Download Preparing for Advanced Algebra Advanced Algebra

Preparing for
Advanced Algebra
Get Started On Chapter 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P2
Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P3
Representing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P4
0-2
FOIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P6
0-3
Factoring Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P7
0-4
Counting Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P9
0-5
Adding Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P13
0-6
Multiplying Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P16
0-7
Congruent and Similar Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P20
0-8
The Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P22
0-9
Measures of Center, Spread, and Position . . . . . . . . . . . . . . . . . . . . . . . . .P24
Table of Contents
0-1
Ed Freeman/Stone/Getty Images
Posttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P29
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Vocabulary
p. P4
Your Digital Math Portal
Multilingual
eGlossary
Personal Tutor
Foldables
p. P6
p. P2
p. P2
i
Unit 1
|
Linear Relations and Functions
Equations and
Inequalities
Mathematical
Content
Get Ready for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1-1 Expressions and Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
A.SSE.1.a, A.SSE.1.b
1-2 Properties of Real Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
A.SSE.2
1-3 Solving Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
A.CED.1
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
1-4 Solving Absolute Value Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
A.SSE.1.b, A.CED.1
1-5 Solving Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
A.CED.1, A.CED.3
Explore: Algebra Lab Interval Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1-6 Solving Compound and Absolute Value Inequalities . . . . . . . . . . . . . . . . . . . .41
A.CED.1, A.CED.3
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
Standardized Test Practice, Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56
Jon Boyes/Photographer’s Choice/Getty Images
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Your Digital Math Portal
Animation
Vocabulary
pp. 12, 84
pp. 5, 69
Multilingual
eGlossary
pp. 4, 60
ii
Personal Tutor
pp. 6, 63
Unit 1
|
Linear Relations and Functions
Linear Relations
and Functions
Mathematical
Content
Get Ready for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2-1 Relations and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61
Extend: Algebra Lab Discrete and Continuous Functions . . . . . . . . . . . . . . . . . . . . . . . 68
2-2 Linear Relations and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
Extend: Algebra Lab Roots of Equations and Zeros of Functions . . . . . . . . . . . . . . . . . . 75
2-3 Rate of Change and Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
2-4 Writing Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83
Extend: Graphing Technology Lab Direct Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
F.IF.4, F.IF.5
F.IF.4
F.IF.4, F.IF.9
F.IF.4
F.IF.4, F.IF.6
A.SSE.1.b, A.CED.2
F.IF.4
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91
2-5 Scatter Plots and Lines of Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92
F.IF.4
Extend: Algebra Lab Correlation and Causation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
F.IF.4
2-6 Special Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Explore: Graphing Technology Lab Families of Lines. . . . . . . . . . . . . . . . . . . . . . . . . . 108
Roine Magnusson/Photodisc/Getty Images
2-7 Parent Functions and Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2-8 Graphing Linear and Absolute Value Inequalities. . . . . . . . . . . . . . . . . . . . . . 117
F.IF.4, F.IF.7.b
F.BF.3
F.IF.4, F.BF.3
A.CED.3
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Standardized Test Practice, Chapters 1–2 . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Virtual
Manipulatives
Graphing
Calculator
pp. 28, 61
p. 90
Foldables
pp. 4, 60
Self-Check
Practice
pp. 7, 127
iii
Unit 1
|
Linear Relations and Functions
Systems of Equations
and Inequalities
Mathematical
Content
Get Ready for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Explore: Graphing Technology Lab Intersections of Graphs . . . . . . . . . . . . . . . . . . . . . 135
3-1 Solving Systems of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
A.CED.3, A.REI.11
3-2 Solving Systems of Inequalities by Graphing . . . . . . . . . . . . . . . . . . . . . . . . . 146
A.CED.3
Extend: Graphing Technology Lab Systems of Linear Inequalities . . . . . . . . . . . . . . . . 153
3-3 Optimization with Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
A.CED.3
3-4 Systems of Equations in Three Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
A.CED.3
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Explore: Spreadsheet Lab Organizing Data with Matrices. . . . . . . . . . . . . . . . . . . . . . 169
3-5 Operations with Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
3-6 Multiplying Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Extend: Graphing Technology Lab Operations with Matrices . . . . . . . . . . . . . . . . . . . 187
3-7 Solving Systems of Equations Using Cramer’s Rule. . . . . . . . . . . . . . . . . . . . 189
A.CED.3
3-8 Solving Systems of Equations Using Inverse Matrices. . . . . . . . . . . . . . . . . . 198
A.CED.3
DreamPictures/Blend Images/Getty Images
Extend: Graphing Technology Lab Augmented Matrices . . . . . . . . . . . . . . . . . . . . . . . 205
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Standardized Test Practice, Chapters 1–3 . . . . . . . . . . . . . . . . . . . . . . . . . . 214
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Animation
Vocabulary
pp. 146, 247
pp. 206, 290
Multilingual
eGlossary
pp. 134, 218
iv
Personal Tutor
pp. 136, 222
Unit 2
|
Quadratic, Polynomial, and Radical Functions and Relations
Quadratic Functions
Functions
Quadratic
and Relations
Relations
and
Mathematical
Content
Get Ready for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
4-1 Graphing Quadratic Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Extend: Graphing Technology Lab Modeling Real-World Data . . . . . . . . . . . . . . . . . . . 228
4-2 Solving Quadratic Equations by Graphing. . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Extend: Graphing Technology Lab Solving Quadratic Equations by Graphing . . . . . . . . 237
A.SSE.1.a, F.IF.9
F.IF.4
A.CED.2, F.IF.4
A.REI.11
4-3 Solving Quadratic Equations by Factoring . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
A.SSE.2, F.IF.8.a
4-4 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
N.CN.1, N.CN.2
Extend: Algebra Lab The Complex Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
4-5 Completing the Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
Extend: Graphing Technology Lab Solving Quadratic Equations. . . . . . . . . . . . . . . . . . 263
4-6 The Quadratic Formula and the Discriminant . . . . . . . . . . . . . . . . . . . . . . . . . 264
Explore: Graphing Technology Lab Families of Parabolas . . . . . . . . . . . . . . . . . . . . . . 273
4-7 Transformations of Quadratic Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Extend: Algebra Lab Quadratics and Rate of Change . . . . . . . . . . . . . . . . . . . . . . . . . 281
Black 100/Allsport Concepts/Getty Images
4-8 Quadratic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
N.CN.7, F.IF.8.a
N.CN.7
N.CN.7, A.SSE.1.b
F.IF.4, F.BF.3
F.IF.8.a, F.BF.3
F.IF.4, F.IF.6
A.CED.1, A.CED.3
Extend: Graphing Technology Lab Modeling Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Standardized Test Practice, Chapters 1–4 . . . . . . . . . . . . . . . . . . . . . . . . . . 298
Virtual
Manipulatives
Graphing
Calculator
pp. 137, 219
pp. 205, 237
Foldables
pp. 134, 218
Self-Check
Practice
pp. 183, 295
v
Unit 2
1
|
FoundationsPolynomial,
Quadratic,
for Functions
and Radical Functions and Relations
5
Polynomialsand
and
Polynomials
P
PolynomialFunctions
Functions
Polynomial
P
Mathematical
Content
Get Ready for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
5-1 Operations with Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
A.APR.1
Extend: Algebra Lab Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
5-2 Dividing Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
A.APR.6
Extend: Graphing Technology Lab Dividing Polynomials . . . . . . . . . . . . . . . . . . . . . . . 318
A.APR.6
Explore: Graphing Technology Lab Power Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 320
F.IF.4
5-3 Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
F.IF.4, F.IF.7.c
5-4 Analyzing Graphs of Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . 330
F.IF.4, F.IF.7.c
Extend: Graphing Technology Lab Modeling Data Using Polynomial Functions . . . . . . 338
F.IF.4, F.IF.7.c
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
Explore: Graphing Technology Lab Solving Polynomial Equations by Graphing . . . . . . 341
5-5 Solving Polynomial Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
A.CED.1
Extend: Graphing Technology Lab Polynomial Identities . . . . . . . . . . . . . . . . . . . . . . . 350
A.REI.11
5-6 The Remainder and Factor Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
A.APR.2, F.IF.7.c
5-7 Roots and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
N.CN.9, A.APR.3
Extend: Graphing Technology Lab Analyzing Polynomial Functions . . . . . . . . . . . . . . . 366
A.APR.4
5-8 Rational Zero Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
Standardized Test Practice, Chapters 1–5 . . . . . . . . . . . . . . . . . . . . . . . . . . 380
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Vocabulary
pp. 306, 387
pp. 303, 400
Multilingual
eGlossary
pp. 302, 384
vi
Personal Tutor
pp. 304, 386
Photodisc/Getty Images
Animation
Unit 2
|
Quadratic, Polynomial, and Radical Functions and Relations
6
I
Inverses
and Radical
F
Functions
and Relations
Mathematical
Content
Get Ready for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
6-1 Operations on Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
F.IF.9, F.BF.1.b
6-2 Inverse Functions and Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
F.IF.4, F.BF.4.a
Extend: Graphing Technology Lab Inverse Functions and Relations. . . . . . . . . . . . . . . 399
6-3 Square Root Functions and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
F.IF.7.b, F.BF.3
6-4 nth Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
A.SSE.2
Extend: Graphing Technology Lab Graphing nth Root Functions . . . . . . . . . . . . . . . . . 413
F.IF.7.b, F.BF.3
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
6-5 Operations with Radical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
A.SSE.2
6-6 Rational Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
6-7 Solving Radical Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . 429
Extend: Graphing Technology Lab Solving Radical Equations and Inequalities. . . . . . . 436
A.REI.2
A.REI.2, A.REI.11
Stockbyte/Getty Images
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
Standardized Test Practice, Chapters 1–6 . . . . . . . . . . . . . . . . . . . . . . . . . . 446
Virtual
Manipulatives
Graphing
Calculator
p. 331
pp. 338, 436
Foldables
pp. 302, 384
Self-Check
Practice
pp. 326, 443
vii
Unit 3
1
|
Foundations
Advanced
Functions
for Functions
and Relations
Exponential and
Logarithmic Functions
and Relations
Mathematical
Content
Get Ready for Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
7-1 Graphing Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
Explore: Graphing Technology Lab Solving Exponential Equations and Inequalities . . . 459
F.IF.7.e, F.IF.8.b
A.REI.11
7-2 Solving Exponential Equations and Inequalities. . . . . . . . . . . . . . . . . . . . . . . 461
A.CED.1, F.LE.4
7-3 Logarithms and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
F.IF.7.e, F.BF.3
Extend: Graphing Technology Lab Choosing the Best Model . . . . . . . . . . . . . . . . . . . . 476
7-4 Solving Logarithmic Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . 478
A.SSE.2, A.CED.1
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
7-5 Properties of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
A.CED.1
7-6 Common Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
A.CED.1
Extend: Graphing Technology Lab Solving Logarithmic Equations and Inequalities . . . 499
A.REI.11
7-7 Base e and Natural Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
A.SSE.2
Explore: Spreadsheet Lab Compound Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
7-8 Using Exponential and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . 509
Extend: Graphing Technology Lab Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
F.IF.8.b, F.LE.4
F.BF.1.b
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522
Standardized Test Practice, Chapters 1–7 . . . . . . . . . . . . . . . . . . . . . . . . . . 524
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Vocabulary
pp. 453, 532
pp. 517, 581
Multilingual
eGlossary
pp. 450, 528
viii
Personal Tutor
pp. 455, 531
Purestock/Getty Images
Animation
Unit 3
|
Advanced Functions and Relations
Rational Functions
and Relations
Mathematical
Content
Get Ready for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
8-1 Multiplying and Dividing Rational Expressions . . . . . . . . . . . . . . . . . . . . . . . 529
A.APR.7
8-2 Adding and Subtracting Rational Expressions . . . . . . . . . . . . . . . . . . . . . . . . 538
A.APR.7
8-3 Graphing Reciprocal Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545
A.CED.2, F.BF.3
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552
8-4 Graphing Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
A.CED.2, F.IF.9
Extend: Graphing Technology Lab Graphing Rational Functions . . . . . . . . . . . . . . . . . 561
8-5 Variation Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562
A.CED.2
8-6 Solving Rational Equations and Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . . 570
A.CED.1, A.REI.2
Extend: Graphing Technology Lab Solving Rational Equations and Inequalities . . . . . . 579
A.REI.2, A.REI.11
Image Source/Masterfile
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585
Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
Standardized Test Practice, Chapters 1–8 . . . . . . . . . . . . . . . . . . . . . . . . . . 588
Virtual
Manipulatives
Graphing
Calculator
pp. 451, 557
pp. 516, 579
Foldables
pp. 450, 528
Self-Check
Practice
pp. 464, 585
ix
Unit 3
1
|
Foundations
Advanced
Functions
for Functions
and Relations
Conic Sections
Mathematical
Content
Get Ready for Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
9-1
Midpoint and Distance Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593
A.CED.4
9-2
Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599
A.SSE.1.b, A.CED.2
Explore: Graphing Technology Lab Equations of Circles . . . . . . . . . . . . . . . . . . . . . 606
9-3
Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607
A.SSE.1.b, A.CED.4
Explore: Algebra Lab Investigating Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614
9-4
Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615
A.SSE.1.b, A.CED.2
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
9-5
Hyperbolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624
A.SSE.1.b, A.CED.2
9-6
Identifying Conic Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632
A.SSE.1.b, F.IF.9
Extend: Graphing Technology Lab Analyzing Quadratic Relations . . . . . . . . . . . . . . 637
Explore: Graphing Technology Lab Linear-Nonlinear Systems . . . . . . . . . . . . . . . . . 639
9-7
Solving Linear-Nonlinear Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640
A.REI.11
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652
Standardized Test Practice, Chapters 1–9 . . . . . . . . . . . . . . . . . . . . . . . . 654
Your Digital Math Portal
Animation
Vocabulary
pp. 641, 659
pp. 599, 710
Multilingual
eGlossary
pp. 592, 658
x
Personal Tutor
pp. 600, 660
Brand X Pictures/PunchStock
c
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Unit 4
|
Discrete Mathematics
Sequences and
Sequences and Series
Series
Mathematical
Content
Get Ready for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657
10-1
Sequences as Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659
F.IF.4
10-2
Arithmetic Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666
A.CED.4
10-3
Geometric Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674
A.SSE.4
Explore: Algebra Lab Area Under a Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
10-4
Infinite Geometric Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683
Extend: Graphing Technology Lab Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691
10-5
Recursion and Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692
Extend: Spreadsheet Lab Amortizing Loans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698
10-6
Martin Child/Photodisc/Getty Images
10-7
The Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699
A.APR.5
Extend: Algebra Lab Combinations and Pascal’s Triangle . . . . . . . . . . . . . . . . . . . . 704
A.APR.5
Proof by Mathematical Induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705
A.SSE.1.b, A.APR.5
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 710
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716
Standardized Test Practice, Chapters 1–10 . . . . . . . . . . . . . . . . . . . . . . . 718
Virtual
Manipulatives
Graphing
Calculator
pp. 594, 681
pp. 639, 690
Foldables
pp. 592, 658
Self-Check
Practice
pp. 603, 715
xi
Unit 4
1
|
Foundations
Discrete
Mathematics
for Functions
Statistics
and Probability
Mathematical
Content
Get Ready for Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721
11-1
Designing a Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723
S.IC.3, S.IC.5
Extend: Graphing Technology Lab Simulations and Margin of Error. . . . . . . . . . . . . 731
S.IC.4, S.IC.6
11-2
Distributions of Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733
S.IC.1
11-3
Probability Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 742
S.MD.7
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751
11-4
The Binomial Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752
S.MD.6, S.MD.7
11-5
The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 760
S.ID.4
Extend: Spreadsheet Lab Normal Approximation of Binomial Distributions . . . . . . . 767
S.ID.4
11-6
Confidence Intervals and Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . 769
S.IC.1, S.IC.4
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782
Standardized Test Practice, Chapters 1–11 . . . . . . . . . . . . . . . . . . . . . . . 784
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Your Digital Math Portal
Vocabulary
pp. 720, 799
pp. 742, 859
Multilingual
eGlossary
pp. 722, 788
xii
Personal Tutor
pp. 724, 789
MIXA/Getty Images
Animation
Unit 5
|
Trigonometry
Trigonometric
Functions
Mathematical
Content
Get Ready for Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787
Explore: Spreadsheet Lab Investigating Special Right Triangles . . . . . . . . . . . . . . . 789
12-1
Trigonometric Functions in Right Triangles. . . . . . . . . . . . . . . . . . . . . . . . . 790
12-2
Angles and Angle Measure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 799
F.TF.1
Extend: Geometry Lab Areas of Parallelograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . 806
12-3
Trigonometric Functions of General Angles . . . . . . . . . . . . . . . . . . . . . . . . 807
12-4
Law of Sines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814
Extend: Geometry Lab Regular Polygons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822
12-5
Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829
12-6
Circular and Periodic Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 830
F.TF.1, F.TF.2
12-7
Graphing Trigonometric Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837
F.IF.7.e, F.TF.5
Dennis Welsh/UpperCut Images/Getty Images
Explore: Graphing Technology Lab Trigonometric Graphs . . . . . . . . . . . . . . . . . . . . 844
F.BF.3
12-8
Translations of Trigonometric Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845
F.IF.7.e, F.BF.3
12-9
Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853
A.CED.2
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866
Standardized Test Practice, Chapters 1–12 . . . . . . . . . . . . . . . . . . . . . . . 868
Virtual
Manipulatives
Graphing
Calculator
pp. 737, 822
pp. 731, 844
Foldables
pp. 722, 788
Self-Check
Practice
pp. 738, 865
xiii
Unit 5
1
|
Foundations for Functions
Trigonometry
Trigonometric Identities
and Equations
Mathematical
Content
Get Ready for Chapter 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871
13-1
Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873
F.TF.8
13-2
Verifying Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880
F.TF.8
13-3
Sum and Difference of Angles Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . 886
F.TF.8
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 892
13-4
Double-Angle and Half-Angle Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . 893
F.TF.8
Explore: Graphing Technology Lab Solving Trigonometric Equations . . . . . . . . . . . . 900
13-5
Solving Trigonometric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901
F.TF.8
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 908
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 911
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 912
Standardized Test Practice, Chapters 1–13 . . . . . . . . . . . . . . . . . . . . . . . 914
Maria Teijeiro/Photodisc/Getty Images
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Animation
Vocabulary
p. 870
p. 873
Your Digital Math Portal
Multilingual
eGlossary
p. 872
xiv
v
Personal Tutor
p. 875
Graphing
Calculator
p. 900
Foldables
p. 872
Self-Check
Practice
p. 897
Student Handbook
Contents
How to Use the Student Handbook
Rubberball/Getty Images
Extra Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R1
Selected Answers and Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R14
Glossary/Glosario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R124
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R149
Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover
Symbols and Parent Functions . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover
xv