IB Mathematics AI HL
Key Concepts

In the IB Mathematics Applications & Interpretation (AI) Higher Level (HL) Key Concepts section, you will find summary videos that will help you review the most important concepts and skills necessary for success. They are ideal for a quick refresher before tackling questions in the Revision Village Questionbank or Practice Exams sections of the website.

Topic 1

Number & Algebra

Topic 1

Number & Algebra

Rounding & Significant Figures

6 mins

Scientific Notation

5 mins

Percentage Error

5 mins

Arithmetic Sequences & Series

7 mins

Geometric Sequences & Series

10 mins

Sigma Notation

5 mins

Compound Interest & Depreciation

8 mins

Loans & Amortization

8 mins

Annuities

7 mins

GDC Tips: Finance Solver (TVM Solver)

6 mins

Introduction to Complex Numbers

9 mins

Forms of Complex Numbers (Rectangular, Polar, Euler)

10 mins

Operations of Complex Numbers

12 mins

GDC Tips: Complex Numbers

9 mins

Introduction to Matrices

12 mins

Solving Simultaneous Equations using Matrices

8 mins

Eigenvalues, Eigenvectors & Matrix Powers

13 mins

GDC Tips: Matrices

5 mins

Topic 1

Number & Algebra

Rounding & Significant Figures

6 mins

Scientific Notation

5 mins

Percentage Error

5 mins

Arithmetic Sequences & Series

7 mins

Geometric Sequences & Series

10 mins

Sigma Notation

5 mins

Compound Interest & Depreciation

8 mins

Loans & Amortization

8 mins

Annuities

7 mins

GDC Tips: Finance Solver (TVM Solver)

6 mins

Introduction to Complex Numbers

9 mins

Forms of Complex Numbers (Rectangular, Polar, Euler)

10 mins

Operations of Complex Numbers

12 mins

GDC Tips: Complex Numbers

9 mins

Introduction to Matrices

12 mins

Solving Simultaneous Equations using Matrices

8 mins

Eigenvalues, Eigenvectors & Matrix Powers

13 mins

GDC Tips: Matrices

5 mins

Topic 2

Functions

Topic 2

Functions

Forms of Linear Lines

7 mins

Gradients & Intercepts of Linear Lines

7 mins

Parallel & Perpendicular Gradients

3 mins

Perpendicular Bisectors

8 mins

GDC Tips: Intersection of Two Lines

4 mins

Functions: Overview & Types

7 mins

GDC Tips: Plotting Functions & Analysis Tools

9 mins

GDC Tips: Using nSolve to Solve Equations

6 mins

Domain & Range, Composite, Inverse

12 mins

Transformations of Functions

9 mins

Topic 2

Functions

Forms of Linear Lines

7 mins

Gradients & Intercepts of Linear Lines

7 mins

Parallel & Perpendicular Gradients

3 mins

Perpendicular Bisectors

8 mins

GDC Tips: Intersection of Two Lines

4 mins

Functions: Overview & Types

7 mins

GDC Tips: Plotting Functions & Analysis Tools

9 mins

GDC Tips: Using nSolve to Solve Equations

6 mins

Domain & Range, Composite, Inverse

12 mins

Transformations of Functions

9 mins

Topic 3

Geometry & Trigonometry

Topic 3

Geometry & Trigonometry

Geometry of 3D Shapes

3 mins

Pythagoras Theorem

6 mins

Right Angled Trig (Sin/Cos/Tan)

7 mins

Sine & Cosine Rule, Area of a Triangle

10 mins

Length of Arc, Area of Sector (Circles)

6 mins

Degrees v Radians

5 mins

Voronoi Diagrams

10 mins

Unit Circle & Trig Ratios

8 mins

Graphs of Trig Functions

8 mins

Graph Theory

11 mins

Vectors Basics

7 mins

Vector Equation of a Line

6 mins

Scalar Product & Angle Between Two Vectors

9 mins

Vector Product

8 mins

Geometric Transformations

10 mins

Topic 3

Geometry & Trigonometry

Geometry of 3D Shapes

3 mins

Pythagoras Theorem

6 mins

Right Angled Trig (Sin/Cos/Tan)

7 mins

Sine & Cosine Rule, Area of a Triangle

10 mins

Length of Arc, Area of Sector (Circles)

6 mins

Degrees v Radians

5 mins

Voronoi Diagrams

10 mins

Unit Circle & Trig Ratios

8 mins

Graphs of Trig Functions

8 mins

Graph Theory

11 mins

Vectors Basics

7 mins

Vector Equation of a Line

6 mins

Scalar Product & Angle Between Two Vectors

9 mins

Vector Product

8 mins

Geometric Transformations

10 mins

Topic 4

Statistics & Probability

Topic 4

Statistics & Probability

Mean, Median, Mode

10 mins

Quartiles, Interquartile Range, Box & Whisker

6 mins

Outliers

4 mins

Data Sampling Methods

5 mins

Independent & Dependent Variables, Scatter Plots

6 mins

Correlation: Pearson's & Spearman's

9 mins

Line of Regression Equation (& Reliability)

8 mins

Coefficient of Determination

10 mins

Non-Linear Regression

9 mins

Tree Diagrams (Probability)

8 mins

Venn Diagrams (Probability)

8 mins

Transition Matrices & Markov Chains

10 mins

Probability Distribution

7 mins

Binomial Distribution

7 mins

Normal Distribution

9 mins

Hypothesis Testing

7 mins

Poisson Distribution

9 mins

Estimation & Confidence Intervals

8 mins

Combination of Random Variables

7 mins

Topic 4

Statistics & Probability

Mean, Median, Mode

10 mins

Quartiles, Interquartile Range, Box & Whisker

6 mins

Outliers

4 mins

Data Sampling Methods

5 mins

Independent & Dependent Variables, Scatter Plots

6 mins

Correlation: Pearson's & Spearman's

9 mins

Line of Regression Equation (& Reliability)

8 mins

Coefficient of Determination

10 mins

Non-Linear Regression

9 mins

Tree Diagrams (Probability)

8 mins

Venn Diagrams (Probability)

8 mins

Transition Matrices & Markov Chains

10 mins

Probability Distribution

7 mins

Binomial Distribution

7 mins

Normal Distribution

9 mins

Hypothesis Testing

7 mins

Poisson Distribution

9 mins

Estimation & Confidence Intervals

8 mins

Combination of Random Variables

7 mins

Topic 5

Calculus

Topic 5

Calculus

Overview of Differential Calculus

6 mins

Basics of Differentiation

8 mins

Gradients of Tangents & Normals

6 mins

Turning Points (Max/Min, Optimization)

7 mins

Further Differentiation Rules

19 mins

Related Rates

12 mins

The Second Derivative

9 mins

Overview of Integral Calculus

7 mins

Basics of Anti-Differentiation

7 mins

Finding Areas Under Curves

7 mins

Trapezoidal Rule

6 mins

Further Integration Rules

13 mins

Integration by Substitution

9 mins

Area Enclosed by a Curve and the x or y-axis

7 mins

Volumes of Revolution about the x or y-axis

8 mins

Kinematics

9 mins

Introduction to Differential Equations

7 mins

Separable Differential Equations

9 mins

Slope Fields

7 mins

Euler's Method

8 mins

Topic 5

Calculus

Overview of Differential Calculus

6 mins

Basics of Differentiation

8 mins

Gradients of Tangents & Normals

6 mins

Turning Points (Max/Min, Optimization)

7 mins

Further Differentiation Rules

19 mins

Related Rates

12 mins

The Second Derivative

9 mins

Overview of Integral Calculus

7 mins

Basics of Anti-Differentiation

7 mins

Finding Areas Under Curves

7 mins

Trapezoidal Rule

6 mins

Further Integration Rules

13 mins

Integration by Substitution

9 mins

Area Enclosed by a Curve and the x or y-axis

7 mins

Volumes of Revolution about the x or y-axis

8 mins

Kinematics

9 mins

Introduction to Differential Equations

7 mins

Separable Differential Equations

9 mins

Slope Fields

7 mins

Euler's Method

8 mins

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More IB Mathematics AI HL Resources

Questionbank

All the questions you could need! Sorted by topic and arranged by difficulty, with mark schemes and video solutions for every question.

Paper 3

This resource offers a collection of mathematical modeling and investigation-style questions designed to help you prepare for the IB Math AI HL Paper 3 exam.

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Practice Exams

Choose your revision tool! Contains topic quizzes for focused study, Revision Village mock exams covering the whole syllabus, and the revision ladder to precisely target your learning.

Key Concepts

Helpful refreshers summarizing exactly what you need to know about the most important concepts covered in the course.

Past Papers

Full worked solutions to all past paper questions, taught by experienced IB instructors.

Bootcamps & IA Toolkit

This resource combines topic-based Bootcamps and an IA Toolkit. Bootcamps review key concepts, while the IA Toolkit supports your Internal Assessment.

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Flashcards

Use multiple-choice questions and study crucial terminology on desktop or mobile app to improve your marks!

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Frequently Asked Questions

What are the AI HL Key Concepts?

The IB Math Applications and Interpretation (AI) HL Key Concepts section is one of the five main features on Revision Village for AI HL students (in addition to Questionbank, Practice Exams, Past Papers and Bootcamps). The Key Concepts section includes a carefully planned set of AI HL Exam Revision Videos that students can use to refresh specific concepts (e.g. Differential Equations using Euler’s Method) that they may have missed or misunderstood in class. The revision videos typically range between 5 and 10 minutes in length and are a short and concise way for students to quickly refresh a concept, before practicing exam questions, either in the Questionbank or Practice Exams section of the Revision Village website.

How should I best use the AI HL Key Concepts?

A great way to improve in mathematics is by practicing lots of questions, but sometimes we forget key pieces of theory. It’s recommended that students use the AI HL Key Concepts in conjunction with solving exam questions. Stuck on a specific question? Go to the Key Concepts section and watch one of the revision videos that recaps the theory. It’s recommended that students then return to the original question and try and solve it again.

Do the AI HL Key Concept videos replace my textbook?

This is not the aim of the AI HL Key Concept section on Revision Village. These videos are short and concise and aim to ‘recap’ the theory, as opposed to teaching and explaining the theory, which is the purpose of textbooks. The AI HL Key Concept section on Revision Village aims to support students’ revision process by providing an easy way to quickly recap the concepts that occur frequently on Applications and Interpretation Higher Level examinations.

Who are the teachers in the AI HL Key Concept videos?

The AI HL Key Concept videos on Revision Village are taught by experienced IB Mathematics teachers and examiners, who are passionate about teaching IB Math AI HL concepts in a simple, intuitive and engaging manner. The team is dedicated to helping each and every student achieve their best possible IB Mathematics grade.

IB Mathematics AI HLKey Concepts

Number & Algebra

Number & Algebra

Number & Algebra

Functions

Functions

Functions

Geometry & Trigonometry

Geometry & Trigonometry

Geometry & Trigonometry

Statistics & Probability

Statistics & Probability

Statistics & Probability

Calculus

Calculus

Calculus

#1 IB Math Resource

34% Grade Increase

80% of IB Students

More IB Mathematics AI HL Resources

Questionbank

Paper 3

Practice Exams

Key Concepts

Past Papers

Bootcamps & IA Toolkit

Flashcards

What are the AI HL Key Concepts?

How should I best use the AI HL Key Concepts?

Do the AI HL Key Concept videos replace my textbook?

Who are the teachers in the AI HL Key Concept videos?

IB Mathematics AI HL
Key Concepts