⯈ 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 
  Proof by Induction  Proof by Contradiction  Proof 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  Solving Inequalities up to Degree 3 

  
  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 

  
  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  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 
RightAngled 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)  Graphing 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 

  
  3Dimensional 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  BoxandWhisker 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 
 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 
 Integrals of Inverse and Reciprocal Functions  Rewriting the Integrand Using Partial Fractions  Integration by Parts  Repeated Integration by Parts  Area Between Curve and the yAxis  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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