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 mins
Scientific Notation
5 mins
Percentage Error
5 mins
Arithmetic Sequences & Series
7 mins
Geometric Sequences & Series
10 mins
Sigma Notation
5 mins
Compound Interest & Depreciation
8 mins
Loans & Amortization
8 mins
Annuities
7 mins
GDC Tips: Finance Solver (TVM Solver)
6 mins
Introduction to Complex Numbers
9 mins
Forms of Complex Numbers (Rectangular, Polar, Euler)
10 mins
Operations of Complex Numbers
12 mins
GDC Tips: Complex Numbers
9 mins
Introduction to Matrices
12 mins
Solving Simultaneous Equations using Matrices
8 mins
Eigenvalues, Eigenvectors & Matrix Powers
13 mins
GDC Tips: Matrices
5 mins
Topic 1
Number & Algebra
Rounding & Significant Figures
6 mins
Scientific Notation
5 mins
Percentage Error
5 mins
Arithmetic Sequences & Series
7 mins
Geometric Sequences & Series
10 mins
Sigma Notation
5 mins
Compound Interest & Depreciation
8 mins
Loans & Amortization
8 mins
Annuities
7 mins
GDC Tips: Finance Solver (TVM Solver)
6 mins
Introduction to Complex Numbers
9 mins
Forms of Complex Numbers (Rectangular, Polar, Euler)
10 mins
Operations of Complex Numbers
12 mins
GDC Tips: Complex Numbers
9 mins
Introduction to Matrices
12 mins
Solving Simultaneous Equations using Matrices
8 mins
Eigenvalues, Eigenvectors & Matrix Powers
13 mins
GDC Tips: Matrices
5 mins
Forms of Linear Lines
7 mins
Gradients & Intercepts of Linear Lines
7 mins
Parallel & Perpendicular Gradients
3 mins
Perpendicular Bisectors
8 mins
GDC Tips: Intersection of Two Lines
4 mins
Functions: Overview & Types
7 mins
GDC Tips: Plotting Functions & Analysis Tools
9 mins
GDC Tips: Using nSolve to Solve Equations
6 mins
Domain & Range, Composite, Inverse
12 mins
Transformations of Functions
9 mins
Topic 2
Functions
Forms of Linear Lines
7 mins
Gradients & Intercepts of Linear Lines
7 mins
Parallel & Perpendicular Gradients
3 mins
Perpendicular Bisectors
8 mins
GDC Tips: Intersection of Two Lines
4 mins
Functions: Overview & Types
7 mins
GDC Tips: Plotting Functions & Analysis Tools
9 mins
GDC Tips: Using nSolve to Solve Equations
6 mins
Domain & Range, Composite, Inverse
12 mins
Transformations of Functions
9 mins
Geometry of 3D Shapes
3 mins
Pythagoras Theorem
6 mins
Right Angled Trig (Sin/Cos/Tan)
7 mins
Sine & Cosine Rule, Area of a Triangle
10 mins
Length of Arc, Area of Sector (Circles)
6 mins
Degrees v Radians
5 mins
Voronoi Diagrams
10 mins
Unit Circle & Trig Ratios
8 mins
Graphs of Trig Functions
8 mins
Graph Theory
11 mins
Vectors Basics
7 mins
Vector Equation of a Line
6 mins
Scalar Product & Angle Between Two Vectors
9 mins
Vector Product
8 mins
Geometric Transformations
10 mins
Topic 3
Geometry & Trigonometry
Geometry of 3D Shapes
3 mins
Pythagoras Theorem
6 mins
Right Angled Trig (Sin/Cos/Tan)
7 mins
Sine & Cosine Rule, Area of a Triangle
10 mins
Length of Arc, Area of Sector (Circles)
6 mins
Degrees v Radians
5 mins
Voronoi Diagrams
10 mins
Unit Circle & Trig Ratios
8 mins
Graphs of Trig Functions
8 mins
Graph Theory
11 mins
Vectors Basics
7 mins
Vector Equation of a Line
6 mins
Scalar Product & Angle Between Two Vectors
9 mins
Vector Product
8 mins
Geometric Transformations
10 mins
Mean, Median, Mode
10 mins
Quartiles, Interquartile Range, Box & Whisker
6 mins
Outliers
4 mins
Data Sampling Methods
5 mins
Independent & Dependent Variables, Scatter Plots
6 mins
Correlation: Pearson's & Spearman's
9 mins
Line of Regression Equation (& Reliability)
8 mins
Coefficient of Determination
10 mins
Non-Linear Regression
9 mins
Tree Diagrams (Probability)
8 mins
Venn Diagrams (Probability)
8 mins
Transition Matrices & Markov Chains
10 mins
Probability Distribution
7 mins
Binomial Distribution
7 mins
Normal Distribution
9 mins
Hypothesis Testing
7 mins
Poisson Distribution
9 mins
Estimation & Confidence Intervals
8 mins
Combination of Random Variables
7 mins
Topic 4
Statistics & Probability
Mean, Median, Mode
10 mins
Quartiles, Interquartile Range, Box & Whisker
6 mins
Outliers
4 mins
Data Sampling Methods
5 mins
Independent & Dependent Variables, Scatter Plots
6 mins
Correlation: Pearson's & Spearman's
9 mins
Line of Regression Equation (& Reliability)
8 mins
Coefficient of Determination
10 mins
Non-Linear Regression
9 mins
Tree Diagrams (Probability)
8 mins
Venn Diagrams (Probability)
8 mins
Transition Matrices & Markov Chains
10 mins
Probability Distribution
7 mins
Binomial Distribution
7 mins
Normal Distribution
9 mins
Hypothesis Testing
7 mins
Poisson Distribution
9 mins
Estimation & Confidence Intervals
8 mins
Combination of Random Variables
7 mins
Overview of Differential Calculus
6 mins
Basics of Differentiation
8 mins
Gradients of Tangents & Normals
6 mins
Turning Points (Max/Min, Optimization)
7 mins
Further Differentiation Rules
19 mins
Related Rates
12 mins
The Second Derivative
9 mins
Overview of Integral Calculus
7 mins
Basics of Anti-Differentiation
7 mins
Finding Areas Under Curves
7 mins
Trapezoidal Rule
6 mins
Further Integration Rules
13 mins
Integration by Substitution
9 mins
Area Enclosed by a Curve and the x or y-axis
7 mins
Volumes of Revolution about the x or y-axis
8 mins
Kinematics
9 mins
Introduction to Differential Equations
7 mins
Separable Differential Equations
9 mins
Slope Fields
7 mins
Euler's Method
8 mins
Topic 5
Calculus
Overview of Differential Calculus
6 mins
Basics of Differentiation
8 mins
Gradients of Tangents & Normals
6 mins
Turning Points (Max/Min, Optimization)
7 mins
Further Differentiation Rules
19 mins
Related Rates
12 mins
The Second Derivative
9 mins
Overview of Integral Calculus
7 mins
Basics of Anti-Differentiation
7 mins
Finding Areas Under Curves
7 mins
Trapezoidal Rule
6 mins
Further Integration Rules
13 mins
Integration by Substitution
9 mins
Area Enclosed by a Curve and the x or y-axis
7 mins
Volumes of Revolution about the x or y-axis
8 mins
Kinematics
9 mins
Introduction to Differential Equations
7 mins
Separable Differential Equations
9 mins
Slope Fields
7 mins
Euler's Method
8 mins
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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 five main features on Revision Village for AI HL students (in addition to Questionbank, Practice Exams, Past Papers and Bootcamps). 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.