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IB

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 video thumbnail

Rounding & Significant Figures

6 mins

Scientific Notation video thumbnail

Scientific Notation

5 mins

Percentage Error video thumbnail

Percentage Error

5 mins

Arithmetic Sequences & Series video thumbnail

Arithmetic Sequences & Series

7 mins

Geometric Sequences & Series video thumbnail

Geometric Sequences & Series

10 mins

Sigma Notation video thumbnail

Sigma Notation

5 mins

Compound Interest & Depreciation video thumbnail

Compound Interest & Depreciation

8 mins

Loans & Amortization video thumbnail

Loans & Amortization

8 mins

Annuities video thumbnail

Annuities

7 mins

GDC Tips: Finance Solver (TVM Solver) video thumbnail

GDC Tips: Finance Solver (TVM Solver)

6 mins

Introduction to Complex Numbers video thumbnail

Introduction to Complex Numbers

9 mins

Forms of Complex Numbers (Rectangular, Polar, Euler) video thumbnail

Forms of Complex Numbers (Rectangular, Polar, Euler)

10 mins

Operations of Complex Numbers video thumbnail

Operations of Complex Numbers

12 mins

GDC Tips: Complex Numbers video thumbnail

GDC Tips: Complex Numbers

9 mins

Introduction to Matrices video thumbnail

Introduction to Matrices

12 mins

Solving Simultaneous Equations using Matrices video thumbnail

Solving Simultaneous Equations using Matrices

8 mins

Eigenvalues, Eigenvectors & Matrix Powers video thumbnail

Eigenvalues, Eigenvectors & Matrix Powers

13 mins

GDC Tips: Matrices video thumbnail

GDC Tips: Matrices

5 mins


Topic 1

Number & Algebra

Rounding & Significant Figures video thumbnail

Rounding & Significant Figures

6 mins

Scientific Notation video thumbnail

Scientific Notation

5 mins

Percentage Error video thumbnail

Percentage Error

5 mins

Arithmetic Sequences & Series video thumbnail

Arithmetic Sequences & Series

7 mins

Geometric Sequences & Series video thumbnail

Geometric Sequences & Series

10 mins

Sigma Notation video thumbnail

Sigma Notation

5 mins

Compound Interest & Depreciation video thumbnail

Compound Interest & Depreciation

8 mins

Loans & Amortization video thumbnail

Loans & Amortization

8 mins

Annuities video thumbnail

Annuities

7 mins

GDC Tips: Finance Solver (TVM Solver) video thumbnail

GDC Tips: Finance Solver (TVM Solver)

6 mins

Introduction to Complex Numbers video thumbnail

Introduction to Complex Numbers

9 mins

Forms of Complex Numbers (Rectangular, Polar, Euler) video thumbnail

Forms of Complex Numbers (Rectangular, Polar, Euler)

10 mins

Operations of Complex Numbers video thumbnail

Operations of Complex Numbers

12 mins

GDC Tips: Complex Numbers video thumbnail

GDC Tips: Complex Numbers

9 mins

Introduction to Matrices video thumbnail

Introduction to Matrices

12 mins

Solving Simultaneous Equations using Matrices video thumbnail

Solving Simultaneous Equations using Matrices

8 mins

Eigenvalues, Eigenvectors & Matrix Powers video thumbnail

Eigenvalues, Eigenvectors & Matrix Powers

13 mins

GDC Tips: Matrices video thumbnail

GDC Tips: Matrices

5 mins

Topic 2

Functions

Topic 2

Functions
Forms of Linear Lines video thumbnail

Forms of Linear Lines

7 mins

Gradients & Intercepts of Linear Lines video thumbnail

Gradients & Intercepts of Linear Lines

7 mins

Parallel & Perpendicular Gradients video thumbnail

Parallel & Perpendicular Gradients

3 mins

Perpendicular Bisectors video thumbnail

Perpendicular Bisectors

8 mins

GDC Tips: Intersection of Two Lines video thumbnail

GDC Tips: Intersection of Two Lines

4 mins

Functions: Overview & Types video thumbnail

Functions: Overview & Types

7 mins

GDC Tips: Plotting Functions & Analysis Tools video thumbnail

GDC Tips: Plotting Functions & Analysis Tools

9 mins

GDC Tips: Using nSolve to Solve Equations video thumbnail

GDC Tips: Using nSolve to Solve Equations

6 mins

Domain & Range, Composite, Inverse video thumbnail

Domain & Range, Composite, Inverse

12 mins

Transformations of Functions video thumbnail

Transformations of Functions

9 mins


Topic 2

Functions

Forms of Linear Lines video thumbnail

Forms of Linear Lines

7 mins

Gradients & Intercepts of Linear Lines video thumbnail

Gradients & Intercepts of Linear Lines

7 mins

Parallel & Perpendicular Gradients video thumbnail

Parallel & Perpendicular Gradients

3 mins

Perpendicular Bisectors video thumbnail

Perpendicular Bisectors

8 mins

GDC Tips: Intersection of Two Lines video thumbnail

GDC Tips: Intersection of Two Lines

4 mins

Functions: Overview & Types video thumbnail

Functions: Overview & Types

7 mins

GDC Tips: Plotting Functions & Analysis Tools video thumbnail

GDC Tips: Plotting Functions & Analysis Tools

9 mins

GDC Tips: Using nSolve to Solve Equations video thumbnail

GDC Tips: Using nSolve to Solve Equations

6 mins

Domain & Range, Composite, Inverse video thumbnail

Domain & Range, Composite, Inverse

12 mins

Transformations of Functions video thumbnail

Transformations of Functions

9 mins

Topic 3

Geometry & Trigonometry

Topic 3

Geometry & Trigonometry
Geometry of 3D Shapes video thumbnail

Geometry of 3D Shapes

3 mins

Pythagoras Theorem video thumbnail

Pythagoras Theorem

6 mins

Right Angled Trig (Sin/Cos/Tan) video thumbnail

Right Angled Trig (Sin/Cos/Tan)

7 mins

Sine & Cosine Rule, Area of a Triangle video thumbnail

Sine & Cosine Rule, Area of a Triangle

10 mins

Length of Arc, Area of Sector (Circles) video thumbnail

Length of Arc, Area of Sector (Circles)

6 mins

Degrees v Radians video thumbnail

Degrees v Radians

5 mins

Voronoi Diagrams video thumbnail

Voronoi Diagrams

10 mins

Unit Circle & Trig Ratios video thumbnail

Unit Circle & Trig Ratios

8 mins

Graphs of Trig Functions video thumbnail

Graphs of Trig Functions

8 mins

Graph Theory video thumbnail

Graph Theory

11 mins

Vectors Basics video thumbnail

Vectors Basics

7 mins

Vector Equation of a Line video thumbnail

Vector Equation of a Line

6 mins

Scalar Product & Angle Between Two Vectors video thumbnail

Scalar Product & Angle Between Two Vectors

9 mins

Vector Product video thumbnail

Vector Product

8 mins

Geometric Transformations video thumbnail

Geometric Transformations

10 mins


Topic 3

Geometry & Trigonometry

Geometry of 3D Shapes video thumbnail

Geometry of 3D Shapes

3 mins

Pythagoras Theorem video thumbnail

Pythagoras Theorem

6 mins

Right Angled Trig (Sin/Cos/Tan) video thumbnail

Right Angled Trig (Sin/Cos/Tan)

7 mins

Sine & Cosine Rule, Area of a Triangle video thumbnail

Sine & Cosine Rule, Area of a Triangle

10 mins

Length of Arc, Area of Sector (Circles) video thumbnail

Length of Arc, Area of Sector (Circles)

6 mins

Degrees v Radians video thumbnail

Degrees v Radians

5 mins

Voronoi Diagrams video thumbnail

Voronoi Diagrams

10 mins

Unit Circle & Trig Ratios video thumbnail

Unit Circle & Trig Ratios

8 mins

Graphs of Trig Functions video thumbnail

Graphs of Trig Functions

8 mins

Graph Theory video thumbnail

Graph Theory

11 mins

Vectors Basics video thumbnail

Vectors Basics

7 mins

Vector Equation of a Line video thumbnail

Vector Equation of a Line

6 mins

Scalar Product & Angle Between Two Vectors video thumbnail

Scalar Product & Angle Between Two Vectors

9 mins

Vector Product video thumbnail

Vector Product

8 mins

Geometric Transformations video thumbnail

Geometric Transformations

10 mins

Topic 4

Statistics & Probability

Topic 4

Statistics & Probability
Mean, Median, Mode video thumbnail

Mean, Median, Mode

10 mins

Quartiles, Interquartile Range, Box & Whisker video thumbnail

Quartiles, Interquartile Range, Box & Whisker

6 mins

Outliers video thumbnail

Outliers

4 mins

Data Sampling Methods video thumbnail

Data Sampling Methods

5 mins

Independent & Dependent Variables, Scatter Plots video thumbnail

Independent & Dependent Variables, Scatter Plots

6 mins

Correlation: Pearson's & Spearman's video thumbnail

Correlation: Pearson's & Spearman's

9 mins

Line of Regression Equation (& Reliability) video thumbnail

Line of Regression Equation (& Reliability)

8 mins

Coefficient of Determination video thumbnail

Coefficient of Determination

10 mins

Non-Linear Regression video thumbnail

Non-Linear Regression

9 mins

Tree Diagrams (Probability) video thumbnail

Tree Diagrams (Probability)

8 mins

Venn Diagrams (Probability) video thumbnail

Venn Diagrams (Probability)

8 mins

Transition Matrices & Markov Chains video thumbnail

Transition Matrices & Markov Chains

10 mins

Probability Distribution video thumbnail

Probability Distribution

7 mins

Binomial Distribution video thumbnail

Binomial Distribution

7 mins

Normal Distribution video thumbnail

Normal Distribution

9 mins

Hypothesis Testing video thumbnail

Hypothesis Testing

7 mins

Poisson Distribution video thumbnail

Poisson Distribution

9 mins

Estimation & Confidence Intervals video thumbnail

Estimation & Confidence Intervals

8 mins

Combination of Random Variables video thumbnail

Combination of Random Variables

7 mins


Topic 4

Statistics & Probability

Mean, Median, Mode video thumbnail

Mean, Median, Mode

10 mins

Quartiles, Interquartile Range, Box & Whisker video thumbnail

Quartiles, Interquartile Range, Box & Whisker

6 mins

Outliers video thumbnail

Outliers

4 mins

Data Sampling Methods video thumbnail

Data Sampling Methods

5 mins

Independent & Dependent Variables, Scatter Plots video thumbnail

Independent & Dependent Variables, Scatter Plots

6 mins

Correlation: Pearson's & Spearman's video thumbnail

Correlation: Pearson's & Spearman's

9 mins

Line of Regression Equation (& Reliability) video thumbnail

Line of Regression Equation (& Reliability)

8 mins

Coefficient of Determination video thumbnail

Coefficient of Determination

10 mins

Non-Linear Regression video thumbnail

Non-Linear Regression

9 mins

Tree Diagrams (Probability) video thumbnail

Tree Diagrams (Probability)

8 mins

Venn Diagrams (Probability) video thumbnail

Venn Diagrams (Probability)

8 mins

Transition Matrices & Markov Chains video thumbnail

Transition Matrices & Markov Chains

10 mins

Probability Distribution video thumbnail

Probability Distribution

7 mins

Binomial Distribution video thumbnail

Binomial Distribution

7 mins

Normal Distribution video thumbnail

Normal Distribution

9 mins

Hypothesis Testing video thumbnail

Hypothesis Testing

7 mins

Poisson Distribution video thumbnail

Poisson Distribution

9 mins

Estimation & Confidence Intervals video thumbnail

Estimation & Confidence Intervals

8 mins

Combination of Random Variables video thumbnail

Combination of Random Variables

7 mins

Topic 5

Calculus

Topic 5

Calculus
Overview of Differential Calculus video thumbnail

Overview of Differential Calculus

6 mins

Basics of Differentiation video thumbnail

Basics of Differentiation

8 mins

Gradients of Tangents & Normals video thumbnail

Gradients of Tangents & Normals

6 mins

Turning Points (Max/Min, Optimization) video thumbnail

Turning Points (Max/Min, Optimization)

7 mins

Further Differentiation Rules video thumbnail

Further Differentiation Rules

19 mins

Related Rates video thumbnail

Related Rates

12 mins

The Second Derivative video thumbnail

The Second Derivative

9 mins

Overview of Integral Calculus video thumbnail

Overview of Integral Calculus

7 mins

Basics of Anti-Differentiation video thumbnail

Basics of Anti-Differentiation

7 mins

Finding Areas Under Curves video thumbnail

Finding Areas Under Curves

7 mins

Trapezoidal Rule video thumbnail

Trapezoidal Rule

6 mins

Further Integration Rules video thumbnail

Further Integration Rules

13 mins

Integration by Substitution video thumbnail

Integration by Substitution

9 mins

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

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

7 mins

Volumes of Revolution about the x or y-axis video thumbnail

Volumes of Revolution about the x or y-axis

8 mins

Kinematics video thumbnail

Kinematics

9 mins

Introduction to Differential Equations video thumbnail

Introduction to Differential Equations

7 mins

Separable Differential Equations video thumbnail

Separable Differential Equations

9 mins

Slope Fields video thumbnail

Slope Fields

7 mins

Euler's Method video thumbnail

Euler's Method

8 mins


Topic 5

Calculus

Overview of Differential Calculus video thumbnail

Overview of Differential Calculus

6 mins

Basics of Differentiation video thumbnail

Basics of Differentiation

8 mins

Gradients of Tangents & Normals video thumbnail

Gradients of Tangents & Normals

6 mins

Turning Points (Max/Min, Optimization) video thumbnail

Turning Points (Max/Min, Optimization)

7 mins

Further Differentiation Rules video thumbnail

Further Differentiation Rules

19 mins

Related Rates video thumbnail

Related Rates

12 mins

The Second Derivative video thumbnail

The Second Derivative

9 mins

Overview of Integral Calculus video thumbnail

Overview of Integral Calculus

7 mins

Basics of Anti-Differentiation video thumbnail

Basics of Anti-Differentiation

7 mins

Finding Areas Under Curves video thumbnail

Finding Areas Under Curves

7 mins

Trapezoidal Rule video thumbnail

Trapezoidal Rule

6 mins

Further Integration Rules video thumbnail

Further Integration Rules

13 mins

Integration by Substitution video thumbnail

Integration by Substitution

9 mins

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

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

7 mins

Volumes of Revolution about the x or y-axis video thumbnail

Volumes of Revolution about the x or y-axis

8 mins

Kinematics video thumbnail

Kinematics

9 mins

Introduction to Differential Equations video thumbnail

Introduction to Differential Equations

7 mins

Separable Differential Equations video thumbnail

Separable Differential Equations

9 mins

Slope Fields video thumbnail

Slope Fields

7 mins

Euler's Method video thumbnail

Euler's Method

8 mins

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Frequently Asked Questions

The IB Math Applications and Interpretation (AI) HL Key Concepts section is one of the four main features on Revision Village for AI HL students (in addition to Questionbank, Practice Exams and Past Papers). 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.

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.

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.

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.