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Tables of Contents for Intermediate Alegbra With Applications
Chapter/Section Title
Page #
Page Count
Preface
xiii
Index of Applications
xxv
Review of Real Numbers
1
52
Introduction to Real Numbers
3
12
Inequality and absolute value
3
3
Set operations and interval notation
6
9
Operations on Rational Numbers
15
13
Operations on integers
15
3
Operations on rational numbers
18
3
Exponential expressions
21
1
The Order of Operations Agreement
22
6
Variable Expressions
28
9
The Properties of the Real Numbers
28
2
Evaluate variable expressions
30
2
Simplify variable expressions
32
5
Verbal Expressions and Variable Expressions
37
16
Translate a verbal expression into a variable expression
37
2
Application problems
39
4
Focus on Problem Solving: Polya's Four-Step Process
43
3
Projects and Group Activities: Water Displacement
46
1
Chapter Summary
47
2
Chapter Review Exercises
49
1
Chapter Test
50
3
First-Degree Equations and Inequalities
53
64
Equations in One Variable
55
10
Solve equations using the Addition and Multiplication Properties of Equations
55
3
Solve equations using the Distributive Property
58
2
Application problems
60
5
Coin, Stamp, and Integer Problems
65
7
Coin and stamp problems
65
2
Integer problems
67
5
Value Mixture and Motion Problems
72
7
Value mixture problems
72
1
Uniform motion problems
73
6
Applications: Problems Involving Percent
79
9
Investment problems
79
2
Percent mixture problems
81
7
Inequalities in One Variable
88
10
Solve inequalities in one variable
88
2
Solve compound inequalities
90
2
Application problems
92
6
Absolute Value Equations and Inequalities
98
19
Absolute value equations
98
2
Absolute value inequalities
100
2
Application problems
102
4
Focus on Problem Solving: Understand the Problem
106
1
Projects and Group Activities: Venn Diagrams
107
1
Absolute Value Equations and Inequalities
108
1
Chapter Summary
109
3
Chapter Review Exercises
112
1
Chapter Test
113
1
Cumulative Review Exercises
114
3
Linear Functions and Inequalities in Two Variables
117
76
The Rectangular Coordinate System
119
10
Points on a rectangular coordinate system
119
2
Find the length and midpoint of a line segment
121
2
Graph a scatter diagram
123
6
Introduction to Functions
129
13
Evaluate a function
129
13
Linear Functions
142
13
Graph a linear function
142
2
Graph an equation of the form Ax + By = C
144
5
Application problems
149
6
Slope of a Straight Line
155
9
Find the slope of a line given two points
155
3
Graph a line given a point and the slope
158
6
Finding Equations of Lines
164
8
Find the equation of a line given a point and the slope
164
2
Find the equation of a line given two points
166
1
Application problems
167
5
Parallel and Perpendicular Lines
172
7
Find equations of parallel and perpendicular lines
172
7
Inequalities in Two Variables
179
14
Graph the solution set of an inequality in two variables
179
3
Focus on Problem Solving: Find a Pattern
182
2
Projects and Group Activities: Evaluating a Function with a Graphing Calculator
184
1
Introduction to Graphing Calculators
184
1
Chapter Summary
185
2
Chapter Review Exercises
187
3
Chapter Test
190
1
Cumulative Review Exercises
191
2
Systems of Equations and Inequalities
193
58
Solving Systems of Linear Equations by Graphing and by the Substitution Method
195
7
Solve a system of linear equations by graphing
195
2
Solve a system of linear equations by the substitution method
197
5
Solving Systems of Linear Equations by the Addition Method
202
10
Solve a system of two linear equations in two variables by the addition method
202
2
Solve a system of three linear equations in three variables by the addition method
204
8
Solving Systems of Equations by Using Determinants and by Using Matrices
212
13
Evaluate determinants
212
2
Solve systems of linear equations by using Cramer's Rule
214
3
Solve systems of linear equations by using matrices
217
8
Application Problems
225
11
Rate-of-wind and water-current problems
225
2
Application problems
227
9
Solving Systems of Linear Inequalities
236
15
Graph the solution set of a system of linear inequalities
236
3
Focus on Problem Solving: Solve an Easier Problem
239
1
Projects and Group Activities: Using a Graphing Calculator to Solve a System of Equations
240
1
Solving a First-Degree Equation with a Graphing Calculator
241
2
Chapter Summary
243
3
Chapter Review Exercises
246
1
Chapter Test
247
2
Cumulative Review Exercises
249
2
Polynomials and Exponents
251
74
Exponential Expressions
253
11
Multiply monomials
253
1
Divide monomials and simplify expressions with negative exponents
254
4
Scientific notation
258
1
Application problems
259
5
Introduction to Polynomials
264
10
Evaluate polynomial functions
264
4
Add or subtract polynomials
268
6
Multiplication of Polynomials
274
8
Multiply a polynomial by a monomial
274
1
Multiply to polynomials
275
1
Multiply polynomials that have special products
276
1
Application problems
277
5
Division of Polynomials
282
7
Divide polynomials
282
1
Synthetic division
283
2
Evaluate a polynomial using synthetic division
285
4
Factoring Polynomials
289
11
Factor a monomial from a polynomial
289
1
Factor by grouping
290
1
Factor trinomials of the form x2 + bx + c
291
2
Factor trinomials of the form ax2 + bx + c
293
7
Special Factoring
300
8
Factor the difference of two perfect squares and factor perfect-square trinomials
300
2
Factor the sum or the difference of two cubes
302
1
Factor trinomials that are quadratic in form
303
1
Factor completely
304
4
Solving Equations by Factoring
308
17
Solve equations by factoring
308
2
Application problems
310
5
Focus on Problem Solving: Find a Counterexample
315
1
Projects and Group Activities: Reverse Polish Notation
316
1
Pythagorean Triples
317
1
Chapter Summary
318
2
Chapter Review Exercises
320
2
Chapter Test
322
1
Cumulative Review Exercises
323
2
Rational Expressions
325
52
Introduction to Rational Functions
327
6
Find the domain of a rational function
327
2
Simplify rational expressions
329
4
Operations on Rational Expressions
333
8
Multiply and divide rational expressions
333
1
Add and subtract rational expressions
334
7
Complex Fractions
341
4
Simplify complex fractions
341
4
Rational Equations
345
10
Solve fractional equations
345
1
Work problems
346
2
Uniform motion problems
348
7
Proportions and Variation
355
10
Proportions
355
2
Variation problems
357
8
Literal Equations
365
12
Solve literal equations
365
2
Focus on Problem Solving: Implication
367
1
Projects and Group Activities: Continued Fractions
368
1
Graphing Rational Expressions
369
1
Chapter Summary
370
2
Chapter Review Exercises
372
2
Chapter Test
374
1
Cumulative Review Exercises
375
2
Rational Exponents and Radicals
377
52
Rational Exponents and Radical Expressions
379
8
Simplify expressions with rational exponents
379
2
Write exponential expressions as radical expressions and radical expressions as exponential expressions
381
1
Simplify radical expressions that are roots of perfect powers
382
5
Operations on Radical Expressions
387
9
Simplify radical expressions
387
1
Add and subtract radical expressions
388
1
Multiply radical expressions
389
1
Divide radical expressions
390
6
Complex Numbers
396
8
Simplify complex numbers
396
2
Add and subtract complex numbers
398
1
Multiply complex numbers
398
2
Divide complex numbers
400
4
Radical Functions
404
6
Find the domain of a radical function
404
1
Graph a radical function
405
5
Solving Equations Containing Radical Expressions
410
19
Solve equations containing one or more radical expressions
410
2
Application problems
412
6
Focus on Problem Solving: Another Look at Polya's Four-Step Process
418
1
Projects and Group Activities: Graphing Complex Numbers
419
2
Solving Radical Equations with a Graphing Calculator
421
1
Chapter Summary
422
1
Chapter Review Exercises
423
2
Chapter Test
425
1
Cumulative Review Exercises
426
3
Quadratic Equations and Inequalities
429
66
Solving Quadratic Equations by Factoring or by Taking Square Roots
431
7
Solve quadratic equations by factoring
431
1
Write a quadratic equation given its solutions
432
1
Solve quadratic equations by taking square roots
433
5
Solving Quadratic Equations by Completing the Square and by Using the Quadratic Formula
438
11
Solve quadratic equations by completing the square
438
3
Solve quadratic equations by using the quadratic formula
441
8
Equations That Are Reducible to Quadratic Equations
449
7
Equations that are quadratic in form
449
2
Radical equations
451
1
Fractional equations
452
4
Applications of Quadratic Equations
456
6
Application problems
456
6
Nonlinear Inequalities
462
4
Solve inequalities by factoring
462
1
Solve rational inequalities
463
3
Properties of Quadratic Functions
466
13
Graph a quadratic function
466
4
Find the x-intercepts of a parabola
470
9
Applications of Quadratic Functions
479
16
Minimum and maximum problems
479
1
Applications of minimum and maximum
480
4
Focus on Problem Solving: Inductive and Deductive Reasoning
484
1
Projects and Group Activities: Completing the Square
485
1
Using a Graphing Calculator to Solve a Quadratic Equation
486
1
Solving Nonlinear Inequalities Using a Graphing Calculator
487
1
Chapter Summary
488
2
Chapter Review Exercises
490
1
Chapter Test
491
1
Cumulative Review Exercises
492
3
Functions and Relations
495
44
Graphs of Functions
497
9
Graph functions
497
9
Translations of Graphs
506
7
Graph by using translations
506
7
Algebra of Functions
513
5
Perform operations on functions
513
2
Find the composition of two functions
515
3
One-to-One and Inverse Functions
518
21
Determine whether a function is one-to-one
518
2
Find the inverse of a function
520
7
Focus on Problem Solving: Proof in Mathematics
527
1
Projects and Group Activities: Derivative Investments
528
2
Properties of Polynomials
530
1
The Greatest-Integer Function
531
1
Chapter Summary
532
2
Chapter Review Exercises
534
2
Chapter Test
536
1
Cumulative Review Exercises
537
2
Exponential and Logarithmic Functions
539
58
Exponential Functions
541
9
Evaluate exponential functions
541
2
Graph exponential functions
543
7
Introduction to Logarithms
550
13
Write equivalent exponential and logarithmic equations
550
3
The Properties of Logarithms
553
10
Graphs of Logarithmic Functions
563
7
Graph logarithmic functions
563
7
Exponential and Logarithmic Equations
570
8
Solve exponential equations
570
2
Solve logarithmic equations
572
6
Applications of Exponential and Logarithmic Functions
578
19
Application problems
578
10
Focus on Problem Solving: Proof by Contradiction
588
1
Projects and Group Activities: Fractals
589
2
Chapter Summary
591
1
Chapter Review Exercises
592
1
Chapter Test
593
1
Cumulative Review Exercises
594
3
Sequences and Series
597
40
Introduction to Sequences and Series
599
6
Write the terms of a sequence
599
1
Find the sum of a series
600
5
Arithmetic Sequences and Series
605
7
Find the nth term of an arithmetic sequence
605
2
Find the sum of an arithmetic series
607
1
Application problems
608
4
Geometric Sequences and Series
612
9
Find the nth term of a geometric sequence
612
1
Finite geometric series
613
2
Infinite geometric series
615
2
Application problems
617
4
Binomial Expansions
621
16
Expand (a + n)n
621
6
Focus on Problem Solving: Forming Negations
627
1
Projects and Group Activities: ISBN and UPC Numbers
628
1
Finding the Proper Dosage
629
2
Chapter Summary
631
1
Chapter Review Exercises
632
2
Chapter Test
634
1
Cumulative Review Exercises
635
2
Conic Sections
637
38
The Parabola
639
5
Graph parabolas
639
5
The Circle
644
6
Find the equation of a circle and then graph the circle
644
2
Write the equation of a circle in standard form and then graph the circle
646
4
The Ellipse and the Hyperbola
650
7
Graph an ellipse with center at the origin
650
2
Graph a hyperbola with center at the origin
652
5
Solving Nonlinear Systems of Equations
657
5
Solve nonlinear systems of equations
657
5
Quadratic Inequalities and Systems of Inequalities
662
13
Graph the solution set of a quadratic inequality in two variables
662
1
Graph the solution set of a nonlinear system of inequalities
663
5
Focus on Problem Solving: Use a Variety of Problem-Solving Strategies
668
1
Projects and Group Activities: Graphing Conic Sections Using a Graphing Utility
668
1
Chapter Summary
669
2
Chapter Review Exercises
671
2
Chapter Test
673
2
Final Exam
675
4
Appendix: Guidelines for Using Graphing Calculators
679
Solutions to Problems
S1
Answers to Odd-Numbered Exercises
A1
Glossary
G1
Index
I1