IB Math AI Worksheet 5.1 - Limits

This IB Maths AI SL 5.1 – Limits worksheet builds students’ foundational understanding of limits as a way of describing how functions behave as inputs approach particular values. Learners develop fluency with limit notation, one-sided limits, and the idea that a function can approach a value even when it is undefined at that point. Core concepts such as approaching values, discontinuities, and the connection between limits and rates of change are introduced through clear, structured tasks.

Guided activities move from estimating limits using tables and algebraic simplification to classifying removable, jump, and infinite discontinuities. Students practise evaluating one-sided limits, applying limit laws, and using factoring and rationalising techniques to resolve indeterminate forms. The resource also supports conceptual reasoning, encouraging learners to explain in words why limits exist or fail to exist and to interpret graphical and algebraic behaviour together.