IB Mathematics AA HL – Log & Exp Functions (Module 5)

Exponential & logarithmic functions, equations, graphs, modelling, and integration — fully aligned with IB AA HL

Created byKonstantinos Kokoris

Last updated 2/2026

English

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

1 section • 15 lectures • 41m total length

Module overview1:27
Exponential Functions: Definition & Structure3:21
This lesson introduces exponential functions through their formal definition and structural properties.
Emphasis is placed on domain, range, growth and decay behaviour, and correct functional notation, as required in IB Mathematics AA HL.
Students learn to recognise exponential structure and explain behaviour mathematically, not just apply formulas.
Logarithmic Functions: Definition & Inverse Relationship3:27
This lesson introduces logarithmic functions through their formal definition as inverses of exponential functions.
Emphasis is placed on domain restrictions, functional notation, and the inverse relationship required in IB Mathematics AA HL.
Students learn to interpret logarithms conceptually, not as mechanical rules.
Laws of Logarithms (Conceptual, not mechanical)3:15
This lesson develops the laws of logarithms from the inverse relationship with exponentials.
Emphasis is placed on meaning, structure, and correct application, rather than rote manipulation, as expected in IB Mathematics AA HL.
Students learn when and why each law applies.
Solving Exponential Equations3:19
This lesson focuses on systematic methods for solving exponential equations using algebraic reasoning and logarithms.
Emphasis is placed on correct structure, justification of steps, and clear communication, as required in IB Mathematics AA HL.
Students learn to recognise appropriate solution strategies and avoid common exam errors.
Solving Logarithmic Equations3:12
This lesson develops systematic methods for solving logarithmic equations using logarithmic laws and algebraic reasoning.
Emphasis is placed on domain restrictions, rejection of invalid solutions, and clear structure, as required in IB Mathematics AA HL.
Students learn to justify solutions rather than rely on manipulation alone.
Graphs of Exponential & Logarithmic Functions3:45
This lesson examines the graphical behaviour of exponential and logarithmic functions.
Emphasis is placed on domain, range, asymptotes, transformations, and the distinction between the cases α > 1 and 0 < α < 1, as required in IB Mathematics AA HL.
Students learn to interpret graphs analytically, not by memorisation.
Modelling with Exponential Functions3:18
This lesson focuses on using exponential functions to model real-world situations.
Emphasis is placed on interpreting parameters, justifying the choice of model, and writing solutions clearly, as required in IB Mathematics AA HL.
Students learn to connect mathematical structure with contextual meaning.
Integrating Exponential Functions3:17
This lesson introduces the integration of exponential functions using standard techniques.
Emphasis is placed on structure, constant factors, and correct notation, as required in IB Mathematics AA HL.
Students learn to interpret integrals as accumulated change.
Integrating Logarithmic Functions3:21
This lesson focuses on the integration of logarithmic functions, including forms that require algebraic manipulation.
Emphasis is placed on correct structure, use of logarithmic expressions, and mathematical justification, as required in IB Mathematics AA HL.
Students learn to recognise integrable forms rather than apply rules mechanically.
Definite Integrals with Exponentials & Logs3:05
This lesson develops the use of definite integrals involving exponential and logarithmic functions.
Emphasis is placed on correct evaluation, limits of integration, and interpretation of results, as required in IB Mathematics AA HL.
Students learn to link integration with total change.
Exponential Models & Integration3:05
This lesson combines exponential modelling with integration to analyse accumulated change in real-world contexts.
Emphasis is placed on correct setup, interpretation of results, and clear mathematical communication, as required in IB Mathematics AA HL.
Students learn to move from rate models to total quantities.
Worked IB-Style Examples (Exam Workshop)2:53
Final Exam Module 50:10
Module Summary and Next Steps0:33

Requirements

Basic algebra skills, including solving linear equations and manipulating expressions.
Familiarity with functions and graphs at pre-IB or early IB level.
Enrollment in or preparation for IB Mathematics AA HL is strongly recommended.

Description

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.

Who this course is for:

IB Mathematics AA HL students who want a structured, exam-aligned understanding of logarithmic and exponential functions.
Students aiming for top IB exam performance, not just procedural practice.
IB teachers or tutors looking for a clear, syllabus-accurate reference for teaching this topic.