Once you’ve benchmarked sample reports, elevate your IA by strategically incorporating more complex mathematical concepts beyond the syllabus. Here’s how:
1. Go Beyond the Syllabus
The main math concept for your IB Math IA should be drawn from the IB Math syllabus, but aim to extend it slightly beyond the syllabus.
Example:
- SL Students: Use HL-only topics (e.g., parametric equations for modeling a bridge, polar coordinates for analyzing planetary orbits).
- HL Students: Incorporate first-year university math (e.g., partial differential equations).
Guiding Questions:
- What HL/university concepts naturally extend my topic?
- Can I replace a basic method (e.g., linear regression) with a more sophisticated technique (e.g., nonlinear least squares)?
- Does my topic intersect with another discipline (e.g., physics, economics) that requires advanced math?
2. Critically Evaluate Different Approaches
You can compare various mathematical approaches in your IB Math IA, justify your choices, and discuss their limitations.
Example:
- Compare Regression of X on Y vs. Y on X: compare regression of X on Y versus Y on X, explaining why their slopes differ and determining which is better suited for your analysis. This concept, introduced in the Haese textbook’s Bivariate chapter, helps you understand how the choice of dependent variable impacts your results.
- Contrast Polynomial Regression vs. Lagrange Interpolation for Modeling: for modeling an object, contrast polynomial regression (easy to implement) with Lagrange interpolation (precise but unstable).
Guidance Questions:
- Open your IB Math textbook to the chapter explaining your mathematical approach, skim through it, and list all the math concepts introduced. Then, consider if there are other related concepts that could enhance your approach.
3. Manual Calculations for showcasing your understanding
You can demonstrate your understanding of the concept by performing key calculations manually.
Example:
- Regression modelling: Manually calculate the least squares regression linear equation.
Guidance Questions:
- Which calculations are simple enough to do manually but complex enough to showcase skill?
- How do manual results compare to software outputs?