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Tables of Contents for Algebra for Students
Chapter/Section Title
Page #
Page Count
To The Student
ix
Review of the Real Number System
Basic Terms
1
10
Operations on Real Numbers
11
11
Properties of Real Numbers
22
9
Chaper 1 Test
28
3
Linear Equations and Inequalities
Linear Equations in One Variable
31
10
Formulas
41
5
Applications of Linear Equations
46
7
More Applications of Linear Equations
53
4
Linear Inequalities in One Variable
57
8
Set Operations and Compound Inequalities
65
5
Absolute Value Equations and Inequalities
70
11
Chaper 2 Test
78
3
Graphs, Linear Equations, and Functions
The Rectangular Coordinate System
81
11
The Slope of a Line
92
10
Linear Equations in Two Variables
102
10
Linear Inequalities in Two Variables
112
7
Introduction to Functions
119
11
Variation
130
12
Chaper 3 Test
137
5
Exponents and Polynomials
Integer Exponents and Scientific Notation
142
12
Addition and Subtraction of Polynomials
154
7
Polynomial Functions
161
7
Multiplication of Polynomials
168
8
Greatest Common Factors; Factoring by Grouping
176
5
Factoring Trinomials
181
7
Special Factoring
188
5
General Methods of Factoring
193
5
Solving Equations by Factoring
198
12
Chaper 4 Test
206
4
Rational Expressions
Rational Expressions and Functions; Multiplication and Division
210
9
Addition and Subtraction of Rational Expressions
219
6
Complex Fractions
225
5
Division of Polynomials
230
6
Graphs and Equations with Rational Expressions
236
7
Applications of Rational Expressions
243
12
Chaper 5 Test
252
3
Roots and Radicals
Rational Exponents and Radicals
255
8
Simplifying Radical Expressions
263
9
Addition and Subtraction of Radical Expressions
272
4
Multiplication and Division of Radical Expressions
276
7
Graphs and Equations with Radical Expressions
283
12
Complex Numbers
295
12
Chaper 6 Test
303
4
Quadratic Equations and Inequalities
Completing the Square
307
8
The Quadratic Formula
315
9
Equations Quadratic in Form
324
9
Formulas and Applications
333
7
Nonlinear Inequalities
340
9
Chaper 7 Test
347
2
Graphing Relations and Functions
The Algebra of Functions
349
9
Quadratic Functions; Translations
358
11
More About Parabolas; Applications
369
10
Symmetry; Increasing and Decreasing Functions
379
9
The Circle and the Ellipse
388
9
The Hyperbola; Conic Sections
397
6
Piecewise Linear Functions
403
14
Chaper 8 Test
413
4
Polynomial and Rational Functions
Synthetic Division
417
8
Zeros of Polynomial Functions
425
7
Graphs and Applications of Polynomial Functions
432
15
Graphs and Applications of Rational Functions
447
21
Chaper 9 Test
463
5
Inverse, Exponential, and Logarithmic Functions
Inverse Functions
468
7
Exponential Functions
475
8
Logarithmic Functions
483
7
Properties of Logarithms
490
5
Evaluating Logarithms
495
5
Exponential and Logarithmic Equations; Applications
500
15
Chaper 10 Test
510
5
Systems of Equations and Inequalities
Linear Systems of Equations in Two Variables
515
12
Linear Systems of Equations in Three Variables
527
6
Applications of Linear Systems of Equations
533
6
Nonlinear Systems of Equations
539
8
Second-Degree Inequalities, Systems of Inequalities, and Linear Programming
547
18
Chaper 11 Test
560
5
Matrices and Determinants
Matrix Solution of Linear Systems
565
8
Properties of Matrices
573
9
Determinants
582
8
Cramer's Rule
590
5
Matrix Inverses
595
14
Chaper 12 Test
606
3
Further Topics in Algebra
Sequences and Series
609
8
Arithmetic Sequences
617
9
Geometric Sequences
626
11
The Binomial Theorem
637
7
Mathematical Induction
644
5
Counting Theory
649
12
Basics of Probability
661
14
Chaper 13 Test
670
5
Answers to Chapter Tests
675