Algebra & Trigonometry

Chapter R: A Review of Basic Concepts and Skills

R-1 The Language, Notation, and Numbers of Mathematics

R-2 Algebraic Expressions and the Properties of Real Numbers

R-3 Exponents, Scientific Notation, and a Review of Polynomials

R-4 Factoring Polynomials

R-5 Rational Expressions

R-6 Radicals and Rational Exponents

Chapter 1: Equations and Inequalities

1-1 Linear Equations, Formulas, and Problem Solving

1-2 Linear Inequalities in One Variable

1-3 Absolute Value Equations and Inequalities

1-4 Complex Numbers

1-5 Solving Quadratic Equations

1-6 Solving Other Types of Equations

Chapter 2: Relations, Functions and Graphs

2-1 Rectangular Coordinates; Graphing Circles and Relations

2-2 Graphs of Linear Equations

2-3 Linear Equations and Rates of Change

2-4 Functions, Notation, and Graphs of Functions

2-5 Analyzing the Graph of a Function

2-6 Toolbox Functions and Transformations

2-7 Piecewise-Defined Functions

2-8 The Algebra and Composition of Functions

Chapter 3: Polynomial and Rational Functions

3-1 Quadratic Functions and Applications

3-2 Synthetic Division; The Remainder and Factor Theorems

3-3 The Zeroes of Polynomial Functions

3-4 Graphing Polynomial Functions

3-5 Graphing Rational Functions

3-6 Additional Insights into Rational Functions

3-7 Polynomial and Rational Inequalities

3-8 Variation: Function Models in Action

Chapter 4: Exponential and Logarithmic Functions

4-1 One-to-One and Inverse Functions

4-2 Exponential Functions

4-3 Logarithms and Logarithmic Functions

4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations

4-5 Applications from Business, Finance, and Science

Chapter 5: Introduction to Trigonometric Functions

5-1 Angle Measure, Special Triangles, and Special Angles

5-2 The Trigonometry of Right Triangles

5-3 Trigonometry and the Coordinate Plane

5-4 Unit Circles and the Trigonometric of Real Numbers

5-5 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions

5-6 Graphs of Tangent and Cotangent Functions

5-7 Transformations and Applications of Trigonometric Graphs

Chapter 6: Trigonometric Identities, Inverses, and Equations

6-1 Fundamental Identities and Families of Identities

6-2 Constructing and Verifying Identities

6-3 The Sum and Difference Identities

6-4 Double Angle, Half Angle & Product-to-Sum Identities

6-5 The Inverse Trigonometric Functions and Their Applications

6-6 Solving Basic Trigonometric Equations

6-7 General Trigonometric Equations and Applications

Chapter 7: Applications of Trigonometry

7-1 Oblique Triangles and the Law of Sines

7-2 The Law of Cosines; Area of a Triangle

7-3 Vectors and Vector Diagrams

7-4 Vector Applications and the Dot Product

7-5 Complex Numbers in Trigonometric Form

7-6 Demoivre’s Theorem and the Theorem on nth Roots

Chapter 8: Systems of Equations and Inequalities

8-1 Linear Systems in Two Variables with Applications

8-2 Linear Systems in Three Variables with Applications

8-3 Nonlinear Systems of Equations and Inequalities

8-4 Systems of Inequalities and Linear Programming

Chapter 9: Matrices and Matrix Applications

9-1 Solving Systems Using Matrices and Row Operations

9-2 The Algebra of Matrices

9-3 Solving Linear Systems Using Matrix Equations

9-4 Applications of Matrices and Determinants: Cramer's Rule, Partial Fractions, and More

Chapter 10: Analytical Geometry and Conic Sections

10-1 Introduction to Analytic Geometry

10-2 The Circle and the Ellipse

10-3 The Hyperbola

10-4 The Analytic Parabola

10-5 Polar Coordinates, Equations, and Graphs

10-6 More on Conic Sections: Rotation of Axes and Polar Form

10-7 Parametric Equations and Graphs

Chapter 11: Additional Topics in Algebra

11-1 Sequences and Series

11-2 Arithmetic Sequences

11-3 Geometric Sequences

11-4 Mathematical Induction

11-5 Counting Techniques

11-6 Introduction to Probability

11-7 The Binomial Theorem Summary and Concept Review

APPENDICES

A-1 More on Synthetic Division

A-2 More on Matrices

A-3 Deriving the Equation of a Conic

A-4 Proof Positive - A Selection of Proofs from Algebra and Trigonometry