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# 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

Topic 1

###### Number & Algebra

Rounding & Significant Figures

6 minutes

Scientific Notation

5 minutes

Percentage Error

5 minutes

Arithmetic Sequences & Series

7 minutes

Geometric Sequences & Series

10 minutes

Sigma Notation

5 minutes

Compound Interest & Depreciation

8 minutes

Loans & Amortization

8 minutes

Annuities

7 minutes

GDC Tips: Finance Solver (TVM Solver)

6 minutes

Introduction to Complex Numbers

9 minutes

Forms of Complex Numbers (Rectangular, Polar, Euler)

10 minutes

Operations of Complex Numbers

12 minutes

GDC Tips: Complex Numbers

9 minutes

Introduction to Matrices

12 minutes

Solving Simultaneous Equations using Matrices

8 minutes

Eigenvalues, Eigenvectors & Matrix Powers

13 minutes

GDC Tips: Matrices

5 minutes

Topic 1

## Number & Algebra

Rounding & Significant Figures

6 minutes

Scientific Notation

5 minutes

Percentage Error

5 minutes

Arithmetic Sequences & Series

7 minutes

Geometric Sequences & Series

10 minutes

Sigma Notation

5 minutes

Compound Interest & Depreciation

8 minutes

Loans & Amortization

8 minutes

Annuities

7 minutes

GDC Tips: Finance Solver (TVM Solver)

6 minutes

Introduction to Complex Numbers

9 minutes

Forms of Complex Numbers (Rectangular, Polar, Euler)

10 minutes

Operations of Complex Numbers

12 minutes

GDC Tips: Complex Numbers

9 minutes

Introduction to Matrices

12 minutes

Solving Simultaneous Equations using Matrices

8 minutes

Eigenvalues, Eigenvectors & Matrix Powers

13 minutes

GDC Tips: Matrices

5 minutes

Topic 2

Topic 2

###### Functions

Forms of Linear Lines

7 minutes

Gradients & Intercepts of Linear Lines

7 minutes

Parallel & Perpendicular Gradients

3 minutes

Perpendicular Bisectors

8 minutes

GDC Tips: Intersection of Two Lines

4 minutes

Functions: Overview & Types

7 minutes

GDC Tips: Plotting Functions & Analysis Tools

9 minutes

GDC Tips: Using nSolve to Solve Equations

6 minutes

Domain & Range, Composite, Inverse

12 minutes

Transformations of Functions

9 minutes

Topic 2

## Functions

Forms of Linear Lines

7 minutes

Gradients & Intercepts of Linear Lines

7 minutes

Parallel & Perpendicular Gradients

3 minutes

Perpendicular Bisectors

8 minutes

GDC Tips: Intersection of Two Lines

4 minutes

Functions: Overview & Types

7 minutes

GDC Tips: Plotting Functions & Analysis Tools

9 minutes

GDC Tips: Using nSolve to Solve Equations

6 minutes

Domain & Range, Composite, Inverse

12 minutes

Transformations of Functions

9 minutes

Topic 3

Topic 3

###### Geometry & Trigonometry

Geometry of 3D Shapes

3 minutes

Pythagoras Theorem

6 minutes

Right Angled Trig (Sin/Cos/Tan)

7 minutes

Sine & Cosine Rule, Area of a Triangle

10 minutes

Length of Arc, Area of Sector (Circles)

6 minutes

Degrees v Radians

5 minutes

Voronoi Diagrams

10 minutes

Unit Circle & Trig Ratios

8 minutes

Graphs of Trig Functions

8 minutes

Graph Theory

11 minutes

Vectors Basics

7 minutes

Vector Equation of a Line

6 minutes

Scalar Product & Angle Between Two Vectors

9 minutes

Vector Product

8 minutes

Geometric Transformations

10 minutes

Topic 3

## Geometry & Trigonometry

Geometry of 3D Shapes

3 minutes

Pythagoras Theorem

6 minutes

Right Angled Trig (Sin/Cos/Tan)

7 minutes

Sine & Cosine Rule, Area of a Triangle

10 minutes

Length of Arc, Area of Sector (Circles)

6 minutes

Degrees v Radians

5 minutes

Voronoi Diagrams

10 minutes

Unit Circle & Trig Ratios

8 minutes

Graphs of Trig Functions

8 minutes

Graph Theory

11 minutes

Vectors Basics

7 minutes

Vector Equation of a Line

6 minutes

Scalar Product & Angle Between Two Vectors

9 minutes

Vector Product

8 minutes

Geometric Transformations

10 minutes

Topic 4

Topic 4

###### Statistics & Probability

Mean, Median, Mode

10 minutes

Quartiles, Interquartile Range, Box & Whisker

6 minutes

Outliers

4 minutes

Data Sampling Methods

5 minutes

Independent & Dependent Variables, Scatter Plots

6 minutes

Correlation: Pearson's & Spearman's

9 minutes

Line of Regression Equation (& Reliability)

8 minutes

Coefficient of Determination

10 minutes

Non-Linear Regression

9 minutes

Tree Diagrams (Probability)

8 minutes

Venn Diagrams (Probability)

8 minutes

Transition Matrices & Markov Chains

10 minutes

Probability Distribution

7 minutes

Binomial Distribution

7 minutes

Normal Distribution

9 minutes

Hypothesis Testing

7 minutes

Poisson Distribution

9 minutes

Estimation & Confidence Intervals

8 minutes

Combination of Random Variables

7 minutes

Topic 4

## Statistics & Probability

Mean, Median, Mode

10 minutes

Quartiles, Interquartile Range, Box & Whisker

6 minutes

Outliers

4 minutes

Data Sampling Methods

5 minutes

Independent & Dependent Variables, Scatter Plots

6 minutes

Correlation: Pearson's & Spearman's

9 minutes

Line of Regression Equation (& Reliability)

8 minutes

Coefficient of Determination

10 minutes

Non-Linear Regression

9 minutes

Tree Diagrams (Probability)

8 minutes

Venn Diagrams (Probability)

8 minutes

Transition Matrices & Markov Chains

10 minutes

Probability Distribution

7 minutes

Binomial Distribution

7 minutes

Normal Distribution

9 minutes

Hypothesis Testing

7 minutes

Poisson Distribution

9 minutes

Estimation & Confidence Intervals

8 minutes

Combination of Random Variables

7 minutes

Topic 5

Topic 5

###### Calculus

Overview of Differential Calculus

6 minutes

Basics of Differentiation

8 minutes

Gradients of Tangents & Normals

6 minutes

Turning Points (Max/Min, Optimization)

7 minutes

Further Differentiation Rules

19 minutes

Related Rates

12 minutes

The Second Derivative

9 minutes

Overview of Integral Calculus

7 minutes

Basics of Anti-Differentiation

7 minutes

Finding Areas Under Curves

7 minutes

Trapezoidal Rule

6 minutes

Further Integration Rules

13 minutes

Integration by Substitution

9 minutes

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

7 minutes

Volumes of Revolution about the x or y-axis

8 minutes

Kinematics

9 minutes

Introduction to Differential Equations

7 minutes

Separable Differential Equations

9 minutes

Slope Fields

7 minutes

Euler's Method

8 minutes

Topic 5

## Calculus

Overview of Differential Calculus

6 minutes

Basics of Differentiation

8 minutes

Gradients of Tangents & Normals

6 minutes

Turning Points (Max/Min, Optimization)

7 minutes

Further Differentiation Rules

19 minutes

Related Rates

12 minutes

The Second Derivative

9 minutes

Overview of Integral Calculus

7 minutes

Basics of Anti-Differentiation

7 minutes

Finding Areas Under Curves

7 minutes

Trapezoidal Rule

6 minutes

Further Integration Rules

13 minutes

Integration by Substitution

9 minutes

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

7 minutes

Volumes of Revolution about the x or y-axis

8 minutes

Kinematics

9 minutes

Introduction to Differential Equations

7 minutes

Separable Differential Equations

9 minutes

Slope Fields

7 minutes

Euler's Method

8 minutes

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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.