| 1.1.1. | Natural Numbers, Integers, and Rational Numbers | |
| 1.1.2. | The Real Number System | |
| 1.1.3. | Writing Repeating Decimals as Fractions | |
| 1.1.4. | Sums and Products of Rational and Irrational Numbers |
| 1.2.1. | Imaginary Numbers | |
| 1.2.2. | Solving Quadratic Equations with Purely Imaginary Solutions | |
| 1.2.3. | Complex Numbers | |
| 1.2.4. | Adding and Subtracting Complex Numbers | |
| 1.2.5. | Multiplying Complex Numbers | |
| 1.2.6. | Solving Quadratic Equations With Complex Roots | |
| 1.2.7. | The Cyclic Property of the Imaginary Unit |
| 2.3.1. | The Least Common Multiple of Two Monomials | |
| 2.3.2. | The Least Common Multiple of Two Polynomials | |
| 2.3.3. | Describing Numerical Relationships Using Polynomial Identities |
| 2.4.1. | Introduction to Quadratic Equations | |
| 2.4.2. | Solving Perfect Square Quadratic Equations | |
| 2.4.3. | Perfect Square Quadratic Equations with One or No Solutions | |
| 2.4.4. | The Zero Product Rule for Solving Quadratic Equations | |
| 2.4.5. | Solving Quadratic Equations Using a Difference of Squares | |
| 2.4.6. | Solving Quadratic Equations with No Constant Term | |
| 2.4.7. | Solving Quadratic Equations by Factoring | |
| 2.4.8. | Solving Quadratic Equations with Leading Coefficients by Factoring | |
| 2.4.9. | Completing the Square | |
| 2.4.10. | Completing the Square With Odd Linear Terms | |
| 2.4.11. | Completing the Square With Leading Coefficients | |
| 2.4.12. | Solving Quadratic Equations by Completing the Square | |
| 2.4.13. | Solving Quadratic Equations With Leading Coefficients by Completing the Square | |
| 2.4.14. | The Quadratic Formula | |
| 2.4.15. | The Discriminant of a Quadratic Equation | |
| 2.4.16. | Modeling With Quadratic Equations |
| 3.5.1. | Graphing Elementary Quadratic Functions | |
| 3.5.2. | Vertical Reflections of Quadratic Functions | |
| 3.5.3. | Graphs of General Quadratic Functions | |
| 3.5.4. | Roots of Quadratic Functions | |
| 3.5.5. | The Discriminant of a Quadratic Function | |
| 3.5.6. | Calculating the Axis of Symmetry of a Parabola | |
| 3.5.7. | The Average of the Roots Formula | |
| 3.5.8. | The Vertex Form of a Parabola | |
| 3.5.9. | Writing the Equation of a Parabola in Vertex Form | |
| 3.5.10. | Domain and Range of Quadratic Functions | |
| 3.5.11. | Finding Intersections of Lines and Quadratic Functions |
| 3.6.1. | Modeling Downwards Vertical Motion | |
| 3.6.2. | Modeling Upwards Vertical Motion | |
| 3.6.3. | Vertical Motion | |
| 3.6.4. | Revenue, Cost, and Profit Functions | |
| 3.6.5. | Constructing Revenue, Cost, and Profit Functions | |
| 3.6.6. | Maximizing Profit and Break-Even Points |
| 4.7.1. | The Arithmetic of Functions | |
| 4.7.2. | Composition of Functions | |
| 4.7.3. | Finding Algebraic Expressions of Composite Functions | |
| 4.7.4. | Local Extrema of Functions | |
| 4.7.5. | One-To-One Functions | |
| 4.7.6. | Introduction to Inverse Functions | |
| 4.7.7. | Calculating the Inverse of a Function | |
| 4.7.8. | Inverses of Quadratic Functions | |
| 4.7.9. | Graphs of Inverse Functions | |
| 4.7.10. | Domain and Range of Inverse Functions | |
| 4.7.11. | Invertible Functions | |
| 4.7.12. | Plotting X as a Function of Y | |
| 4.7.13. | Periodic Functions | |
| 4.7.14. | Even and Odd Functions | |
| 4.7.15. | Unbounded Behavior of Functions Near a Point | |
| 4.7.16. | The Average Rate of Change of a Function |
| 4.8.1. | Vertical Translations of Functions | |
| 4.8.2. | Horizontal Translations of Functions | |
| 4.8.3. | Vertical Stretches of Functions | |
| 4.8.4. | Horizontal Stretches of Functions | |
| 4.8.5. | Vertical Reflections of Functions | |
| 4.8.6. | Horizontal Reflections of Functions | |
| 4.8.7. | Combining Graph Transformations: Two Operations | |
| 4.8.8. | Combining Graph Transformations: Three or More Operations | |
| 4.8.9. | Constructing Functions Using Transformations | |
| 4.8.10. | Combining Reflections With Other Graph Transformations | |
| 4.8.11. | Finding Points on Transformed Curves | |
| 4.8.12. | The Domain and Range of Transformed Functions | |
| 4.8.13. | Absolute Value Graph Transformations |
| 5.9.1. | Absolute Value Graphs | |
| 5.9.2. | Vertical Reflections of Absolute Value Graphs | |
| 5.9.3. | Stretches of Absolute Value Graphs | |
| 5.9.4. | Combining Transformations of Absolute Value Graphs | |
| 5.9.5. | Domain and Range of Absolute Value Functions | |
| 5.9.6. | Roots of Absolute Value Functions | |
| 5.9.7. | Equations Connecting Absolute Value and Linear Functions | |
| 5.9.8. | Absolute Value Equations With Extraneous Solutions |
| 6.10.1. | Converting From Exponential to Logarithmic Form | |
| 6.10.2. | Converting From Logarithmic to Exponential Form | |
| 6.10.3. | Evaluating Logarithms | |
| 6.10.4. | The Natural Logarithm | |
| 6.10.5. | The Common Logarithm | |
| 6.10.6. | Simplifying Logarithmic Expressions |
| 6.11.1. | The Product Rule for Logarithms | |
| 6.11.2. | The Quotient Rule for Logarithms | |
| 6.11.3. | The Power Rule for Logarithms | |
| 6.11.4. | Combining the Laws of Logarithms | |
| 6.11.5. | The Change of Base Formula for Logarithms |
| 6.12.1. | Vertical Translations of Exponential Growth Functions | |
| 6.12.2. | Vertical Translations of Exponential Decay Functions | |
| 6.12.3. | Interpreting Graphs of Exponential Functions | |
| 6.12.4. | Combining Graph Transformations of Exponential Functions | |
| 6.12.5. | Properties of Transformed Exponential Functions |
| 6.13.1. | Graphing Logarithmic Functions | |
| 6.13.2. | Combining Graph Transformations of Logarithmic Functions | |
| 6.13.3. | Properties of Transformed Logarithmic Functions | |
| 6.13.4. | Inverses of Exponential and Logarithmic Functions |
| 6.14.1. | Solving Exponential Equations Using Logarithms | |
| 6.14.2. | Solving Equations Containing the Exponential Function | |
| 6.14.3. | Solving Exponential Equations With Different Bases | |
| 6.14.4. | Solving Exponential Equations With Different Bases Using Logarithms | |
| 6.14.5. | Solving Exponential Equations Using the Zero-Product Property |
| 6.15.1. | Solving Logarithmic Equations | |
| 6.15.2. | Solving Logarithmic Equations Containing the Natural Logarithm | |
| 6.15.3. | Solving Logarithmic Equations Using the Laws of Logarithms | |
| 6.15.4. | Solving Logarithmic Equations by Combining the Laws of Logarithms | |
| 6.15.5. | Solving Logarithmic Equations With Logarithms on Both Sides | |
| 6.15.6. | Solving Logarithmic Equations Using the Zero-Product Property |
| 6.16.1. | Modeling With Compound Interest | |
| 6.16.2. | Continuously Compounded Interest | |
| 6.16.3. | Converting Between Exponents |
| 7.17.1. | Introduction to Geometric Sequences | |
| 7.17.2. | The Recursive Formula for a Geometric Sequence | |
| 7.17.3. | Finding the Nth Term of a Geometric Sequence | |
| 7.17.4. | Translating Between Explicit and Recursive Formulas for Geometric Sequences | |
| 7.17.5. | Finding the Common Ratio of a Geometric Sequence Given Two Terms | |
| 7.17.6. | Finding the Index of a Term in a Geometric Sequence |
| 7.18.1. | Introduction to Sigma Notation | |
| 7.18.2. | Properties of Finite Series | |
| 7.18.3. | Expressing an Arithmetic Series in Sigma Notation | |
| 7.18.4. | Finding the Sum of an Arithmetic Series | |
| 7.18.5. | Finding the First Term of an Arithmetic Series | |
| 7.18.6. | Calculating the Number of Terms in an Arithmetic Series | |
| 7.18.7. | Modeling With Arithmetic Series |
| 7.19.1. | Pascal's Triangle and the Binomial Coefficients | |
| 7.19.2. | Expanding a Binomial Using Binomial Coefficients | |
| 7.19.3. | The Special Case of the Binomial Theorem | |
| 7.19.4. | Approximating Values Using the Binomial Theorem |
| 8.20.1. | Solving Radical Equations | |
| 8.20.2. | Solving Advanced Radical Equations |
| 9.21.1. | Similarity and Similar Polygons | |
| 9.21.2. | Side Lengths and Angle Measures of Similar Polygons | |
| 9.21.3. | Areas of Similar Polygons | |
| 9.21.4. | Working With Areas of Similar Polygons | |
| 9.21.5. | Geometric Transformations and Similarity | |
| 9.21.6. | The Angle-Angle (AA) Criterion for Similar Triangles | |
| 9.21.7. | The Side-Side-Side (SSS) Criterion for Similar Triangles | |
| 9.21.8. | The Side-Angle-Side (SAS) Criterion for Similar Triangles | |
| 9.21.9. | Combining Similarity Criteria for Triangles | |
| 9.21.10. | The Midpoint Theorem | |
| 9.21.11. | The Triangle Proportionality Theorem |
| 9.22.1. | The Inscribed Angle Theorem | |
| 9.22.2. | Problem Solving Using the Inscribed Angle Theorem | |
| 9.22.3. | Thales' Theorem | |
| 9.22.4. | Angles in Inscribed Right Triangles | |
| 9.22.5. | Inscribed Quadrilaterals | |
| 9.22.6. | Tangent Lines to Circles | |
| 9.22.7. | Circle Similarity |
| 10.23.1. | The Center and Radius of a Circle in the Coordinate Plane | |
| 10.23.2. | Equations of Circles Centered at the Origin | |
| 10.23.3. | Equations of Circles Centered at a General Point | |
| 10.23.4. | Finding the Center and Radius of a Circle by Completing the Square | |
| 10.23.5. | Calculating Intercepts of Circles | |
| 10.23.6. | Intersections of Circles with Lines |
| 10.24.1. | Upward and Downward Opening Parabolas | |
| 10.24.2. | Left and Right Opening Parabolas | |
| 10.24.3. | The Vertex of a Parabola | |
| 10.24.4. | Calculating the Vertex of a Parabola by Completing the Square | |
| 10.24.5. | The Focus-Directrix Property of a Parabola | |
| 10.24.6. | Calculating the Focus of a Parabola | |
| 10.24.7. | Calculating the Directrix of a Parabola | |
| 10.24.8. | Calculating Intercepts of Parabolas | |
| 10.24.9. | Intersections of Parabolas With Lines |
| 11.25.1. | Identifying Three-Dimensional Shapes | |
| 11.25.2. | Faces, Vertices, and Edges of Polyhedrons | |
| 11.25.3. | Nets of Polyhedrons | |
| 11.25.4. | Finding Surface Areas Using Nets | |
| 11.25.5. | The Distance Formula in Three Dimensions | |
| 11.25.6. | Euler's Formula for Polyhedra | |
| 11.25.7. | The Five Platonic Solids |
| 11.26.1. | Volumes of Cubes | |
| 11.26.2. | Surface Areas of Cubes | |
| 11.26.3. | Face Diagonals of Cubes | |
| 11.26.4. | Diagonals of Cubes | |
| 11.26.5. | Volumes of Rectangular Solids | |
| 11.26.6. | Surface Areas of Rectangular Solids | |
| 11.26.7. | Diagonals of Rectangular Solids | |
| 11.26.8. | Volumes of Pyramids | |
| 11.26.9. | Surface Areas of Pyramids |
| 11.27.1. | Volumes of Cylinders | |
| 11.27.2. | Surface Areas of Cylinders | |
| 11.27.3. | Volumes of Right Cones | |
| 11.27.4. | Slant Heights of Right Cones | |
| 11.27.5. | Surface Areas of Right Cones | |
| 11.27.6. | Volumes of Spheres | |
| 11.27.7. | Surface Areas of Spheres | |
| 11.27.8. | Conical Frustums | |
| 11.27.9. | Volumes of Revolution |
| 12.28.1. | Angles and Sides in Right Triangles | |
| 12.28.2. | The Trigonometric Ratios | |
| 12.28.3. | Calculating Trigonometric Ratios Using the Pythagorean Theorem | |
| 12.28.4. | Calculating Side Lengths of Right Triangles Using Trigonometry | |
| 12.28.5. | Calculating Angles in Right Triangles Using Trigonometry | |
| 12.28.6. | Modeling With Trigonometry | |
| 12.28.7. | The Reciprocal Trigonometric Ratios | |
| 12.28.8. | Trigonometric Ratios in Similar Right Triangles | |
| 12.28.9. | Trigonometric Functions of Complementary Angles | |
| 12.28.10. | Special Trigonometric Ratios | |
| 12.28.11. | Calculating the Area of a Right Triangle Using Trigonometry | |
| 12.28.12. | Solving Multiple Right Triangles Using Trigonometry |
| 12.29.1. | Introduction to Radians | |
| 12.29.2. | Calculating Arc Length Using Angles in Radians | |
| 12.29.3. | Calculating Areas of Sectors Using Angles in Radians | |
| 12.29.4. | Trigonometric Ratios With Radians |
| 12.30.1. | Angles in the Coordinate Plane | |
| 12.30.2. | Negative Angles in the Coordinate Plane | |
| 12.30.3. | Coterminal Angles | |
| 12.30.4. | Calculating Reference Angles | |
| 12.30.5. | Properties of the Unit Circle in the First Quadrant | |
| 12.30.6. | Extending the Trigonometric Ratios Using the Unit Circle | |
| 12.30.7. | Extending the Trigonometric Ratios Using Angles in Radians | |
| 12.30.8. | Extending the Trigonometric Ratios to Negative Angles | |
| 12.30.9. | Extending the Trigonometric Ratios to Large Angles | |
| 12.30.10. | Using the Pythagorean Identity in the First Quadrant | |
| 12.30.11. | Extending the Pythagorean Identity to All Quadrants |
| 12.31.1. | Finding Trigonometric Ratios of Quadrantal Angles | |
| 12.31.2. | Trigonometric Ratios of Quadrantal Angles Outside the Standard Range | |
| 12.31.3. | Finding Trigonometric Ratios of Special Angles Using the Unit Circle | |
| 12.31.4. | Evaluating Trigonometric Expressions | |
| 12.31.5. | Further Extensions of the Special Trigonometric Ratios |
| 12.32.1. | Graphing Sine and Cosine | |
| 12.32.2. | Graphing Tangent and Cotangent | |
| 12.32.3. | Graphing Secant and Cosecant |
| 12.33.1. | Describing Properties of the Sine Function | |
| 12.33.2. | Describing Properties of the Cosine Function | |
| 12.33.3. | Describing Properties of the Tangent Function | |
| 12.33.4. | Describing Properties of the Secant Function | |
| 12.33.5. | Describing Properties of the Cosecant Function | |
| 12.33.6. | Describing Properties of the Cotangent Function |
| 12.34.1. | Vertical Translations of Trigonometric Functions | |
| 12.34.2. | Vertical Stretches of Trigonometric Functions | |
| 12.34.3. | Horizontal Translations of Trigonometric Functions | |
| 12.34.4. | Horizontal Stretches of Trigonometric Functions | |
| 12.34.5. | Combining Graph Transformations of Sine and Cosine | |
| 12.34.6. | Graph Transformations of Tangent and Cotangent | |
| 12.34.7. | Combining Graph Transformations of Tangent and Cotangent | |
| 12.34.8. | Combining Graph Transformations of Secant and Cosecant | |
| 12.34.9. | Graphing Reflections of Trigonometric Functions | |
| 12.34.10. | Graphing Reflections of Trigonometric Functions: Three or More Transformations |
| 12.35.1. | Properties of Transformed Sine and Cosine Functions | |
| 12.35.2. | Properties of Transformed Tangent and Cotangent Functions | |
| 12.35.3. | Properties of Transformed Secant and Cosecant Functions | |
| 12.35.4. | Modeling With Trigonometric Functions |
| 13.36.1. | Probability From Experimental Data | |
| 13.36.2. | Sample Spaces and Events in Probability | |
| 13.36.3. | Single Events in Probability | |
| 13.36.4. | The Complement of an Event | |
| 13.36.5. | Introduction to Sets | |
| 13.36.6. | The Union of Sets | |
| 13.36.7. | The Intersection of Sets | |
| 13.36.8. | Venn Diagrams in Probability | |
| 13.36.9. | Geometric Probability |
| 13.37.1. | Compound Events in Probability From Experimental Data | |
| 13.37.2. | Computing Probabilities for Compound Events Using Venn Diagrams | |
| 13.37.3. | Computing Probabilities for Three Events Using Venn Diagrams | |
| 13.37.4. | The Addition Law of Probability | |
| 13.37.5. | Mutually Exclusive Events |
| 13.38.1. | The Rule of Sum and the Rule of Product | |
| 13.38.2. | Factorials | |
| 13.38.3. | Factorials in Variable Expressions | |
| 13.38.4. | Ordering Objects | |
| 13.38.5. | Permutations | |
| 13.38.6. | Combinations | |
| 13.38.7. | Computing Probabilities Using Combinatorics |
| 14.39.1. | Sampling | |
| 14.39.2. | The Mean of a Data Set | |
| 14.39.3. | Variance and Standard Deviation | |
| 14.39.4. | Covariance | |
| 14.39.5. | The Z-Score |
| 14.40.1. | The Linear Correlation Coefficient | |
| 14.40.2. | Linear Regression | |
| 14.40.3. | Residuals and Residual Plots |
