IBMathsDPApplications & Interpretation (AI)HLRevision Notes

DP IB Applications & Interpretation (AI): HL Revision Notes

Achieve exam success with our DP IB Applications & Interpretation (AI): HL revision notes—expertly crafted to align with your syllabus. These concise, high-quality study resources are designed to help you master complex concepts and apply them with confidence. From clear explanations to downloadable PDFs, everything you need for effective exam preparation is right here. Written by experienced teachers and examiners, Save My Exams gives you the insight and support to boost your performance. Build confidence, sharpen your skills, and feel fully prepared to tackle your HL exams.

1. Number & Algebra

Upper & Lower Bounds

Percentage Error

Accuracy & Estimation

Solving Equations using a GDC

Laws of Indices

Introduction to Logarithms

Laws of Logarithms

Language of Sequences & Series

Arithmetic Sequences & Series

Geometric Sequences & Series

Applications of Sequences & Series

Compound Interest & Depreciation

Introduction to Complex Numbers

Operations with Complex Numbers

Complex Roots of Quadratics

Modulus & Argument

Introduction to Argand Diagrams

Geometry of Complex Numbers

Modulus-Argument (Polar) Form

Exponential (Euler's) Form

Conversion between Forms of Complex Numbers

Frequency & Phase of Trig Functions

Introduction to Matrices

Operations with Matrices

Determinants & Inverses

Solving Systems of Linear Equations with Matrices

The Characteristic Polynomial, Eigenvalues & Eigenvectors

Diagonalisation & Powers of Matrices

3. Geometry & Trigonometry

Coordinate Geometry

Perpendicular Bisectors

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

Simple Identities

Graphs of Trigonometric Functions

Solving Equations Using Trigonometric Graphs

Drawing Voronoi Diagrams

Interpreting Voronoi Diagrams

Toxic Waste Dump Problem

Matrix Transformations

Matrices of Geometric Transformations

Matrices of Composite Transformations

Determinant of a Transformation Matrix

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

Components of Vectors

Geometric Proof with Vectors

Equation of a Line in Vector Form

Equation of a Line in Parametric Form

Angle Between Two Lines

Shortest Distance Between a Point and a Line

Shortest Distance Between Two Lines

Kinematics with Vectors

Constant & Variable Velocity

Introduction to Graph Theory

Walks & Adjacency Matrices

Minimum Spanning Trees (Kruskal's Algorithm)

Minimum Spanning Trees (Prim's Algorithm)

Chinese Postman Problem

Travelling Salesman Problem

Nearest Neighbour & Deleted Vertex Algorithms

4. Statistics & Probability

Reliability & Validity of Data Collection Methods

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

Spearman's Rank Correlation Coefficient

Comparison of Correlation Coefficients

Linear Regression

Least Squares Regression Curves & Coefficient of Determination

Logarithmic Scales

Linearising using Logarithms

Probability & Types of Events

Independent & Mutually Exclusive Events

Conditional Probability

Discrete Probability Distributions

Expected Values

Linear Combinations of Random Variables

Unbiased Estimates

The Binomial Distribution

Calculating Binomial Probabilities

The Normal Distribution

Calculations with Normal Distribution

Sample Mean Distribution

Central Limit Theorem

Confidence Interval for the Mean

Poisson Distribution

Calculating Poisson Probabilities

Introduction to Hypothesis Testing

Chi-squared Test for Independence

Goodness of Fit Test

Hypothesis Testing for Mean (One Sample)

Hypothesis Testing for Mean (Two Sample)

Binomial Hypothesis Testing

Poisson Hypothesis Testing

Hypothesis Testing for Correlation

Type I & Type II Errors

Transition Matrices

Powers of Transition Matrices

Steady State & Long-term Probabilities

5. Calculus

Introduction to Derivatives

Differentiating Powers of x

Gradients, Tangents & Normals

Increasing & Decreasing Functions

Local Minimum & Maximum Points

Modelling with Differentiation

Differentiating Special Functions

Related Rates of Change

Second Order Derivatives

Stationary Points

Concavity & Points of Inflection

Numerical Integration using the Trapezoidal Rule

Introduction to Integration

Integrating Powers of x

Finding the Constant of Integration

Finding Areas Using a GDC

Integrating Special Functions

Reverse Chain Rule

Integration by Substitution

Definite Integrals

Negative Integrals

Area Between Curve & y-axis

Area Between a Curve and a Line

Volumes of Revolution

Displacement, Velocity & Acceleration

Calculus for Kinematics

Separation of Variables

Modelling with Differential Equations

Approximate Solutions to Differential Equations using Euler's Method

Coupled Differential Equations

Phase Portraits

Equilibrium Points

Sketching Solution Trajectories

Second Order Differential Equations

Exam boards

Study tools

Related links