10/20
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10/20
0
10
20
6.1·Weakness
Page 14• Click to view
The rationale for dividing extra parts into areas A, B, and C needs elaboration; specify why these regions capture all non-model segments.
Criteria A: Presentation
3/4
0
2
4
Criteria Strands
Good
Coherence and logical development
Good
Organization and structure
Moderate
Conciseness and relevance
Criteria Feedback
Clear academic flow with recognizable structure (introduction, methodology, exploration, conclusion).
Use of headings, table of contents and page numbers provides easy navigation.
Coherent logical development where arguments proceed in a cause-and-effect sequence.
Explanations are sometimes verbose and repetitive, affecting conciseness.
Sections of historical background and repeated R² definitions are not directly relevant.
Inconsistent page numbering in contents (e.g., bibliography).
1.1·Suggestion
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The research question is clear but could specify the quantitative metric (e.g. 2D area ratio) to sharpen the focus on material use efficiency.
1.2·Strength
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The title and research question are articulated clearly, establishing a focused investigation into material use efficiency. This strong framing guides the reader on the study’s intent from the outset.
1.3·Weakness
Page 2• Click to view
The table of contents shows a mismatch in page numbering for the bibliography entry (listed as Page 2). Ensure consistency to aid navigation.
1.4·Weakness
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The introductory background on viewership statistics, while interesting, is not directly relevant to the mathematical modeling and could be condensed.
1.5·Weakness
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Bibliography entries vary in formatting style and lack consistent indentation; apply a standard citation format for professionalism.
Criteria B: Mathematical Communication
2/4
0
2
4
Criteria Strands
Moderate
Mathematical language and notation
Good
Multiple representations
Moderate
Logical structure and clarity
Criteria Feedback
Effective use of multiple representations (tables, diagrams, coloured overlays) to support understanding.
Detailed integration steps are clearly laid out in a logical sequence.
Precise rounding of regression outcomes to four decimal places enhances clarity.
Mathematical notation is inconsistent: units missing or superscripts misplaced.
Some long derivations contain transcription mistakes and missing final numeric evaluations.
Inline notation for function domains is dense and could be better formatted.
2.1·Strength
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Figure 2 provides an effective visual preview of expected functions, aiding clarity through a multiple-representation approach.
2.2·Suggestion
Page 5• Click to view
The inline notation for function domains is dense and could be reformatted into a clear table or separate lines for improved mathematical communication.
2.3·Strength
Page 8• Click to view
The list of regression outcomes is meticulously rounded to 4 dp, promoting precision and clarity in the presentation of functions.
2.4·Strength
Page 9• Click to view
Figures 5 and 6 showcase model applications of quartic and linear functions effectively, supporting the logical structure of the exploration.
2.5·Suggestion
Page 9• Click to view
Image axes and scales are not always annotated; include axis labels for clarity in your GeoGebra model screenshots.
2.6·Weakness
Page 12• Click to view
The final numeric evaluation of the integral is omitted; include the computed value immediately after the antiderivative to complete the derivation.
2.7·Strength
Page 12• Click to view
The detailed integration steps are presented clearly, enhancing mathematical communication through a logical sequence of expressions.
2.8·Weakness
Page 17• Click to view
Model height is reported in cm² rather than cm; correct units to maintain mathematical communication integrity.
Criteria C: Personal Engagement
2/3
0
2
3
Criteria Strands
Good
Independent thinking
Good
Personal approach
Good
Creativity and initiative
Criteria Feedback
Strong personal connection to the topic through the student’s interest in football.
Evidence of independent thinking in designing a unique point-by-point modelling approach.
Use of R² diagnostics and manual area corrections shows initiative beyond minimal requirements.
Creativity is somewhat repetitive, relying on similar regression techniques without a fundamentally novel strategy.
Personal approach is clear but does not push boundaries with innovative methodology.
Opportunities for further personal insight (e.g. alternate modelling techniques) are not fully explored.
3.1·Strength
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The student’s personal connection and passion for football are convincingly linked to the choice of topic, demonstrating genuine engagement.
Criteria D: Reflection
1/3
0
2
3
Criteria Strands
Good
Depth of reflection
Poor
Critical analysis
Poor
Evaluation of outcomes
Criteria Feedback
Includes some reflection on future 3D modelling, showing awareness of methodological limitations.
Reflection is intermittent and largely descriptive rather than critically analytical.
Discussion of negative R² and error propagation is absent, limiting depth of analysis.
Evaluation of outcomes is brief, without quantified error analysis or concrete improvement plans.
4.1·Weakness
Page 18• Click to view
The conclusion’s interpretation of the radius efficiency ratio could be clarified; a value <1 indicates more efficient material use, not less.
4.2·Strength
Page 20• Click to view
Reflection on future 3D modeling shows thoughtful evaluation, indicating an awareness of methodological limitations and possible improvements.
Criteria E: Use of Mathematics
2/6
0
3
6
Criteria Strands
Moderate
Relevance of mathematics
Moderate
Level appropriateness
Poor
Understanding and accuracy
Criteria Feedback
Relevant SL mathematics used (integration, quartic regression, scale factors) directly addresses the research question.
Procedural steps such as sum of integrals and area decompositions are carried out correctly in many parts.
Awareness of regression diagnostics (R² calculations) demonstrates appropriate use of mathematical tools.
Conceptual misunderstandings: negative R² and unit inconsistencies weaken accuracy.
Arithmetic errors in area subtraction and boundary interval continuity issues are present.
GeoGebra methodology lacks sufficient detail on coordinate scaling and axis setup.
5.1·Weakness
Page 4• Click to view
The description of GeoGebra usage lacks specific details on coordinate scaling and axis setup; include these to enhance reproducibility.
5.2·Strength
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The methodology section effectively situates your approach in the context of existing research, demonstrating a strong literature linkage.
5.3·Suggestion
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Point‐density concerns are noted, but a brief discussion on the trade-off between point number and regression accuracy would strengthen the modeling rationale.
5.4·Strength
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The assumption of quartic and linear forms for the contour functions is clearly stated, reflecting thoughtful classification of model segments.
5.5·Weakness
Page 7• Click to view
The standard quartic and linear function forms are given, but a justification for choosing quartic over lower-degree polynomials is missing.
5.6·Suggestion
Page 8• Click to view
There is no commentary on the negative leading coefficients or their impact on curve shape; interpret these signs to deepen mathematical understanding.
5.7·Weakness
Page 10• Click to view
The choice of intervals for each function is documented clearly, but overlapping or small gaps could affect the enclosed area; verify boundary continuity.
5.8·Strength
Page 11• Click to view
Including the R² calculations demonstrates awareness of regression diagnostics and reflects appropriate use of mathematics to gauge model accuracy.
5.9·Suggestion
Page 11• Click to view
Negative R² results are calculated but not interpreted; discuss why RSS>TSS produces negative values and its implication for curve fit.
5.10·Strength
Page 14• Click to view
Sum of integrals is computed correctly, leading to a total area including extra parts, which shows strong procedural accuracy.
5.11·Weakness
Page 15• Click to view
There is an arithmetic inconsistency in Area A: the triangle1 area is listed as 9 cm² without explanation, and the total sum formula is incorrect.
5.12·Strength
Page 17• Click to view
Area C decomposition with triangles and rectangle is consistently applied, reinforcing systematic problem-solving approach.
Mathematics Analysis and Approaches (AA) IA Exemplar: FIFA World Cup… | RevisionDojo
