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

The inclusion of a standalone “Page Count” line interrupts the academic flow and is unnecessary within the main body.

The title prominently identifies the subject and level of inquiry, providing clear context for the reader.

Consider adding a brief abstract or aim statement on the title page to outline objectives and scope.

The first TOC entry reads “In traditional action,” which appears unrelated to the investigation’s content—review for accuracy.

The table of contents provides section names but omits page references, making navigation cumbersome.

Consider aligning all TOC entries in a consistent format and include page numbers for each section.

Footnotes interrupt readability; integrate key references in-text or use endnotes to enhance conciseness.

Repeating the list of series tested adds redundancy; consolidate into one concise paragraph.

The final sentence trails off mid–thought; complete the aim statement to clarify the scope of series under study.

The harmonic series section repeats the definition style; consider referring back to the standard form to avoid redundancy.

Bibliography entries vary in style and are missing access dates; adopt a consistent citation convention.

The introduction clearly defines infinite sequences and series, establishing foundational concepts effectively.

Consider summarizing the four limit comparison outcomes in a small table to enhance multiple representations.

The statement of limit comparison test conditions is conflated—L=0 and L=∞ clauses need clearer separation.

The generalised geometric series’ formula uses “ar2” instead of proper exponent notation $a{r}^2$—adjust for consistency.

Including a small table of values of $a_n$ versus $n$ would improve clarity of how $|r|$ controls term size.

The graph visually supports divergence reasoning, but it is a stock image; generating your own CAS plot would be more authentic.

The explanation of how the area under $f(x)$ bounds the series is clear and logically structured.

The conditions for the integral test on $f(x)=1/x$ are systematically verified, demonstrating clear methodical communication.

In the limit calculation, the step “ln 1=0” is omitted; include explicit evaluation to maintain rigor.

The personal connection to finance in perpetuity valuation demonstrates genuine engagement with real-world applications.

The exploration shows clear personal interest in finance, linking theory to real‐world motivation effectively.

Reflection on why certain tests were inapplicable is noted but would benefit from deeper critical analysis.

Describing how each test complements others in the evaluation section would deepen reflection on methodology.

The evaluation acknowledges limitations but lacks discussion on error sources or sensitivity of tests.

Suggest extending to p-series or root test as noted, and specify expected outcomes to sharpen future directions.

The definition of the generalised arithmetic series is accurately presented with summation notation.

The conclusion that integral test cannot apply due to an increasing derivative needs referencing derivative sign tests.

The limit calculation correctly shows that L=d, a constant >0, proving divergence via limit comparison.

Use of both ratio and integral tests demonstrates effective selection of HL convergence techniques.

The integral test application correctly computes $${\int }_1^{\infty }a{r}^{x}dx$$, but justification for continuity on $[1,\infty )$ is minimal.

In the alternating series test section, rationale is sound but could be improved by referencing Leibniz’s original theorem source.