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| Equations and Inequalities | |
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| Linear Equations, Formulas, and Problem Solving | |
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| Linear Inequalities in One Variable | |
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| Absolute Value Equations and Inequalities | |
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| Complex Numbers | |
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| Solving Quadratic Equations | |
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| Solving Other Types of Equations | |
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| Relations, Functions and Graphs | |
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| Rectangular Coordinates; Graphing Circles and Relations | |
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| Graphs of Linear Equations | |
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| Linear Equations and Rates of Change | |
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| Functions, Notation, and Graphs of Functions | |
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| Analyzing the Graph of a Function | |
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| Toolbox Functions and Transformations | |
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| Piecewise-Defined Functions | |
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| The Algebra and Composition of Functions | |
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| Polynomial and Rational Functions | |
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| Quadratic Functions and Applications | |
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| Synthetic Division; The Remainder and Factor Theorems | |
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| The Zeroes of Polynomial Functions | |
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| Graphing Polynomial Functions | |
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| Graphing Rational Functions | |
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| Additional Insights into Rational Functions | |
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| Polynomial and Rational Inequalities | |
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| Variation: Function Models in Action | |
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| Exponential and Logarithmic Functions | |
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| One-to-One and Inverse Functions | |
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| Exponential Functions | |
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| Logarithms and Logarithmic Functions | |
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| Properties of Logarithms; Solving Exponential and Logarithmic Equations | |
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| Applications from Business, Finance, and Science | |
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| Business, Finance, and Science Applications | |
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| Introduction to Trigonometric Functions | |
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| Angle Measure, Special Triangles, and Special Angles | |
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| Unit Circles and the Trigonometry of Real Numbers | |
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| Graphs of Sine and Cosine Functions; Cosecant and Secant Functions | |
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| Graphs of Tangent and Cotangent Functions | |
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| Transformations and Applications of Trigonometric Graphs | |
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| The Trigonometry of Right Triangles | |
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| Trigonometry and the Coordinate Plane | |
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| Trigonometric Identities, Inverses, and Equations | |
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| Fundamental Identities and Families of Identities | |
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| Constructing and Verifying Identities | |
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| The Sum and Difference Identities | |
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| Double Angle, Half Angle & Product-to-Sum Identities | |
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| The Inverse Trigonometric Functions and Their Applications | |
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| Solving Basic Trigonometric Equations | |
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| General Trigonometric Equations and Applications | |
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| Applications of Trigonometry | |
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| Oblique Triangles and the Law of Sines | |
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| The Law of Cosines; Area of a Triangle | |
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| Vectors and Vector Diagrams | |
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| Vector Applications and the Dot Product | |
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| Complex Numbers in Trigonometric Form | |
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| DemoivreG++s Theorem and the Theorem on nth Roots | |
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| Systems of Equations and Inequalities | |
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| Linear Systems in Two Variables with Applications | |
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| Linear Systems in Three Variables with Applications | |
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| Partial Fraction Decomposition | |
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| Systems of Inequalities and Linear Programming | |
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| Solving Systems Using Matrices and Row Operations | |
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| The Algebra of Matrices | |
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| Solving Linear Systems Using Matrix Equations | |
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| Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More | |
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| Analytical Geometry | |
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| Introduction to Analytic Geometry | |
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| The Circle and the Ellipse | |
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| The Hyperbola | |
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| The Analytic Parabola | |
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| Nonlinear Systems of Equations and Inequalities | |
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| Polar Coordinates, Equations, and Graphs | |
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| More on Conic Sections: Rotation of Axes and Polar Form | |
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| Parametric Equations and Graphs | |
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| Additional Topics in Algebra | |
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| Sequences and Series | |
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| Arithmetic Sequences | |
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| Geometric Sequences | |
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| Mathematical Induction | |
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| Counting Techniques | |
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| Introduction to Probability | |
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| The Binomial Theorem | |
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| Bridges to Calculus | |
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| An Introduction to Limits | |
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| Finding Limits Numerically and Graphically | |
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| Algebraic Methods for Finding Limits; One-Sided Limits and Continuity | |