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Mathematics Analysis and Approaches (AA) IA Exemplar: Least Surface… | RevisionDojo
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IB Mathematics Analysis and Approaches (AA) HL Internal Assessment Exemplar: to find the design that have the least surface area so that I can choose which design that benefits me the most by having fewer amount of paint
to find the design that have the least surface area so that I can choose which design that benefits me the most by having fewer amount of paint
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4
Official IB Result
11/20
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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 division into introduction, methodology, individual designs, own design, and conclusion
Use of headings, numbered tables and graphs provides a navigable structure
Overall coherence and logical sequence of ideas is solid
Transitions between sections are sometimes abrupt and wording can be confusing
Inconsistent heading styles and formatting across sections
Repeated explanations and informal digressions reduce conciseness
1.1·Strength
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The title clearly states the exploration’s focus and candidate number, providing immediate context for the reader.
1.2·Weakness
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The title page omits the author’s name and submission date, which are standard in formal IB reports. Consider adding this information for completeness.
1.3·Suggestion
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The research question is implied rather than explicitly stated. Frame a clear question such as: “Which vase design minimizes paint requirement based on surface area?”
1.4·Weakness
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The opening paragraph includes informal phrasing and some grammatical errors that distract from the mathematical aim. Revise for clarity and precision.
1.5·Suggestion
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The step stating “I will model using quadratic and linear equations” would benefit from a brief rationale for selecting those functions.
1.6·Weakness
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Diagrams lack descriptive captions beyond “Diagram 1” and “Diagram 2.” Add concise captions explaining what each illustration represents.
1.7·Suggestion
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Clarify the phrase “Since the equation applying the derivative” by rephrasing to “The derivatives of each piecewise function are shown below.”
1.8·Weakness
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The heading “Design 2” is formatted differently from “Design 1.” Use consistent heading levels and styles throughout.
1.9·Weakness
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The text indicates a proposed new design but omits the corresponding surface‐area calculations. Include the integral computations for this design.
1.10·Weakness
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The “My own design” heading uses a different font weight and level than previous sections. Ensure consistent styling for coherence.
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
Standard notation for integrals, derivatives and piecewise functions is used
Inclusion of algebraic, numerical and graphical representations
Derivative and surface-area tables support the mathematical discussion
Graphs and tables often lack axis labels, scales and units
Logical progression is intermittent; some steps and choices are unexplained
2.1·Weakness
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The citation “(Business Bliss Consultants FZE, 2024:” is incomplete and stops abruptly. Provide full bibliographic details in APA or IB format.
2.2·Suggestion
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The modelling paragraph could be tightened by focusing on key steps. Remove filler text and specify tools and scales in bullet form.
2.3·Weakness
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The surface-area integral formula is reproduced twice without commentary. Avoid unnecessary repetition and explain any derivation steps succinctly.
2.4·Weakness
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The piecewise function in Design 1 uses inconsistent punctuation and spacing around domain intervals. Standardize each piece for readability.
2.5·Strength
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The derivative table correctly lists each dy/dx, demonstrating accurate application of differentiation to the piecewise segments.
2.6·Weakness
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An empty table appears below; either populate it with data or remove it to avoid confusion.
2.7·Suggestion
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Include units (cm²) in the table header for surface‐area values to reinforce mathematical accuracy.
2.8·Suggestion
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Graphs lack clearly labeled axes and scales, reducing interpretability. Add axis titles and grid lines to improve clarity.
Criteria C: Personal Engagement
1/3
0
2
3
Criteria Strands
Poor
Independent thinking
Poor
Personal approach
Poor
Creativity and initiative
Criteria Feedback
Personal context (mother’s planting hobby) grounds the task
Creation of an additional 'own' design shows some initiative
Independent thinking is limited; the mathematical approach closely follows standard references
Personal anecdotes do not significantly inform the modeling choices
Creativity and innovation are minimal
3.1·Suggestion
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The personal anecdote about painting adds context but does not advance the mathematics. Focus narrative on modeling choices to strengthen engagement with the task.
3.2·Weakness
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The informal comment “The result satisfied me” adds personality but does not advance analysis. Refocus on interpreting why Design 1 differs.
Criteria D: Reflection
1/3
0
2
3
Criteria Strands
Poor
Depth of reflection
Poor
Critical analysis
Poor
Evaluation of outcomes
Criteria Feedback
Basic comparison of surface-area results
Acknowledgment of possible graphing errors and suggestions for 3-D software
Reflection is mainly descriptive with limited insight
Critical analysis of assumptions and errors is superficial
Evaluation of outcomes lacks quantitative error bounds or deeper implications
4.1·Weakness
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The narrative around the difference in area between Designs 1 and 2 lacks deeper mathematical insight. Discuss how curvature and arc length interact.
4.2·Suggestion
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The reflection on methodological limitations is brief. Expand on how use of Desmos and GDC might introduce systematic errors and propose mitigation.
Criteria E: Use of Mathematics
4/6
0
3
6
Criteria Strands
Moderate
Relevance of mathematics
Good
Level appropriateness
Moderate
Understanding and accuracy
Criteria Feedback
Appropriate application of surface-area-of-revolution calculus at AA-HL level
Modelling multiple piecewise functions with correct derivative tables
Consistent use of technology to evaluate integrals and control volume variables
Minor notational errors (e.g. sign error in a derivative)
Modelling choices (bounds, function selection) are not always justified
Incomplete tables for the 'own design' and lack of a summary total row
5.1·Strength
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Noting that all three vases share a 1 liter volume is a strong methodological choice to control variables consistently.
5.2·Strength
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Table 2 on page 7 presents surface‐area totals clearly, linking each function to its integral result.
5.3·Weakness
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In Table 5 the derivative of 1.001x2−28.5x+206.427 is given as 2.002x+28.5 rather than 2.002x−28.5. Correcting this will affect subsequent area calculations.
5.4·Suggestion
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Table totals are presented well, but it would help to cross-check each integral result with an independent method (e.g., numerical approximation) to validate accuracy.
5.5·Weakness
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For the own-design model, no computed surface areas are shown alongside the derivative table. Present a completed table of integrals and totals.
5.6·Weakness
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Table 8 lists individual areas but omits a “TOTAL” row. Summarize the sum of these values to support the final comparison.
