Advanced Mathematical Concepts: Precalculus With Applications, Student Edition https://www.mheducation.com/cover-images/Jpeg_250-high/0028341759.jpeg 11 - 12 9780028341750
Advanced Mathematical Concepts: Precalculus With Applications, Student Edition

Advanced Mathematical Concepts: Precalculus With Applications, Student Edition

Grade Levels: 11 - 12
By McGraw-Hill Education
Copyright: 2001
Publication Date: May 26, 2000
MHID: 0028341759
ISBN 13: 9780028341750

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New Features

A full-color design, a wide range of exercise sets, relevant special features, and an emphasis on graphing and technology invite your students to experience the excitement of understanding and applying higher-level mathematics skills.

Graphing calculator instruction is provided in the Graphing Calculator Appendix.  Each Graphing Calculator Exploration provides a unique problem-solving situation.

Calculus concepts and skills are integrated throughout the course.

Advanced Mathematical Concepts: Precalculus With Applications, Student Edition

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

 

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