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

The title page lacks essential IB details such as the candidate name, number, subject, and date. Including these will align with IB presentation standards.

The separate “Number of pages: 12” notation is unnecessary. Removing it will improve conciseness and adhere to standard IB formatting.

The lengthy definitions of Pearson’s $r$ and $r^2$ are repeated across paragraphs, which interrupts flow. Streamline these to maintain relevance.

Citations for statistical definitions appear inline. Consider referencing once and directing readers to the Works Cited for cleaner presentation.

The table caption and source note are separate entries. Merge these into a single caption below the table to improve organization.

The caption describing Table 3 appears above the table; IB convention places captions below. Relocate it for better organization.

Add a concise caption for Table 3 that specifies rounding conventions and column headings in a unified format.

The conclusion and reflection are merged within the results narrative, obscuring clear organization. Separate these sections for coherence.

Consider applying a consistent citation format (e.g., MLA or APA) with italics, authors, and dates to enhance presentation quality.

The bibliography entries are inconsistently formatted (line breaks disrupt URLs, missing authors/titles). Standardize using a recognized style.

The final page of references includes an orphaned entry and lacks a concluding statement. Ensure only fully cited sources remain.

The main data table presents all 15 points clearly, which supports subsequent manual and calculator-based analyses.

Column headers lack unit labels (e.g., lbs, %). Adding units directly to headers will strengthen mathematical communication.

The scatter-plot effectively visualizes the inverse linear trend between body weight and BAC, providing a clear multiple representation.

Axes on the graph are unlabeled with scales or units, reducing clarity. Add numeric tick marks and unit labels to each axis.

When substituting values into the slope equation, annotate each number with its symbolic origin (e.g., $\Sigma xy=563.36$) to enhance clarity.

Terminology shifts between “slope/y-intercept formula” and $y=mx+b$. Use consistent notation to avoid confusion.

The Pearson formula denominator is written as $[n\Sigma y^2-(\Sigma y{)}^2]$ but ensure consistency with the numerator’s bracketed form for clarity.

The introduction effectively uses personal context—interest in healthcare and class experience—to motivate the investigation and engage the reader.

The reflection connecting correlation to experiences in biology and physics shows insightful interdisciplinary engagement.

Consider performing a residual analysis to evaluate how well the linear model fits the data and discuss any systematic deviations.

Directly compare your manual and GDC values for $m$, $b$, and $r$ in a summary table to highlight consistency and deepen analysis.

Discuss the assumptions underlying Pearson’s $r$ (linearity, homoscedasticity) to enhance critical analysis of the correlation.

Propose further exploration such as residual pattern analysis or comparison with non-linear models, beyond the suggested chi-square test.

Discuss why a linear model was chosen in terms of goodness-of-fit (e.g., $r^2$) beyond visual inspection to justify model selection rigorously.

The least-squares slope formula $m=\frac{n\Sigma xy-\Sigma x\Sigma y}{n\Sigma x^2-(\Sigma x{)}^2}$ is correctly presented, demonstrating solid use of SL mathematics.

The intermediate calculation $m=\frac{-622.5}{420000}$ and its approximation to three significant figures could be accompanied by a brief note on rounding error.

The contextual interpretation of slope $m\approx -0.00148$ (“BAC decreases by 0.00148 per pound”) is clear and mathematically accurate.

The y-intercept calculation is correctly performed and its physical meaning at $x=0$ is thoughtfully discussed.

Steps for GDC verification are listed, but the calculator’s reported correlation coefficient $r$ is omitted. Include it to confirm manual calculations.

Including the $y^2$ column in Table 3 demonstrates thorough understanding of Pearson’s coefficient components.

The manual computation of $r\approx -0.972$ is correctly executed and its interpretation (strong inverse correlation) is accurate.