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.
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
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
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
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
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
What are the AI HL Key Concepts?
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.
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.