Julie Miller and Donna Gerken wrote their developmental math series because students were coming into their courses underprepared. They weren’t mathematically mature enough to understand the concepts of math nor were they fully engaged with the material. This series strives to help bridge that gap for students, with the text strengthened by its offering in ALEKS, now featuring Custom Question Authoring, Video Assignments, interactive tools, and more!
ALEKS is a course assistant that helps math instructors forge Constructive Learning Paths for their students – blending personalized modules with instructor-driven assignments to ensure every student always has another block to build on their knowledge base.
Author(s): Julie Miller, Donna Gerken
Edition: 2
Publisher: McGraw-Hill
Year: 2023
Language: English
Pages: 1266
Review of Prerequisites 1
Erik Isakson/Tetra Images/SuperStock
Section R.1 Sets and the Real Number Line 2
Section R.2 Exponents and Radicals 17
Section R.3 Polynomials and Factoring 31
Problem Recognition Exercises: Simplifying Algebraic Expressions 45
Section R.4 Rational Expressions and More Operations on Radicals 45
Section R.5 Equations with Real Solutions 56
Section R.6 Complex Numbers and More Quadratic Equations 73
Section R.7 Applications of Equations 86
Section R.8 Linear, Compound, and Absolute Value Inequalities 99
Problem Recognition Exercises: Recognizing and Solving Equations and Inequalities 110
Algebra for Calculus 110
Equations and Inequalities for Calculus 111
Key Concepts 112
Review Exercises 116
Test 119
CHAPTER 1 Functions and Relations 121
Andrey Popov/Shutterstock
Section 1.1 The Rectangular Coordinate System and Graphing Utilities 122
Section 1.2 Circles 135
Section 1.3 Functions and Relations 141
Section 1.4 Linear Equations in Two Variables and Linear Functions 155
Section 1.5 Applications of Linear Equations and Modeling 172
Problem Recognition Exercises: Comparing Graphs of Equations 188
Section 1.6 Transformations of Graphs 189
Section 1.7 Analyzing Graphs of Functions and Piecewise-Defined Functions 204
Section 1.8 Algebra of Functions and Function Composition 224
Key Concepts 238
Review Exercises 240
Test 245
Cumulative Review Exercises 246
CHAPTER 2 Polynomial and Rational Functions 249
Laboratory for Atmospheres, NASA Goddard Space Flight Center
Section 2.1 Quadratic Functions and Applications 250
Section 2.2 Introduction to Polynomial Functions 265
Section 2.3 Division of Polynomials and the Remainder and Factor Theorems 282
Section 2.4 Zeros of Polynomials 295
Section 2.5 Introduction to Rational Functions 311
Page v
Section 2.6 Graphs of Rational Functions 328
Problem Recognition Exercises: Polynomial and Rational Functions 341
Section 2.7 Polynomial and Rational Inequalities 342
Problem Recognition Exercises: Solving Equations and Inequalities 356
Section 2.8 Variation 357
Key Concepts 365
Review Exercises 368
Test 372
Cumulative Review Exercises 374
CHAPTER 3 Exponential and Logarithmic Functions 375
Justin Lewis/Digital Vision/Getty Images
Section 3.1 Inverse Functions 376
Section 3.2 Exponential Functions 388
Section 3.3 Logarithmic Functions 403
Problem Recognition Exercises: Analyzing Functions 418
Section 3.4 Properties of Logarithms 419
Section 3.5 Exponential and Logarithmic Equations and Applications 429
Section 3.6 Modeling with Exponential and Logarithmic Functions 443
Key Concepts 460
Review Exercises 462
Test 465
Cumulative Review Exercises 466
CHAPTER 4 Trigonometric Functions 467
Nick Koudis/Photodisc/Getty Images
Section 4.1 Angles and Their Measure 468
Section 4.2 Trigonometric Functions Defined on the Unit Circle 485
Section 4.3 Right Triangle Trigonometry 503
Section 4.4 Trigonometric Functions of Any Angle 520
Section 4.5 Graphs of Sine and Cosine Functions 531
Section 4.6 Graphs of Other Trigonometric Functions 551
Problem Recognition Exercises: Comparing Graphical Characteristics of Trigonometric Functions 563
Section 4.7 Inverse Trigonometric Functions 564
Key Concepts 580
Review Exercises 585
Test 588
Cumulative Review Exercises 590
CHAPTER 5 Analytic Trigonometry 591
Carmen MartA-nez BanAs/Maica/E+/ Getty Images
Section 5.1 Fundamental Trigonometric Identities 592
Section 5.2 Sum and Difference Formulas 603
Section 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas 615
Section 5.4 Product-to-Sum and Sum-to-Product Formulas 625
Problem Recognition Exercises: Verifying Trigonometric Identities 631
Section 5.5 Trigonometric Equations 631
Page vi
Problem Recognition Exercises: Trigonometric Identities and Trigonometric Equations 646
Key Concepts 647
Review Exercises 649
Test 651
Cumulative Review Exercises 652
CHAPTER 6 Applications of Trigonometric Functions 653
Digital Vision/Getty Images
Section 6.1 Applications of Right Triangles 654
Section 6.2 The Law of Sines 666
Section 6.3 The Law of Cosines 681
Problem Recognition Exercises: Solving Triangles Using a Variety of Tools 692
Section 6.4 Harmonic Motion 693
Key Concepts 703
Review Exercises 705
Test 707
Cumulative Review Exercises 709
CHAPTER 7 Trigonometry Applied to Polar Coordinate Systems and Vectors 711
Ryan McGinnis/Flickr/Getty Images
Section 7.1 Polar Coordinates 712
Section 7.2 Graphs of Polar Equations 723
Problem Recognition Exercises: Comparing Equations in Polar and Rectangular Form 738
Section 7.3 Complex Numbers in Polar Form 740
Section 7.4 Vectors 754
Section 7.5 Dot Product 771
Key Concepts 785
Review Exercises 787
Test 790
Cumulative Review Exercises 791
CHAPTER 8 Systems of Equations and Inequalities 793
Michael Hitoshi/Digital Vision/Getty Images
Section 8.1 Systems of Linear Equations in Two Variables and Applications 794
Section 8.2 Systems of Linear Equations in Three Variables and Applications 808
Section 8.3 Partial Fraction Decomposition 820
Section 8.4 Systems of Nonlinear Equations in Two Variables 830
Section 8.5 Inequalities and Systems of Inequalities in Two Variables 839
Problem Recognition Exercises: Equations and Inequalities in Two Variables 850
Section 8.6 Linear Programming 851
Key Concepts 860
Review Exercises 862
Test 864
Cumulative Review Exercises 865
Page vii
CHAPTER 9 Matrices and Determinants and Applications 867
Jasper White/Image Source
Section 9.1 Solving Systems of Linear Equations Using Matrices 868
Section 9.2 Inconsistent Systems and Dependent Equations 879
Section 9.3 Operations on Matrices 889
Section 9.4 Inverse Matrices and Matrix Equations 906
Section 9.5 Determinants and Cramer’s Rule 918
Problem Recognition Exercises: Using Multiple Methods to Solve Systems of Linear Equations 931
Key Concepts 931
Review Exercises 933
Test 936
Cumulative Review Exercises 937
CHAPTER 10 Analytic Geometry 939
Nick M Do/Photodisc/Getty Images
Section 10.1 The Ellipse 940
Section 10.2 The Hyperbola 958
Section 10.3 The Parabola 976
Problem Recognition Exercises: Comparing Equations of Conic Sections and the General Equation 990
Section 10.4 Rotation of Axes 992
Section 10.5 Polar Equations of Conics 1005
Section 10.6 Plane Curves and Parametric Equations 1015
Key Concepts 1030
Review Exercises 1033
Test 1037
Cumulative Review Exercises 1039
CHAPTER 11 Sequences, Series, Induction, and Probability 1041
Image Source/Getty Images
Section 11.1 Sequences and Series 1042
Section 11.2 Arithmetic Sequences and Series 1054
Section 11.3 Geometric Sequences and Series 1065
Problem Recognition Exercises: Comparing Arithmetic and Geometric Sequences and Series 1079
Section 11.4 Mathematical Induction 1079
Section 11.5 The Binomial Theorem 1086
Section 11.6 Principles of Counting 1093
Section 11.7 Introduction to Probability 1105
Key Concepts 1122
Review Exercises 1124
Test 1128
Cumulative Review Exercises 1130
CHAPTER 12 Preview of Calculus (Online)
Section 12.1 Introduction to Limits Through Tables and Graphs
Section 12.2 Algebraic Properties of Limits
Problem Recognition Exercises: Limits and Continuity
Section 12.3 The Tangent Line Problem: Introduction to Derivatives
Page viii
Section 12.4 Limits at Infinity and Limits of Sequences
Section 12.5 Area Under a Curve
Key Concepts
Review Exercises
Test
Student Answer Appendix SA-1
Instructor Answer Appendix IA-1 (AIE only)
Subject Index I-1
Appendix A Additional Topics (Online)
Section A.1 Proof of the Binomial Theorem
Section A.2 Conic Sections Defined by a Fixed Point and a Fixed Line
Additional Online Content
Detailed Chapter Summaries
Group Activities
