Table of Contents

Chapter 1: Equations and Inequalities

1. Linear Equations & Applications
2. Systems of Linear Equations & Applications
3. Linear Inequalities
4. Absolute Value in Equations and Inequalities
5. Complex Numbers
6. Quadratic Equations & Applications
7. Equations Reducible to Quadratic Form
8. Polynomial & Rational Inequalities

1. Basic Tools; Circles
2. Straight Lines
3. Functions
4. Graphing Functions
5. Combining Functions
6. Inverse Functions

1. Polynomial Functions and Graphs
2. Finding Rational Zeros of Polynomials
3. Approximating Real Zeros of Polynomials
4. Rational Functions
5. Partial Fractions

1. Exponential Functions
2. The Exponential Function With Base e
3. Logarithmic Functions
4. Common and Natural Logarithms
5. Exponential & Logarithmic Equations

1. The Wrapping Function
2. Circular Functions
3. Angles and Their Measure
4. Trigonometric Functions
5. Solving Right Triangles
6. Graphing Basic Trigonometric Functions
7. Graphing y= k + A sin(Bx+C) and y= k + A cos(Bx + C)
8. Graphing More General Tangent, Cotangent, Secant and Cosecant Functions
9. Inverse Trigonometric Functions

1. Basic Identities and Their Use
2. Sum, Difference, and Cofunction Identities
3. Double-Angle and Half-Angle Identities
4. Product-Sum and Sum-Product Identities
5. Trigonometric Equations

1. Law of Sines
2. Law of Cosines
3. Geometric Vectors
4. Algebraic Vectors
5. Polar Coordinates and Graphs
6. Complex Numbers in Rectangular and Polar Forms
7. De Moivreís Theorem

1. Systems of Linear Equations and Augmented Matrices
2. Gauss-Jordan Elimination
3. Systems Involving Second-Degree Equations
4. Systems of Linear Inequalities in Two Variables
5. Linear Programming

1. Matrices: Basic Operations
2. Inverse of a Square Matrix
3. Matrix Equations and Systems of Linear Equations
4. Determinants
5. Properties of Determinants
6. Cramerís Rule

1. Sequences and Series
2. Mathematical Induction
3. Arithmetic & Geometric Sequences
4. Binomial Formula
5. Multiplication Principle, Permutations, and Combinations

1. Conic Sections; Parabola
2. Ellipse
3. Hyperbola
4. Translation of Axes
5. Parametric Equations

A: Basic Algebraic Operations

A-1 Algebra & Real Numbers

A-2 Polynomials: Basic Operations

A-3 Polynomials: Factoring

A-4 Rational Expressions: Basic Operations

A-5 Integer Exponents

A-6 Rational Exponents

A-7 Radicals

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