DP IB Analysis & Approaches (AA): HL Exam Questions By Topic

Standard Form, Laws of Indices, Partial Fractions

Introduction to Logarithms, Laws of Logarithms, Solving Exponential Equations

Language of Sequences & Series, Sigma Notation, 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, Permutations, Combinations

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

Equations of a Straight Line, Parallel & Perpendicular Lines

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

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 Division, Factor & Remainder Theorem, Graphs & Roots of Polynomial Functions, Sum & Product of Roots of Polynomials

Solving Inequalities Graphically, Polynomial Inequalities

Modulus Functions, Modulus Transformations, Modulus Equations & Inequalities, Reciprocal Transformations, Square Transformations

Coordinate Geometry, 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, Exact Values

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

Sampling & Data Collection, 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, Linear Regression

Probability & Types of Events, Independent & Mutually Exclusive Events, Conditional Probability, Bayes' Theorem, Venn Diagrams, Tree Diagrams

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

Introduction to Derivatives, Differentiating Powers of x, Gradients, Tangents & Normals, Increasing & Decreasing Functions

Differentiating Trigonometric, Exponential & Logarithmic Functions, Chain Rule, Product Rule, Quotient Rule, 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, Euler's Method, 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