Absolute value, 32–33
definition of, 32
evaluating, 33
Addition
associative property of, 61
commutative property of, 60
of complex numbers, 576
of fractions, 6
with grouping symbols, 40–41
identity element for, 62
identity property of, 62
inverse for, 63
of like terms, 320
of multivariable polynomials, 324
of negative numbers, 37
on a number line, 37
in order of operations, 16
of polynomials, 322
properties of, 60–61
of radicals, 513
of rational expressions, 440–442
of real numbers, 37, 59
of signed numbers, 38, 59
summary of properties of, 66
word phrases for, 41
Addition property
of equality, 87
of inequality, 153
Additive identity element, 62
Additive inverse, 31–32, 40, 63
definition of, 32
Algebraic expressions, 22
distinguishing from equations, 25
evaluating, 22–23, 54
from word phrases, 23–24, 72, 104
simplifying, 69–70
Angles
complementary, 113
measure of, 114, 122–123
right, 113
straight, 113, 122
supplementary, 113
vertical, 122
Approximately equal to, 497
symbol for, 497
Area of geometric figures, 120, 302,
339–340, 559
Associative properties, 61
distinguishing from commutative, 61–62
Average, 58
Axes of a coordinate system, 180
Axis
of a parabola, 325, 580
of symmetry, 580
Base
comparing percentage to, 134
of an exponential expression, 15, 296
Basic principle of fractions, 3
Bhaskara, 503
Binomials, 321
greater powers of, 337
multiplication by FOIL method, 331
squares of, 335
steps to multiply by FOIL method, 331
Boundary line, 224
Braces, 597
Brackets, 16–17
Break-even quantity, 278Cartesian coordinate system, 180
plotting points on, 181
Celsius-Fahrenheit relationship, 124
Circle
area of, 559
circumference of, 126
graph, 9
Classifying polynomials, 321
Coefficient, 70, 320
Combining like terms, 71, 320
Common denominator, 6
Common factor, 360
Commutative properties, 60
distinguishing from associative,
61–62
Complement of a set, 599
symbol for, 599
Complementary angles, 113
Completing the square method for solving
quadratic equations, 561
steps to solve by completing the
square, 562
Complex fractions, 448
steps to simplify, 448, 450
Complex numbers, 574–575
chart of, 575
conjugate of, 577
imaginary part of, 575
operations on, 576–577
real part of, 575
standard form of, 575
Components of an ordered pair, 229
Composite number, 3
Compound interest, 303
Concours d’elegance, 447
Conditional equation, 102–103
Conjugates
of complex numbers, 577multiplication of, 525, 577
of radicals, 525
Consecutive integers, 112, 401
even, 113, 401
odd, 113, 401
Consistent system, 251
Constant of variation, 476
Contradiction, 103
Coordinate system, 180
Cartesian, 180
origin of, 180
quadrants of, 180
rectangular, 180
Coordinates of a point, 29, 180
Cost, unit, 130
Cross multiplication, 131
Cross products, 131–132
Cube(s)
difference of, 385
of a number, 15
perfect, 499, 520
sum of, 386
volume of, 512
Cube root, 499
rationalizing deonominators with, 520
symbol for, 499Data, interpreting, 33
Data set, 216
Decimal approximation of an irrational
number, 496
Decimal numbers
converting to percents, 134
linear equations with, 102
operations on, 134
solving linear systems with, 261
Decimal numeration system, 347
Degree, 113
of a polynomial, 321
of a term, 321
Denominator(s), 2, 421
common, 6
with cube roots, 520
least common, 6, 435
rationalizing, 517
using conjugates to rationalize, 525–526
Dependent equations, 251
elimination method for solving, 268
substitution method for solving, 260
Depreciation, 197
Descartes, René, 180
Descending powers, 321
Difference, 7, 39, 42
of cubes, 384
of squares, 381D
C
A B
Index