DP IB Maths: AA HL
Exam Questions

Standard Form, 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

Proof by Induction, Proof by Contradiction

Binomial Theorem, Extension of The Binomial Theorem

Counting Principles, Permutations & Combinations

Intro 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

Equations of a Straight Line

Quadratic Functions, Factorising & Completing the Square, Solving Quadratics, Quadratic Inequalities, Discriminants

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 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

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, Exact Values

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 Trig Functions, Inverse Trig 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

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

Bivariate Data, Correlation & Regression

Probability & Types of Events, Conditional Probability, Bayes' Theorem, Sample Space Diagrams

Discrete Probability Distributions, Mean & Variance

The Binomial Distribution, Calculating Binomial Probabilities

The Normal Distribution, Calculations with Normal Distribution, Standardisation of Normal Variables

Probability Density Function

Introduction to Differentiation, Applications of Differentiation

Differentiating Special Functions, Techniques of Differentiation, Higher Order Derivatives, Further Applications of Differentiation, Concavity & Points of Inflection, Derivatives & Graphs

Introduction to Integration, Applications of Integration

Integrating Special Functions, Techniques of Integration, Definite Integrals, Further Applications of Integration

Modelling with Differentiation

Kinematics Toolkit, Calculus for Kinematics

Basic Limits & Continuity

First Principles Differentiation, Applications of Chain Rule, Implicit Differentiation, Differentiating Further Functions

Integrating Further Functions, Further Techniques of Integration, Integrating with Partial Fractions, Advanced Applications of Integration, 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

Further Limits