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

The student states a clear research question and keeps the investigation broadly connected to it throughout.

The student uses a logical modelling sequence from assumptions to equations to numerical solution.

The student shows awareness of the vehicle context and chooses a method suited to a nonlinear coupled system.

The investigation would be stronger if the target quantity were defined more precisely from the start.

Some modelling choices are not justified clearly enough, especially the fixed yaw-rate assumption and the conditions under which the maximum is being sought.

The purpose is sometimes narrowed by the computation, so the final answer feels more like a model output than a fully framed investigation.

The student uses a strong range of relevant subject terminology, including vehicle-dynamics and numerical-method language.

The student demonstrates sound understanding of core mathematical ideas such as coupled differential equations, root finding, and Runge-Kutta iteration.

The student applies the concepts in a way that usually supports the physical problem rather than remaining purely abstract.

Several terms and symbols are not used with complete consistency, which makes parts of the derivation harder to follow.

Some notation is imprecise, such as using a term that is later assigned a different meaning, or using a broader term where a more exact one is needed.

A few formulae and variable links are not explained cleanly enough, so the mathematical ideas are not always applied with full control.