IB Mathematics Analysis and Approaches (AA) SL Extended Essay Example

The topic and purpose are communicated accurately and effectively through a clear title, introduction, signposts, and conclusion.

The research question is prominently stated, focused, and consistently linked to the analysis throughout the essay.

The three-stage methodology is coherent and generally appropriate, with logical progression from delay-embedding to Lyapunov exponent to fractal dimension.

The phrasing of the research question shifts slightly in later sections, reducing consistency of focus.

Scope is overambitious given the limited seven-week data window, weakening practical applicability.

Delay-embedding parameter choices (τ=5, ω=7) are asserted without justification or sensitivity testing, and replicability details are only partially provided.

Consistent and accurate use of subject-specific terminology (Lyapunov exponent, fractal dimension, bifurcation) with clear definitions and application.

Demonstrates good conceptual understanding of chaos-theory constructs and their relevance to financial markets through worked numerical examples.

Notation is occasionally inconsistent (e.g., X(t) vs Xₙ) and contains minor typos (e.g., logistic map formula).

Explanatory passages sometimes blur mathematical precision with colloquial language, and there is no error analysis or validation of key calculations.

Repetitive definitions and reliance on secondary sources (e.g., Google Search) undermine academic rigor.