Exponential & logarithmic functions, equations, graphs, modelling, and integration — fully aligned with IB AA HL
This course covers Module 5 of IB Mathematics AA HL, focusing on logarithmic and exponential functions and their use in equations, graphs, modelling, and integration.
What you’ll learn
- Understand the structure of exponential and logarithmic functions, including domain, range, inverse relationships, and growth or decay..
- Solve exponential and logarithmic equations correctly, stating domain restrictions and rejecting invalid solutions as required in IB exams..
- Analyse and sketch exponential and logarithmic graphs, including transformations and the cases a>1 and 0<a<1.
- Model real-world situations using exponential functions, interpret parameters, and justify the choice of model in IB-style questions..
- Integrate exponential and logarithmic functions, including definite integrals, and interpret results as accumulated change..
- Solve full IB-style exam questions on logs, exponentials, and integration, using clear reasoning and correct mathematical notation..
Course Content
- Module 5: Logarithmic & Exponential Functions –> 15 lectures • 41min.
Requirements
This course covers Module 5 of IB Mathematics AA HL, focusing on logarithmic and exponential functions and their use in equations, graphs, modelling, and integration.
In IB Mathematics, these topics are not assessed as isolated techniques. Examiners expect students to understand structure, domain restrictions, functional behaviour, and interpretation, not just perform calculations. This course is designed to reflect exactly that expectation.
You will begin by studying the definition and structure of exponential and logarithmic functions, including their inverse relationship and growth or decay behaviour. The course then develops a conceptual understanding of logarithmic laws, followed by systematic methods for solving exponential and logarithmic equations, with careful attention to domain restrictions and invalid solutions.
Graphical behaviour is treated in full, including transformations and the critical distinction between the cases α > 1 and 0 < α < 1, which frequently appears in IB exam questions. You will then apply exponential functions to real-world modelling problems and learn how IB expects parameters to be interpreted and justified.
The second half of the course focuses on integration of exponential and logarithmic functions, including definite integrals and applications involving accumulated change. These ideas are then combined in modelling contexts, preparing you for multi-step IB exam questions.
The module concludes with worked IB-style exam examples and a full test with review, allowing you to practise writing solutions with correct notation, structure, and reasoning, exactly as required in IB assessments.
This course is part of a structured IB Mathematics AA HL pathway and is designed to function both as a standalone module and as preparation for further topics in the syllabus.
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.