IB Mathematics Applications & Interpretation (AI) SL Internal Assessment Example

The introduction’s narrative is engaging but overly lengthy, leading to repetition and digressions from the mathematical focus. Condense personal background to strengthen coherence and maintain relevance to the aim.

Section headers are used but the transition from Introduction to subsequent sections is abrupt. Consider adding a brief roadmap at the end of the introduction to improve logical flow.

Although the aim is stated, the methodology in the introduction could be more concise. Focus on precise objectives rather than narrative to maintain relevance.

The methodology outlines key steps clearly but would benefit from a structured flowchart or bullet list to strengthen coherence and aid reader navigation.

Figure 1 is referenced in the text but the numbering in the caption and the reference in the narrative do not match consistently, disrupting clarity.

The heading level for “Surface area of cushion rim:” is an H4, inconsistent with the H3 style used elsewhere. Standardize heading hierarchy to improve structure.

The narrative on price averaging mentions methodology but omits the explicit formula used. Including $\text{Average}=\frac{\sum prices}{n}$ would clarify the calculation.

The explanation of sector angles uses inline math but lacks consistent LaTeX formatting. Use $\frac{1}{8}$ and $120^{\circ }$ in block form for clarity.

Units in the volume calculation table are inconsistent: areas are in cm² but later multiplied to give cm³. Ensure units are precise at each step.

The boldface notation for variables $\mathbf{R}$ and $r$ is inconsistent with earlier plain-text usage. Adopt a uniform notation style for clarity.

The calculation for the torus surface area omits the unit on the final result. Add “cm²” after $S=2370$ for completeness.

The cuboid cross-section calculation is correct and tabled neatly, aiding readability and confirming understanding.

The text summarizing material quantities is clear, but including the formula $extTotalVolume=29712.76{\text{cm}}^3$ alongside would strengthen mathematical communication.

The average price for wood in Table 2 is rounded to 65.5€, yet earlier averages use 65.56€. Align rounding conventions to maintain consistency.

The fabric cost table uses unconventional notation “2.53E988€”. Standardize to a clear currency format (e.g., 2.53 €) for consistency.

The average fabric price is correctly calculated but embedding the general formula $\frac{988+469.3}{2}$ in the narrative would improve clarity.

The student clearly articulates a strong personal motivation rooted in their aspiration to become an interior designer. This personal context enhances engagement and drives the exploration.

Introducing a torus-and-ellipsoid cushion is a creative touch that demonstrates initiative and enhances the personal approach.

The discussion of wood and fabric selection demonstrates clear personal decision-making based on practical considerations, reinforcing engagement.

The approximation formula for the ellipsoid surface area is well cited, but the student could discuss the percentage error that this approximation might introduce.

Acknowledgment of calculus limitation is honest but reflection stops at description. Propose alternative non-calculus methods or literature to deepen critique.

The conclusion restates results accurately but does not reflect on how mathematical understanding deepened. Introduce insight on how geometric modelling informed decision-making.

The evaluation notes limitations of brand selection but lacks quantitative analysis of how these would alter results. Suggest estimating impact percentages to deepen critique.

The explanation of calculating volumes and surface areas for wood, metal, and fabric is precise and appropriate to the task context.

The student sensibly decomposes the desk chair into cylinder and sector components and explains this process clearly.

The student correctly sums the volumes of seat, legs, and backrest to find the total chair volume. Consider rounding intermediate results to a consistent decimal place for readability.

The formula in the table for the large sector area shows $A=\frac{0}{360}\times \pi r^2$, which appears to be a placeholder error. Please correct the numerator to reflect the actual angle.

The sphere formula in Table 3 is mistyped as $V=\frac{4}{3}\pi r^2$ rather than $\frac{4}{3}\pi r^3$. Correct this to ensure mathematical accuracy.

Breaking the nightstand legs into spheres and multiplying is a clear and effective use of composite solids to find total volume.

The divisor in the wood calculation table appears as 19.2 without explanation. Clarify that 19.2 arises from 19200 cm³ ÷ 1000 cm³ to avoid confusion.