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IBMathsDPAnalysis & Approaches (AA)HLRevision Notes

DP IB Analysis & Approaches (AA): HL
Revision Notes

Concise resources for the DP IB Analysis & Approaches (AA): HL course.

1. Number & Algebra

Laws of Indices

Partial Fractions

Introduction to Logarithms

Laws of Logarithms

Solving Exponential Equations

Language of Sequences & Series

Arithmetic Sequences & Series

Geometric Sequences & Series

Applications of Sequences & Series

Compound Interest & Depreciation

Proof by Induction

Proof by Contradiction

Binomial Theorem

Extension of The Binomial Theorem

Counting Principles

Permutations & Combinations

Introduction to Complex Numbers

Modulus & Argument

Introduction to Argand Diagrams

Geometry of Complex Numbers

Forms of Complex Numbers

Complex Roots of Polynomials

De Moivre's Theorem

Roots of Complex Numbers

Systems of Linear Equations

Algebraic Solutions

2. Functions

Equations of a Straight Line

Quadratic Functions

Factorising & Completing the Square

Solving Quadratics

Quadratic Inequalities

Language of Functions

Composite & Inverse Functions

Symmetry of Functions

Graphing Functions

Exponential & Logarithmic Functions

Solving Equations

Modelling with Functions

Reciprocal & Rational Functions

Translations of Graphs

Reflections of Graphs

Stretches of Graphs

Composite Transformations of Graphs

Factor & Remainder Theorem

Polynomial Division

Polynomial Functions

Roots of Polynomials

Solving Inequalities Graphically

Polynomial Inequalities

Modulus Functions

Modulus Transformations

Modulus Equations & Inequalities

Reciprocal & Square Transformations

3. Geometry & Trigonometry

Coordinate Geometry

3D Coordinate Geometry

Volume & Surface Area

Pythagoras & Right-Angled Trigonometry

Non Right-Angled Trigonometry

Applications of Trigonometry & Pythagoras

The Unit Circle

Graphs of Trigonometric Functions

Transformations of Trigonometric Functions

Modelling with Trigonometric Functions

Simple Identities

Compound Angle Formulae

Double Angle Formulae

Relationship Between Trigonometric Ratios

Linear Trigonometric Equations

Quadratic Trigonometric Equations

Reciprocal Trigonometric Functions

Inverse Trigonometric Functions

Trigonometric Proof

Strategy for Trigonometric Equations

Introduction to Vectors

Position & Displacement Vectors

Magnitude of a Vector

The Scalar Product

The Vector Product

Geometric Proof with Vectors

Vector Equations of Lines

Applications to Kinematics

Pairs of Lines in 3D

Shortest Distances with Lines

Vector Equations of Planes

Intersections of Lines & Planes

Angles Between Lines & Planes

Shortest Distances with Planes

5. Calculus

Introduction to Differentiation

Applications of Differentiation

Differentiating Trigonometric, Exponential & Logarithmic Functions

Techniques of Differentiation

Higher Order Derivatives

Stationary Points

Concavity & Points of Inflection

Derivatives & Graphs

Introduction to Integration

Applications of Integration

Integrating Trigonometric, Exponential & Reciprocal Functions

Techniques of Integration

Definite Integrals

Modelling with Differentiation

Displacement, Velocity & Acceleration

Calculus for Kinematics

Basic Limits & Continuity

First Principles Differentiation

Applications of Chain Rule

Implicit Differentiation

Differentiating Further Functions

Integrating Further Functions

Integration by Substitution & by Parts

Integrating with Partial Fractions

Areas & Volumes of Revolution

Modelling with Volumes of Revolution

Numerical Solutions to Differential Equations

Analytical Solutions to Differential Equations

Modelling with Differential Equations

Maclaurin Series

Maclaurin Series from Differential Equations

Exam boards

Study tools

Related links