DP IB Applications & Interpretation (AI): HL Exam Questions By Topic

Standard Form, Approximation, 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, Sigma Notation, Arithmetic Sequences & Series, Geometric Sequences & Series, Applications of Sequences & Series

Compound Interest & Depreciation, Amortisation, Annuities

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

Equations of a Straight Line, Parallel & Perpendicular Lines

Functions & Mappings, Graphing Functions & Their Key Features, Intersecting Graphs, Quadratic Functions & Graphs, Cubic Functions & Graphs, Exponential Functions & Graphs, Sinusoidal Functions & Graphs

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

Composite Functions, Inverse Functions

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

Natural Logarithmic Models, Logistic Models, Piecewise Models

Coordinate Geometry, Perpendicular Bisectors, Arcs & Sectors Using Degrees, Radian Measure, 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

Sampling, Reliability & Validity of Data Collection Methods, Measures of Central Tendency, Measures of Dispersion, Frequency Tables, Linear Transformations of Data, Outliers, Box & Whisker Diagrams, Cumulative Frequency Graphs, Histograms, 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, Venn Diagrams, Tree 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, 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

Markov Chains, Transition Matrices, Powers of Transition Matrices, Steady State & Long-term Probabilities

Introduction to Derivatives, Differentiating Powers of x, Gradients, Tangents & Normals, Increasing & Decreasing Functions, Local Minimum & Maximum Points, Modelling with Differentiation

Differentiating Special Functions, Chain Rule, Product Rule, Quotient Rule, 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, Slope Fields, Approximate Solutions to Differential Equations using Euler's Method

Coupled Differential Equations, Phase Portraits, Equilibrium Points, Sketching Solution Trajectories, Second Order Differential Equations