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Act as an IB Math IA supervisor with extensive experience marking explorations. Help me plan my Math IA exploration:
1. **Choosing a Topic**: Suggest engaging topics that connect mathematics to a personal interest area
2. **Research Question**: Formulate a clear, focused question that allows for mathematical exploration
3. **Mathematical Content**: Identify which areas of the syllabus you can demonstrate (e.g., calculus, statistics, modelling)
4. **Criterion A — Presentation** (4 marks): Structure your exploration logically with introduction, body, and conclusion; use appropriate mathematical language and define key terms
5. **Criterion B — Mathematical Communication** (4 marks): Use proper notation, define variables, label graphs, and format expressions with LaTeX: $$f(x) = ax^2 + bx + c$$
6. **Criterion C — Personal Engagement** (3 marks): Show genuine interest and make the exploration YOUR OWN — reflect on choices, explain WHY this topic matters to you
7. **Criterion D — Reflection** (3 marks): Discuss the significance of results, consider limitations, and suggest extensions
8. **Criterion E — Use of Mathematics** (6 marks): Demonstrate mathematics commensurate with your level (AA HL vs AI SL have different expectations)
**Topic Ideas by Course:**
- **AA HL**: Modelling with differential equations, complex number geometry, proof by induction applications
- **AA SL**: Optimization problems, exponential growth modelling, trigonometric applications
- **AI HL**: Statistical analysis of real data, Voronoi diagrams, network optimization
- **AI SL**: Correlation studies, linear programming, financial mathematics
**Word Count Guidance:** Aim for 12–20 pages (roughly 6,000–12,000 words including calculations)
**Common Mistakes:**
- Choosing a topic that is too broad or too narrow
- Relying on technology without showing understanding
- Forgetting to reflect throughout (not just at the end)
- Insufficient personal engagement — avoid generic textbook problems
**IB Tip:** The best explorations connect mathematics to something YOU genuinely care about. Moderators can tell when engagement is authentic.
**My interests and course level:** [DESCRIBE YOUR INTERESTS AND MATH COURSE]