Table of Contents

1 • Graphs
 The Coordinate Plane: Four Quadrants
 Midpoint on the Coordinate Plane
 Distance on the Coordinate Plane: Pythagorean Formula
 Distance on the Coordinate Plane: Horizontal and Vertical
 Symmetry of Graphs and Functions
 Slope of a Line through Two Points
 Equation of a Straight Line: General Form
 Equation of a Straight Line: Standard and Point–Slope Forms
 Equation of a Straight Line: Slope–Intercept Form
 Slopes and Intercepts of Linear Functions
 Equations of Parallel and Perpendicular Lines
 Equation of a Circle

2 • Functions and Their Graphs
 Relations and Functions
 Polynomial Functions
 Combining Functions
 Domain and Range from Function Graphs
 Even and Odd Functions
 Increasing and Decreasing Intervals of a Function
 Average and Instantaneous Rates of Change
 Graphs of Piecewise Functions
 Function Transformations: Dilation
 Function Transformations: Translations
 3 • Linear and Quadratic Functions

4 • Polynomial and Rational Functions
 Graphs of Rational Functions
 Polynomial Inequalities
 Rational Inequalities
 Remainder and Factor Theorem with Synthetic Division
 Descartes’ Rule of Signs
 Rational Zeros Theorem
 Upper and Lower Bound Tests for Polynomial Functions
 Intermediate Value Theorem
 Linear Factorization and Conjugate Root Theorems
 Real and Complex Roots of Polynomials
 5 • Exponential and Logarithmic Functions

6 • Trigonometric Functions
 Angles in Degrees, Minutes, and Seconds
 Arc Lengths and Sectors
 Conversion between Radians and Degrees
 Exact Values of Trigonometric Ratios
 Evaluating Trigonometric Functions Using Cofunction Identities
 Amplitude and Period of Trigonometric Functions
 Graphs of Trigonometric Functions
 Transformation of Trigonometric Functions

7 • Analytic Trigonometry
 Inverse Trigonometric Functions
 Simple Trigonometric Equations
 Solving a Trigonometric Equation
 Simplifying Trigonometric Expressions Using Trigonometric Identities
 Angle Sum and Difference Identities
 DoubleAngle and HalfAngle Identities
 Solving Trigonometric Equations with the DoubleAngle Identity
 ProducttoSum Identities

8 • Applications of Trigonometric Functions
 Trigonometric Ratios in Right Triangles
 Right Triangle Trigonometry: Solving for an Angle
 Evaluating Trigonometric Function Values with Angles 30, 45, and 60
 Evaluating Trigonometric Functions Using Pythagorean Identities
 Right Triangle Trigonometry: Solving for a Side
 Ambiguous Case of the Law of Sines
 Law of Sines
 Heron’s Formula
 Applications on Sine and Cosine Laws
 Law of Cosines
 Finding the Area of a Triangle Using Trigonometry
 Modeling with Trigonometric Functions

9 • Polar Coordinates; Vectors
 Polar Coordinates
 Graphing Polar Curves
 Argand Diagram
 Multiplying Complex Numbers
 Magnitude of a 2D Vector
 Graphical Operations on Vectors
 Adding and Subtracting Vectors in 2D
 Vector Operations in 2D
 Dot Product in 2D
 Points, Midpoints, and Distances in Space
 Dot Product in 3D
 Angle between Two Vectors in Space
 Direction Angles and Direction Cosines
 Cross Product in 3D
 10 • Analytic Geometry

11 • Systems of Equations and Inequalities
 Solving Systems of Linear Equations Using Substitution
 Solving Systems of Linear Equations Using Elimination
 Consistency and Dependency of Linear Systems
 Investigating Profits
 Applications on Systems of Linear Equations
 Applications on Systems of Linear Equations in Three Variables
 Systems of Linear Equations in Three Variables
 Solving a System of Two Equations Using a Matrix Inverse
 TwobyTwo Determinants
 ThreebyThree Determinants
 Cramer’s Rule
 Properties of Determinants
 Adding and Subtracting Matrices
 Scalar Multiplication of Matrices
 Properties of Matrix Multiplication
 Matrix Multiplication
 Inverse of a 2 × 2 Matrix
 Inverse of a Matrix: The Adjoint Method
 Partial Fractions: Nonrepeated Linear Factors
 Partial Fractions: Repeated Linear Factors
 Partial Fractions: Nonrepeated Irreducible Quadratic Factors
 Solving Systems of Quadratic Equations
 LinearQuadratic Systems of Equations
 TwoVariable Linear Inequalities
 Linear Programming

12 • Sequences; Induction; the Binomial Theorem
 Introduction to Sequences
 Calculations with Arithmetic Sequences
 Using Arithmetic Sequence Formulas
 Arithmetic Series
 Geometric Sequences
 Finding the nth Term of a Geometric Sequence
 Sum of a Finite Geometric Sequence
 Infinite Geometric Series
 Mathematical Induction
 Properties of Combinations
 Pascal’s Triangle and the Binomial Theorem
 The Binomial Theorem
 13 • Counting and Probability
 14 • A Preview of Calculus: The Limit, Derivative, and Integral of a Function