Absolute value, 9–10

• equations involving, 158–161

• inequalities involving, 160–163

Absolute value function, 255, 257

Acid(s), 490

Acid rain, 489–490

Adams, Evelyn Marie, 778

Addition. See also Sum(s)

• of complex numbers, 121

• of fractions, 14

• of matrices, 607–608, 609

• of polynomials, 32

• of radical expressions, 65–66

• of rational expressions, 53–56

Addition method, for solving systems of linear equations, 519–520

Additive Rule, probability and, 781–782

Air search, 158, 161–162

Algebra

• Fundamental Theorem of Algebra and, 377

• medieval, 514

• origin of word, 514

Algebraic expressions, 14–16

• defined, 14

• value of, 14–15

Algebraic numbers, 436

Algorithms

• Division Algorithm, 352–354

• origin of word, 514

Al-Khwarizmi, Muhammad ibn Musa, 514

Alternating current, 119, 125

American Journal of Mathematics, 607

Annual compounding, 432

Annuities, 744–745

Apollonius of Perga, 659

Apparent brightness, 497

Applied problems. See also Modeling

• composite functions and, 288–290

• with ellipses, 684–685

• with exponential equations, 478–479

• with geometric sequences, 744–745

• with hyperbolas, 701–702

• inverse functions and, 301–302

• with linear programming, 574–575

• with matrix inverses, 628–629

• with polynomial functions, 359–360

• procedure for solving, 92–93

• with quadratic equations, 113–114

• with quadratic functions, 324–326

• with systems of linear equations, 521–522, 534–535

• with systems of nonlinear equations, 554–555

• tracking moving objects, 324–325

Area

• maximum, finding, 325

• of a rectangle, 220

• of a transformed polygon, 643–644

Arithmetic expressions

• evaluating, 11–12

• order of operations for, 11–12

Arithmeticorum Libri Duo (Maurolico), 754

Arithmetic progressions. See Arithmetic sequences

Arithmetic sequences, 729–734

• common difference of, 729–730, 732

• defined, 729

• finite, sum of, 732–735

• graphing, 731–732

• recursive definition of, 730

Ars Magna (Cardano), 376

Associative property of real numbers, 12

Astronomia Nova (Kepler), 332

Asymptotes

• of a hyperbola, 694–696

• oblique, of rational functions, 395–396

• vertical and horizontal, of a rational function, 386–388, 389, 391–392

Augmented matrices, 590–592

Average rate of change, of a function, 241–244

Axes

• of an ellipse, 676, 678

• coordinate, 175

• of a hyperbola, 691, 692

• of a parabola, 319, 662

• of symmetry, 188, 319, 662