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Mathematics Analysis and Approaches (AA) IA Exemplar: Tire… | RevisionDojo
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IB Mathematics Analysis and Approaches (AA) HL Internal Assessment Exemplar: To what extent can integration and differential equations develop an accurate
tire degradation model for modern F1 cars, with factors including track temperature, tire compound, and track geometry and elevation?
To what extent can integration and differential equations develop an accurate
tire degradation model for modern F1 cars, with factors including track temperature, tire compound, and track geometry and elevation?
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5
Official IB Result
13/20
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13/20
0
10
20
6.1·Weakness
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The citation displays HTML artifacts and inconsistent formatting. Clean up footnotes and ensure uniform referencing.
Criteria A: Presentation
3/4
0
2
4
Criteria Strands
Moderate
Coherence and logical development
Good
Organization and structure
Moderate
Conciseness and relevance
Criteria Feedback
Clear three-level structure with numbered headings and a contents page guiding the reader
Overall readable flow that supports the main storyline
Frequent digressions and repetition interrupt coherence
Mis-numbered and inconsistent headings, empty sub-headings
Verbose sections and typographical errors detract from conciseness
1.1·Weakness
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The title is overly long and combines multiple elements, which reduces immediacy and clarity. Consider streamlining to focus on the core topic and research question.
1.2·Strength
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The research question is clearly stated and directly aligned with the exploration’s aims, providing strong focus for the subsequent methodology.
1.3·Weakness
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Entries in the Table of Contents are mis-numbered and some headings do not match the main text. Ensure consistency between contents and section titles.
1.4·Suggestion
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The historical overview of Formula 1 in the introduction is lengthy and only loosely connected to the mathematical focus. Trim this to improve coherence.
1.5·Weakness
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There is an empty sub-heading here, which interrupts flow. Remove or replace it with appropriate content to maintain structure.
1.6·Suggestion
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The “Fun Fact” box interrupts the technical discussion. Consider its relevance or move it to an appendix.
1.7·Weakness
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These images are informative but lack captions, making it hard for the reader to know what they represent. Add descriptive captions and figure numbers.
1.8·Weakness
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The placeholder “Example:” table is empty and interrupts the narrative. Remove or populate it with meaningful content.
1.9·Weakness
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The section header “5.4” is misaligned with the previous numbering. Ensure all headings are numbered consistently.
1.10·Weakness
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The conclusion recapitulates the work but is overly verbose. Condense into key findings and explicitly link back to the research question.
1.11·Weakness
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Bibliography entries show inconsistent formatting (italics, URLs, authors). Adopt a uniform IB referencing style throughout.
Criteria B: Mathematical Communication
2/4
0
2
4
Criteria Strands
Moderate
Mathematical language and notation
Moderate
Multiple representations
Moderate
Logical structure and clarity
Criteria Feedback
Use of standard calculus symbols (∫, dT/dt, ln) and display-mode equations
Step-by-step derivations support reader comprehension
A variables table clarifies symbol meanings
Notation mis-uses (e.g. conflicting definitions of T and C, misplaced absolute-value bars)
Limited student-generated representations; heavy reliance on clipped images
Logical gaps in the argument (treating variables as constants without explanation)
2.1·Suggestion
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The list of factors affecting tire degradation lacks clear linkage to the subsequent models. Explicitly state how each factor enters your equations.
2.2·Weakness
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The result “0.0833 unit²” is presented without discussing units or approximation error. Explain the unit derivation and rounding.
2.3·Weakness
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Relying on technology for simple arithmetic undercuts the mathematical argument. Show the Riemann sum calculation manually for clarity.
2.4·Weakness
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The example differential equation dxdy=3x5y omits a multiplication operator. Correct it to dxdy=15xy for precision.
2.5·Strength
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The methodology list is concise and provides a clear roadmap for model construction and testing.
2.6·Strength
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The separation-of-variables step is laid out correctly, helping the reader follow the integration process.
2.7·Suggestion
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Several integrals are enclosed in absolute-value notation. Since T<100 during a lap, absolute bars may be unnecessary—consider removing them.
Criteria C: Personal Engagement
2/3
0
2
3
Criteria Strands
Good
Independent thinking
Good
Personal approach
Good
Creativity and initiative
Criteria Feedback
Personal passion for Formula 1 clearly informs the modelling framework
Independent derivation of four linked differential equations
Evidence of research and simulator testing to choose constants
Model structure largely follows a familiar template
Limited novelty in the mathematical approach
3.1·Strength
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Personal reflections on your passion for F1 lend authenticity and demonstrate clear ownership of the exploration topic.
Criteria D: Reflection
2/3
0
2
3
Criteria Strands
Good
Depth of reflection
Good
Critical analysis
Good
Evaluation of outcomes
Criteria Feedback
Meaningful evaluation of outcomes against simulator telemetry
Clear identification of limitations and suggestions for improvement
Thoughtful discussion of why different tracks yield different wear rates
Reflection lacks quantitative error analysis (e.g. residuals or percentage errors)
Limited depth in critiquing parameter-estimation methods
4.1·Weakness
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The final expression includes the term e100(μT/2)t2+C without discussing how constants are chosen. Reflect on parameter estimation methods.
4.2·Suggestion
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The narrative on comparing simulator outputs is descriptive but lacks quantitative error analysis. Include percentage errors or residuals to strengthen validation.
4.3·Weakness
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The ‘Uniformity of variables’ row lists no possible improvement. Propose a specific strategy (e.g., time-varying functions) to address this limitation.
4.4·Strength
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The limitations table effectively summarizes errors and improvements, showing clear critical reflection on model constraints.
Criteria E: Use of Mathematics
4/6
0
3
6
Criteria Strands
Poor
Relevance of mathematics
Moderate
Level appropriateness
Poor
Understanding and accuracy
Criteria Feedback
Appropriate use of differential equations and integration techniques
Mathematics consistently at or above SL course level
Clear demonstration of methods such as separation of variables
Standard textbook derivations unrelated to the model consume space
Incomplete parameter values and symbol misuse in tables
5.1·Weakness
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The extensive textbook comparison between differentiation and integration could be condensed; focus on the novel aspects relevant to your model.
5.2·Weakness
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The Riemann-sum summation indices and Δx are not defined; clarify the general form i=1∑nΔxf(xi) with explicit limits.
5.3·Weakness
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Variables table uses generic letters C, G, E which may be confused with constants. Assign meaningful symbols (e.g., θ for camber) and define them clearly.
5.4·Weakness
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In the differential equation dtdT=μTt(1−100T), T is used for both dependent variable and track temperature. Rename one for clarity.
5.5·Weakness
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In the camber differential equation, the symbol C is used both for camber angle and integration constant. Rename one symbol to avoid confusion.
5.6·Weakness
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The “Coefficient of friction” entry is blank in the circuit data list. Provide the numeric value to complete the model inputs.
5.7·Weakness
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In the Marina Bay circuit data list, the frictional force entry lacks value. Ensure all relevant parameters are provided for reproducibility.
