Schaum's outline of theory and problems of elementary algebra Book

Chapter 1	From Arithemetic to Algebra	1
1.	Representing Numbers by Letters	1
2.	Interchanging Numbers in Addition	2
3.	Interchanging Numbers in Multiplication	3
4.	Symbolizing the Operations in Algebra	4
5.	Expressing Addition and Subtraction Algebraically	5
6.	Expressing Multiplication and Division Algebraically	6
7.	Expressing Two or More Operations Algebraically	6
8.	Order in Which Fundamental Operations Are Performed	8
9.	The Uses of Parentheses: Changing the Order of Operations	9
10.	Multiplying Factors in Terms: Numerical and Literal Coefficients	10
11.	Repeated Multiplying of a Factor: Base, Exponent, and Power	11
12.	Combining Like and Unlike Terms	13
Chapter 2	Simple Equations and Their Solutions	21
1.	Kinds of Equalities: Equations and Identities	21
2.	Translating Verbal Statements into Equations	22
3.	Solving Simple Equations by Using Inverse Operations	23
4.	Rules of Equality for Solving Equations	25
5.	Using Division to Solve an Equation	26
6.	Using Multiplication to Solve an Equation	28
7.	Using Subtraction to Solve an Equation	30
8.	Using Addition to Solve an Equation	31
9.	Using Two or More Operations to Solve an Equation	32
Chapter 3	Signed Numbers	43
1.	Understanding Signed Numbers: Positive and Negative Numbers	43
2.	Using Number Scales for Signed Numbers	44
3.	Adding Signed Numbers	48
4.	Simplifying the Addition of Signed Numbers	50
5.	Subtracting Signed Numbers	51
6.	Multiplying Signed Numbers	53
7.	Finding Powers of Signed Numbers	55
8.	Dividing Signed Numbers	56
9.	Evaluating Expressions Having Signed Numbers	58
Chapter 4	Introduction to Monomials and Polynomials	64
1.	Understanding Monomials and Polynomials	64
2.	Adding Monomials	65
3.	Arranging and Adding Polynomials	66
4.	Subtracting Monomials	67
5.	Subtracting Polynomials	68
6.	Using Parentheses and Other Grouping Symbols to Add or Subtract Polynomials	69
7.	Multiplying Monomials and Powers of the Same Base	71
8.	Multiplying a Polynomial by a Monomial	72
9.	Multiplying Polynomials	73
10.	Dividing Powers and Monomials	74
11.	Dividing a Polynomial by a Monomial	76
12.	Dividing a Polynomial by a Polynomial	77
Chapter 5	First-Degree Equations	86
1.	Reviewing the Solution of First-Degree Equations Having Positive Roots	86
2.	Solving First-Degree Equations Having Negative Solutions	88
3.	Solving Equations by Transposing	90
4.	Solving Equations Containing Parentheses	91
5.	Solving Equations Containing One Fraction or Fractions Having the Same Denominator	92
6.	Solving Equations Containing Fractions Having Different Denominators: Lowest Common Denominator	93
7.	Solving Equations Containing Decimals	95
8.	Solving Literal Equations	96
9.	The Graphing Calculator	97
Chapter 6	Formulas	105
1.	Points and Lines	105
2.	Understanding Polygons, Circles, and Solids	106
3.	Formulas for Perimeters and Circumferences: Linear Measure	111
4.	Formulas for Areas: Square Measure	115
5.	Formulas for Volumes: Cubic Measure	120
6.	Deriving Formulas	124
7.	Transforming Formulas	126
8.	Finding the Value of an Unknown in a Formula	128
Chapter 7	Graphs of Linear Equations	137
1.	Understanding Graphs	137
2.	Graphing Linear Equations	141
3.	Solving a Pair of Linear Equations Graphically	147
4.	Deriving a Linear Equation from a Table of Values	150
5.	Midpoint of a Segment	152
6.	Distance between Two Points	153
Chapter 8	Introduction to Simultaneous Equations	163
1.	Solving a Pair of Equations by Addition or Subtraction	163
2.	Solving a Pair of Equations by Substitution	166
Chapter 9	Problem Solving and Mathematical Modeling	169
1.	Number Problems Having One Unknown: Introduction to Problem Solving	169
2.	Number Problems Having Two Unknowns	171
3.	Consecutive-Integer Problems	173
4.	Age Problems	175
5.	Ratio Problems	176
6.	Angle Problems	179
7.	Perimeter Problems	182
8.	Coin or Stamp Problems	185
9.	Cost and Mixture Problems	187
10.	Investment or Interest Problems	189
11.	Motion Problems	191
12.	Mathematical Modeling	197
Chapter 10	Products and Factoring	213
1.	Understanding Factors and Products	213
2.	Factoring a Polynomial Having a Common Monomial Factor	214
3.	Squaring a Monomial	215
4.	Finding the Square Root of a Monomial	216
5.	Finding the Product of the Sum and Difference of Two Numbers	217
6.	Factoring the Difference of Two Squares	218
7.	Finding the Product of Two Binomials with Like Terms	219
8.	Factoring Trinomials in Form of x[superscript 2] + bx + c	221
9.	Factoring a Trinomial in Form of ax[superscript 2] + bx + c	222
10.	Squaring a Binomial	223
11.	Factoring a Perfect-Square Trinomial	223
12.	Completely Factoring Polynomials	225
13.	The Variable: Direct and Inverse Variation	226
14.	Understanding Direct Variation: y = kx or y / x = k	227
15.	Understanding Inverse Variation: xy = k	230
Chapter 11	Fractions	241
1.	Understanding Fractions	241
2.	Changing Fractions to Equivalent Fractions	243
3.	Reciprocals and Their Uses	244
4.	Reducing Fractions to Lowest Terms	246
5.	Multiplying Fractions	248
6.	Dividing Fractions	249
7.	Adding or Subtracting Fractions Having the Same Denominator	250
8.	Adding or Subtracting Fractions Having Different Denominators	251
9.	Simplifying Complex Fractions	253
Chapter 12	Roots and Radicals	262
1.	Understanding Roots and Radicals	262
2.	Understanding Rational and Irrational Numbers	264
3.	Finding the Square Root of a Number by Using a Graph	265
4.	Finding the Square Root of a Number by Using a Table or Calculator	266
5.	Simplifying the Square Root of a Product	267
6.	Simplifying the Square Root of a Fraction	269
7.	Adding and Subtracting Square Roots of Numbers	271
8.	Multiplying Square Roots of Numbers	272
9.	Dividing Square Roots of Numbers	273
10.	Rationalizing the Denominator of a Fraction	274
11.	Solving Radical Equations	276
Chapter 13	Quadratic Equations	284
1.	Understanding Quadratic Equations in One Unknown	284
2.	Solving Quadratic Equations by Factoring	285
3.	Solving Incomplete Quadratic Equations	287
4.	Solving a Quadratic Equation by Completing the Square	289
5.	Solving a Quadratic Equation by Quadratic Formula	291
6.	Solving Quadratic Equations Graphically	293
Chapter 14	The Pythagorean Theorem and Similar Triangles	301
1.	Law of Pythagoras	301
2.	Proportions: Equal Ratios	305
3.	Similar Triangles	307
Chapter 15	Introduction to Trigonometry	315
1.	Understanding Trigonometric Ratios	315
2.	Trigonometric Functions of an Acute Angle	315
3.	Trigonometric Functions of Complementary Angles	316
4.	Trigonometric Functions of 30[degree], 45[degree], 60[degree]	316
Chapter 16	Introduction to Geometry	323
1.	Solving Problems Graphically	323
2.	Understanding the Slope of a Line	324
3.	Understanding Congruent Triangles	326
4.	Understanding Symmetry	330
5.	Transformations	331
Appendix A	Review of Arithmetic	343
1.	The Whole Numbers	343
2.	Fractions	345
3.	Decimals	348
4.	Reviewing Percents and Percentage	350
Appendix B	The Use of Calculators	353
1.	Using a Calculator to Perform the Fundamental Operations of Arithmetic	353
2.	Introduction to the Graphing Calculator	354
	Index	359