Elementary and intermediate algebra

Cover......Page 1
Title Page......Page 8
Copyright......Page 10
CONTENTS......Page 13
ABOUT THE AUTHORS......Page 12
PREFACE......Page 19
INDEX OF APPLICATIONS......Page 31
CHAPTER 1 An Introduction to Algebra......Page 37
1 Read Tables and Graphs.......Page 38
2 Use the Basic Vocabulary and Notation of Algebra.......Page 39
3 Identify Expressions and Equations.......Page 40
4 Use Equations to Construct Tables of Data.......Page 42
1 Factor and Prime Factor Natural Numbers.......Page 45
2 Recognize Special Fraction Forms.......Page 46
3 Multiply and Divide Fractions.......Page 47
4 Build Equivalent Fractions.......Page 48
5 Simplify Fractions.......Page 50
6 Add and Subtract Fractions.......Page 51
8 Compute with Mixed Numbers.......Page 54
1 Define the Set of Integers.......Page 58
2 Define the Set of Rational Numbers.......Page 59
4 Classify Real Numbers.......Page 61
5 Graph Sets of Real Numbers on the Number Line.......Page 62
6 Find the Absolute Value of a Real Number.......Page 64
1 Add Two Numbers That Have the Same Sign.......Page 68
2 Add Two Numbers That Have Different Signs.......Page 69
3 Use Properties of Addition.......Page 71
4 Identify Opposites (Additive Inverses).......Page 72
1 Use the Definition of Subtraction.......Page 76
2 Solve Application Problems Using Subtraction.......Page 79
1 Multiply Signed Numbers.......Page 83
2 Use Properties of Multiplication.......Page 85
3 Divide Signed Numbers.......Page 87
4 Use Properties of Division.......Page 89
1 Evaluate Exponential Expressions.......Page 94
2 Use the Order of Operations Rule.......Page 96
3 Evaluate Expressions Containing Grouping Symbols.......Page 98
4 Find the Mean (Average).......Page 100
1 Identify Terms and Coefficients of Terms.......Page 104
2 Translate Word Phrases to Algebraic Expressions.......Page 106
3 Analyze Problems to Determine Hidden Operations.......Page 108
4 Evaluate Algebraic Expressions.......Page 109
1 Use the Commutative and Associative Properties.......Page 114
2 Simplify Products.......Page 115
3 Use the Distributive Property.......Page 116
4 Identify Like Terms.......Page 119
5 Combine Like Terms.......Page 120
CHAPTER SUMMARY AND REVIEW......Page 124
CHAPTER TEST......Page 133
GROUP PROJECT......Page 135
CHAPTER 2 Equations, Inequalities, and Problem Solving......Page 137
1 Determine Whether a Number Is a Solution.......Page 138
2 Use the Addition Property of Equality.......Page 139
3 Use the Subtraction Property of Equality.......Page 141
4 Use the Multiplication Property of Equality.......Page 142
5 Use the Division Property of Equality.......Page 144
1 Use More Than One Property of Equality to Solve Equations.......Page 148
2 Simplify Expressions to Solve Equations.......Page 150
3 Clear Equations of Fractions and Decimals.......Page 152
4 Identify Identities and Contradictions.......Page 154
2 Solve Percent Problems by Direct Translation.......Page 158
3 Solve Applied Percent Problems.......Page 159
4 Find Percent of Increase and Decrease.......Page 160
5 Solve Discount and Commission Problems.......Page 161
1 Use Formulas from Business.......Page 166
2 Use Formulas from Science.......Page 167
3 Use Formulas from Geometry.......Page 169
4 Solve for a Specified Variable.......Page 171
1 Apply the Steps of a Problem-Solving Strategy.......Page 178
2 Solve Consecutive Integer Problems.......Page 181
3 Solve Geometry Problems.......Page 182
1 Solve Investment Problems.......Page 187
2 Solve Uniform Motion Problems.......Page 189
3 Solve Liquid Mixture Problems.......Page 191
4 Solve Dry Mixture Problems.......Page 192
5 Solve Number-Value Problems.......Page 193
1 Determine Whether a Number Is a Solution of an Inequality.......Page 198
2 Graph Solution Sets and Use Interval Notation.......Page 199
3 Solve Linear Inequalities.......Page 200
4 Solve Compound Inequalities.......Page 205
5 Solve Inequality Applications.......Page 206
CHAPTER SUMMARY AND REVIEW......Page 211
CHAPTER TEST......Page 218
GROUP PROJECT......Page 219
CHAPTER 3 Graphing Linear Equations and Inequalities in Two Variables; Functions......Page 221
1 Construct a Rectangular Coordinate System.......Page 222
2 Plot Ordered Pairs and Determine the Coordinates of a Point.......Page 223
3 Graph Paired Data.......Page 225
4 Read Line Graphs.......Page 226
1 Determine Whether an Ordered Pair Is a Solution of an Equation.......Page 231
2 Complete Ordered-Pair Solutions of Equations.......Page 232
3 Construct a Table of Solutions.......Page 233
4 Graph Linear Equations by Plotting Points.......Page 234
5 Use Graphs of Linear Equations to Solve Applied Problems.......Page 238
1 Identify Intercepts of a Graph.......Page 242
2 Graph Linear Equations by Finding Intercepts.......Page 243
3 Identify and Graph Horizontal and Vertical Lines.......Page 247
4 Obtain Information from Intercepts.......Page 248
1 Find the Slope of a Line from Its Graph.......Page 253
2 Find the Slope of a Line Given Two Points.......Page 255
3 Find Slopes of Horizontal and Vertical Lines.......Page 257
4 Solve Applications of Slope.......Page 258
5 Calculate Rates of Change.......Page 259
6 Determine Whether Lines Are Parallel or Perpendicular Using Slope.......Page 260
1 Use Slope–Intercept Form to Identify the Slope and y-Intercept of a Line.......Page 266
2 Write a Linear Equation in Slope–Intercept Form.......Page 267
3 Write an Equation of a Line Given Its Slope and y-Intercept.......Page 268
4 Use the Slope and y-Intercept to Graph a Linear Equation.......Page 269
5 Recognize Parallel and Perpendicular Lines.......Page 271
6 Use Slope–Intercept Form to Write an Equation to Model Data.......Page 272
1 Use Point–Slope Form to Write an Equation of a Line.......Page 276
2 Write an Equation of a Line Given Two Points on the Line.......Page 277
3 Write Equations of Horizontal and Vertical Lines.......Page 278
4 Use a Point and the Slope to Graph a Line.......Page 279
5 Write Linear Equations That Model Data.......Page 280
1 Determine Whether an Ordered Pair Is a Solution of an Inequality.......Page 285
2 Graph a Linear Inequality in Two Variables.......Page 286
3 Graph Inequalities with a Boundary through the Origin.......Page 289
4 Solve Applied Problems Involving Linear Inequalities in Two Variables.......Page 290
3.8 An Introduction to Functions......Page 294
2 Identify Functions and Their Domains and Ranges.......Page 295
3 Use Function Notation.......Page 296
4 Graph Functions.......Page 299
5 Use the Vertical Line Test.......Page 300
6 Solve Applications Involving Functions.......Page 302
CHAPTER SUMMARY AND REVIEW......Page 306
CHAPTER TEST......Page 315
CUMULATIVE REVIEW......Page 317
CHAPTER 4 Systems of Linear Equations and Inequalities......Page 319
4.1 Solving Systems of Equations by Graphing......Page 320
1 Determine Whether a Given Ordered Pair Is a Solution of a System.......Page 321
2 Solve Systems of Linear Equations by Graphing.......Page 322
3 Use Graphing to Identify Inconsistent Systems and Dependent Equations.......Page 323
4 Identify the Number of Solutions of a Linear System Without Graphing.......Page 325
5 Use a Graphing Calculator to Solve a Linear System (Optional).......Page 326
1 Solve Systems of Linear Equations by Substitution.......Page 330
2 Find a Substitution Equation.......Page 332
3 Solve Systems of Linear Equations that Contain Fractions.......Page 334
4 Use Substitution to Identify Inconsistent Systems and Dependent Equations.......Page 335
1 Solve Systems of Linear Equations by the Elimination Method.......Page 340
2 Use Multiplication to Eliminate a Variable.......Page 341
3 Use the Elimination Method Twice to Solve a System.......Page 344
4 Use Elimination to Identify Inconsistent Systems and Dependent Equations.......Page 345
5 Determine the Most Efficient Method to Use to Solve a Linear System.......Page 346
1 Assign Variables to Two Unknowns.......Page 350
2 Use Systems to Solve Geometry Problems.......Page 352
3 Use Systems to Solve Number-Value Problems.......Page 354
4 Use Systems to Solve Interest, Uniform Motion, and Mixture Problems.......Page 355
1 Solve a System of Linear Inequalities by Graphing.......Page 364
2 Solve Application Problems Involving Systems of Linear Inequalities.......Page 369
CHAPTER SUMMARY AND REVIEW......Page 373
CHAPTER TEST......Page 378
CUMULATIVE REVIEW......Page 380
CHAPTER 5 Exponents and Polynomials......Page 383
1 Identify Bases and Exponents.......Page 384
2 Multiply Exponential Expressions That Have Like Bases.......Page 386
3 Divide Exponential Expressions That Have Like Bases.......Page 387
4 Raise Exponential Expressions to a Power.......Page 389
5 Find Powers of Products and Quotients.......Page 390
1 Use the Zero Exponent Rule.......Page 395
2 Use the Negative Integer Exponent Rule.......Page 396
3 Use Exponent Rules to Change Negative Exponents in Fractions to Positive Exponents.......Page 398
4 Use All Exponent Rules to Simplify Expressions.......Page 400
1 Convert from Scientific to Standard Notation.......Page 405
2 Write Numbers in Scientific Notation.......Page 407
3 Perform Calculations with Scientific Notation.......Page 408
1 Know the Vocabulary for Polynomials.......Page 412
2 Evaluate Polynomials.......Page 414
3 Graph Equations Defined by Polynomials.......Page 416
1 Simplify Polynomials by Combining Like Terms.......Page 421
2 Add Polynomials.......Page 422
3 Subtract Polynomials.......Page 424
1 Multiply Monomials.......Page 430
2 Multiply a Polynomial by a Monomial.......Page 431
3 Multiply Binomials.......Page 432
4 Multiply Polynomials.......Page 434
1 Square a Binomial.......Page 439
2 Multiply the Sum and Difference of the Same Two Terms.......Page 441
3 Find Higher Powers of Binomials.......Page 442
4 Simplify Expressions Containing Polynomial Multiplication.......Page 443
1 Divide a Monomial by a Monomial.......Page 447
2 Divide a Polynomial by a Monomial.......Page 448
3 Divide a Polynomial by a Polynomial.......Page 449
CHAPTER SUMMARY AND REVIEW......Page 456
CHAPTER TEST......Page 463
GROUP PROJECT......Page 464
CUMULATIVE REVIEW......Page 465
CHAPTER 6 Factoring and Quadratic Equations......Page 467
6.1 The Greatest Common Factor; Factoring by Grouping......Page 468
1 Find the Greatest Common Factor of a List of Terms.......Page 469
2 Factor Out the Greatest Common Factor.......Page 470
3 Factor by Grouping.......Page 473
1 Factor Trinomials of the Form x[sup(2)] + bx + c.......Page 479
2 Factor Trinomials of the Form After Factoring Out the GCF x[sup(2)] + bx + c.......Page 484
3 Factor Trinomials of the Form Using the Grouping Method x[sup(2)] + bx + c.......Page 485
6.3 Factoring Trinomials of the Form ax[sup(2)] + bx + c......Page 490
1 Factor Trinomials Using the Trial-and-Check Method.......Page 491
2 Factor Trinomials After Factoring Out the GCF.......Page 494
3 Factor Trinomials Using the Grouping Method.......Page 495
6.4 Factoring Perfect-Square Trinomials and the Difference of Two Squares......Page 500
1 Recognize Perfect-Square Trinomials.......Page 501
2 Factor Perfect-Square Trinomials.......Page 502
3 Factor the Difference of Two Squares.......Page 503
1 Factor the Sum and Difference of Two Cubes.......Page 508
1 Use a General Strategy for Factoring Polynomials.......Page 513
1 Define Quadratic Equations.......Page 518
2 Solve Quadratic Equations Using the Zero-Factor Property.......Page 519
3 Solve Third-Degree Equations by Factoring.......Page 523
1 Solve Problems Involving Geometric Figures.......Page 526
2 Solve Problems Involving Consecutive Integers.......Page 528
3 Solve Problems Using the Pythagorean Theorem.......Page 529
4 Solve Problems Given the Quadratic Equation Model.......Page 530
CHAPTER SUMMARY AND REVIEW......Page 535
CHAPTER TEST......Page 541
GROUP PROJECT......Page 543
CUMULATIVE REVIEW......Page 544
CHAPTER 7 Rational Expressions and Equations......Page 547
1 Evaluate Rational Expressions.......Page 548
2 Find Numbers That Cause a Rational Expression to Be Undefined.......Page 549
3 Simplify Rational Expressions.......Page 550
4 Simplify Rational Expressions That Have Factors That Are Opposites.......Page 554
1 Multiply Rational Expressions.......Page 558
2 Divide Rational Expressions.......Page 561
3 Convert Units of Measurement.......Page 563
1 Add and Subtract Rational Expressions That Have the Same Denominator.......Page 567
2 Find the Least Common Denominator.......Page 570
3 Build Rational Expressions into Equivalent Expressions.......Page 572
7.4 Adding and Subtracting with Unlike Denominators......Page 576
1 Add and Subtract Rational Expressions That Have Unlike Denominators.......Page 577
2 Add and Subtract Rational Expressions That Have Denominators That Are Opposites.......Page 581
1 Simplify Complex Fractions Using Division.......Page 585
2 Simplify Complex Fractions Using the LCD.......Page 588
7.6 Solving Rational Equations......Page 593
1 Solve Rational Equations.......Page 594
2 Solve for a Specified Variable in a Formula.......Page 598
7.7 Problem Solving Using Rational Equations......Page 602
2 Solve Uniform Motion Problems.......Page 603
3 Solve Shared-Work Problems.......Page 605
4 Solve Investment Problems.......Page 607
1 Write Ratios and Rates in Simplest Form.......Page 612
2 Solve Proportions.......Page 613
3 Use Proportions to Solve Problems.......Page 616
4 Use Proportions to Solve Problems Involving Similar Triangles.......Page 618
CHAPTER SUMMARY AND REVIEW......Page 623
CHAPTER TEST......Page 631
GROUP PROJECT......Page 632
CUMULATIVE REVIEW......Page 633
CHAPTER 8 Transition to Intermediate Algebra......Page 635
1 Use Properties of Equality to Solve Linear Equations.......Page 636
2 Identify Identities and Contradictions.......Page 639
3 Solve Formulas for a Specified Variable.......Page 640
4 Solve Linear Inequalities.......Page 641
1 Define Relation, Domain, and Range.......Page 649
2 Identify Functions.......Page 650
3 Use Function Notation.......Page 652
4 Find the Domain of a Function.......Page 654
5 Graph Linear Functions.......Page 655
6 Write Equations of Linear Functions.......Page 656
7 Evaluate Polynomial Functions.......Page 659
1 Find Function Values Graphically.......Page 664
2 Find the Domain and Range of a Function Graphically.......Page 665
3 Graph Nonlinear Functions.......Page 666
4 Translate Graphs of Functions.......Page 669
5 Reflect Graphs of Functions.......Page 671
6 Find Function Values and the Domain and Range of Polynomial Functions Graphically.......Page 672
7 Use the Vertical Line Test.......Page 673
1 Find the Intersection and the Union of Two Sets.......Page 679
2 Solve Compound Inequalities Containing the Word And.......Page 680
3 Solve Double Linear Inequalities.......Page 683
4 Solve Compound Inequalities Containing the Word Or.......Page 685
1 Solve Equations of the Form | X | = k.......Page 691
2 Solve Equations with Two Absolute Values.......Page 694
3 Solve Inequalities of the Form | X | < k.......Page 695
4 Solve Inequalities of the Form | X | > k.......Page 697
1 Factor Out the Greatest Common Factor.......Page 703
2 Factor by Grouping.......Page 704
3 Use Factoring to Solve Formulas for a Specified Variable.......Page 705
4 Factor Trinomials.......Page 706
6 Use the Grouping Method to Factor Trinomials.......Page 709
1 Factor the Difference of Two Squares.......Page 713
2 Factor the Sum and Difference of Two Cubes.......Page 717
8.8 Review of Rational Expressions and Rational Equations; Rational Functions......Page 722
2 Find the Domain of a Rational Function.......Page 723
3 Recognize the Graphs of Rational Functions.......Page 724
4 Simplify Rational Expressions.......Page 725
5 Multiply and Divide Rational Expressions.......Page 726
6 Add and Subtract Rational Expressions.......Page 728
7 Solve Rational Equations.......Page 731
1 Solve Problems Involving Direct Variation.......Page 736
2 Solve Problems Involving Inverse Variation.......Page 738
3 Solve Problems Involving Joint Variation.......Page 739
4 Solve Problems Involving Combined Variation.......Page 740
CHAPTER SUMMARY AND REVIEW......Page 744
CHAPTER TEST......Page 759
GROUP PROJECT......Page 761
CHAPTER 9 Radical Expressions and Equations......Page 763
1 Find Square Roots.......Page 764
2 Find Square Roots of Expressions Containing Variables.......Page 766
3 Graph the Square Root Function.......Page 767
4 Evaluate Radical Functions.......Page 769
5 Find Cube Roots.......Page 770
6 Graph the Cube Root Function.......Page 772
7 Find nth Roots.......Page 773
1 Simplify Expressions of the Form a{sup(1/n)].......Page 779
2 Simplify Expressions of the Form a[sup(m/n)].......Page 781
4 Simplify Expressions with Negative Rational Exponents.......Page 784
5 Use Rules for Exponents to Simplify Expressions.......Page 785
6 Simplify Radical Expressions.......Page 786
9.3 Simplifying and Combining Radical Expressions......Page 790
1 Use the Product Rule to Simplify Radical Expressions.......Page 791
2 Use Prime Factorization to Simplify Radical Expressions.......Page 793
3 Use the Quotient Rule to Simplify Radical Expressions.......Page 794
4 Add and Subtract Radical Expressions.......Page 796
1 Multiply Radical Expressions.......Page 801
2 Find Powers of Radical Expressions.......Page 803
3 Rationalize Denominators.......Page 804
4 Rationalize Denominators That Have Two Terms.......Page 808
5 Rationalize Numerators.......Page 809
1 Solve Equations Containing One Radical.......Page 813
2 Solve Equations Containing Two Radicals.......Page 818
3 Solve Formulas Containing Radicals.......Page 820
1 Use the Pythagorean Theorem to Solve Problems.......Page 824
2 Solve Problems Involving 45°– 45°– 90° Triangles.......Page 826
3 Solve Problems Involving 30°– 60°– 90° Triangles.......Page 827
4 Use the Distance Formula to Solve Problems.......Page 829
5 Find the Midpoint of a Line Segment.......Page 830
9.7 Complex Numbers......Page 836
1 Express Square Roots of Negative Numbers in Terms of i.......Page 837
2 Write Complex Numbers in the Form a + bi.......Page 838
4 Multiply Complex Numbers.......Page 839
5 Divide Complex Numbers.......Page 841
6 Perform Operations Involving Powers of i.......Page 844
CHAPTER SUMMARY AND REVIEW......Page 848
CHAPTER TEST......Page 857
GROUP PROJECT......Page 859
CHAPTER 10 Quadratic Equations, Functions, and Inequalities......Page 861
10.1 The Square Root Property and Completing the Square......Page 862
1 Use the Square Root Property to Solve Quadratic Equations.......Page 863
2 Solve Quadratic Equations by Completing the Square.......Page 866
10.2 The Quadratic Formula......Page 874
1 Derive the Quadratic Formula.......Page 875
2 Solve Quadratic Equations Using the Quadratic Formula.......Page 876
3 Write Equivalent Equations to Make Quadratic Formula Calculations Easier.......Page 878
4 Use the Quadratic Formula to Solve Application Problems.......Page 879
10.3 The Discriminant and Equations That Can Be Written in Quadratic Form......Page 887
1 Use the Discriminant to Determine Number and Type of Solutions.......Page 888
2 Solve Equations That Are Quadratic in Form.......Page 889
3 Solve Application Problems Using Quadratic Equations.......Page 893
1 Graph Functions of the Form f(x ) = ax[sup(2)] and f(x) = ax[sup(2)] + k.......Page 897
2 Graph Functions of the Form f(x) = a(x - h)[sup(2)] and f(x) = a(x - h)[sup(2)] + k.......Page 900
3 Graph Functions of the Form f(x) = ax[sup(2)] + bx + c by Completing the Square.......Page 901
4 Find the Vertex Using -b/2a.......Page 903
5 Determine Minimum and Maximum Values.......Page 906
6 Solve Quadratic Equations Graphically.......Page 907
10.5 Quadratic and Other Nonlinear Inequalities......Page 911
1 Solve Quadratic Inequalities.......Page 912
2 Solve Rational Inequalities.......Page 914
3 Graph Nonlinear Inequalities in Two Variables.......Page 918
CHAPTER SUMMARY AND REVIEW......Page 922
CHAPTER TEST......Page 928
GROUP PROJECT......Page 930
CUMULATIVE REVIEW......Page 931
CHAPTER 11 Exponential and Logarithmic Functions......Page 935
1 Add, Subtract, Multiply, and Divide Functions.......Page 936
2 Find the Composition of Functions.......Page 939
3 Use Graphs to Evaluate Functions.......Page 941
4 Use Composite Functions to Solve Problems.......Page 942
1 Determine Whether a Function Is a One-to-One Function.......Page 947
2 Use the Horizontal Line Test to Determine Whether a Function Is One-to-One.......Page 948
3 Find the Equation of the Inverse of a Function.......Page 950
4 Find the Composition of a Function and Its Inverse.......Page 951
5 Graph a Function and Its Inverse.......Page 952
11.3 Exponential Functions......Page 957
1 Define Exponential Functions.......Page 958
2 Graph Exponential Functions.......Page 959
3 Use Exponential Functions in Applications Involving Growth or Decay.......Page 963
11.4 Logarithmic Functions......Page 971
1 Define Logarithm.......Page 972
3 Write Exponential Equations as Logarithmic Equations.......Page 973
4 Evaluate Logarithmic Expressions.......Page 975
5 Graph Logarithmic Functions.......Page 977
6 Use Logarithmic Formulas and Functions in Applications.......Page 979
11.5 Base-e Exponential and Logarithmic Functions......Page 984
2 Graph the Natural Exponential Function.......Page 985
3 Use Base-e Exponential Formulas and Functions in Applications.......Page 987
4 Define Base-e Logarithms.......Page 988
5 Evaluate Natural Logarithmic Expressions.......Page 989
6 Graph the Natural Logarithmic Function.......Page 990
7 Use Base-e Logarithmic Formulas and Functions in Applications.......Page 992
1 Use the Four Basic Properties of Logarithms.......Page 998
2 Use the Product Rule for Logarithms.......Page 999
3 Use the Quotient Rule for Logarithms.......Page 1000
4 Use the Power Rule for Logarithms.......Page 1001
5 Write Logarithmic Expressions as a Single Logarithm.......Page 1003
6 Use the Change-of-Base Formula.......Page 1005
7 Use Properties of Logarithms to Solve Application Problems.......Page 1006
11.7 Exponential and Logarithmic Equations......Page 1009
1 Solve Exponential Equations.......Page 1010
2 Solve Logarithmic Equations.......Page 1014
3 Use Exponential and Logarithmic Equations to Solve Application Problems.......Page 1017
CHAPTER SUMMARY AND REVIEW......Page 1022
CHAPTER TEST......Page 1033
GROUP PROJECT......Page 1035
CHAPTER 12 More on Systems of Equations......Page 1037
1 Determine Whether an Ordered Pair Is a Solution of a System.......Page 1038
2 Solve Systems of Linear Equations by Graphing.......Page 1039
3 Use Graphing to Identify Inconsistent Systems and Dependent Equations.......Page 1040
4 Solve Systems of Linear Equations by Substitution.......Page 1044
5 Solve Systems of Linear Equations by the Elimination (Addition) Method.......Page 1046
6 Use Substitution and Elimination (Addition) to Identify Inconsistent Systems and Dependent Equations.......Page 1047
7 Solve Application Problems Using Systems of Equations.......Page 1048
1 Determine Whether an Ordered Triple Is a Solution of a System.......Page 1055
2 Solve Systems of Three Linear Equations in Three Variables.......Page 1056
3 Solve Systems of Equations with Missing Variable Terms.......Page 1058
4 Identify Inconsistent Systems and Dependent Equations.......Page 1061
1 Assign Variables to Three Unknowns.......Page 1066
2 Use Systems to Solve Curve-Fitting Problems.......Page 1069
2 Write the Augmented Matrix for a System.......Page 1074
3 Perform Elementary Row Operations on Matrices.......Page 1075
4 Use Matrices to Solve a System of Two Equations.......Page 1077
5 Use Matrices to Solve a System of Three Equations.......Page 1078
6 Use Matrices to Identify Inconsistent Systems and Dependent Equations.......Page 1080
12.5 Solving Systems of Equations Using Determinants......Page 1084
1 Evaluate 2 x 2 and 3 x 3 Determinants.......Page 1085
2 Use Cramer’s Rule to Solve Systems of Two Equations.......Page 1088
3 Use Cramer’s Rule to Solve Systems of Three Equations.......Page 1090
CHAPTER SUMMARY AND REVIEW......Page 1095
CHAPTER TEST......Page 1104
GROUP PROJECT......Page 1105
CUMULATIVE REVIEW......Page 1106
CHAPTER 13 Conic Sections; More Graphing......Page 1111
1 Identify Conic Sections and Some of Their Applications.......Page 1112
2 Graph Equations of Circles Written in Standard Form.......Page 1114
4 Convert the General Form of the Equation of a Circle to Standard Form.......Page 1116
6 Convert the General Form of the Equation of a Parabola to Standard Form to Graph It.......Page 1118
1 Define an Ellipse.......Page 1125
2 Graph Ellipses Centered at the Origin.......Page 1126
3 Graph Ellipses Centered at (h, k).......Page 1128
4 Solve Application Problems Involving Ellipses.......Page 1130
2 Graph Hyperbolas Centered at the Origin.......Page 1134
3 Graph Hyperbolas Centered at (h, k).......Page 1137
4 Graph Equations of the Form xy = k.......Page 1138
5 Solve Application Problems Involving Hyperbolas.......Page 1139
6 Identify Conic Sections by Their Equations.......Page 1140
1 Solve Systems by Graphing.......Page 1143
2 Solve Systems by Substitution.......Page 1144
3 Solve Systems by Elimination (Addition).......Page 1146
CHAPTER SUMMARY AND REVIEW......Page 1150
CHAPTER TEST......Page 1155
GROUP PROJECT......Page 1156
CHAPTER 14 Miscellaneous Topics......Page 1157
14.1 The Binomial Theorem......Page 1158
1 Use Pascal’s Triangle to Expand Binomials.......Page 1159
2 Use Factorial Notation.......Page 1161
3 Use the Binomial Theorem to Expand Binomials.......Page 1162
4 Find a Specific Term of a Binomial Expansion.......Page 1164
1 Find Terms of a Sequence Given the General Term.......Page 1167
2 Find Terms of an Arithmetic Sequence by Identifying the First Term and the Common Difference.......Page 1168
3 Find Arithmetic Means.......Page 1170
4 Find the Sum of the First n Terms of an Arithmetic Sequence.......Page 1171
5 Solve Application Problems Involving Arithmetic Sequences.......Page 1172
6 Use Summation Notation.......Page 1173
1 Find Terms of a Geometric Sequence by Identifying the First Term and the Common Ratio.......Page 1177
2 Find Geometric Means.......Page 1179
3 Find the Sum of the First n Terms of a Geometric Sequence.......Page 1181
4 Define and Use Infinite Geometric Series.......Page 1182
5 Solve Application Problems Involving Geometric Sequences.......Page 1184
CHAPTER SUMMARY AND REVIEW......Page 1189
CHAPTER TEST......Page 1193
GROUP PROJECT......Page 1194
CUMULATIVE REVIEW......Page 1195
APPENDIXES 1 Roots and Powers......Page 1201
2 Synthetic Division......Page 1202
3 Answers to Selected Problems......Page 1209
INDEX......Page 1277