IB Mathematics AI SL - Topic 5: Calculus | Complete Student Notes

IB Mathematics AI SL – Topic 5: Calculus | Complete Lesson Notes

A complete set of structured lesson notes for IB Mathematics: Applications and Interpretation SL, covering the full Topic 5 Calculus syllabus from SL 5.1 to SL 5.8.

This 100+ page digital book is designed to help students build a clear understanding of calculus rather than simply memorising procedures. Each section develops the ideas carefully, combines algebraic reasoning with appropriate GDC use, and includes worked examples, diagrams, practice questions and answer keys.

The book covers:

• 5.1 Limits and the Derivative

• 5.2 Increasing and Decreasing Functions

• 5.3 Power Rule Differentiation

• 5.4 Tangents and Normals

• 5.5 Integration and Area

• 5.6 Stationary Points

• 5.7 Optimisation

• 5.8 Trapezoidal Rule for Integration

Particular attention is given to the way calculus is actually used in AI SL Mathematics. Students are shown when a result should be obtained algebraically, when technology is expected, and how the two approaches connect.

The notes develop the relationship between the sign of the derivative and the behaviour of the original function, show how stationary points can be located and classified using the derivative function, and use both calculus and GDC methods appropriately in optimisation problems.

Integration is treated not only as a calculation, but also as an accumulated quantity and as area where appropriate. The notes reinforce the use of boundary conditions, definite integrals and correct interpretation in context.

Optimisation develops the full modelling process: identifying the quantity to maximise or minimise, forming a one-variable model, considering the meaningful domain, using calculus and/or technology, checking endpoints when required, and interpreting the final answer.

Throughout the book, students will find:

• Clear and concise explanations

• Fully worked examples

• Graphs and mathematical illustrations

• GDC guidance and calculator screenshots

• Common-error warnings and exam advice

• Practice questions of increasing difficulty

• Complete answer keys

• IB exam-focused support

The book is especially useful for students who want to become more confident using their graphic display calculator alongside calculus, while still understanding the mathematics behind the calculator output.

Suitable for learning Topic 5 for the first time, consolidating classwork, independent study, or revision before assessments.

Format: Digital PDF

Course: IB Mathematics: Applications and Interpretation SL

Topic: Topic 5 – Calculus

Author: John Radford, Radford Mathematics

This resource has been developed independently by Radford Mathematics and is not approved or endorsed by the International Baccalaureate Organization.