Using kinematics, how do variations in a velocity-time graph between Charles Leclerc and Oscar Piastri during Turn 1 of the 2024 Azerbaijan Grand Prix explain differences in their cornering performance?HL
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5
Official IB Result
12/20
Criteria A: Presentation
3/4
0
2
4
Criteria Strands
A.1Coherence and logical development
Good
A.2Organization and structure
Good
A.3Conciseness and relevance
Moderate
Criteria Feedback
- Clear investigative sequence with logical flow through rationale, modelling, results and conclusion
- Effective use of headings, sub‐headings, numbered sections and a table of contents to organize content
- Material is predominantly relevant to the research question
- Occasional narrative digressions interrupt the logical development
- Repetition of definitions (derivative, integral) reduces conciseness
- Raw data tables split across pages and inconsistent citation formatting detract from organization
1.1·Suggestion
Page 2
The table of contents effectively maps sections to page numbers, improving navigation. To enhance readability, align section titles and their page numbers consistently across columns.
1.2·Weakness
Page 3
Background on F1 regulations is extensive but partially distracts from the mathematical focus. Trim narrative digressions to improve conciseness and maintain relevance.
1.3·Suggestion
Page 4
Repeated definitions of derivatives and integrals later in the report reduce conciseness. Merge these explanations into a single, concise overview.
1.4·Weakness
Page 5
The raw data tables are split across the page and interrupt the flow. Combine or position tables closer to the narrative to improve organization.
1.5·Suggestion
Page 22
Bibliography entries show essential sources but citation formatting is inconsistent. Apply a uniform referencing style and include complete access dates.
Criteria B: Mathematical Communication
2/4
0
2
4
Criteria Strands
B.1Mathematical language and notation
Good
B.2Multiple representations
Good
B.3Clarity and consistency
Good
Criteria Feedback
- Key formulae are presented with correct symbols and variables defined
- Use of multiple representations (scatterplots, logistic/polynomial curves, integration diagrams) is effective
- Explanations generally reference the accompanying mathematical representations
- Inconsistent formatting of negative signs and exponents in pasted software output
- Axis labels or units are sometimes missing or faint on graphs
- Excessive numerical precision and inconsistent significant figures hinder clarity
2.1·Strength
Page 1
The research question is clearly stated, specifying the kinematics context and drivers compared. Consider defining variables like velocity in m/s in this section to enhance clarity.
2.2·Strength
Page 4
The modeling paragraph clearly explains why logistic and polynomial functions are chosen and how piecewise modeling applies here, demonstrating sound mathematical communication.
2.3·Suggestion
Page 5
Decimal precision varies across the tables. Standardize the number of significant figures to improve mathematical consistency and readability.
2.4·Suggestion
Page 6
The anomaly graph is clear, but some axis labels and units are faint or missing. Ensure all graph axes include legible labels and units.
2.5·Suggestion
Page 7
The general logistic formula is presented correctly. Explicitly note the sign convention in the exponent (−kx) to avoid confusion in interpretation.
2.6·Suggestion
Page 8
Logistic model parameter values are reported to many decimal places. Round parameters to three significant figures for clearer presentation.
2.7·Suggestion
Page 9
The degree-8 polynomial coefficients are displayed with excessive precision, which hinders readability. Consider rounding to three significant figures.
2.8·Suggestion
Page 10
Graph 6 effectively overlays logistic and polynomial models but the axes lack clear units and labels. Label both axes and include units (s, m/s).
2.9·Strength
Page 10
The piecewise modeling rationale is articulated clearly. For completeness, state the exact domain intervals for each piece in the narrative.
2.10·Suggestion
Page 11
The piecewise function is well formatted but uses inconsistent interval notation (≤ versus <). Standardize this to ensure mathematical precision.
2.11·Strength
Page 13
Quotient‐rule derivation of the logistic derivative is shown step-by-step, enhancing clarity of methodology.
2.12·Suggestion
Page 15
Overlaid acceleration curves in Graph 12 facilitate comparison of braking and acceleration profiles. Adding a legend directly on the plot would further improve readability.
2.13·Suggestion
Page 16
Definite integrals are correctly set up for each phase. Explicitly state the resulting units (meters) when reporting the integrated distances.
2.14·Suggestion
Page 18
The force‐time table is extensive; visualizing force vs. time in a plot would help identify braking and acceleration phases more effectively.
2.15·Suggestion
Page 18
The force equation is stated clearly, but include units for each quantity (m, s, kg) within the formula to maintain consistency.
Criteria C: Personal Engagement
2/3
0
2
3
Criteria Strands
C.1Independent thinking
Good
C.2Personal approach
Good
C.3Creativity and initiative
Good
Criteria Feedback
- Strong personal motivation established through the student’s passion for F1
- Clear justification of data‐collection and modelling choices shows independent thinking
- Creative initiative in blending logistic and high-degree polynomial models
- Mathematical methods largely follow standard procedures without further extension
- No advanced or novel parameter‐estimation techniques were developed
3.1·Strength
Page 3
The introduction shows strong personal engagement: the student integrates their passion for F1 with classroom kinematics, driving a clear motivation for the exploration.
Criteria D: Reflection
2/3
0
2
3
Criteria Strands
D.1Depth of reflection
Good
D.2Critical analysis
Good
D.3Connection to understanding
Good
Criteria Feedback
- Meaningful reflection on model limitations, data anomalies and their impact
- Clear links made between mathematical results and racing understanding
- Justification of outlier removal demonstrates thoughtful analysis of data quality
- Reflection lacks deeper statistical diagnostics or sensitivity analyses
- Critical analysis is present but not penetrating or rigorous
4.1·Strength
Page 6
Identification and removal of anomalous points is justified with clear visual reasoning, demonstrating meaningful reflection on data quality.
4.2·Suggestion
Page 17
Fuel mass assumption is transparent but likely overestimates qualifying load. Conduct a sensitivity check on fuel mass to assess its impact on force calculations.
4.3·Suggestion
Page 19
Conclusion integrates findings well but could explicitly restate the research question to reinforce how results answer it.
4.4·Suggestion
Page 21
Limitations are acknowledged thoughtfully. To strengthen reflection, suggest statistical diagnostics (e.g., residual plots) to evaluate model fit inaccuracies.
Criteria E: Use of Mathematics
3/6
0
3
6
Criteria Strands
E.1Relevance and level
Moderate
E.2Accuracy and correctness
Moderate
E.3Knowledge and understanding
Moderate
Criteria Feedback
- Application of HL-level mathematics (logistic modelling, 8th-degree polynomials, differentiation, integration) appropriate to the exploration
- Analytic differentiation and definite integrals are set up correctly
- Conceptual links between calculus techniques and kinematic interpretation are clear
- Minor recurring accuracy errors (logistic derivative sign, missing units)
- Mathematical methods are routine with limited justification of model choice (no fit statistics)
- Some arithmetic slips in manual coefficient computation
5.1·Strength
Page 5
The sampling method is well described: systematic sampling at every 5 frames is appropriate, and the conversion from km/h to m/s is clearly shown.
5.2·Suggestion
Page 6
Anomaly removal remains qualitative. Incorporate a statistical criterion (e.g., interquartile range) for outlier detection to increase rigor.
5.3·Suggestion
Page 7
Parameter fitting is done via GDC but lacks description of the fitting criterion. Briefly describe how best fit was determined (e.g., least squares) to improve transparency.
5.4·Suggestion
Page 8
Linking parameter k to deceleration rate is insightful; including its unit (s⁻¹) explicitly would improve the precision of interpretation.
5.5·Suggestion
Page 9
The rationale for choosing an 8th-degree polynomial lacks quantitative support. Include model fit statistics (e.g., R² or SSE) to justify degree selection.
5.6·Suggestion
Page 11
Quantitative evaluation of the continuity of piecewise functions (e.g., matching derivatives at the join point) would deepen the analysis of smooth transitions.
5.7·Weakness
Page 12
Check the arithmetic of one differentiated coefficient (e.g., the x⁴ term) to ensure no minor slip occurred in the manual computation.
5.8·Strength
Page 12
Differentiation rules are presented concisely in Formula 2. This general approach is communicated clearly and consistently.
5.9·Weakness
Page 13
The substituted logistic derivative shows a negative‐sign inconsistency compared to standard form; verify the exponential term handling to correct this sign error.
5.10·Suggestion
Page 15
Linking peak acceleration values to driving technique is insightful; present those numeric extremes in a small table for quick reference.
5.11·Suggestion
Page 17
Comparison of integrated distances is clear and quantifies performance difference. Discuss how changing car mass (fuel burn-off) might alter distance outcomes.
5.12·Suggestion
Page 19
Summary table of key force metrics effectively highlights comparative performance. Adding percentage differences would quantify the magnitude of those differences.