Extra Examples, Mathematics: Advanced Concepts & Applications, Edition, Mathematics, Glencoe

Extra Examples

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Chapter 1 Linear Relations and Functions

  1-1 Relations and Functions
  1-2 Composition of Functions
  1-3 Graphing Linear Equations
  1-4 Writing Equations
  1-5 Writing Equations of Parallel and Perpendicular Lines
  1-6 Modeling Real-World Data with Linear Functions
  1-7 Piecewise and Absolute Value Functions
  1-8 Graphing Linear Inequalities

Chapter 2 Systems of Linear Equations and Inequalities

  2-1 Solving Systems of Equations in Two Variables
  2-2 Solving Systems of Equations in Three Variables
  2-3 Using Matrices to Model Real-World Data
  2-4 Modeling Motion with Matrices
  2-5 Determinants and Multiplicative Inverses of Matrices
  2-6 Solving Systems of Inequalities
  2-7 Linear Programming

Chapter 3 The Nature of Graphs

  3-1 Symmetry and Coordinate Graphs
  3-2 Families of Graphs
  3-3 Graphs of Nonlinear Inequalities
  3-4 Inverse Functions and Relations
  3-5 Continuity and End Behavior
  3-6 Critical Points and Extrema
  3-7 Graphs of Rational Functions
  3-8 Direct, Indirect, and Joint Variation

Chapter 4 Polynomial and Rational Functions

  4-1 Polynomial Functions
  4-2 Quadratic Equations
  4-3 The Remainder and Factor Theorems
  4-4 The Rational Root Theorem
  4-5 Locating Zeros of a Polynomial Function
  4-6 Rational Equations and Partial Fractions
  4-7 Radical Equations and Inequalities
  4-8 Modeling Real-World Data with Polynomial Functions

Chapter 5 The Trigonometric Functions

  5-1 Angles and Degree Measure
  5-2 Trigonometric Ratios in Right Triangles
  5-3 Trigonometric Functions on the Unit Circle
  5-4 Applying Trigonometric Functions
  5-5 Solving Right Triangles
  5-6 The Law of Sines
  5-7 The Ambiguous Case for the Law of Sines
  5-8 The Law of Cosines

Chapter 6 Graphs of Trigonometric Functions

  6-1 Angles and Radian Measure
  6-2 Linear and Angular Velocity
  6-3 Graphing Sine and Cosine Functions
  6-4 Amplitude and Period of Sine and Cosine Functions
  6-5 Horizontal and Vertical Shifts of Sine and Cosine Functions
  6-6 Modeling Real-World Data with Sinusoidal Functions
  6-7 Graphing Other Trigonometric Functions
  6-8 Trigonometric Inverses and Their Graphs

Chapter 7 Trigonometric Identities and Equations

  7-1 Basic Trigonometric Identities
  7-2 Verifying Trigonometric Identities
  7-3 Sum and Difference Identities
  7-4 Double-Angle and Half-Angle Identities
  7-5 Solving Trigonometric Equations
  7-6 Normal Form of a Linear Equation
  7-7 Distance from a Point to a Line

Chapter 8 Vectors and Parametric Equations

  8-1 Geometric Vectors
  8-2 Algebraic Vectors
  8-3 Vectors in Three-dimensional Space
  8-4 Perpendicular Vectors
  8-5 Applications with Vectors
  8-6 Vectors and Parametric Equations
  8-7 Modeling Motion Using Parametric Equations
  8-8 Transformational Matrices in Three-dimensional Space

Chapter 9 Polar Coordinates and Complex Numbers

  9-1 Polar Coordinates
  9-2 Graphs of Polar Equations
  9-3 Polar and Rectangular Coordinates
  9-4 Polar Form of a Linear Equation
  9-5 Simplifying Complex Numbers
  9-6 The Complex Plan and Polar Form of Complex Numbers
  9-7 Products and Quotients of Complex Numbers in Polar Form
  9-8 Powers and Roots of Complex Numbers

Chapter 10 Conics

  10-1 Introduction to Analytic Geometry
  10-2 Circles
  10-3 Ellipses
  10-4 Hyperbolas
  10-5 Parabolas
  10-6 Rectangular and Parametric Forms of Conic Sections
  10-7 Transformations of Conics
  10-8 Systems of Second-Degree Equations and Inequalities

Chapter 11 Exponential and Logarithmic Functions

  11-1 Real Exponents
  11-2 Exponential Functions
  11-3 The Number e
  11-4 Logarithmic Functions
  11-5 Common Logarithms
  11-6 Natural Logarithms
  11-7 Modeling Real-World Data with Exponential and Logarithmic Functions

Chapter 12 Sequences and Series

  12-1 Arithmetic Sequences and Series
  12-2 Geometric Sequences and Series
  12-3 Infinite Sequences and Series
  12-4 Convergent and Divergent Series
  12-5 Sigma Notation and the nth Term
  12-6 The Binomial Theorem
  12-7 Special Sequences and Series
  12-8 Sequences and Iterations
  12-9 Mathematical Induction

Chapter 13 Combinatorics and Probability

  13-1 Permutations and Combinations
  13-2 Permutations with Repetitions and Circular Permutations
  13-3 Probability and Odds
  13-4 Probabilities of Compound Events
  13-5 Conditional Probabilities
  13-6 The Binomial Theorem and Probability

Chapter 14 Statistics and Data Analysis

  14-1 The Frequency Distribution
  14-2 Measures of Central Tendency
  14-3 Measures of Variability
  14-4 The Normal Distribution
  14-5 Sample Sets of Data

Chapter 15 Introduction to Calculus

  15-1 Limits
  15-2 Derivatives and Antiderivatives
  15-3 Area Under a Curve
  15-4 The Fundamental Theorem of Calculus