preparing for...
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00Preparing for Precalculus
Multilingual eGlossary p. P1
Vocabulary p. P3
Table of Contents©
Dan
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Multilingual eGlossary p. P1
Vocabulary p. P3
connectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com Your Digital Math Portal
00Get Started on Chapter 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P2
Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P2
0-1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P3
0-2 Operations with Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P6
0-3 Quadratic Functions and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P9
0-4 n th Roots and Real Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P14
0-5 Systems of Linear Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . .P18
0-6 Matrix Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P23
0-7 Probability with Permutations and Combinations. . . . . . . . . . . . . . . . . . . .P28
0-8 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P32
Posttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P38
00Preparing for Precalculus
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Your Digital Math PortalconnectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com
Unit 1 | Linear Relations and Functions
11Functions from a Calculus Perspective
Multilingual eGlossary p. 85
Vocabulary p. 86
Animation p. 98
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22Get Ready for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2-1 Power and Radical Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86
Explore: Graphing Technology Lab Behavior of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 96
2-2 Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97
Extend: Graphing Technology Lab Hidden Behavior of Graphs. . . . . . . . . . . . . . . . . . . 108
2-3 The Remainder and Factor Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118
2-4 Zeros of Polynomial Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119
2-5 Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130
2-6 Nonlinear Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153
Connect to AP Calculus: Area Under a Curve. . . . . . . . . . . . . . . . . . . . . . . .154
22Power, Polynomial, and Rational Functions
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Personal Tutor p. 56
Graphing Calculator pp. 74-75
Self-Check Practice p. 44
11Get Ready for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1-1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1-2 Analyzing Graphs of Functions and Relations . . . . . . . . . . . . . . . . . . . . . . . . .13
1-3 Continuity, End Behavior, and Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
1-4 Extrema and Average Rates of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44
1-5 Parent Functions and Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
Extend : Graphing Technology Lab Nonlinear Inequalities . . . . . . . . . . . . . . . . . . . . . . . 56
1-6 Function Operations and Composition of Functions. . . . . . . . . . . . . . . . . . . . .57
1-7 Inverse Relations and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
Extend: Graphing Technology Lab Graphing Inverses Using Parametric Equations . . . . 74
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81
Connect to AP Calculus: Rate of Change at a Point . . . . . . . . . . . . . . . . . . . .82
11Functions from a Calculus Perspective
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Personal Tutor p. 56
Graphing Calculator pp. 74-75
Self-Check Practice p. 44
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iii iii
Unit 1 | Linear Relations and Functions
Power, Polynomial, Power, Polynomial, and Rational Functionsand Rational Functions
Get Ready for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2-1 Power and Radical Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86
Explore: Graphing Technology Lab Behavior of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 96
2-2 Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97
Extend: Graphing Technology Lab Hidden Behavior of Graphs. . . . . . . . . . . . . . . . . . . 108
2-3 The Remainder and Factor Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118
2-4 Zeros of Polynomial Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119
2-5 Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130
2-6 Nonlinear Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153
Connect to AP Calculus: Area Under a Curve. . . . . . . . . . . . . . . . . . . . . . . .154
Power, Polynomial, and Rational Functions
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Mag
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Multilingual eGlossary p. 85
Vocabulary p. 86
Animation p. 98
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Your Digital Math PortalconnectED.mcgraw-hill.comccccc
Unit 1 | Linear Relations and Functions
Exponential and Exponential and Logarithmic FunctionsLogarithmic Functions
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Get Ready for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
3-1 Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .158
Extend: Graphing Technology Lab Financial Literacy: Exponential Functions . . . . . . . . 170
3-2 Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172
3-3 Properties of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .189
3-4 Exponential and Logarithmic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .190
Extend: Graphing Technology Lab Exponential and Logarithmic Inequalities . . . . . . . 199A
3-5 Modeling with Nonlinear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .200
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .211
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .215
Connect to AP Calculus: Approximating Rates of Change . . . . . . . . . . . . .216
Exponential and Logarithmic Functions
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Liss
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Personal Tutor pp. 170-171
Graphing Calculator pp. 170-171
Self-Check Practice p. 185
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v v
Unit 1 | Linear Relations and Functions
Trigonometric FunctionsTrigonometric Functions
Get Ready for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
4-1 Right Triangle Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .220
4-2 Degrees and Radians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .231
4-3 Trigonometric Functions on the Unit Circle. . . . . . . . . . . . . . . . . . . . . . . . . . .242
Explore: Graphing Technology Lab Graphing the Sine Function Parametrically . . . . . . 254
4-4 Graphing Sine and Cosine Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256
Extend: Graphing Technology Lab Sums and Differences of Sinusoids . . . . . . . . . . . . 267
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .268
4-5 Graphing Other Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . .269
4-6 Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .280
4-7 The Law of Sines and the Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . . . . .291
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .302
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .307
Connect to AP Calculus: Related Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . .308
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Auro
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Multilingual eGlossary p. 219
Vocabulary p. 269
Animation p. 244
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Your Digital Math PortalconnectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com
Unit 2 | Quadratic, Polynomial, and Radical Functions and Relations
5555Trigonometric Identities and Equations
connectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com Your Digital Math Portal
Multilingual eGlossary p. 363
Vocabulary pp. 388
Animation p. 375
Systems of Equations and Matrices66666Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations 6and Matrices6and Matricesand Matrices6and Matrices
Get Ready for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
6-1 Multivariable Linear Systems and Row Operations . . . . . . . . . . . . . . . . . . . .364
6-2 Matrix Multiplication, Inverses, and Determinants. . . . . . . . . . . . . . . . . . . . .375
Extend: Graphing Technology Lab Determinants and Areas of Polygons . . . . . . . . . . . 387
6-3 Solving Linear Systems Using Inverses and Cramer’s Rule . . . . . . . . . . . . . .388
Extend: Graphing Technology Lab Matrices and Cryptography . . . . . . . . . . . . . . . . . . 395
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .397
6-4 Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .398
6-5 Linear Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .405
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .413
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .417
Connect to AP Calculus: Nonlinear Optimization . . . . . . . . . . . . . . . . . . . . .418
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Self-Check Practice p. 352
Graphing Calculator pp. 344–345
Personal Tutor p. 334
Trigonometric Identities and Equations55555Trigonometric Identities 5Trigonometric Identities Trigonometric Identities 5Trigonometric Identities Trigonometric Identities 5Trigonometric Identities Trigonometric Identities 5Trigonometric Identities 5and Equations5and Equationsand Equations5and Equations
Get Ready for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
5-1 Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .312
5-2 Verifying Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .320
5-3 Solving Trigonometric Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .327
Extend: Graphing Technology Lab Solving Trigonometric Inequalities . . . . . . . . . . . . . 334
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .335
5-4 Sum and Difference Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .336
Extend: Graphing Technology Lab Reduction Identities . . . . . . . . . . . . . . . . . . . . . . . . 344
5-5 Multiple-Angle and Product-to-Sum Identities. . . . . . . . . . . . . . . . . . . . . . . .346
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .355
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .359
Connect to AP Calculus: Rate of Change for Sine and Cosine . . . . . . . . . .360
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Self-Check Practice p. 352
Graphing Calculator pp. 344–345
Personal Tutor p. 334
© C
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vii vii
Unit 2 | Quadratic, Polynomial, and Radical Functions and RelationsUnit 2 | Quadratic, Polynomial, and Radical Functions and Relations
6666Systems of Equations and Matrices
connectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com Your Digital Math Portal
Multilingual eGlossary p. 363
Vocabulary pp. 388
Animation p. 375
Systems of Equations and Matrices66666Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations 6and Matrices6and Matricesand Matrices6and Matrices
Get Ready for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
6-1 Multivariable Linear Systems and Row Operations . . . . . . . . . . . . . . . . . . . .364
6-2 Matrix Multiplication, Inverses, and Determinants. . . . . . . . . . . . . . . . . . . . .375
Extend: Graphing Technology Lab Determinants and Areas of Polygons . . . . . . . . . . . 387
6-3 Solving Linear Systems Using Inverses and Cramer’s Rule . . . . . . . . . . . . . .388
Extend: Graphing Technology Lab Matrices and Cryptography . . . . . . . . . . . . . . . . . . 395
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .397
6-4 Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .398
6-5 Linear Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .405
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .413
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .417
Connect to AP Calculus: Nonlinear Optimization . . . . . . . . . . . . . . . . . . . . .418
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Multilingual eGlossary p. 363
Vocabulary pp. 388
Animation p. 375
© C
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©Pe
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viii viii
Your Digital Math PortalconnectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com
Unit 2 | Quadratic, Polynomial, and Radical Functions and Relations
7777Conic Sections and Parametric Equations
connectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com Your Digital Math Portal
Multilingual eGlossary p. 481
Vocabulary p. 500
Animation p. 484
Vectors88888Vectors8VectorsVectors8VectorsVectors8VectorsVectors8VectorsVectors8VectorsVectors8Vectors
Get Ready for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
8-1 Introduction to Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .482
8-2 Vectors in the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .492
8-3 Dot Products and Vector Projections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .500
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .509
8-4 Vectors in Three-Dimensional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .510
Extend: Graphing Technology Lab Vector Transformations with Matrices. . . . . . . . . . . 517
8-5 Dot and Cross Products of Vectors in Space . . . . . . . . . . . . . . . . . . . . . . . . .518
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .525
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .529
Connect to AP Calculus: Vector Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . .530
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Self-Check Practice p. 453
Graphing Calculator p. 472
Personal Tutor pp. 462–463
Conic Sections and Parametric Equations77777Conic Sections and 7Conic Sections and Conic Sections and 7Conic Sections and 7Parametric Equations7Parametric EquationsParametric Equations7Parametric Equations
Get Ready for Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
7-1 Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .422
7-2 Ellipses and Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .432
7-3 Hyperbolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .442
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .453
7-4 Rotations of Conic Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .454
Extend: Graphing Technology Lab Systems of Nonlinear Equations and Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
7-5 Parametric Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .464
Extend: Graphing Technology Lab Modeling with Parametric Equations . . . . . . . . . . . 472
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .473
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .477
Connect to AP Calculus: Solids of Revolution . . . . . . . . . . . . . . . . . . . . . . .478
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Self-Check Practice p. 453
Graphing Calculator p. 472
Personal Tutor pp. 462–463
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ix ix
Unit 3 | Advanced Functions and RelationsUnit 2 | Quadratic, Polynomial, and Radical Functions and Relations
8888Vectors
connectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com Your Digital Math Portal
Multilingual eGlossary p. 481
Vocabulary p. 500
Animation p. 484
Vectors88888Vectors8VectorsVectors8VectorsVectors8VectorsVectors8VectorsVectors8VectorsVectors8Vectors
Get Ready for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
8-1 Introduction to Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .482
8-2 Vectors in the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .492
8-3 Dot Products and Vector Projections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .500
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .509
8-4 Vectors in Three-Dimensional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .510
Extend: Graphing Technology Lab Vector Transformations with Matrices. . . . . . . . . . . 517
8-5 Dot and Cross Products of Vectors in Space . . . . . . . . . . . . . . . . . . . . . . . . .518
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .525
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .529
Connect to AP Calculus: Vector Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . .530
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Multilingual eGlossary p. 481
Vocabulary p. 500
Animation p. 484
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Your Digital Math PortalconnectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com
Unit 3 | Advanced Functions and Relations
9999Polar Coordinates and Complex Numbers
connectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com Your Digital Math Portal
Multilingual eGlossary p. 589
Vocabulary p. 608
Animation p. 629
Sequences and Series 1010101010Sequences and Series 10Sequences and Series Sequences and Series 10Sequences and Series
Get Ready for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588
10-1 Sequences, Series, and Sigma Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .590
10-2 Arithmetic Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .599
10-3 Geometric Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .608
Extend: Graphing Technology Lab Continued Fractions . . . . . . . . . . . . . . . . . . . . . . . . 619
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .620
10-4 Mathematical Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .621
10-5 The Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .628
10-6 Functions as Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .636
Extend: Spreadsheet Lab Detecting Patterns in Data . . . . . . . . . . . . . . . . . . . . . . . . 644A
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .645
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .649
Connect to AP Calculus: Riemann Sum . . . . . . . . . . . . . . . . . . . . . . . . . . . .650
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viii_xxi_FM_TOC_664183.indd 18 7/17/12 11:38 AM
Self-Check Practice p. 577
Graphing Calculator p. 541
Personal Tutor p. 541
Polar Coordinates and Complex Numbers99999Polar Coordinates and 9Polar Coordinates and Polar Coordinates and 9Polar Coordinates and 9Complex Numbers9Complex NumbersComplex Numbers9Complex Numbers
Get Ready for Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
9-1 Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .534
Explore: Graphing Technology Lab Investigate Graphs of Polar Equations . . . . . . . . . . 541
9-2 Graphs of Polar Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .542
9-3 Polar and Rectangular Forms of Equations. . . . . . . . . . . . . . . . . . . . . . . . . . .551
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .560
9-4 Polar Forms of Conic Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .561
9-5 Complex Numbers and DeMoivre’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . .569
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .580
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .585
Connect to AP Calculus: Arc Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .586
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Self-Check Practice p. 577
Graphing Calculator p. 541
Personal Tutor p. 541
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xi xi
Unit 3 | Advanced Functions and RelationsUnit 3 | Advanced Functions and Relations
101010Sequences and Series
connectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com Your Digital Math Portal
Multilingual eGlossary p. 589
Vocabulary p. 608
Animation p. 629
Sequences and Series 1010101010Sequences and Series 10Sequences and Series Sequences and Series 10Sequences and Series
Get Ready for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588
10-1 Sequences, Series, and Sigma Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .590
10-2 Arithmetic Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .599
10-3 Geometric Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .608
Extend: Graphing Technology Lab Continued Fractions . . . . . . . . . . . . . . . . . . . . . . . . 619
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .620
10-4 Mathematical Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .621
10-5 The Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .628
10-6 Functions as Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .636
Extend: Spreadsheet Lab Detecting Patterns in Data . . . . . . . . . . . . . . . . . . . . . . . . 644A
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .645
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .649
Connect to AP Calculus: Riemann Sum . . . . . . . . . . . . . . . . . . . . . . . . . . . .650
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Multilingual eGlossary p. 589
Vocabulary p. 608
Animation p. 629
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xii xii
Your Digital Math PortalconnectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com
Unit 4 | Discrete Mathematics
111111Inferential Statistics
Multilingual eGlossary p. 735
Vocabulary p. 735
connectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com Your Digital Math Portal
1212Get Ready for Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734
12-1 Estimating Limits Graphically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .736
12-2 Evaluating Limits Algebraically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .746
Explore: Graphing Technology Lab The Slope of a Curve. . . . . . . . . . . . . . . . . . . . . . . 757
12-3 Tangent Lines and Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .758
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .765
12-4 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .766
12-5 Area Under a Curve and Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .775
12-6 The Fundamental Theorem of Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .784
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .792
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .797
Connect to AP Calculus: The Chain Rule . . . . . . . . . . . . . . . . . . . . . . . . . . .798
1212Limits and Derivatives
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viii_xxi_FM_TOC_664183.indd 20 7/17/12 11:40 AM
Self-Check Practice p. 695
Graphing Calculator pp. 723–724
Personal Tutor p. 684
Inferential Statistics1111111111Inferential Statistics11Inferential StatisticsInferential Statistics11Inferential Statistics
Get Ready for Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652
11-1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .654
11-2 Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .664
11-3 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .674
Extend: Graphing Technology Lab Transforming Skewed Data . . . . . . . . . . . . . . . . . . 684
11-4 The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .685
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .695
11-5 Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .696
11-6 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .705
11-7 Correlation and Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .713
Extend: Graphing Technology Lab Median-Fit Lines . . . . . . . . . . . . . . . . . . . . . . . . . . 723
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .725
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .731
Connect to AP Calculus: Population Proportions . . . . . . . . . . . . . . . . . . . . .732
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viii_xxi_FM_TOC_664183.indd 19 7/17/12 11:39 AM
Self-Check Practice p. 695
Graphing Calculator pp. 723–724
Personal Tutor p. 684
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xiii xiii
Unit 4 | Discrete MathematicsUnit 4 | Discrete Mathematics
121212Limits and Derivatives
Multilingual eGlossary p. 735
Vocabulary p. 735
connectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com Your Digital Math Portal
1212Get Ready for Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734
12-1 Estimating Limits Graphically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .736
12-2 Evaluating Limits Algebraically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .746
Explore: Graphing Technology Lab The Slope of a Curve. . . . . . . . . . . . . . . . . . . . . . . 757
12-3 Tangent Lines and Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .758
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .765
12-4 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .766
12-5 Area Under a Curve and Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .775
12-6 The Fundamental Theorem of Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .784
ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .792
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .797
Connect to AP Calculus: The Chain Rule . . . . . . . . . . . . . . . . . . . . . . . . . . .798
1212Limits and Derivatives
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Multilingual eGlossary p. 735
Vocabulary p. 735
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Student Handbook
Reference
Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R1
Selected Answers and Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R29
Glossary/Glosario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R148
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R178
Trigonometric Functions and Identities . . . . . . . . . . . . . . . . . . Inside Back Cover
Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover
Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover
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