Internal Assessment

The math exploration is not a lab report. There is no experiment, no data collection in the traditional sense, and no apparatus. Instead, you investigate a mathematical idea — proving something, modelling a real phenomenon mathematically, exploring the applications of a theorem, or analysing a mathematical pattern. The emphasis is on mathematical reasoning, communication, and personal engagement with the mathematics itself.

This criterion assesses the overall organisation and readability of your exploration. A well-presented exploration has a clear introduction stating the aim, logical sections that flow naturally, appropriate use of mathematical notation and technology-generated graphs/diagrams, and a conclusion that ties the work together. The reader should be able to follow your reasoning from start to finish without confusion. References and a bibliography are expected.

This assesses how well you use mathematical language, notation, and terminology. You should define any variables or symbols you introduce, use correct mathematical notation consistently, and explain your reasoning in coherent sentences — not just present a string of equations. The exploration should read as a piece of mathematical writing, not as scribbled working-out. Technology output (graphs, tables, screenshots) should be integrated into the narrative with clear captions and references in the text.

This criterion rewards evidence that you explored the topic out of genuine personal interest rather than obligation. Signs of personal engagement include: exploring a topic connected to your own hobby, curiosity, or experience; making the exploration your own by adapting or extending a known idea rather than just summarising it; and showing independent thinking — for example, testing your own conjectures or reflecting on surprising results. An exploration that reads like a textbook chapter with no personal voice will score poorly here.

This is about critically evaluating your own mathematical work. It is not enough to just do the mathematics — you should step back and comment on it. Strong reflection includes: discussing the limitations of your approach or model (what assumptions did you make, and how do they constrain your conclusions?); considering alternative methods or extensions; and linking your findings back to the original aim. Reflection should be woven throughout the exploration where natural, not dumped into a single paragraph at the end.

This is the heaviest-weighted criterion. It assesses the depth, sophistication, and accuracy of the mathematics you use. This is not about using the most advanced mathematics possible — it is about using mathematics that is commensurate with the level of the course and applying it correctly and meaningfully. An HL exploration that only uses SL-level mathematics without demonstrating deeper understanding will score poorly, while a well-executed exploration using appropriate HL content (e.g. calculus, complex numbers, vectors, differential equations) can score highly. Errors in fundamental mathematics will reduce the mark regardless of ambition.