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

The table of contents is overly detailed, including minor subsections that clutter navigation. Consider consolidating entries and focusing on main sections to improve conciseness and reader orientation.

The introduction contains lengthy background copied from sources without synthesis. Trim redundant definitions and focus on your rationale to enhance coherence and maintain reader engagement.

Listing empirical percentages in bullet form increases length. Consider summarizing the 68–95–99.7% checks in a concise table to aid readability and relevance.

Graph 2’s caption omits parameter values. Add mean and standard deviation on the figure or in caption to reinforce mathematical communication of the normal curve.

The paragraph ends abruptly and seems incomplete, disrupting flow. Ensure the text is complete and provides a full conclusion or transition to the hypothesis test.

The extensive chi-square distribution table in the body disrupts flow. Relocate the full table to an appendix or summary section, citing only relevant critical values in the main text.

The raw data table is appropriately placed in the appendix, keeping the main report concise and focused on analysis.

The distribution-vs-weights table lacks clear axis labels or units, making interpretation difficult. Add headings and units for each column to improve presentation.

In the frequency table class intervals mix “<” and “≤” inconsistently, and notation for observed frequency appears as “0₁” in formulae. Ensure consistent use of $<$ vs $\le$ and correct symbol notation throughout.

The histogram image is low resolution and axes labels are faint. Improve figure quality and explicitly justify scale choices to enhance clarity and support your analysis.

The text describing skewness uses informal language and does not link observation to later statistical tests. Tighten mathematical language and connect visual skewness to hypothesis outcomes.

The description of the GDC function $\mathrm{normPdf}(x,\bar{x},\sigma )$ lacks specification of domain and units. Explicitly define input ranges and units to improve clarity.

The criteria table lists “Not yet met” for expected frequencies before merging. Update the table after combining intervals to reflect accurate met status.

The large table of expected frequencies and probabilities could be streamlined by focusing on final merged intervals only. Move detailed interval calculations to appendix.

In the chi-square calculation block, the notation uses “0_i” instead of “$O_i$”. Correct this typographical error to maintain clear mathematical communication.

The degrees of freedom definition is uncited in text. Include an in-text citation for the formula $df=k-1$ to strengthen academic rigor in mathematical communication.

Figure 1’s legend and units are missing. Include axis labels, units (g for weight), and a legend explaining curve vs data points for full mathematical communication.

The recommendations for increasing sample size and expanding crates show personal engagement and initiative in refining methodology.

The sampling description is clear but lacks critical reflection at this stage. Introduce brief commentary on potential bias from using a single crate to demonstrate deeper awareness of methodology.

The empirical rule bullets are described in prose only. Reflect on reasons for the observed 75% vs theoretical 68% and 91.67% vs 95%, linking deviation to sampling or distributional assumptions.

The narrative separates graphical observations from the final test. Integrate comments on skewness and bimodality into your evaluation to deepen critical reflection.

The conclusion succinctly evaluates sampling bias and test outcomes, demonstrating meaningful reflection on limitations and improvements.

The standard deviation value is quoted as produced by the GDC without showing the formula. Display the calculation or formula $\sigma =\sqrt{\frac{\sum (x-\bar{x}{)}^2}{n}}$ to strengthen mathematical rigor.

Adjusting min/max x-values without justification may mislead. Provide reasoning or calculate support points (e.g., mean±3σ) to justify axis limits mathematically.

The superimposed histogram and curve are interpreted qualitatively. Quantify misfit (e.g., area difference or KS statistic) to strengthen the connection between visual and statistical assessments.

The null and alternative hypotheses are conventionally reversed: typically $H_0$ assumes normality. Align hypothesis statements with standard conventions to avoid confusion.

Merging class intervals yields uneven widths and reduces df; discuss the impact on test sensitivity and degrees of freedom to show comprehensive use of mathematics.