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Advanced Mathematical Concepts: Precalculus with Applications, ©2001
Table of Contents
UNIT 1 RELATIONS, FUNCTIONS, AND GRAPHS
CHAPTER 1 LINEAR RELATIONS AND FUNCTIONS
1-1 Relations and Functions (old 1-1)
1-2 Composition of Functions (part of old 1-2)
1-3 Graphing Linear Equations (part of old 1-3, slope, intercepts)
1-3B Analyzing Families of Linear Graphs
1-4 Writing Linear Equations (old 1-5)
1-5 Writing Equations of Parallel and Perpendicular Lines (old 1-6)
1-6 Modeling Real-World Data with Linear Functions (parts of old 15-6)
1-7 Piecewise and Absolute Value Functions (NEW)
1-8 Graphing Linear Inequalities (old 1-3)
CHAPTER 2 SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES
2-1 Solving Systems of Equations in Two Variables (old 2-1)
2-2 Solving Systems of Equations in Three Variables (NEW)
2-3 Using Matrices to Model Real-World Data (old 2-2)
2-4A Transformation matrices
2-4 Modeling Motion with Matrices (NEW)
2-5 Determinants and Multiplicative Inverses of Matrices (old 2-3)
2-5B Augmented Matrices and Reduced Row-Echelon Form
2-6 Solving Systems of Inequalities (old 2-5)
2-7 Linear Programming (old 2-6)
chapter 3 The nature of Graphs
3-1 Symmetry and Coordinate Graphs (old 3-1)
3-2 Families of Graphs (old 3-2)
3-3 Graphs of Nonlinear Inequalities (old 3-5)
3-4 Inverse Functions and Relations (old 3-3)
3-5 Continuity and End Behavior (old 3-8)
3-5B Gap Discontinuities (NEW)
3-6 Critical Points and Extrema (old 3-7)
3-7 Graphs of Rational Functions (old 3-4)
3-8 Direct, Indirect, and Joint Variation (NEW)
CHAPTER 4 POLYNOMIAL AND RATIONAL FUNCTIONS
4-1 Polynomial Functions (old 4-1)
4-2 Quadratic Equations (old 4-2)
4-3 The Remainder and Factor Theorems (old 4-3)
4-4 The Rational Root Theorem (old 4-4)
4-5 Locating Zeros of a Polynomial Function (old 4-5)
4-6 Rational Equations and Partial Fractions (old 4-6)
4-7 Radical Equations and Inequalities (old 4-7)
4-8 Modeling Real-World Data with Polynomial Functions (NEW)
4-8B Fitting a Polynomial Function to a Set of Points (NEW)
UNIT 2 TRIGONOMETRY
CHAPTER 5 THE TRIGONOMETRIC FUNCTIONS
5-1 Angles and Degree Measure (old 5-1)
5-2 Trigonometric Ratios in Right Triangles (parts of old 5-4, 5-5)
5-3 Trigonometric Functions on the Unit Circle (old 5-3, 5-4)
5-4 Applying Trigonometric Functions (part of old 5-5)
5-5 Solving Right Triangles (parts of old 5-5, 6-4)
5-6 The Law of Sines (old 5-6, 5-8)
5-7 The Ambiguous Case for the Law of Sines (part of old 5-6)
5-8 The Law of Cosines (old 5-7, 5-8)
5-8B Solving Triangles
CHAPTER 6 GRAPHS OF THE TRIGONOMETRIC FUNCTIONS
6-1 Angles and Radian Measure (old 5-2)
6-2 Linear and Angular Velocity (old 5-2)
6-3 Graphing Sine and Cosine Functions (old 6-1)
6-4 Amplitude and Period of Sine and Cosine Functions (old 6-2)
6-5 Translations of Sine and Cosine Functions (old 6-2, 6-3)
6-6 Modeling Real-World Data with Sinusoidal Functions (NEW)
6-7 Graphing Other Trigonometric Functions (remnants from Ch. 6)
6-7B Graphing Calculator Exploration Sound Beats
6-8 Trigonometric Inverses and Their Graphs (6-4, 6-6)
CHAPTER 7 TRIGONOMETRIC IDENTITIES AND EQUATIONS
7-1 Basic Trigonometric Identities (old 7-1)
7-2 Verifying Trigonometric Identities (old 7-2)
7-3 Sum and Difference Identities (old 7-3)
7-3B Reduction Identities (NEW)
7-4 Double-Angle and Half-Angle Identities (old 7-4)
7-5 Solving Trigonometric Equations (old 7-5)
7-6 Normal Form of a Linear Equation (old 7-6)
7-7 Distance from a Point to a Line (old 7-7)
CHAPTER 8 VECTORS AND PARAMETRIC EQUATIONS
8-1 Geometric Vectors (old 8-1)
8-2 Algebraic Vectors (old 8-2)
8-3 Vectors in Three-Dimensional Space (old 8-3)
8-4 Perpendicular Vectors (old 8-4)
8-4B Finding Cross Products (new)
8-5 Applications with Vectors (old 8-5)
8-6 Vectors and Parametric Equations (old 8-6)
8-6B Modeling With Parametric Equations (new)
8-7 Using Parametric Equations to Model Motion (old 8-7)
8-8 Transformational Matrices in Three-Dimensional Space (new)
UNIT 3 ADVANCED FUNCTIONS AND GRAPHING
CHAPTER 9 POLAR COORDINATES AND COMPLEX NUMBERS
9-1 Polar Coordinates (old 9-1)
9-2 Graphs of Polar Equations (old 9-2)
9-3 Polar and Rectangular Coordinates (old 9-3)
9-4 Polar Form of a Linear Equation (old 9-4)
9-5 Simplifying Complex Numbers (old 9-5)
9-6 The Complex Plane and Polar Form of Complex Numbers (old 9-6)
9-6B Geometry in the Complex Plane (NEW)
9-7 Products and Quotients of Complex Numbers in Polar Form (old 9-7)
9-8 Powers and Roots of Complex Numbers (old 9-8)
chapter 10 Conics
10-1 Analytic Geometry (old 1-4, distance, midpoint, coordinate proofs)
10-2 Circles (old 10-1)
10-3 Ellipses (old 10-3)
10-4 Hyperbolas (old 10-4)
10-5 Parabolas (old 10-2)
10-6 Rectangular and Parametric Forms of Conic Sections (old 10-5)
10-7 Transformations of Conics (old 10-6)
10-8 Systems of Second-Degree Equations and Inequalities (old 10-7)
10-8B Shading Areas on a Graph (NEW)
chapter 11 exponential and logarithmic functions
11-1 Real Exponents (old 11-1)
11-2 Exponential Functions (old 11-2)
11-3 The Number e (old 11-3)
11-4 Logarithmic Functions (old 11-4)
11-5 Common Logarithms (old 11-5, include equations from old 11-6)
11-6 Natural Logarithms (old 11-7, include equations from old 11-6)
11-6B Natural Logarithms and Area (NEW)
11-7 Modeling Real-World Data with Exponential and Logarithmic Functions (NEW)
unit 4 discrete mathematics
CHAPTER 12 SEQUENCES AND SERIES
12-1 Arithmetic Sequences and Series (old 12-1)
12-2 Geometric Sequences and Series (old 12-2)
12-3 Infinite Sequences and Series (old 12-3)
12-3B Continued Fractions (NEW)
12-4 Convergent and Divergent Series (old 12-4)
12-5 Sigma Notation and the nth Term (old 12-5)
12-6 The Binomial Theorem (old 12-6)
12-7 Special Sequences and Series (old 12-7)
12-8 Sequences and Iterations (NEW- adapted from old Chapter 13)
12-9 Mathematical Induction (old 12-8)
chapter 13 combinatorics and probability
13-1 Permutations and Combinations (old 14-1 and 14-3)
13-2 Permutations with Repetitions and Circular Permutations (old 14-2)
13-3 Probability and Odds (old 14-4)
13-4 Probabilities of Compound Events (old 14-5 and 14-6)
13-5 Conditional Probability (old 14-7)
13-6 The Binomial Theorem and Probability (old 14-8)
chapter 14 statistics and data analysis
14-1 The Frequency Distribution (old 15-1)
14-2 Measures of Central Tendency (old 15-2)
14-3 Measures of Variability (old 15-3)
14-4 The Normal Distribution (old 15-4)
14-4B Graphing Calculator Exploration The Standard Normal Curve
14-5 Sample Sets of Data (old 15-5)
UNIT 5 CALCULUS
CHAPTER 15 INTRODUCTION TO CALCULUS
15-1 Limits (old 17-1)
15-2A The Slope of a Curve (New)
15-2 Derivatives and Antiderivatives (old 3-6, 17-2, 17-4)
15-3 Area Under a Curve (old 17-3)
15-4 The Fundamental Theorem of Calculus (old 17-5)
· GRAPHING CALCULATOR APPENDIX
GC-1 Introduction to the Graphing Calculator
Commonly used settings for MODE, Most commonly used menus, Performing Calculations, 2nd and ALPHA keys
GC-2 Graphing Functions
Linear, Quadratic, Other Polynomial, Exponential and Logarithmic Systems
GC-3 Analyzing Functions
How to Use Table; Using ZOOM, TRACE;
Special Menus (Intersection points, Roots, Maximum, Minimum)
GC-4 Graphing Inequalities
Linear Inequalities, Polynomial inequalities, Using the Shade command
GC-5 Matrices
Defining and entering elements in matrices, Find inverses, determinants;
special matrix functions
GC-6 Graphing Trigonometric
Trigonometric Functions; Inverse Trigonometric Functions
GC-7 Graphing Special Functions
Absolute value; Greatest Integer function
GC-8 Parametric and Polar Equations
Parametric Equations; Polar Equations
GC-9 Statistical Graphs
Lists and statistics measures; Different types of statistical graphs