GeoGebra for dynamic geometry
Illustrate invariants and dynamic relationships visually, turning abstract properties into interactive demonstrations that support your argument.
Choosing the right Internal Assessment topic shapes the entire experience of the Mathematics: Analysis and Approaches Higher Level exploration. A well-chosen focus lets you demonstrate mathematical communication, personal engagement, and the depth of reasoning the criteria reward.
Strong explorations often come from areas where the mathematics naturally invites clear communication, structured presentation, and meaningful reflection. Topics that let you define notation, explain steps, and evaluate your own methods tend to score well across the criteria.
Look for directions where you can move beyond calculation into justification, where visual or computational tools clarify the argument, and where the conclusion opens a genuine reflective comment on limitations or extensions.
Explore divisibility patterns, modular arithmetic, or properties of special sequences with rigorous justification.
Examine convergence of unusual series, parametric or polar curves, or applications of the Mean Value Theorem in non-standard settings.
Extend a known result or construct a proof for a conjecture you formulate, comparing proof techniques along the way.
Investigate different approaches to the same problem to highlight the structure of mathematical reasoning.
Illustrate invariants and dynamic relationships visually, turning abstract properties into interactive demonstrations that support your argument.
Generate data for conjectures, run simulations, or automate repetitive calculations while keeping the mathematical narrative central.
Show asymptotic behaviour, bifurcations, or curve families that clarify the mathematical development.
Include screenshots or code snippets only when they support the narrative. Explain what the tool does, why you chose it, and how the output informs your reasoning.
Turn computational work into clear mathematical communication by linking each output to a step in your argument.
Open with a clear aim and a research question that defines the mathematical object, method, and intended outcome.
Introduce notation, definitions, and any theorems you will use so the development reads as a self-contained argument.
Present calculations and reasoning in a readable order, moving from foundations to results with justifications at each step.
End with a reflection that addresses limitations, possible extensions, and what you learned about the mathematics itself.
Frequent issues include insufficient depth for HL, weak personal engagement shown by following a textbook example without adaptation, and mathematical reasoning that states results without justification. Over-reliance on software output without explanation also weakens communication.
Avoid topics that are purely descriptive or that stay at Standard Level depth. Check that every claim has a reason, that your voice appears in the choices made, and that the reflection goes beyond a summary of steps.
Use supervisor checkpoints to confirm the question is viable and the structure works.
Share drafts with peers for clarity of communication and logical flow.
Targeted tutoring can help deepen the mathematics, improve notation, or strengthen the reflection.
Treat feedback as part of the process; documenting your responses demonstrates engagement and strengthens the final submission.
Check whether the mathematics uses HL-only syllabus content such as proof by induction, complex numbers, differential equations, or advanced calculus. If the core argument could be done at SL, extend it with a generalization, a proof, or a deeper analysis.
You can start from a known problem, but you must adapt it with your own question, method, or extension. Personal engagement is shown by the choices you make, not by replicating a worked example.
Include only what supports the mathematical narrative. A short snippet or a key graph with explanation is better than pages of output. The focus remains on your reasoning, not the tool.
A strong reflection discusses limitations of the method, assumptions that could be relaxed, alternative approaches, and what the exploration taught you about the mathematics itself, not just the process.
Finalize after you have sketched the background and the first steps of the development. If the sketch reveals gaps or repetition, adjust the question before investing in the full write-up.
Bring your ideas or draft question to a consultation. We help you check the scope, align with the criteria, and plan the mathematical development so your exploration meets AA HL expectations.