IB Mathematics Analysis and Approaches (AA) HL Internal Assessment Example

Multiple entries for “Conclusion” and “Evaluation” may confuse the reader; streamline headings to maintain a clear structure.

The table of contents spans a large area; consider adjusting spacing and alignment to improve readability and coherence.

The background paragraph is informative but overly long; consider splitting complex sentences and focusing on key concepts.

The photograph lacks a scale bar or dimension annotation; include a clear reference to translate pixel measurements to physical units.

Raw data table is comprehensive but lacks a caption and clear unit notation in the header; adding these will improve presentation.

The transition to model fitting is abrupt; add a linking sentence explaining why starting with a linear model establishes a useful baseline.

Reflection text on this page ends mid-sentence; ensure all sentences are complete for clarity and professionalism.

The final summary succinctly states the outcome and relevance of the quadratic model, enhancing the reader’s takeaway.

Two separate “Conclusion” headings appear; consolidate to prevent structural confusion.

Variables in the equation should be introduced inline before or immediately after the block; ensure $v=\sqrt{2gh}$ is preceded by clear definitions.

Explain the rationale for rounding to four significant figures explicitly; this clarifies the connection between measurement precision and data processing.

The analysis introduction clearly states the use of GeoGebra for curve fitting, reflecting sound mathematical communication.

The term “v intercept” is incorrect; replace with “y-intercept” to use standard mathematical terminology.

Include units for slope and intercept in the caption (e.g., cm/s and cm) to clarify the dimensions of Geogebra’s line parameters.

The quadratic model is praised but its explicit form isn’t displayed in the text; include the equation for completeness.

The logarithmic model uses $\ln (x)$ but the independent variable is time $t$; revise to $h(t)=a\ln (t)+b$ for consistency.

Symbols “ν” and “v” are used interchangeably for velocity; maintain consistent notation to avoid confusion.

Integration step omits absolute-value notation for $h$; include $\int h^{-1/2}dh$ justification to ensure mathematical rigor.

The final function uses $\Delta h$ but earlier context defines $h$; clarify variables so the reader tracks what is being modeled.

Constant notation switches between uppercase $C$ and lowercase $c$; maintain one symbol to avoid ambiguity.

The personal introduction demonstrates genuine engagement, but the aim statement repeats itself; condense to avoid unnecessary repetition.

Describing camera placement to reduce parallax shows thoughtful experimental design and enhances data integrity.

The first reflection insightfully identifies setup issues, demonstrating meaningful consideration of experimental design.

Reflection acknowledges several limitations but does not quantify their impact; consider estimating the magnitude of error introduced by each.

Critique of the linear model is clear but would benefit from a quantitative residual or error analysis to support the claims.

Discuss the percentage error or residuals when comparing predicted emptying time to observed behavior to deepen critical analysis.

Reflection on derivation challenges exhibits substantial critical thinking and acknowledges modeling trade-offs.

Comparing empirical and derived curves is insightful; include a quantitative goodness-of-fit metric (e.g., R²) to strengthen analysis.

Final reflection proposes concrete improvements (geometric detail, resistance factors), showing thoughtful forward-planning.

Time values stop at 24.5 s; consider discussing why the experiment ends there or extending to full emptying to validate model predictions.

The description of polynomial flexibility is well articulated, effectively linking theory to model choice.

In the outflow rate equation, include a negative sign explicitly when defining $dV/dt$ to denote volume loss over time.

Using 980 for $g$ in cm/s² mixes unit systems; clarify if all calculations use cgs or SI consistently.