Subjects

# 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

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

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

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

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

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

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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