Subjects

# IB Math AI HL - Key Concepts

In the IB Math Applications & Interpretation (AI) 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

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

###### 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

###### 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

###### 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

###### 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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