► 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 |
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| | 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 |
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| | Proof |
| | Proof by Induction | Proof by Contradiction | Disproof by Counterexample |
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| | 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 |
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| | Other Topics |
| | Solutions of Systems of Linear Equations | Partial Fractions |
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► 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 |
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| | 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 |
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| | 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 |
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► 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 |
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| | 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 |
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| | 3-Dimensional Shapes |
Volume and Surface Area of 3D Solids |
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► 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 |
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| | Representing Data |
Histograms | Cumulative Frequency Graphs | Box-and-Whisker Diagrams | Scatter Diagrams, Lines of Best Fit |
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| | 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) |
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| | 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 Continuous Random Variables | Linear Transformations of Random Variables |
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► 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 |
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| | 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 |
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| | 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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