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

Consider adding a concise abstract or overview on the title page summarizing the investigation’s aim, methodology, and key findings to guide the reader from the outset.

The title is clear and descriptive, specifying the object, mathematical method, and context effectively, which helps set reader expectations.

The introductory anecdote is lengthy and detracts from focus. Streamline this section by removing repetitive details to maintain conciseness and relevance.

The aim is clearly and succinctly stated, providing a focused research question and objectives. This helps structure the subsequent methodology.

The large table of Desmos functions would benefit from a side‐by‐side schematic diagram. This visual link would reinforce the connection between equations and shape.

Final Desmos outline lacks a scale bar or numeric axes labels. Adding a scale marker would enable the reader to verify dimensions visually.

Handwritten calculations interrupt the professional format. Consider moving detailed GDC screenshots or handwritten work to an appendix to maintain flow.

There is a typo in the heading “Scalling.” Correct spelling to “Scaling” for presentation polish.

Repetitive explanation of the volume scale factor could be consolidated earlier. Streamline by defining VSF once and referring back for coherence.

Ensure bibliography entries follow a consistent referencing style (e.g. MLA, APA), including uniform date formats, punctuation, and italics for sources.

The figure of the dumbbell lacks a descriptive caption and axis labels. Add a concise caption and scale indicators to improve clarity of the image.

Notation for the linear scale factor uses mixed comma and period decimal symbols. Use a consistent decimal point format to avoid confusion.

The data table is well placed, but headers and units are misaligned. Ensure each column label and unit (cm, cm³) is consistently formatted for clarity.

Clarify what one cubic unit on Desmos represents in real‐world volume. A brief sentence tying Desmos units to cm³ would enhance mathematical communication.

The intentional use of quadratic fits to approximate spherical parts demonstrates effective multiple representation techniques using Desmos.

The coordinate table lacks units and context for each point. Add labels (x, y in cm) and a brief caption to clarify the data source.

The plotted Desmos function figure needs a concise caption explaining which segment of the dumbbell it represents. This will guide interpretation.

Equation list for fitted functions is comprehensive, but domain intervals are formatted inconsistently. Standardize interval notation and spacing.

Describe briefly how curve alignment was verified in Desmos (e.g. grid snap, manual adjustment) to strengthen your explanation of mapping accuracy.

Two of the block equations lack explicit domain constraints, making the outline ambiguous. Include missing bounds to ensure full mathematical clarity.

The integral notation is introduced clearly with proper definitions of variables and limits, enhancing reader understanding of the calculus process.

The substitution equations for P and Q are densely formatted; grouping terms more clearly (e.g. line breaks) would improve readability.

Significant figures vary across your volume table (sometimes five decimals, sometimes three). Adopt a consistent precision aligned with measurement accuracy.

The personal rationale provides strong insight into motivation, demonstrating genuine personal engagement through an authentic and meaningful context.

Reliance on an online solver is efficient but undercuts demonstration of manual skill. Reflect on the trade‐off between accuracy and independent proof.

Clarify in the narrative why the first function was done manually and the rest via GDC, highlighting how this approach demonstrates understanding and efficiency.

The discussion of measurement challenges identifies key issues but lacks quantitative error estimates. Include uncertainty bounds for tape‐measure readings to enhance critical analysis.

Consider discussing potential lens distortion or photographic error when taking the Desmos image to highlight model assumptions and limitations.

The tiny volume result for V₁ (0.012738 cm³) is surprising. Reflect on whether this makes physical sense and discuss its significance.

Future improvements are noted but remain general. Provide specific numerical approaches or tools (e.g. error analysis techniques) for deeper critical reflection.

The conclusion effectively summarizes the process and result, but could be strengthened by quantifying potential error margins or model limitations.

Measurement procedure is described in detail but lacks discussion of instrument accuracy or repeated‐measure consistency. Add a brief note on measurement error to strengthen rigor.

The density range is well introduced, providing a realistic interval for acceptable volume. This grounds the investigation in practical material properties.

Algebraic steps in the simultaneous equations are correct but lack explanatory commentary. Adding brief rationale for each manipulation would improve clarity.

Only the first integral result is shown manually. Include the numeric outcome directly below your manual steps before delegating the rest to the GDC for coherence.