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

The title is clear and descriptive, immediately informing the reader of the investigation focus on tin size, shape, and cake rise.

The inclusion of word count and student number adds administrative clutter; consider relocating these details to a cover sheet or appendix.

Aim section repeats similar statements and could be more concise; refine wording to focus on one clear research question.

Bibliography entries are present but formatting is inconsistent; use a standard citation style (e.g., APA) and ensure uniformity.

Definitions of linear and exponential variables use inconsistent notation and lack units; standardize symbols and specify units where applicable.

The data table lacks axis labels and units; add clear labels (e.g., time in minutes, rise in mm) to enhance clarity.

Figure 1 provides a helpful visual of the setup, aiding reader comprehension of how measurements were taken.

Bake time specified as “50.01 minutes” suggests overprecision; round to a practical value (e.g., 50 min) and include units consistently.

Temperature annotation “210°c” uses lowercase “c”; standardize to “210 °C” to align with SI notation.

The text refers to axes T and R without defining them in the caption; explicitly label axes as time (min) and rise (mm).

Exponent difference uses x=17.02 in one section and x=17.03 elsewhere; ensure consistency of data points in all calculations.

Figure 8 for medium tin lacks axis labels and scale markers; adding these would make the comparison clearer.

The calculation label “1/x ≈17.754” should read $\overline{x}\approx 17.754$; correct this notation to avoid confusion.

Summation table demonstrates all intermediate values clearly, supporting transparency of the correlation calculation.

The introductory paragraph effectively uses personal narrative to engage the reader and demonstrate genuine interest in the topic.

Evaluation of the unsuccessful trial thoughtfully identifies key sources of error, demonstrating meaningful reflection on methodology challenges.

The interpretation in the combined plot claims tin shape affects rate but earlier correlation results show weak relationships for medium tin; reconcile this inconsistency.

Interpretation of $r\approx 0.160$ treats any positive as meaningful; discuss the low magnitude and its statistical insignificance.

The evaluation section comprehensively discusses practical errors (oven door, positioning, timing) demonstrating thoughtful critical analysis.

Reflection on personal learning demonstrates awareness of how mathematical and experimental processes interact, enhancing depth of insight.

The first-attempt method list lacks details on repeated trials and controls; include number of repetitions and control variables for reliability.

The improved-trial data table is well laid out, showing clear comparative data across tin sizes.

The gradient calculation uses points (36.14,20) and (17.03,10) but the resulting m ≈0.520 conflicts with the quotient ~0.523; re-check arithmetic.

The presentation of a and b values in the exponential model is correct and shows good understanding of simultaneous equations.

Best-fit discussion describes visual fit but lacks quantitative metrics (e.g. residuals or $r^2$); include these to strengthen justification.

The Pearson correlation formula is stated accurately using correct summation notation, aiding clarity for statistical analysis.

Square-root step shows $\sqrt{908.62\times 250}$ but intermediate product value is omitted; include it (e.g. $908.62\times 250=227155$).