IB Mathematics AA HL – Limits & Derivatives (Calculus Module

Master Limits and Differentiation with IB-Style Examples, Exam Technique, and Strong Calculus Foundations
What you'll learn
✓ Understand and interpret average and instantaneous rates of change using graphs and algebra.
✓ Understand and interpret average and instantaneous rates of change using graphs and algebra.
✓ Differentiate functions using power, sum, product, quotient, and chain rules at IB HL level.
✓ Differentiate trigonometric functions and composite expressions accurately using the chain rule.
✓ Set up and write full IB-style solutions with correct notation, structure, and method marks.
✓ Identify and avoid the most common IB examiner traps in differentiation questions.
Requirements
● Students should have completed the core foundations of IB Mathematics AA HL, including basic functions, algebraic manipulation, and graphical interpretation. Familiarity with rates of change and simple gradients is recommended. No prior knowledge of calculus is required, as all concepts are developed from first principles.
Description
This course is the second module of a structured IB Mathematics AA Higher Level series and provides a rigorous introduction to limits and differentiation, the foundation of all IB calculus.
Rather than memorising formulas or applying shortcuts, this course develops the conceptual understanding, precision, and mathematical structure required by the IB assessment criteria. Every topic is taught exactly as it is expected in IB exams, with emphasis on correct notation, logical reasoning, and exam-style presentation.
You will study
• average and instantaneous rates of change
• the concept of limits and approaching a value
• secant and tangent lines
• the formal definition of the derivative from first principles
• differentiation rules and techniques
• IB-style interpretation of graphs and rate problems
Each lesson is carefully designed with
• clear step-by-step explanations
• IB-style worked examples
• common examiner mistakes and traps
• structured practice and consolidation
This course is not based on tricks or shortcuts. It is designed to build deep understanding so that students can confidently handle advanced calculus, optimization, motion problems, and later IB topics.
It is ideal as
• a foundation before advanced calculus
• structured support alongside school lessons
• focused preparation for IB Math AA HL exams
By the end of this module, students will be able to approach differentiation problems with confidence, accuracy, and correct IB exam technique.
Who this course is for
■ This course is designed for IB Mathematics AA Higher Level students who are beginning calculus and want a clear, structured, and exam-oriented introduction to differentiation. It is ideal for students who want to build strong foundations before advanced calculus, improve their problem-solving technique, and learn how to write correct IB-style solutions. It is also suitable for teachers and tutors looking for structured IB-aligned material.
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