IB Mathematics AA HL – Apps of Derivatives (Module 4)

Maxima & Minima, Optimisation, Curve Sketching and Real IB Applications
What you'll learn
✓ Use first and second derivatives to analyse the behaviour of functions, including increasing/decreasing intervals and concavity.
✓ Identify and classify stationary points using derivative-based methods, following IB marking expectations.
✓ Apply derivatives to real IB-style contexts, such as optimisation, motion, and curve behaviour interpretation.
✓ Interpret derivative results mathematically, not just compute them, using correct IB mathematical language.
✓ Justify conclusions clearly and logically, as required in IB Mathematics AA HL examination questions.
✓ Avoid common IB exam errors when applying derivatives to unfamiliar or multi-step problems.
Requirements
● A basic understanding of functions and graphs, including domain and range.
● Familiarity with limits and differentiation rules at the level covered in IB Mathematics AA HL.
● Completion of Module 2 (Limits & Derivatives) or equivalent IB-level calculus preparation.
● Completion of Module 2 (Limits & Derivatives) or equivalent IB-level calculus preparation.
Description
This course is Module 4 of a structured IB Mathematics AA Higher Level series and focuses on one of the most heavily assessed areas of the syllabus: applications of derivatives.
In IB Mathematics, differentiation is only the starting point. What truly matters is how derivatives are used to analyse, interpret, and justify conclusions about real mathematical situations. This module is designed to bridge the gap between mechanical differentiation and the type of reasoning the IB expects in exam questions.
You will study how derivatives are applied to
• identify and classify maxima and minima
• perform optimisation with clear mathematical justification
• analyse tangents and normals
• sketch curves using first and second derivative information
• interpret rates of change in applied contexts
• solve related rates and motion problems using derivatives
Each lesson emphasizes
• correct mathematical language
• structured IB-style reasoning
• common examiner expectations and pitfalls
• clear interpretation of results, not just calculation
This course avoids shortcuts and memorisation. Instead, it develops the analytical thinking required to score consistently in IB Mathematics AA HL, particularly in Paper 1 and Paper 2 questions involving applications of calculus.
The module is ideal as
• structured support alongside school teaching
• targeted preparation for IB exam-style application questions
• a bridge between learning differentiation and applying calculus effectively
By the end of this course, learners will be able to use derivatives confidently, justify their conclusions clearly, and approach application questions with structure and precision—exactly as required by the IB assessment criteria.
Students under the age of 18 may only access this course through an account created and managed by a parent or legal guardian, in accordance with Udemy's policies.
Who this course is for
■ Parents or guardians of IB Mathematics AA HL students who want structured, high-quality academic support aligned with IB assessment standards.
■ Parents or guardians of IB Mathematics AA HL students who want structured, high-quality academic support aligned with IB assessment standards.
■ IB Mathematics AA HL students (via a parent or guardian account) who want to understand how derivatives are used, not just how they are calculated.
■ IB teachers and tutors looking for a clear, structured resource focused on correct mathematical thinking and IB-style justification.
■ Adult learners or educators interested in a rigorous, exam-oriented approach to calculus applications.
■ This course is intended for purchase by adults and may be used by students under 18 only under parental or guardian supervision, in line with Udemy policy.
Homepage

https://www.udemy.com/course/ib-mathematics-aa-hl-apps-of-derivatives-module-4/

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