IB Mathematics Analysis and Approaches (AA) SL Extended Essay Example

You stated a clear and measurable research question early in the report.

Your topic is focused and sustained, with a strong real-world modelling context.

You linked your method to the question well by using residuals and RMSE to test model accuracy.

The question could be even sharper by naming the exact system, conditions, and accuracy threshold.

Some methodological choices are not fully justified or reproducible.

The transition between cooling phases is based partly on a subjective observation.

You use a strong range of mathematical terminology such as equilibrium temperature, differential equations, asymptotes, residuals, and RMSE.

You apply relevant mathematical techniques appropriately, including separation of variables and piecewise modelling.

You generally use the theory in a way that is connected to your own data and modelling context.

There are a few important inconsistencies in notation and model form, including the sign of the exponent in the final standard model.

Some of the parameter-fitting choices are not fully justified mathematically.

A few terms are used more strongly than the evidence fully supports.