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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

Arithmetic Sequences & Series video thumbnail

8 minutes

Geometric Sequences & Series

Geometric Sequences & Series video thumbnail

11 minutes

Sigma Notation

Sigma Notation video thumbnail

5 minutes

Exponent Laws & Solving Equations

Exponent Laws & Solving Equations video thumbnail

9 minutes

Log Laws & Solving Equations

Log Laws & Solving Equations video thumbnail

11 minutes

The Binomial Theorem

The Binomial Theorem video thumbnail

11 minutes

Counting Principles, Combinations & Permutations

Counting Principles, Combinations & Permutations video thumbnail

6 minutes

Proof by Mathematical Induction

Proof by Mathematical Induction video thumbnail

8 minutes

Complex Numbers & De Moivre's Theorem

Complex Numbers & De Moivre's Theorem video thumbnail

11 minutes

Systems of Linear Equations

Systems of Linear Equations video thumbnail

9 minutes

Proof by Deduction

Proof by Deduction video thumbnail

7 minutes

Partial Fractions

Partial Fractions video thumbnail

8 minutes

Proof by Contradiction

Proof by Contradiction video thumbnail

3 minutes

Binomial Theorem for Fractional & Negative Indices

Binomial Theorem for Fractional & Negative Indices video thumbnail

6 minutes


Topic 1

Number & Algebra

Arithmetic Sequences & Series

Arithmetic Sequences & Series video thumbnail

8 minutes

Geometric Sequences & Series

Geometric Sequences & Series video thumbnail

11 minutes

Sigma Notation

Sigma Notation video thumbnail

5 minutes

Exponent Laws & Solving Equations

Exponent Laws & Solving Equations video thumbnail

9 minutes

Log Laws & Solving Equations

Log Laws & Solving Equations video thumbnail

11 minutes

The Binomial Theorem

The Binomial Theorem video thumbnail

11 minutes

Counting Principles, Combinations & Permutations

Counting Principles, Combinations & Permutations video thumbnail

6 minutes

Proof by Mathematical Induction

Proof by Mathematical Induction video thumbnail

8 minutes

Complex Numbers & De Moivre's Theorem

Complex Numbers & De Moivre's Theorem video thumbnail

11 minutes

Systems of Linear Equations

Systems of Linear Equations video thumbnail

9 minutes

Proof by Deduction

Proof by Deduction video thumbnail

7 minutes

Partial Fractions

Partial Fractions video thumbnail

8 minutes

Proof by Contradiction

Proof by Contradiction video thumbnail

3 minutes

Binomial Theorem for Fractional & Negative Indices

Binomial Theorem for Fractional & Negative Indices video thumbnail

6 minutes

Topic 2

Functions

Topic 2

Functions

Domain & Range, Composite, Inverse

Domain & Range, Composite, Inverse video thumbnail

12 minutes

Transformations of Functions

Transformations of Functions video thumbnail

9 minutes

Factorising Quadratic Functions & Equations

Factorising Quadratic Functions & Equations video thumbnail

11 minutes

Completing the Square (Quadratics)

Completing the Square (Quadratics) video thumbnail

6 minutes

Discriminant Test (Quadratics)

Discriminant Test (Quadratics) video thumbnail

7 minutes

Rational Functions, Asymptotes & Graphs

Rational Functions, Asymptotes & Graphs video thumbnail

9 minutes

Exponential & Logarithmic Functions

Exponential & Logarithmic Functions video thumbnail

5 minutes

Sketching Functions with a Calculator

Sketching Functions with a Calculator video thumbnail

5 minutes

Polynomial Theorems: Remainder, Factor, Division

Polynomial Theorems: Remainder, Factor, Division video thumbnail

10 minutes

Sum & Product of Roots (Polynomials)

Sum & Product of Roots (Polynomials) video thumbnail

5 minutes


Topic 2

Functions

Domain & Range, Composite, Inverse

Domain & Range, Composite, Inverse video thumbnail

12 minutes

Transformations of Functions

Transformations of Functions video thumbnail

9 minutes

Factorising Quadratic Functions & Equations

Factorising Quadratic Functions & Equations video thumbnail

11 minutes

Completing the Square (Quadratics)

Completing the Square (Quadratics) video thumbnail

6 minutes

Discriminant Test (Quadratics)

Discriminant Test (Quadratics) video thumbnail

7 minutes

Rational Functions, Asymptotes & Graphs

Rational Functions, Asymptotes & Graphs video thumbnail

9 minutes

Exponential & Logarithmic Functions

Exponential & Logarithmic Functions video thumbnail

5 minutes

Sketching Functions with a Calculator

Sketching Functions with a Calculator video thumbnail

5 minutes

Polynomial Theorems: Remainder, Factor, Division

Polynomial Theorems: Remainder, Factor, Division video thumbnail

10 minutes

Sum & Product of Roots (Polynomials)

Sum & Product of Roots (Polynomials) video thumbnail

5 minutes

Topic 3

Geometry & Trigonometry

Topic 3

Geometry & Trigonometry

Radians, Length of Arc, Area of Sector

Radians, Length of Arc, Area of Sector video thumbnail

4 minutes

Unit Circle & Trigonometric Ratios

Unit Circle & Trigonometric Ratios video thumbnail

8 minutes

Trig Identities

Trig Identities video thumbnail

5 minutes

Trig Graphs & Circular Functions

Trig Graphs & Circular Functions video thumbnail

8 minutes

Solving Trigonometric Functions & Equations

Solving Trigonometric Functions & Equations video thumbnail

7 minutes

Sine & Cosine Rule, Area of a Triangle

Sine & Cosine Rule, Area of a Triangle video thumbnail

10 minutes

Degrees v Radians

Degrees v Radians video thumbnail

3 minutes

Vector Basics

Vector Basics video thumbnail

7 minutes

Scalar Product & Angle Between Two Vectors

Scalar Product & Angle Between Two Vectors video thumbnail

9 minutes

Vector Equation of a Line

Vector Equation of a Line video thumbnail

6 minutes

Intersection of 2 Vector Lines

Intersection of 2 Vector Lines video thumbnail

6 minutes

Vector Product

Vector Product video thumbnail

8 minutes

Equation of a Plane (Vectors)

Equation of a Plane (Vectors) video thumbnail

8 minutes

Intersection of a Line & Plane

Intersection of a Line & Plane video thumbnail

5 minutes


Topic 3

Geometry & Trigonometry

Radians, Length of Arc, Area of Sector

Radians, Length of Arc, Area of Sector video thumbnail

4 minutes

Unit Circle & Trigonometric Ratios

Unit Circle & Trigonometric Ratios video thumbnail

8 minutes

Trig Identities

Trig Identities video thumbnail

5 minutes

Trig Graphs & Circular Functions

Trig Graphs & Circular Functions video thumbnail

8 minutes

Solving Trigonometric Functions & Equations

Solving Trigonometric Functions & Equations video thumbnail

7 minutes

Sine & Cosine Rule, Area of a Triangle

Sine & Cosine Rule, Area of a Triangle video thumbnail

10 minutes

Degrees v Radians

Degrees v Radians video thumbnail

3 minutes

Vector Basics

Vector Basics video thumbnail

7 minutes

Scalar Product & Angle Between Two Vectors

Scalar Product & Angle Between Two Vectors video thumbnail

9 minutes

Vector Equation of a Line

Vector Equation of a Line video thumbnail

6 minutes

Intersection of 2 Vector Lines

Intersection of 2 Vector Lines video thumbnail

6 minutes

Vector Product

Vector Product video thumbnail

8 minutes

Equation of a Plane (Vectors)

Equation of a Plane (Vectors) video thumbnail

8 minutes

Intersection of a Line & Plane

Intersection of a Line & Plane video thumbnail

5 minutes

Topic 4

Statistics & Probability

Topic 4

Statistics & Probability

Mean, Standard Deviation & Variance

Mean, Standard Deviation & Variance video thumbnail

8 minutes

Bivariate Statistics

Bivariate Statistics video thumbnail

10 minutes

Venn Diagrams & Probability

Venn Diagrams & Probability video thumbnail

7 minutes

Conditional Probability

Conditional Probability video thumbnail

6 minutes

Probability Distribution

Probability Distribution video thumbnail

7 minutes

Binomial Distribution

Binomial Distribution video thumbnail

8 minutes

Normal Distribution

Normal Distribution video thumbnail

8 minutes

Bayes Theorem

Bayes Theorem video thumbnail

6 minutes

Probability Density Functions

Probability Density Functions video thumbnail

8 minutes


Topic 4

Statistics & Probability

Mean, Standard Deviation & Variance

Mean, Standard Deviation & Variance video thumbnail

8 minutes

Bivariate Statistics

Bivariate Statistics video thumbnail

10 minutes

Venn Diagrams & Probability

Venn Diagrams & Probability video thumbnail

7 minutes

Conditional Probability

Conditional Probability video thumbnail

6 minutes

Probability Distribution

Probability Distribution video thumbnail

7 minutes

Binomial Distribution

Binomial Distribution video thumbnail

8 minutes

Normal Distribution

Normal Distribution video thumbnail

8 minutes

Bayes Theorem

Bayes Theorem video thumbnail

6 minutes

Probability Density Functions

Probability Density Functions video thumbnail

8 minutes

Topic 5

Calculus

Topic 5

Calculus

Differentiation Rules

Differentiation Rules video thumbnail

11 minutes

Equation of a Tangent

Equation of a Tangent video thumbnail

4 minutes

Optimization & Calculus Curves

Optimization & Calculus Curves video thumbnail

10 minutes

Integration Rules

Integration Rules video thumbnail

9 minutes

Integration by Substitution

Integration by Substitution video thumbnail

8 minutes

Kinematics

Kinematics video thumbnail

9 minutes

Integration by Parts

Integration by Parts video thumbnail

7 minutes

Volume of Revolution

Volume of Revolution video thumbnail

6 minutes

L'Hôpital's Rule

L'Hôpital's Rule video thumbnail

6 minutes

Implicit Differentiation

Implicit Differentiation video thumbnail

6 minutes

Related Rates

Related Rates video thumbnail

8 minutes

Differential Equations

Differential Equations video thumbnail

12 minutes

Maclaurin Series

Maclaurin Series video thumbnail

7 minutes


Topic 5

Calculus

Differentiation Rules

Differentiation Rules video thumbnail

11 minutes

Equation of a Tangent

Equation of a Tangent video thumbnail

4 minutes

Optimization & Calculus Curves

Optimization & Calculus Curves video thumbnail

10 minutes

Integration Rules

Integration Rules video thumbnail

9 minutes

Integration by Substitution

Integration by Substitution video thumbnail

8 minutes

Kinematics

Kinematics video thumbnail

9 minutes

Integration by Parts

Integration by Parts video thumbnail

7 minutes

Volume of Revolution

Volume of Revolution video thumbnail

6 minutes

L'Hôpital's Rule

L'Hôpital's Rule video thumbnail

6 minutes

Implicit Differentiation

Implicit Differentiation video thumbnail

6 minutes

Related Rates

Related Rates video thumbnail

8 minutes

Differential Equations

Differential Equations video thumbnail

12 minutes

Maclaurin Series

Maclaurin Series video thumbnail

7 minutes

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Frequently Asked Questions

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.

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.

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.

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.