Foundations of Algebra text book

468 Pages·2011·52.71 MB·English

Alfred S. Posamentier
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iiiiii
Introduction to Foundations of Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii–xviii
Chapter Chapter
Rational Numbers Real Numbers
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . 35
1-1 The Rational Numbers. . . . . . . . . . 2 2-1 Scientific Notation . . . . . . . . . . . . 36
1-2 The Rational Numbers on 2-2 Multiply and Divide in
a Number Line . . . . . . . . . . . . . . . . . . . . . 4 Scientific Notation . . . . . . . . . . . . . . . . . 38
1-3 Greatest Common Factor 2-3 Perfect Squares and
(GCF). . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Square Roots. . . . . . . . . . . . . . . . . . . . . 40
1-4 Multiples: LCM and LCD . . . . . . . . 8 2-4 Estimate Square Roots . . . . . . . . 42
1-5 Compare and Order Check Your Progress I (Lessons 1–4)
Rational Numbers. . . . . . . . . . . . . . . . . . 10 2-5 Irrational Numbers. . . . . . . . . . . . 44
Check Your Progress I (Lessons 1–5)
2-6 Square Roots as
1-6 Estimate with Irrational Numbers . . . . . . . . . . . . . . . . . 46
Rational Numbers. . . . . . . . . . . . . . . . . . 12 2-7 The Real Number System. . . . . . 48
1-7 Add Rational Numbers. . . . . . . . . 14 2-8 Properties of Real Numbers . . . . 50
1-8 Subtract Rational Numbers. . . . . 16 Check Your Progress II (Lessons 5–8)
1-9 Multiply Rational Numbers. . . . . . 18 2-9 Pythagorean Theorem. . . . . . . . . 52
1-10 Divide Rational Numbers. . . . . . . 20 2-10 Special Right Triangles . . . . . . . . 54
Check Your Progress II (Lessons 6–10)
Check Your Progress III (Lessons 9–10)
1-11 Properties of 2-11 Technology:
Rational Numbers. . . . . . . . . . . . . . . . . . 22 Evaluate Powers and Roots. . . . . . . . . . 56
1-12 Integral Exponents. . . . . . . . . . . . 24 2-12 Problem-Solving Strategy:
1-13 Powers and Exponents . . . . . . . . 26 Organize Data . . . . . . . . . . . . . . . . . . . . 58
1-14 Order of Operations with Enrichment:
Rational Numbers. . . . . . . . . . . . . . . . . . 28 Pythagorean Triples . . . . . . . . . . . . . . . . 60
Check Your Progress III (Lessons 11–14) Test Prep . . . . . . . . . . . . . . . . . . . . . . . . 61
1-15 Problem-Solving Strategy:
Make a Drawing. . . . . . . . . . . . . . . . . . . 30
Enrichment:
Matrices . . . . . . . . . . . . . . . . . . . . . . . . . 32
Test Prep . . . . . . . . . . . . . . . . . . . . . . . . 34
iv
Chapter Chapter
Expressions and Equations Inequalities
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . 63 Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . 95
3-1 Mathematical Expressions . . . . . 64 4-1 Inequalities . . . . . . . . . . . . . . . . . 96
3-2 Simplify and Evaluate 4-2 Inequalities: Solution Sets. . . . . . 98
Algebraic Expressions . . . . . . . . . . . . . . 66 4-3 One-Step Addition
3-3 Equations . . . . . . . . . . . . . . . . . . 68 Inequalities. . . . . . . . . . . . . . . . . . . . . . 100
3-4 One-Step Addition and 4-4 One-Step Subtraction
Subtraction Equations . . . . . . . . . . . . . . 70 Inequalities. . . . . . . . . . . . . . . . . . . . . . 102
3-5 One-Step Multiplication and Check Your Progress I (Lessons 1–4)
Division Equations . . . . . . . . . . . . . . . . . 72 4-5 One-Step Multiplication
Check Your Progress I (Lessons 1–5) Inequalities. . . . . . . . . . . . . . . . . . . . . . 104
3-6 Model Two-Step Equations. . . . . 74 4-6 One-Step Division
3-7 Two-Step Equations . . . . . . . . . . 76 Inequalities. . . . . . . . . . . . . . . . . . . . . . 106
3-8 Multistep Equations with 4-7 Two-Step Inequalities . . . . . . . . 108
Grouping Symbols . . . . . . . . . . . . . . . . . 78 4-8 Multistep Inequalities with
3-9 Multistep Equations with Grouping Symbols . . . . . . . . . . . . . . . . 110
Variables on Both Sides. . . . . . . . . . . . . 80 Check Your Progress II (Lessons 5–8)
3-10 Multistep Equations: 4-9 Multistep Inequalities with
Fractions and Decimals . . . . . . . . . . . . . 82 Variables on Both Sides. . . . . . . . . . . . 112
Check Your Progress II (Lessons 6–10) 4-10 Multistep Inequalities:
3-11 Equations: Repeating Fractions and Decimals . . . . . . . . . . . . 114
Decimals as Rational Numbers . . . . . . . 84 4-11 Compound Inequalities . . . . . . . 116
3-12 Absolute-Value Equations. . . . . . 86 Check Your Progress III(Lessons 9–11)
3-13 Literal Equations . . . . . . . . . . . . . 88 4-12 Problem Solving:
Check Your Progress III (Lessons 11–13) Review of Strategies . . . . . . . . . . . . . . 118
3-14 Problem-Solving Strategy: Enrichment:
Guess and Test . . . . . . . . . . . . . . . . . . . 90 Geometric Inequalities. . . . . . . . . . . . . 120
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 121
Enrichment:
Writing Numbers in Different Bases. . . . 92
for all exercise sets.
Test Prep . . . . . . . . . . . . . . . . . . . . . . . . 93
for all exercise sets.
v
Chapter Chapter
Polynomials and Factoring Linear Functions and
Inequalities
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 123
5-1 Polynomials. . . . . . . . . . . . . . . . 124 Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 155
5-2 Degree of a Polynomial. . . . . . . 126 6-1 Relations and Functions . . . . . . 156
5-3 Modeling Polynomials. . . . . . . . 128 6-2 Graphs of Functions . . . . . . . . . 158
5-4 Add Polynomials . . . . . . . . . . . . 130 6-3 Scatter Plots . . . . . . . . . . . . . . . 160
5-5 Subtract Polynomials. . . . . . . . . 132 6-4 Slope of a Line . . . . . . . . . . . . . 162
Check Your Progress I(Lessons 1–5) 6-5 The x- and y-Intercepts
5-6 Multiply by Monomials. . . . . . . . 134 of a Line. . . . . . . . . . . . . . . . . . . . . . . . 164
Check Your Progress I (Lessons 1–5)
5-7 Multiply Binomials . . . . . . . . . . . 136
5-8 More Binomials 6-6 Linear Functions: Standard
Special Cases . . . . . . . . . . . . . . . . . . . 138 Form and Slope-Intercept Form. . . . . . 166
5-9 Divide by Monomials. . . . . . . . . 140 6-7 Linear Functions:
Point-Slope Form. . . . . . . . . . . . . . . . . 168
5-10 Factoring Using the GCF. . . . . . 142
6-8 Parallel and Perpendicular
Check Your Progress II (Lessons 6–10) Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . 170
5-11 Factoring Trinomials: 6-9 Direct Variation . . . . . . . . . . . . . 172
x2 + bx+ c . . . . . . . . . . . . . . . . . . . . . . 144
Check Your Progress II (Lessons 6–9)
5-12 Factoring Special Products. . . . 146
6-10 Solve Systems of Equations
5-13 Factoring Trinomials: by Graphing . . . . . . . . . . . . . . . . . . . . . 174
ax2 + bx+ c . . . . . . . . . . . . . . . . . . . . . 148
6-11 Solve Systems of Equations
Check Your Progress III (Lessons 11–13) by Substitution and Elimination . . . . . . 176
5-14 Problem-Solving Strategy: 6-12 Linear Inequalities in
Find a Pattern. . . . . . . . . . . . . . . . . . . . 150 Two Variables . . . . . . . . . . . . . . . . . . . 178
Enrichment: 6-13 Systems of Linear
Rational Expressions. . . . . . . . . . . . . . 152 Inequalities. . . . . . . . . . . . . . . . . . . . . . 180
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 154 Check Your Progress III (Lessons 10–13)
6-14 Problem-Solving Strategy:
for all exercise sets. Reason Logically . . . . . . . . . . . . . . . . . 182
Enrichment:
Algebraic Fallacies. . . . . . . . . . . . . . . . 184
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 185
for all exercise sets.
vi
Chapter Chapter
Ratio and Proportion Percent Applications
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 187 Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 215
7-1 Ratios, Rates, and Unit Rates . . . . . . . 188 8-1 Fractions, Decimals,
7-2 Proportions . . . . . . . . . . . . . . . . 190 and Percents . . . . . . . . . . . . . . . . . . . . 216
7-3 Conversion Factors and 8-2 Estimate Percents . . . . . . . . . . . . . . . . 218
Measurement Systems . . . . . . . . . . . . 192 8-3 Percentage and Applications. . . 220
7-4 Dimensional Analysis . . . . . . . . 194 Check Your Progress I (Lessons 1–3)
Check Your Progress I (Lessons 1–4) 8-4 Rate and Applications. . . . . . . . 222
7-5 Direct Proportions . . . . . . . . . . . 196 8-5 Base and Applications. . . . . . . . 224
7-6 Partitive Proportions . . . . . . . . . 198 Check Your Progress II (Lessons 4–5)
7-7 Inverse Proportions. . . . . . . . . . 200 8-6 Percent of Change . . . . . . . . . . 226
7-8 Scale Drawings and 8-7 Simple and Compound
Scale Models . . . . . . . . . . . . . . . . . . . . 202 Interests. . . . . . . . . . . . . . . . . . . . . . . . 228
Check Your Progress II (Lessons 5–8) Check Your Progress III (Lessons 6–7)
7-9 Similarity . . . . . . . . . . . . . . . . . . 204 8-8 Problem Solving:
7-10 Trigonometric Ratios. . . . . . . . . 206 Review of Strategies . . . . . . . . . . . . . . 230
7-11 Indirect Measurement . . . . . . . . 208 Enrichment:
Fractals . . . . . . . . . . . . . . . . . . . . . . . . 232
Check Your Progress III (Lessons 9–11)
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 234
7-12 Problem-Solving Strategy:
Solve a Simpler Problem . . . . . . . . . . . 210
for all exercise sets.
Enrichment:
The Golden Ratio. . . . . . . . . . . . . . . . . 212
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 214
for all exercise sets.
vii
Chapter Chapter
Two-Dimensional Geometric Measures and
Geometry Coordinate Geometry
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 235 Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 265
9-1 Angle Pairs . . . . . . . . . . . . . . . . 236 10-1 Precision and Significant Digits . . . . . . 266
9-2 Angles of Parallel Lines. . . . . . . 238 10-2 Perimeter and Missing
9-3 Classifying Polygons . . . . . . . . . . . . . . 240 Dimensions . . . . . . . . . . . . . . . . . . . . . 268
9-4 Angles of Polygons. . . . . . . . . . . . . . . . 242 10-3 Area of Polygons. . . . . . . . . . . . 270
Check Your Progress I (Lessons 1–4) 10-4 Circumference and Area
of Circles . . . . . . . . . . . . . . . . . . . . . . . 272
9-5 Congruent Polygons. . . . . . . . . . . . . . . 244
Check Your Progress I (Lessons 1–4)
9-6 Circles . . . . . . . . . . . . . . . . . . . . . . . . . 246
10-5 Area of Complex Figures. . . . . . 274
9-7 Make Circle Graphs . . . . . . . . . . . . . . . 248
10-6 Area and Missing Dimensions. . 276
9-8 Angle Constructions. . . . . . . . . . . . . . . 250
10-7 Coordinate Plane and
9-9 Line Constructions. . . . . . . . . . . . . . . . 252 Polygons. . . . . . . . . . . . . . . . . . . . . . . . 278
Check Your Progress II (Lessons 5–9) 10-8 Coordinate Plane:
9-10 Triangle Constructions . . . . . . . . . . . . . 254 Reflections and Translations. . . . . . . . . 280
9-11 Angles of Elevation and Depression . . 256 Check Your Progress II(Lessons 5–8)
9-12 Tessellations. . . . . . . . . . . . . . . . . . . . . 258 10-9 Coordinate Plane: Rotations . . . 282
Check Your Progress III (Lessons 10–12) 10-10 Coordinate Plane: Dilations. . . . 284
9-13 Problem-Solving Strategy: 10-11 Combine Transformations . . . . . 286
Adopt a Different Point of View. . . . . . . 260 Check Your Progress III (Lessons 9–11)
Enrichment: 10-12 Problem-Solving Strategy:
Optical Illusions . . . . . . . . . . . . . . . . . . 262 Work Backward . . . . . . . . . . . . . . . . . . 288
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 264 Enrichment:
Heron’s Formula. . . . . . . . . . . . . . . . . . 290
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 291
viii
Chapter Chapter
Patterns and Nonlinear Three-Dimensional
Functions Geometry
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 293 Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 317
11-1 Extend and Create Patterns . . . 294 12-1 Polyhedrons and Other
11-2 Arithmetic Patterns Three-Dimensional Figures . . . . . . . . . 318
and Tables. . . . . . . . . . . . . . . . . . . . . . 296 12-2 Draw Views of Three-Dimensional
11-3 Geometric Patterns Figures. . . . . . . . . . . . . . . . . . . . . . . . . 320
and Tables. . . . . . . . . . . . . . . . . . . . . . 298 12-3 Surface Area of Prisms
Check Your Progress I (Lessons 1–3) and Cylinders. . . . . . . . . . . . . . . . . . . . 322
11-4 Relationships and Graphs. . . . . 300 12-4 Surface Area of Pyramids
and Cones . . . . . . . . . . . . . . . . . . . . . . 324
11-5 Find Function Values. . . . . . . . . 302
Check Your Progress I (Lessons 1–4)
11-6 Nonlinear Functions:
Quadratic . . . . . . . . . . . . . . . . . . . . . . . 304 12-5 Volume of Prisms
and Cylinders. . . . . . . . . . . . . . . . . . . . 326
Check Your Progress II (Lessons 4–6)
12-6 Volume of Pyramids
11-7 Other Nonlinear Functions . . . . 306 and Cones . . . . . . . . . . . . . . . . . . . . . . 328
11-8 Inverse Variation. . . . . . . . . . . . 308 12-7 Volume of Spheres . . . . . . . . . . 330
Check Your Progress III (Lessons 7–8) Check Your Progress II (Lessons 5–7)
11-9 Technology: 12-8 Similar Three-Dimensional
Graphs of Nonlinear Functions . . . . . . 310 Figures. . . . . . . . . . . . . . . . . . . . . . . . . 332
11-10 Problem-Solving Strategy: 12-9 Effect of Changing
Account for All Possibilities . . . . . . . . . 312 Dimensions . . . . . . . . . . . . . . . . . . . . . 334
Enrichment: 12-10 Explore Properties of
Fibonacci Sequence and Nature . . . . . 314 Three-Dimensional Figures . . . . . . . . . 336
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 316 Check Your Progress III (Lessons 8–10)
12-11 Problem Solving:
for all exercise sets. Review of Strategies . . . . . . . . . . . . . . 338
Enrichment:
Platonic Solids . . . . . . . . . . . . . . . . . . . 340
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 342
for all exercise sets.
ix