Table of Contents

1 • Functions and Their Graphs
 The Coordinate Plane: Four Quadrants
 Midpoint on the Coordinate Plane
 Translations on a Coordinate Plane
 Distance on the Coordinate Plane: Pythagorean Formula
 Intercepts and Symmetry of Graphs of Functions
 Equation of a Circle
 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
 Equations of Parallel and Perpendicular Lines
 Relations and Functions
 Polynomial Functions
 Domain and Range from Function Graphs
 Increasing and Decreasing Intervals of a Function
 Extrema of a Function Graph
 Even and Odd Functions
 Average and Instantaneous Rates of Change
 Graphs of Piecewise Functions
 Function Transformations: Translations
 Combining Functions
 Composite Functions
 Graphs of Inverses of Functions
 Inverse of a Function
 Least Squares Regression Line

2 • Polynomial and Rational Functions
 Graphing Quadratic Functions
 Quadratic Functions in Different Forms
 Features of Quadratic Functions
 Zeros of Polynomial Functions
 Graphing Using Derivatives
 Intermediate Value Theorem
 Remainder and Factor Theorem with Synthetic Division
 Polynomial Long Division with Remainder
 Equating, Adding, and Subtracting Complex Numbers
 Multiplying Complex Numbers
 Complex Number Conjugates
 Solving Quadratic Equation with Complex Roots
 Rational Zeros Theorem
 Linear Factorization and Conjugate Root Theorems
 Descartes’ Rule of Signs
 Upper and Lower Bound Tests for Polynomial Functions
 Domain and Range of a Rational Function
 Horizontal and Vertical Asymptotes of a Function
 Graphs of Rational Functions
 Polynomial Inequalities
 OneVariable Quadratic Inequalities
 Rational Inequalities

3 • Exponential and Logarithmic Functions
 Graphs of Exponential Functions
 Solving Exponential Equations Using Exponent Properties
 Applications of Exponential Functions
 Graphs of Logarithmic Functions
 Laws of Logarithms
 Simplifying Natural Logarithmic Expressions
 Solving Exponential Equations Using Logarithms
 Logarithmic Equations with Like Bases
 Exponential Growth and Decay Models
 Compound Interest
 Exponential Growth and Decay

4 • Trigonometry
 Conversion between Radians and Degrees
 Complementary and Supplementary Angles
 Arc Lengths and Sectors
 Exact Values of Trigonometric Ratios
 Trigonometric Ratios in Right Triangles
 Right Triangle Trigonometry: Solve for an Angle
 Evaluating Trigonometric Function Values with Angles 30,45, and 60
 Evaluating Trigonometric Functions Using Pythagorean Identities
 Right Triangle Trigonometry: Solve for a Side
 Trigonometric Ratios on the Unit Circle
 Trigonometric Functions Values with Reference Angles
 Trigonometric Functions of Standard Position Angle
 Transformation of Trigonometric Functions
 The Graphs of Reciprocal Trigonometric Functions
 Inverse Trigonometric Functions
 Angles of Elevation and Depression
 5 • Analytic Trigonometry

6 • Additional Topics in Trigonometry
 Law of Sines
 Finding the Area of Triangle Using Trigonometry
 Ambiguous Case of the Law of Sines
 Heron’s Formula
 Applications on Sine and Cosine Laws
 Law of Cosines
 Scalars, Vectors, and Directed Line Segments
 Magnitude of a 2D Vector
 Components of a Vector
 Vectors in Terms of Fundamental Unit Vectors
 Dot Product
 The Angle between Two Vectors in the Coordinate Plane
 Work Done by a Force Expressed in Vector Notation
 Argand Diagram

7 • Systems of Equations and Inequalities
 Solving Systems of Linear Equations Using Substitution
 Solving Systems of Linear Equations Using Elimination
 Applications on Systems of Linear Equations in Three Variables
 Systems of Linear Equations in Three Variables
 Partial Fractions: Nonrepeated Linear Factors
 Partial Fractions: Repeated Linear Factors
 Partial Fractions: Nonrepeated Irreducible Quadratic Factors
 Applications on Systems of Inequalities
 Solving Systems of Linear Inequalities
 Linear Programming

8 • Matrices and Determinants
 Introduction to Matrices
 Introduction to The System of Linear Equations
 The General Solution of a System of Linear Equations
 Matrix Operations
 Equal Matrices
 Adding and Subtracting Matrices
 Inverse of a 2x2 Matrix
 Inverse of a Matrix: The Adjoint Method
 Solving a System of Two Equations Using a Matrix Inverse
 ThreebyThree Determinants
 TwobyTwo Determinants
 Properties of Determinants
 Cramer’s Rule
 Using Determinants to Calculate Areas

9 • Sequences, Series, and Probability
 Recursive Formula of a Sequence
 Sigma Notation
 Calculations with Arithmetic Sequences
 Using Arithmetic Sequence Formulas
 Finding the Arithmetic Sequence
 Arithmetic Series
 Geometric Sequences
 Finding the nth Term of a Geometric Sequence
 Sum of a Finite Geometric Sequence
 Sum of an Infinite Geometric Sequence
 Mathematical Induction
 Properties of Combinations
 Pascal’s Triangle and the Binomial Theorem
 The Binomial Theorem
 Fundamental Counting Principle
 Properties of Permutations
 Counting Using Permutations
 Counting Using Combinations
 Probability of Simple Events
 Complementary Events
 Using Permutations to Find Probability
 Mutually Exclusive Events
 Compound Events

10 • Topics in Analytic Geometry
 Slope of a Line from a Graph or a Table
 Perpendicular Distance from a Point to a Line on the Coordinate Plane
 Angle between Two Straight Lines in the Coordinate Plane
 Distance on the Coordinate Plane: Horizontal and Vertical
 Equation of a Parabola
 Equation of an Ellipse
 Equation of a Hyperbola
 Eccentricity of Conic Sections
 Polar Coordinates
 Graphing Polar Curves
 Polar Equation of a Conic