Review Chapter
R.1 Real Numbers
R.2 The Order of Operations and Algebraic Expressions
R.3 The Laws of Exponents; Radicals
R.4 Polynomials
R.5 Factoring Polynomials
R.6 Rational Expressions
1. Equations, Inequalities, and Applications
1.1 Linear Equations
1.2 Applications of Linear Equations
1.3 Complex Numbers
1.4 Quadratic Equations
1.5 Applications of Quadratic Equations
1.6 Other Types of Equations
1.7 Linear Inequalities
1.8 Absolute Value Equations and Inequalities
1.9 Polynomial and Rational Inequalities
2. The Rectangular Coordinate System, Lines, and Circles
2.1 The Rectangular Coordinate System
2.2 Circles
2.3 Lines
2.4 Parallel and Perpendicular Lines
3. Functions
3.1 Relations and Functions
3.2 Properties of a Function's Graph
3.3 Graphs of Basic Functions; Piecewise Functions
3.4 Transformations of Functions
3.5 The Algebra of Functions; Composite Functions
3.6 One-to-One Functions; Inverse Functions
4. Polynomial and Rational Functions
4.1 Quadratic Functions
4.2 Applications and Modeling of Quadratic Functions
4.3 The Graphs of Polynomial Functions
4.4 Synthetic Division; The Remainder and Factor Theorems
4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra
4.6 Rational Functions and Their Graphs
4.7 Variation
5. Exponential and Logarithmic Functions and Equations
5.1 Exponential Functions
5.2 Logarithmic Functions
5.3 Properties of Logarithms
5.4 Exponential and Logarithmic Equations
5.5 Applications of Exponential and Logarithmic Functions
6. An Introduction to Trigonometric Functions
6.1 An Introduction to Angles: Degree and Radian Measure
6.2 Applications of Radian Measure
6.3 Triangles
6.4 Right Triangle Trigonometry
6.5 Trigonometric Functions of General Angles
6.6 The Unit Circle
7. The Graphs of Trigonometric Functions
7.1 The Graphs of Sine and Cosine
7.2 More on Graphs of Sine and Cosine; Phase Shift
7.3 The Graphs of the Tangent, Cosecant, Secant, and Cotangent Functions
7.4 Inverse Trigonometric Functions I
7.5 Inverse Trigonometric Functions II
8. Trigonometric Identities, Formulas, and Equations
8.1 Trigonometric Identities
8.2 The Sum and Difference Formulas
8.3 The Double-Angle and Half-Angle Formulas
8.4 The Product-to-Sum and Sum-to-Product Formulas
8.5 Trigonometric Equations
9. Applications of Trigonometry
9.1 Right Triangle Applications
9.2 The Law of Sines
9.3 The Law of Cosines
9.4 Area of Triangles
10. Polar Equations, Complex Numbers, and Vectors
10.1 Polar Coordinates and Polar Equations
10.2 Graphing Polar Equations
10.3 Complex Numbers in Polar Form; DeMoivre’s Theorem
10.4 Vectors
10.5 The Dot Product
11. Conic Sections and Parametric Equations
11.1 The Parabola
11.2 The Ellipse
11.3 The Hyperbola
11.4 Conic Sections in Polar Form
11.5 Parametric Equations
12. Systems of Equations and Inequalities
12.1 Solving Systems of Linear Equations in Two Variables
12.2 Solving Systems of Linear Equations in Three Variables Using the Elimination Method
12.3 Solving Systems of Linear Equations in Three Variables Using Gaussian Elimination and Gauss-Jordan Elimination
12.4 Partial Fraction Decomposition
12.5 Systems of Nonlinear Equations
12.6 Systems of Inequalities
13. Matrices
13.1 Matrix Operations
13.2 Inverses of Matrices and Matrix Equations
13.3 Determinants and Cramer's Rule
14. Sequences and Series; Counting and Probability
14.1 Introduction to Sequences and Series
14.2 Arithmetic Sequences and Series
14.3 Geometric Sequences and Series
14.4 The Binomial Theorem
14.5 Mathematical Induction
14.6 The Theory of Counting
14.7 An Introduction to Probability
Appendix A: Degree, Minute, Second Form and Degree Decimal Form
Appendix B: Conic Section Proofs