DP IB Maths: AI HL
Exam Questions

Standard Form, Approximation & Estimation, GDC: Solving Equations

Exponents, Logarithms

Language of Sequences & Series, Arithmetic Sequences & Series, Geometric Sequences & Series, Applications of Sequences & Series

Compound Interest & Depreciation, Amortisation & Annuities

Intro to Complex Numbers, Modulus & Argument, Introduction to Argand Diagrams

Geometry of Complex Numbers, Forms of Complex Numbers, Applications of Complex Numbers

Introduction to Matrices, Operations with Matrices, Determinants & Inverses, Solving Systems of Linear Equations with Matrices

Eigenvalues & Eigenvectors, Applications of Matrices

Equations of a Straight Line

Functions, Graphing Functions, Properties of Graphs

Linear Models, Quadratic & Cubic Models, Exponential Models, Direct & Inverse Variation, Sinusoidal Models, Strategy for Modelling Functions

Composite & Inverse Functions

Translations of Graphs, Reflections of Graphs, Stretches of Graphs, Composite Transformations of Graphs

Properties of Further Graphs, Natural Logarithmic Models, Logistic Models, Piecewise Models

Coordinate Geometry, Radian Measure, Arcs & Sectors

3D Coordinate Geometry, Volume & Surface Area

Pythagoras & Right-Angled Trigonometry, Non Right-Angled Trigonometry, Applications of Trigonometry & Pythagoras

The Unit Circle, Simple Identities, Solving Trigonometric Equations

Voronoi Diagrams, Toxic Waste Dump Problem

Matrix Transformations, Determinant of a Transformation Matrix

Introduction to Vectors, Position & Displacement Vectors, Magnitude of a Vector, The Scalar Product, The Vector Product, Components of Vectors, Geometric Proof with Vectors

Vector Equations of Lines, Shortest Distances with Lines

Kinematics with Vectors, Constant & Variable Velocity

Introduction to Graph Theory, Walks & Adjacency Matrices, Minimum Spanning Trees, Chinese Postman Problem, Travelling Salesman Problem, Bounds for Travelling Salesman Problem

Sampling, Data Collection, Statistical Measures, Frequency Tables, Linear Transformations of Data, Outliers, Univariate Data, Interpreting Data

Bivariate Data, Correlation Coefficients, Linear Regression

Non-linear Regression, Logarithmic Scales, Linearising using Logarithms

Probability & Types of Events, Conditional Probability, Sample Space Diagrams

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, Confidence Interval for the Mean

Poisson Distribution, Calculating Poisson Probabilities

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

Markov Chains, Transition Matrices

Introduction to Differentiation, Applications of Differentiation, Modelling with Differentiation

Differentiating Special Functions, Techniques of Differentiation, Related Rates of Change, Second Order Derivatives, Further Applications of Differentiation, Concavity & Points of Inflection

Trapezoid Rule: Numerical Integration, Introduction to Integration, Applications of Integration

Integrating Special Functions, Techniques of Integration, Further Applications of Integration, Volumes of Revolution

Kinematics Toolkit, Calculus for Kinematics

Modelling with Differential Equations, Separation of Variables, Slope Fields, Approximate Solutions to Differential Equations

Coupled Differential Equations, Second Order Differential Equations