IB Mathematics AA HL - Key Concepts

In the IB Mathematics Analysis & Approaches (AA) 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

Number & Algebra

Topic 1

Number & Algebra

Arithmetic Sequences & Series

8 minutes

Geometric Sequences & Series

11 minutes

Sigma Notation

5 minutes

Exponent Laws & Solving Equations

9 minutes

Log Laws & Solving Equations

11 minutes

The Binomial Theorem

11 minutes

Counting Principles, Combinations & Permutations

6 minutes

Proof by Mathematical Induction

8 minutes

Complex Numbers & De Moivre's Theorem

11 minutes

Systems of Linear Equations

9 minutes

Proof by Deduction

7 minutes

Partial Fractions

8 minutes

Proof by Contradiction

3 minutes

Binomial Theorem for Fractional & Negative Indices

6 minutes

Topic 1

Number & Algebra

Arithmetic Sequences & Series

8 minutes

Geometric Sequences & Series

11 minutes

Sigma Notation

5 minutes

Exponent Laws & Solving Equations

9 minutes

Log Laws & Solving Equations

11 minutes

The Binomial Theorem

11 minutes

Counting Principles, Combinations & Permutations

6 minutes

Proof by Mathematical Induction

8 minutes

Complex Numbers & De Moivre's Theorem

11 minutes

Systems of Linear Equations

9 minutes

Proof by Deduction

7 minutes

Partial Fractions

8 minutes

Proof by Contradiction

3 minutes

Binomial Theorem for Fractional & Negative Indices

6 minutes

Topic 2

Functions

Topic 2

Functions

Domain & Range, Composite, Inverse

12 minutes

Transformations of Functions

9 minutes

Factorising Quadratic Functions & Equations

11 minutes

Completing the Square (Quadratics)

6 minutes

Discriminant Test (Quadratics)

7 minutes

Rational Functions, Asymptotes & Graphs

9 minutes

Exponential & Logarithmic Functions

5 minutes

Sketching Functions with a Calculator

5 minutes

Polynomial Theorems: Remainder, Factor, Division

10 minutes

Sum & Product of Roots (Polynomials)

5 minutes

Topic 2

Functions

Domain & Range, Composite, Inverse

12 minutes

Transformations of Functions

9 minutes

Factorising Quadratic Functions & Equations

11 minutes

Completing the Square (Quadratics)

6 minutes

Discriminant Test (Quadratics)

7 minutes

Rational Functions, Asymptotes & Graphs

9 minutes

Exponential & Logarithmic Functions

5 minutes

Sketching Functions with a Calculator

5 minutes

Polynomial Theorems: Remainder, Factor, Division

10 minutes

Sum & Product of Roots (Polynomials)

5 minutes

Topic 3

Geometry & Trigonometry

Topic 3

Geometry & Trigonometry

Radians, Length of Arc, Area of Sector

4 minutes

Unit Circle & Trigonometric Ratios

8 minutes

Trig Identities

5 minutes

Trig Graphs & Circular Functions

8 minutes

Solving Trigonometric Functions & Equations

7 minutes

Sine & Cosine Rule, Area of a Triangle

10 minutes

Degrees v Radians

3 minutes

Vector Basics

7 minutes

Scalar Product & Angle Between Two Vectors

9 minutes

Vector Equation of a Line

6 minutes

Intersection of 2 Vector Lines

6 minutes

Vector Product

8 minutes

Equation of a Plane (Vectors)

8 minutes

Intersection of a Line & Plane

5 minutes

Topic 3

Geometry & Trigonometry

Radians, Length of Arc, Area of Sector

4 minutes

Unit Circle & Trigonometric Ratios

8 minutes

Trig Identities

5 minutes

Trig Graphs & Circular Functions

8 minutes

Solving Trigonometric Functions & Equations

7 minutes

Sine & Cosine Rule, Area of a Triangle

10 minutes

Degrees v Radians

3 minutes

Vector Basics

7 minutes

Scalar Product & Angle Between Two Vectors

9 minutes

Vector Equation of a Line

6 minutes

Intersection of 2 Vector Lines

6 minutes

Vector Product

8 minutes

Equation of a Plane (Vectors)

8 minutes

Intersection of a Line & Plane

5 minutes

Topic 4

Statistics & Probability

Topic 4

Statistics & Probability

Mean, Standard Deviation & Variance

8 minutes

Bivariate Statistics

10 minutes

Venn Diagrams & Probability

7 minutes

Conditional Probability

6 minutes

Probability Distribution

7 minutes

Binomial Distribution

8 minutes

Normal Distribution

8 minutes

Bayes Theorem

6 minutes

Probability Density Functions

8 minutes

Topic 4

Statistics & Probability

Mean, Standard Deviation & Variance

8 minutes

Bivariate Statistics

10 minutes

Venn Diagrams & Probability

7 minutes

Conditional Probability

6 minutes

Probability Distribution

7 minutes

Binomial Distribution

8 minutes

Normal Distribution

8 minutes

Bayes Theorem

6 minutes

Probability Density Functions

8 minutes

Topic 5

Calculus

Topic 5

Calculus

Differentiation Rules

11 minutes

Equation of a Tangent

4 minutes

Optimization & Calculus Curves

10 minutes

Integration Rules

9 minutes

Integration by Substitution

8 minutes

Kinematics

9 minutes

Integration by Parts

7 minutes

Volume of Revolution

6 minutes

L'Hôpital's Rule

6 minutes

Implicit Differentiation

6 minutes

Related Rates

8 minutes

Differential Equations

12 minutes

Maclaurin Series

7 minutes

Topic 5

Calculus

Differentiation Rules

11 minutes

Equation of a Tangent

4 minutes

Optimization & Calculus Curves

10 minutes

Integration Rules

9 minutes

Integration by Substitution

8 minutes

Kinematics

9 minutes

Integration by Parts

7 minutes

Volume of Revolution

6 minutes

L'Hôpital's Rule

6 minutes

Implicit Differentiation

6 minutes

Related Rates

8 minutes

Differential Equations

12 minutes

Maclaurin Series

7 minutes

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More IB Math Analysis & Approaches HL Resources

Questionbank

All the questions you could need! Sorted by topic and arranged by difficulty, with mark schemes and video solutions for every question.

Practice Exams

Choose your revision tool! Contains topic quizzes for focused study, Revision Village mock exams covering the whole syllabus, and the revision ladder to precisely target your learning.

Key Concepts

Helpful refreshers summarizing exactly what you need to know about the most important concepts covered in the course.

Past Papers

Full worked solutions to all past paper questions, taught by experienced IB instructors.

Frequently Asked Questions

What are the AA HL Key Concepts?

The IB Math Analysis & Approaches (AA) HL Key Concepts section is one of the four main features on Revision Village for AA HL students (in addition to Questionbank, Practice Exams and Past Papers). The Key Concepts section includes a carefully planned set of AA HL Exam Revision Videos that students can use to refresh specific concepts (e.g. Integration by Parts) 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 AA 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 AA 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 AA HL Key Concept videos replace my textbook?

This is not the aim of the AA 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 AA 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 Analysis and Approaches Higher Level examinations.

Who are the teachers in the AA HL Key Concept videos?

The AA HL Key Concept videos on Revision Village are taught by experienced IB Mathematics teachers and examiners, who are passionate about teaching IB Math AA 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.