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Number and Algebra
Number and Algebra
Core SL
Analysis & Approaches SL
Analysis & Approaches HL
Sequences, Series and Patterns
 Arithmetic Sequences and Series Geometric Sequences and Series Finance
 Infinite Geometric Series Binomial Theorem Binomial Coefficients
 Binomial Theorem (Rational Indices) Counting Principles
Exponents and Logarithms
 Scientific Notation Laws of (Integer) Exponents Logarithms in Bases 10 and e
 Laws of (Rational) Exponents Laws of Logarithms Change of Base of Logarithms Exponential Equations
Proof
 Simple Deductive Proof
 Proof by Induction Proof by Contradiction Disproof by Counterexample
Complex Numbers
 Properties of Complex Numbers The Complex Plane The Polar and Euler Forms of Complex Numbers Complex Roots of Real Polynomials De Moivre's Theorem Powers and Roots of Complex Numbers
Other Topics
 Solutions of Systems of Linear Equations Partial Fractions
Functions
Functions
Core SL
Analysis & Approaches SL
Analysis & Approaches HL
Polynomials
 Linear Equations and Their Graphs
 Quadratic Functions and Their Graphs Solving Quadratic Equations and Inequalities The Discriminant
 Polynomial Functions, Their Equations and Graphs The Factor and Remainder Theorems The Sum and Product of the Roots of a Polynomial
Properties of Functions
 Functions: Notation, Domain, and Range Graphing and Sketching Functions Key Features of Graphs The Intersection of Graphs
 Composite Functions Rational Functions (Linear) and Their Graphs Exponential and Logarithmic Functions and Their Graphs Solving Equations Graphically and Analytically Using Technology to Solve Equations
 Rational Functions (Quadratic) and Their Graphs Solving Inequalities Graphically and Analytically
Transformations
 Graphing Inverse Functions
 Determining Inverse Functions Transformations of Graphs Composite Transformations
 Odd and Even Functions Domain Restrictions of Inverse Functions Self Inverse Functions Transformations Involving the Modulus Function Transformations Involving Squaring Reciprocal Functions Modulus Equations and Inequalities
Geometry and Trigonometry
Geometry and Trigonometry
Core SL
Analysis & Approaches SL
Analysis & Approaches HL
Lines and Planes
 Distance and Midpoint Between Two Points (2D & 3D) Angles Between Lines, and a Line and Plane Construction of Diagrams From Given Information
 Vectors: Adding, Subtracting, Scalar Multiplication Magnitude of Vectors The Scalar and Vector Products The Angle Between Two Vectors The Vector Equation of a Line The Relationship Between Two Lines Equations of Planes The Intersection of Planes, and Planes and Lines The Angle Between Planes, and Planes and Lines
Trigonometry
 Right-Angled Triangle Trigonometry The Sine and Cosine Rules The Area of a Triangle
 Circles: Radians, Arcs, Sectors The Unit Circle Exact Values of Trigonometric Ratios The Ambiguous Case of the Sine Rule Pythagorean and Double Angle Identities (sin and cos) Circular Functions Solving Trigonometric Equations Quadratic Trigonometric Equations
 Reciprocal Trigonometric Functions and Their Graphs Inverse Trigonometric Functions and Their Graphs Compound Angle Identities Double Angle Identity for tan Relationships Between Graphs of Trigonometric Functions
3-Dimensional Shapes
 Volume and Surface Area of 3D Solids
Statistics and Probability
Statistics and Probability
Core SL
Analysis & Approaches SL
Analysis & Approaches HL
Analyzing Data
 Reliability and Bias Outliers Sampling Techniques Quartiles, Percentiles, Range and the IQR Mean, Mode and Median Standard Deviation and Variance The Effect of Constant Change of Data Linear Correlation The Correlation Coefficient
Representing Data
 Histograms Cumulative Frequency Graphs Box-and-Whisker Diagrams Scatter Diagrams, Lines of Best Fit
Probability of Events
 Simple Probability Complementary Events Venn, Tree, Sample Space Diagrams Addition Rule Mutual Exclusivity Dependent and Independent Events Conditional Probability
 Bayes' Theorem (Up to Three Events)
Probability Distributions
 Binomial Distribution Mean and Variance of Binomial Distribution The Normal Distribution Inverse Normal Calculations Discrete Probability Distributions Expectation
 Standardized Normal Distribution Inverse Normal (Unknown Mean and Standard Deviation)
 Variance of Discrete Probability Distributions Continuous Random Variables Mode and Median of Continuous Random Variables Mean, Variance and Standard Deviation of Random Variables Linear Transformations of Random Variables
Calculus
Calculus
Core SL
Analysis & Approaches SL
Analysis & Approaches HL
Differential Calculus
 Limits Increasing and Decreasing Functions Derivatives With Integer Exponents Tangents and Normals to Curves Rates of Change
 Derivatives With Rational Exponents Derivatives of other functions Chain Rule Product Rule Quotient Rule The Second Derivative The Graphs of a Function and its Derivatives Maximum and Minimum Points Optimization Points of Inflection Kinematics
 Convergence and Divergence of Limits Differentiation from First Principles Higher Derivatives l'Hôpital's Rule Implicit Differentiation Related Rates Derivatives of Inverse and Reciprocal Functions
Integral Calculus
 Integrals With Integer Exponents Determining Constant Terms Definite Integrals and Area Using Technology
 Indefinite Integrals Integration By Substitution Definite Integrals The Area Between Curves
 Integration By a Given Substitution Integrals of Inverse and Reciprocal Functions Rewriting the Integrand Using Partial Fractions Integration by Parts Repeated Integration by Parts Area Between Curve and the y-Axis Volumes of Revolution
Series & Differential Equations
 First Order Differential Equations Euler's Method of Numerical Solutions Separation of Variables Homogeneous Differential Equations The Integrating Factor Maclaurin Series Creating New Maclaurin Series from Others Maclaurin Series From Differential Equations

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