This site uses cookie tracking technologies. Learn more in our Cookie Policy.
Mathematics Analysis and Approaches (AA) IA Exemplar: Wine Glass… | RevisionDojo
Loading document preview...
IB Mathematics Analysis and Approaches (AA) SL Internal Assessment Exemplar: Investigating the serving size and air-to-wine ratio of a wine glass using modelling
Investigating the serving size and air-to-wine ratio of a wine glass using modelling
Loading scores...
5
Official IB Result
14/20
Was this exemplar helpful?
Want a report just like this?
Free mini report for your own coursework
Fast feedback on what to improve next
Annotated highlights on your writing
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, logical narrative from introduction through modelling to conclusion
Well‐structured with descriptive headings, subheadings and labelled figures
Descriptive title immediately orients the reader to the investigation’s focus
Occasional unnecessary detail and repetition reduce conciseness
Long algebraic derivations are embedded rather than summarized
Inconsistent table captions and missing units hinder interpretability
1.1·Strength
Page 1• Click to view
The clear, descriptive title establishes the investigation’s focus immediately and supports reader orientation.
1.2·Suggestion
Page 2• Click to view
Table 1 and Table 2 should be titled and captioned consistently, and units for x and y must be specified for full interpretability.
1.3·Suggestion
Page 4• Click to view
The description of concavity misfits in the quartic function shows thoughtful critique; summarise this rather than overly detailed narrative for conciseness.
1.4·Suggestion
Page 5• Click to view
The narrative description of stretching the parabola would be clearer with annotated equations showing each transformation step-by-step.
1.5·Suggestion
Page 8• Click to view
Your simultaneous-equation solution is well executed; summarizing key formulas in a table could improve logical presentation.
1.6·Suggestion
Page 9• Click to view
The matrix solution figure aids understanding, but the handwritten layout is hard to read; typeset the matrix for consistent presentation.
1.7·Suggestion
Page 17• Click to view
The detailed integration steps for the exponential segment are accurate; consider summarizing final expressions to maintain conciseness.
Criteria B: Mathematical Communication
3/4
0
2
4
Criteria Strands
Good
Mathematical language and notation
Good
Multiple representations
Moderate
Logical structure and clarity
Criteria Feedback
Consistent use of appropriate calculus and regression notation for the most part
Effective use of multiple representations (tables, GeoGebra/Desmos graphs, derivative plots)
Logical sequence of argument is generally clear
Dense algebraic paragraphs obscure key steps at times
Some graphs lack axis labels and scales, reducing clarity
The graph in Figure 4 lacks axis labels and scales, making it difficult to assess fits quantitatively; add labels to improve clarity.
2.2·Suggestion
Page 4• Click to view
The equation parameters lack differential or function notation consistency; ensure all superscripts and signs are clear (e.g. x³ term).
2.3·Suggestion
Page 6• Click to view
Show explicitly the natural-log transformation steps in the linearisation to aid clarity and reproducibility of your regression process.
2.4·Suggestion
Page 7• Click to view
The expanded normal equations for least squares are derived correctly, but summation notation is dense; consider breaking into numbered steps for clarity.
Criteria C: Personal Engagement
2/3
0
2
3
Criteria Strands
Good
Independent thinking
Good
Personal approach
Good
Creativity and initiative
Criteria Feedback
Choice of a unique glass and personal narrative demonstrate clear engagement
Evidence of independent thought in deriving bespoke regression methods
Good creativity in combining technology with custom derivations
Some sections revert to textbook exposition rather than personal insight
Decisions sometimes rely heavily on technology without full student‐led justification
3.1·Strength
Page 1• Click to view
The personal narrative in the rationale effectively situates the exploration within the student’s experience, demonstrating genuine engagement.
3.2·Strength
Page 1• Click to view
The student’s choice of a unique glass (Josephine No. 3) illustrates independent thinking and personal motivation for this investigation.
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 modelling choices and their limitations
Clear evaluation of outcomes, including comparison to manufacturer volume and air‐to‐wine ratio
Suggestions for plausible extensions and improvements
Critical analysis remains surface level in places (e.g., volume discrepancy)
Depth of reflection could be enhanced by discussing sensitivity (e.g., z-test p-value effects)
4.1·Suggestion
Page 1• Click to view
The connection between higher ABV and required air space needs clearer justification or a reference to quantify the relationship rather than general reasoning.
4.2·Suggestion
Page 2• Click to view
Consider explaining why the data interval of 0.5 cm was chosen and how many data points ensure a reliable model outline.
4.3·Suggestion
Page 3• Click to view
When defining piecewise intervals by slope sign changes, specify the quantitative slope thresholds used to partition the curve.
4.4·Strength
Page 3• Click to view
The analysis of the quartic’s concavity is insightful; consider quantifying the curvature error to strengthen the critique.
4.5·Suggestion
Page 11• Click to view
In the z-test inversion, sensitivity to p-values near 1 should be discussed; mention how small changes affect σ to justify method limitations.
4.6·Suggestion
Page 18• Click to view
The concluding evaluation summarizes results effectively; adding a critical discussion of the 12.5 cm³ volume discrepancy would deepen reflection.
Criteria E: Use of Mathematics
4/6
0
3
6
Criteria Strands
Good
Relevance of mathematics
Good
Level appropriateness
Moderate
Understanding and accuracy
Criteria Feedback
Mathematics directly targets the aim with effective application of calculus, regression and trigonometry
Work is fully commensurate with SL level, including limits, integration and least‐squares
Insightful application of one‐sided limits and Riemann sums demonstrates strong understanding
Minor algebraic errors in manual cubic construction
Heavy reliance on technology for some integrals without full manual verification
Goodness‐of‐fit metrics (SSE, R²) are not numerically computed
5.1·Suggestion
Page 4• Click to view
When proposing both quadratic and exponential fits, include a plan for comparing their goodness of fit numerically (e.g. SSE or R²).
5.2·Suggestion
Page 10• Click to view
The stepwise derivation of cosine parameters is clear, but residual plots or SSE values would strengthen model selection beyond visual fit.
5.3·Suggestion
Page 12• Click to view
The use of the standard deviation formula refocuses on reliable statistics; include the computed σ value and show substitution for transparency.
5.4·Weakness
Page 13• Click to view
The manual cubic construction shows initiative but has algebraic errors in both integrand and exponent; re-derive f(x) carefully with correct terms.
5.5·Strength
Page 14• Click to view
The application of one-sided limits to enforce continuity is insightful and demonstrates strong understanding of piecewise function behaviour.
5.6·Strength
Page 15• Click to view
The Riemann-sum derivation for volume is well explained; cite the theorem name and link to classical volume of revolution concept.
5.7·Suggestion
Page 18• Click to view
The WolframAlpha-aided cubic volume computation is efficient but should include a screenshot or copy of the integral input for reproducibility.
