IBMathsDPAnalysis & Approaches (AA)HLRevision Notes

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

Revise effectively with our DP IB Analysis & Approaches (AA) revision notes—expertly written to match the IB syllabus and support your exam success. From calculus and algebra to functions and proofs, our clear explanations, examiner insights, and downloadable PDFs help you build confidence and boost your grades. Save My Exams provides trusted, high-quality resources designed to simplify complex maths topics and ensure you're fully prepared for your IB AA exams.

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 Deduction

Disproof by Counter Example

Proof by Induction

Proof by Contradiction

Binomial Theorem

Binomial Coefficients & Pascal's Triangle

Extension of The Binomial Theorem

Counting Principles

Introduction to Complex Numbers

Operations with Complex Numbers

Introduction to Argand Diagrams

Modulus & Argument

Geometry of Complex Numbers

Modulus-Argument (Polar) Form

Exponential (Euler's) Form

Conversion between Forms of Complex Numbers

Complex Roots of Polynomials

De Moivre's Theorem

Proof of De Moivre's Theorem

Roots of Complex Numbers

Systems of Linear Equations

Solving Systems Using Row Reduction

Number of Solutions to a System

2. Functions

Equations of a Straight Line

Parallel & Perpendicular Lines

Quadratic Functions

Factorising Quadratics

Completing the Square

Solving Quadratic Equations

Quadratic Inequalities

Language of Functions

Composite Functions

Inverse Functions

Odd & Even Functions

Periodic Functions

Self-Inverse Functions

Graphing Functions & Their Key Features

Intersecting Graphs

Exponential & Logarithmic Functions

Solving Equations Analytically

Solving Equations Graphically

Modelling with Functions

Reciprocal & Rational Functions

Rational Functions with Quadratics

Translations of Graphs

Reflections of Graphs

Stretches of Graphs

Composite Transformations of Graphs

Polynomial Functions

Polynomial Division

Factor & Remainder Theorem

Roots of Polynomials

Solving Inequalities Graphically

Polynomial Inequalities

Modulus Functions

Modulus Transformations

Modulus Equations & Inequalities

Reciprocal Transformations

Square Transformations

3. Geometry & Trigonometry

Coordinate Geometry

Arcs & Sectors Using Degrees

Arcs & Sectors Using Radians

3D Coordinate Geometry

Volume & Surface Area

Pythagoras & Right-Angled Trigonometry

Sine Rule, Cosine Rule & Area of a Triangle

Angles of Elevation & Depression

Bearings & Constructions

The Unit Circle

Graphs of Trigonometric Functions

Solving Equations Using Trigonometric Graphs

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

Parallel Vectors

Adding & Subtracting Vectors

Position & Displacement Vectors

Magnitude of a Vector & Unit Vectors

The Scalar Product

Angle Between Two Vectors & Perpendicular Vectors

The Vector Product

Areas using the Vector Product

Geometric Proof with Vectors

Equation of a Line in Vector Form

Equation of a Line in Parametric Form

Equation of a Line in Cartesian Form

Applications to Kinematics

Coincident, Parallel, Intersecting & Skew Lines

Angle Between Two Lines

Shortest Distance Between a Point and a Line

Shortest Distance Between Two Lines

Equation of a Plane in Vector Form

Equation of a Plane in Cartesian Form

Intersections of a Line & a Plane

Intersections of Two Planes

Angles Between a Line & a Plane

Angles Between Two Planes

Shortest Distances with Planes

4. Statistics & Probability

Sampling & Data Collection

Measures of Central Tendency

Measures of Dispersion

Frequency Tables

Linear Transformations of Data

Box & Whisker Diagrams

Cumulative Frequency Graphs

Interpreting Data

Scatter Diagrams & Correlation

Pearson's Product-Moment Correlation Coefficient

Linear Regression

Probability & Types of Events

Independent & Mutually Exclusive Events

Conditional Probability

Discrete Probability Distributions

Mean & Variance

Transformation of a Single Variable

The Binomial Distribution

Calculating Binomial Probabilities

The Normal Distribution

Calculations with Normal Distribution

Standardisation of Normal Variables & z-Values

Finding Unknown Parameters

Probability Density Function

Median & Mode of a CRV

Mean & Variance of a CRV

5. Calculus

Introduction to Derivatives

Differentiating Powers of x

Gradients, Tangents & Normals

Increasing & Decreasing Functions

Differentiating Trigonometric, Exponential & Logarithmic Functions

Higher Order Derivatives

Stationary Points

Concavity & Points of Inflection

Derivatives & Graphs

Introduction to Integration

Integrating Powers of x

Finding the Constant of Integration

Finding Areas Using a GDC

Integrating Trigonometric, Exponential & Reciprocal Functions

Reverse Chain Rule

Integration by Substitution

Definite Integrals

Negative Integrals

Area Between a Curve and a Line

Area Between 2 Curves

Modelling with Differentiation

Displacement, Velocity & Acceleration

Calculus for Kinematics

Introduction to Limits

Continuity & Differentiability

First Principles Differentiation

Differentiating Inverse Functions

Implicit Differentiation

Related Rates of Change

Differentiating Reciprocal Trigonometric Functions

Differentiating Inverse Trigonometric Functions

Differentiating Exponential & Logarithmic Functions

Integrating with Reciprocal Trigonometric Functions

Integrating with Inverse Trigonometric Functions

Integrating with Exponential & Logarithmic Functions

Integration by Substitution

Integration by Parts

Integrating with Partial Fractions

Area Between Curve & y-axis

Volumes of Revolution

Modelling with Volumes of Revolution

Introduction to First Order Differential Equations

Separation of Variables

Homogeneous Differential Equations

Integrating Factor

Modelling with Differential Equations

The Logistic Equation

Maclaurin Series of Standard Functions

Maclaurin Series of Composites & Products

Differentiating & Integrating Maclaurin Series

Maclaurin Series from Differential Equations

l'Hôpital's Rule

Limits using Maclaurin Series

Exam boards

Study tools

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