IB Maths AI SL 2.5 - Modelling with Functions Notes

This IB Maths AI SL 2.5 resource introduces modelling with functions in real-world contexts, and is fully aligned with the IB Applications and Interpretation SL syllabus.

Students learn how mathematical models can be used to describe and predict relationships between quantities. The notes introduce the idea of choosing a model based on the pattern in the data or context, including constant rates of change, turning points, repeated cycles, proportional relationships, and inverse variation.

The resource develops key function models used throughout the course, including linear, quadratic, exponential, sinusoidal, cubic, direct variation, and inverse variation models. Students learn how to interpret important parameters such as gradient, intercepts, roots, vertex, amplitude, period, horizontal asymptotes, and constants of variation.

Structured examples guide students through modelling practical situations, including rideshare costs, the height of a baseball, bacteria population growth, the motion of a point on a circular exercise wheel, particle velocity, and an inverse variation gas problem. Each example encourages students to connect the algebraic model with the meaning of the variables in context.

The notes also emphasize the importance of checking whether a model is reasonable. Students are reminded to consider domain restrictions, units, and the real-world meaning of inputs, such as why negative time is not usually valid in a time-after-event model.

The resource finishes by connecting different function types to their characteristic features, helping students decide which model is appropriate for a given situation and interpret results in context.

Ideal for IB Maths AI SL teachers teaching mathematical modelling, linear models, quadratic models, exponential models, sinusoidal models, cubic models, direct variation, inverse variation, and contextual interpretation of functions.

This pairs great with our slidedeck!