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Mathematics Analysis and Approaches (AA) Extended Essay Exemplar:… | RevisionDojo
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IB Mathematics Analysis and Approaches (AA) SL Extended Essay Example
How good are mathematical methods like counting and combinatorics at
evaluating the efficiency and ergonomics of two of the most popular methods for solving the
Rubik's Cube?SL
B
Official IB Result
25/34
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Criteria A: Focus and Method
5/6
0
3
6
Criteria Strands
A.1Topic communication and explanation
Excellent
A.2Research question clarity and focus
Excellent
A.3Research methodology
Good
Criteria Feedback
The research question is explicitly stated, narrowly focused, and remains central throughout the investigation.
Topic communication is accurate and effective with clear sign-posting and alignment to the stated purpose.
Methodology lacks justification for choice of statistical measures (e.g., geometric mean) and sample-size decisions.
Minor digressions (extended historical narrative) slightly dilute the core focus; trimming non-essential context would sharpen the approach.
1.1·Strength
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The research question is explicitly stated and narrowly focused, providing a strong foundation for the investigation’s purpose and maintaining clear alignment throughout the essay.
1.2·Weakness
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The split line ending with “How” disrupts reader flow. Ensure the research question is presented intact on one line for clarity.
1.3·Suggestion
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The introduction establishes historical context effectively, but the connection to the research question could be made more explicit to reinforce focus from the outset.
1.4·Suggestion
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The historical narrative is engaging; however, trimming non-essential details will sharpen focus on the comparative analysis of CFOP and ZZ.
1.5·Suggestion
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The methodology paragraph outlines combined literature review and original data collection, but lacks justification for using geometric mean and sample size choices.
Criteria B: Knowledge and Understanding
5/6
0
3
6
Criteria Strands
B.1Subject knowledge application
Excellent
B.2Use of terminology and concepts
Excellent
Criteria Feedback
Consistently accurate application of mathematical concepts (permutations, orientations, parity) to the research context.
Terminology and notation (e.g., EOLine, ZBLL, geometric mean) are applied accurately and supported by LaTeX formulae.
Occasional informal phrasing (e.g., “superhuman speeds”) and minor computational slips interrupt the otherwise rigorous presentation.
Some definitions (e.g., parity, n-gen) lack formal mathematical precision and could be stated more rigorously.
2.1·Suggestion
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The definition of edge orientation (EO) is clear but could benefit from a formal mathematical statement of the orientation group property.
2.2·Strength
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The CFOP overview succinctly introduces the method and its acronym, demonstrating mastery of subject-specific terminology.
2.3·Suggestion
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Introducing the concept of n-gen here would improve clarity, as it is later used quantitatively without an early formal definition.
2.4·Strength
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The OLL and PLL sections use consistent notation and case counts, reinforcing the accurate application of combinatorial terminology.
2.5·Suggestion
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The parity definition (“equivalence or of equal value”) is imprecise; refine this to the mathematical concept of even and odd permutation parity.
2.6·Strength
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The use of LaTeX to present permutation and orientation formulae is exemplary and enhances mathematical clarity.
Criteria C: Critical Thinking
8/12
0
6
12
Criteria Strands
C.1Research quality
Moderate
C.2Analysis depth
Moderate
C.3Discussion and evaluation
Moderate
Criteria Feedback
The research draws on a good mix of authoritative literature and original data, all clearly relevant to the research question.
Multi-step quantitative analyses (move-count statistics, combinatorial derivations) are well linked to ergonomic and efficiency conclusions.
Key assumptions (e.g., linear relation of rotations to time lost) lack rigorous validation or sensitivity analysis.
Critical evaluation is uneven: statistical uncertainty and alternative interpretations are noted only briefly.
3.1·Suggestion
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Stating the total count of 493 ZBLL algorithms highlights cognitive load but could be supported by a brief discussion of memorization strategies.
3.2·Suggestion
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The F2L description correctly references block-building mechanics. Consider adding a brief example move sequence to illustrate the 1×2×3 block creation.
3.3·Suggestion
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The definitions of counting and combinatorics are clear; consider integrating a simple enumeration example to illustrate permutations in context.
3.4·Suggestion
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The explanation of edge/corner parity is accurate; adding a concrete example move sequence would deepen reader understanding of parity constraints.
3.5·Suggestion
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The quoted fractions from MIT are correctly formatted; consider specifying the exact source page to strengthen citation accuracy.
Criteria D: Presentation
3/4
0
2
4
Criteria Strands
D.1Structure appropriateness
Excellent
D.2Layout and formatting
Good
Criteria Feedback
The structure is clear and appropriate, with a detailed table of contents and logical sectional headings.
Consistent styling of tables, formulae, and images supports readability.
Page numbering is inconsistent or misaligned in places (e.g., ‘IKV462’ reference).
Some figure captions and footnotes (e.g., duplicated phrases, cramped spacing) detract from professional polish.
4.1·Suggestion
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The ‘IKV462’ page reference in the table of contents appears misaligned; consider verifying page numbering consistency to avoid reader confusion.
4.2·Strength
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The detailed table of contents facilitates navigation and demonstrates coherent structure, supporting reader understanding of the essay’s logical flow.
4.3·Weakness
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The duplicated phrase in the figure caption (“All visible edges on this cube are All visible edges…”) should be corrected for professional presentation.
4.4·Weakness
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The footnote ‘Fig 8’ sits very close to the main text, affecting readability; adding spacing would improve visual presentation.
