IB Mathematics Applications & Interpretation (AI) SL Extended Essay Example

The student identifies a clear mathematical topic and keeps returning to reflection matrices as the central idea.

The student uses a sensible method by building transformations from basis vectors and geometric properties.

The student includes relevant verification steps with software and examples, which helps show intent to test results.

The research question is broader than the investigation can fully support.

The focus shifts from a narrower 2D question to a much wider 2D/3D treatment without enough justification.

Some derivations are weakened by unclear notation and incomplete or malformed algebraic steps.

The student uses a good range of relevant mathematical ideas, including matrices, perpendicularity, normals, homogeneous coordinates, and composition of transformations.

The student shows sound understanding in several places, especially where they derive a reflection matrix from geometric conditions.

The student generally uses subject terminology correctly enough to support the investigation.

Some important mathematical distinctions are not handled precisely, especially the difference between linear and affine transformations.

There are recurring notation and labeling errors that reduce confidence in the mathematics.

A few claims are stated too broadly or imprecisely, which weakens the reliability of the overall argument.