Test Bank – Algebra and Trigonometry Enhanced with Graphing Utilities, 8th edition (Sullivan, 2020)

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Test Bank – Algebra and Trigonometry Enhanced with Graphing Utilities, 8th edition (Sullivan, 2020)

Table of Contents

Chapter R Review
R.1 Real Numbers ………………………………………………………………………………………………………….. 1
R.2 Algebra Essentials ……………………………………………………………………………………………………. 5
R.3 Geometry Essentials ……………………………………………………………………………………………….. 11
R.4 Polynomials …………………………………………………………………………………………………………… 16
R.5 Factoring Polynomials …………………………………………………………………………………………….. 23
R.6 Synthetic Division ………………………………………………………………………………………………….. 28
R.7 Rational Expressions ………………………………………………………………………………………………. 30
R.8 nth Roots; Rational Exponents …………………………………………………………………………………. 40

Chapter 1 Graphs, Equations, and Inequalities
1.1 Graphing Utilities; Introduction to Graphing Equations ………………………………………………. 50
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations ………………….. 57
1.3 Quadratic Equations ……………………………………………………………………………………………….. 71
1.4 Complex Numbers; Quadratic Equations in the Complex Number System …………………….. 90
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ………………………………………………………………………………………………. 96
1.6 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Jobs ……………… 117
1.7 Solving Inequalities ………………………………………………………………………………………………. 125
Chapter Review ……………………………………………………………………………………………………………. 137
Chapter Test ………………………………………………………………………………………………………………… 147
Chapter Projects …………………………………………………………………………………………………………… 151

Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ……………………………………………………………………… 152
2.2 Intercepts; Symmetry; Graphing Key Equations ……………………………………………………….. 165
2.3 Lines …………………………………………………………………………………………………………………… 182
2.4 Circles …………………………………………………………………………………………………………………. 200
2.5 Variation ……………………………………………………………………………………………………………… 215
Chapter Review ……………………………………………………………………………………………………………. 220
Chapter Test ………………………………………………………………………………………………………………… 226
Cumulative Review ………………………………………………………………………………………………………. 228
Chapter Projects …………………………………………………………………………………………………………… 230

Chapter 3 Functions and Their Graphs
3.1 Functions …………………………………………………………………………………………………………….. 231
3.2 The Graph of a Function ………………………………………………………………………………………… 249
3.3 Properties of Functions ………………………………………………………………………………………….. 258
3.4 Library of Functions; Piecewise-defined Functions …………………………………………………… 275
3.5 Graphing Techniques: Transformations …………………………………………………………………… 287
3.6 Mathematical Models: Building Functions ……………………………………………………………….. 305
Chapter Review ……………………………………………………………………………………………………………. 313
Chapter Test ………………………………………………………………………………………………………………… 320
Cumulative Review ………………………………………………………………………………………………………. 323
Chapter Projects …………………………………………………………………………………………………………… 327

Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models …………………………………………………….. 329
4.2 Building Linear Models from Data ………………………………………………………………………….. 340
4.3 Quadratic Functions and Their Properties ………………………………………………………………… 346
4.4 Build Quadratic Models from Verbal Descriptions and from Data ………………………………. 370
4.5 Inequalities Involving Quadratic Functions ………………………………………………………………. 378
Chapter Review ……………………………………………………………………………………………………………. 397
Chapter Test ………………………………………………………………………………………………………………… 405
Cumulative Review ………………………………………………………………………………………………………. 408
Chapter Projects …………………………………………………………………………………………………………… 411

Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions ……………………………………………………………………………………………. 414
5.2 The Graph of a Polynomial Function; Models ………………………………………………………….. 425
5.3 The Real Zeros of a Polynomial Function ………………………………………………………………… 445
5.4 Complex Zeros; Fundamental Theorem of Algebra …………………………………………………… 482
5.5 Properties of Rational Functions …………………………………………………………………………….. 491
5.6 The Graph of a Rational Function …………………………………………………………………………… 501
5.7 Polynomial and Rational Inequalities ………………………………………………………………………. 557
Chapter Review ……………………………………………………………………………………………………………. 579
Chapter Test ………………………………………………………………………………………………………………… 593
Cumulative Review ………………………………………………………………………………………………………. 597
Chapter Projects …………………………………………………………………………………………………………… 602

Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions …………………………………………………………………………………………….. 603
6.2 One-to-One Functions; Inverse Functions ………………………………………………………………… 621
6.3 Exponential Functions …………………………………………………………………………………………… 644
6.4 Logarithmic Functions …………………………………………………………………………………………… 665
6.5 Properties of Logarithms ……………………………………………………………………………………….. 687
6.6 Logarithmic and Exponential Equations …………………………………………………………………… 696
6.7 Financial Models ………………………………………………………………………………………………….. 717
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ………………………………………………………………………………………………… 725
6.9 Building Exponential, Logarithmic, and Logistic Models from Data …………………………… 736
Chapter Review ……………………………………………………………………………………………………………. 741
Chapter Test ………………………………………………………………………………………………………………… 763
Cumulative Review ………………………………………………………………………………………………………. 757
Chapter Projects …………………………………………………………………………………………………………… 760

Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ………………………………………………………………… 763
7.2 Right Triangle Trigonometry ………………………………………………………………………………….. 772
7.3 Computing the Values of Trigonometric Functions of Acute Angles …………………………… 788
7.4 Trigonometric Functions of Any Angle ……………………………………………………………………. 801
7.5 Unit Circle Approach; Properties of the Trigonometric Functions ……………………………….. 817
7.6 Graphs of the Sine and Cosine Functions …………………………………………………………………. 826
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions…………………………….. 848
7.8 Phase Shift; Sinusoidal Curve Fitting ………………………………………………………………………. 858
Chapter Review ……………………………………………………………………………………………………………. 871
Chapter Test ………………………………………………………………………………………………………………… 880
Cumulative Review ………………………………………………………………………………………………………. 884
Chapter Projects …………………………………………………………………………………………………………… 888

Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions ……………………………………………………… 891
8.2 The Inverse Trigonometric Functions (Continued) ……………………………………………………. 905
8.3 Trigonometric Equations ……………………………………………………………………………………….. 917
8.4 Trigonometric Identities ………………………………………………………………………………………… 938
8.5 Sum and Difference Formulas ………………………………………………………………………………… 951
8.6 Double-Angle and Half-Angle Formulas …………………………………………………………………. 976
8.7 Product-to-Sum and Sum-to-Product Formulas……………………………………………………….. 1004
Chapter Review ………………………………………………………………………………………………………….. 1017
Chapter Test ………………………………………………………………………………………………………………. 1032
Cumulative Review …………………………………………………………………………………………………….. 1037
Chapter Projects …………………………………………………………………………………………………………. 1043

Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles …………………………………………………………………. 1047
9.2 The Law of Sines ………………………………………………………………………………………………… 1055
9.3 The Law of Cosines …………………………………………………………………………………………….. 1070
9.4 Area of a Triangle ……………………………………………………………………………………………….. 1082
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ……………………………….. 1092
Chapter Review ………………………………………………………………………………………………………….. 1102
Chapter Test ………………………………………………………………………………………………………………. 1108
Cumulative Review …………………………………………………………………………………………………….. 1111
Chapter Projects …………………………………………………………………………………………………………. 1117

Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates ……………………………………………………………………………………………….. 1121
10.2 Polar Equations and Graphs ………………………………………………………………………………….. 1130
10.3 The Complex Plane; De Moivre’s Theorem ……………………………………………………………. 1159
10.4 Vectors ………………………………………………………………………………………………………………. 1172
10.5 The Dot Product ………………………………………………………………………………………………….. 1185
Chapter Review ………………………………………………………………………………………………………….. 1191
Chapter Test ………………………………………………………………………………………………………………. 1200
Cumulative Review …………………………………………………………………………………………………….. 1203
Chapter Projects …………………………………………………………………………………………………………. 1205

Chapter 11 Analytic Geometry
11.2 The Parabola ………………………………………………………………………………………………………. 1209
11.3 The Ellipse …………………………………………………………………………………………………………. 1225
11.4 The Hyperbola ……………………………………………………………………………………………………. 1242
11.5 Rotation of Axes; General Form of a Conic ……………………………………………………………. 1262
11.6 Polar Equations of Conics ……………………………………………………………………………………. 1275
11.7 Plane Curves and Parametric Equations …………………………………………………………………. 1284
Chapter Review ………………………………………………………………………………………………………….. 1299
Chapter Test ………………………………………………………………………………………………………………. 1308
Cumulative Review …………………………………………………………………………………………………….. 1313
Chapter Projects …………………………………………………………………………………………………………. 1315

Chapter 12 Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination ……………………………………… 1319
12.2 Systems of Linear Equations: Matrices ………………………………………………………………….. 1342
12.3 Systems of Linear Equations: Determinants ……………………………………………………………. 1367
12.4 Matrix Algebra …………………………………………………………………………………………………… 1381
12.5 Partial Fraction Decomposition …………………………………………………………………………….. 1400
12.6 Systems of Nonlinear Equations ……………………………………………………………………………. 1419
12.7 Systems of Inequalities ………………………………………………………………………………………… 1447
12.8 Linear Programming ……………………………………………………………………………………………. 1462
Chapter Review ………………………………………………………………………………………………………….. 1476
Chapter Test ………………………………………………………………………………………………………………. 1491
Cumulative Review …………………………………………………………………………………………………….. 1499
Chapter Projects …………………………………………………………………………………………………………. 1503

Chapter 13 Sequences; Induction; the Binomial Theorem
13.1 Sequences ………………………………………………………………………………………………………….. 1505
13.2 Arithmetic Sequences ………………………………………………………………………………………….. 1519
13.3 Geometric Sequences; Geometric Series ………………………………………………………………… 1528
13.4 Mathematical Induction ……………………………………………………………………………………….. 1539
13.5 The Binomial Theorem ………………………………………………………………………………………… 1549
Chapter Review ………………………………………………………………………………………………………….. 1556
Chapter Test ………………………………………………………………………………………………………………. 1560
Cumulative Review …………………………………………………………………………………………………….. 1563
Chapter Projects …………………………………………………………………………………………………………. 1566

Chapter 14 Counting and Probability
14.1 Counting ……………………………………………………………………………………………………………. 1569
14.2 Permutations and Combinations ……………………………………………………………………………. 1572
14.3 Probability …………………………………………………………………………………………………………. 1577
Chapter Review ………………………………………………………………………………………………………….. 1584
Chapter Test ………………………………………………………………………………………………………………. 1586
Cumulative Review …………………………………………………………………………………………………….. 1587
Chapter Projects …………………………………………………………………………………………………………. 1590