Index
• A •
absolute value equations. See radical and absolute value equations
absolute value inequalities, 90–91
absolute value operation, 8
adding and addition
decimals, 19
distributing multiplication over subtraction and, 15
fractions, 18
like terms, 36
signed numbers, 9
terms in arithmetic sequences, 97
age story problems, 106
Algebra I Essentials For Dummies (Sterling), 3
Algebra I For Dummies (Sterling), 3
Algebra II For Dummies (Sterling), 4
answers to practice problems. See specific topics
applying
Descartes's Rule of Sign, 80
properties to expressions, 16
quadratic formula to quadratic equations, 75–76
Rational Root Theorem to list roots, 80
square root rule to quadratic equations, 74
traditional grouping symbols, 14
arithmetic sequences, adding terms in, 97
arranging terms with associative property, 15
associative property, 15
average of n numbers formula, 96
• B •
binomials. See also factoring binomials
distributing over trinomials, 43
dividing with long division, 49
dividing with synthetic division, 50
factoring trinomials into products of, 62–63
finding special products of, 45
multiplying using distributing, 42
multiplying using FOIL, 43
raising to third power, 44
squaring, 44
boxes, volume of, 102
Business Math For Dummies (Sterling), 4
• C •
calculating. See also solving
distance between points, 119–120
slopes of lines from two points, 114–115
changing
base to perform operations, 26
decimals to fractions, 21
degrees to radians, 102
interval notation to inequality notation, 88–89
radians to degrees, 102
circles, sketching graphs of, 122
combining operations on exponentials, 25
common GCF, 56
commutative property, 16
completing the square, 76
complex inequalities, 91
compound inequalities, 89
compound interest formula, 98
coordinate system, plotting points on, 112
cylinders, volume of, 102
• D •
decimals. See fractions and decimals
degrees, changing to/from radians, 102
denominators, rationalizing, 30–31
difference of perfect squares, 58
difference of two perfect cubes, 58–59
distance formula, 95
distributing
binomials over trinomials, 43
multiplication over addition and subtraction, 15
multiplying binomials using, 42
one term over sums and differences, 42
using division, 42
dividing and division
about, 47
answers to practice problems, 210–233
binomials using synthetic division, 50
binomials with long division, 49
decimals, 20
exponentials with same base, 24
factors, 36
with higher power divisors, 50–51
• E •
equation of a line, 118. See also lines
equations. See specific types
estimating values of radicals, 33–34
evaluating expressions, 32, 38
exponential expressions. See expressions, exponential
expressions, algebraic
about, 35
adding like terms, 36
answers to practice problems, 184–198
dividing factors, 36
factorials, 39
function notation, 39
multiplying factors, 36
subtracting like terms, 36
expressions, applying properties to, 16
expressions, exponential
about, 23
answers to practice problems, 158–169
changing base to perform operations, 26
combining operations on, 25
dividing exponentials with same base, 24
multiplying exponentials with same base, 24
raising powers to a power, 24–25
• F •
factorials, 39
factoring
answers to practice problems, 233–242, 258–265
combining techniques with grouping, 66
finding divisors using rules of divisibility, 54
by grouping, 66
out a GCF, 55
practice problems, 54–56, 66–67
reducing fractions with a common GCF, 56
solving quadratic equations using, 74–75
writing prime factorizations, 54
factoring binomials
about, 57
answers to practice problems, 242–251
difference of perfect squares, 58
sum or difference of two perfect cubes, 58–59
factoring quadratic trinomials
about, 61
answers to practice problems, 251–258
factoring out GCF of trinomials, 62
quadratic-like expressions, 63
trinomials into products of binomials, 62–63
using more than one technique, 63–64
figures, transforming graphs of, 123–124
FOIL, multiplying binomials using, 43
formulas
adding terms in arithmetic sequences, 97
answers to practice problems, 344–356, 356–368
area and perimeter of rectangles, 100, 101
area and perimeter of squares, 100
area and perimeter of triangles, 101–102, 103
area of hexagons, 101
area of trapezoids, 100
average of n numbers, 96
changing radians to degrees and degrees to radians, 102
compound interest, 98
distance, 95
finding terms of a sequence, 97
height of objects, 103
practice problems, 94–98, 100–103
simple interest, 94
sum of cubes, 97
summing squares of numbers, 96
sums of anterior angles, 96
temperature, 94
volume of boxes, 102
volume of cylinders, 102
fractions and decimals
about, 17
adding decimals, 19
adding fractions, 18
answers to practice problems, 142–158
changing decimals to fractions, 21
changing fractions to decimals, 20–21
dividing decimals, 20
fractions in linear equations, 71–72
multiplying fractions, 18
reducing fractions with a common GCF, 56
simplifying complex fractions, 19
subtracting decimals, 19
subtracting fractions, 18
function notation, 39
• G •
graphing
answers to practice problems, 386–396, 407–424
calculating slopes of lines, 114–115
determining quadrants of points, 113
finding intercepts of lines, 114, 122
plotting points on coordinate system, 112
sketching graphs of circles, 122
sketching graphs of lines from their equations, 115
sketching lines using two points, 116
sketching parabolas, 123
transforming of figures, 123–124
grouping, factoring by, 66
grouping symbols, 14
• H •
height of objects formula, 103
Heron's Formula, 103
hexagons, area of, 101
• I •
inequalities
about, 87
answers to practice problems, 323–344
changing interval notation to inequality notation, 88–89
complex, 91
compound, 89
finding solutions of nonlinear inequalities, 90
performing operations on, 88
rewriting and solving absolute value inequalities, 90–91
solving linear inequalities, 89
solving quadratic inequalities, 89–90
writing using interval notation, 88
interest formula, 94
• L •
like terms, adding and subtracting, 36
line slope, determining, 114–115
linear equations
about, 69
answers to practice problems, 265–277
solving using basic operations, 70–71
linear inequalities, solving, 89
lines
about, 117
answers to practice problems, 396–406
computing distance between points, 119–120
determining midpoint, 120
finding equations of, 119
slopes of parallel and perpendicular, 119
writing equations of, 118
long division, dividing binomials with, 49
• M •
Math Word Problems For Dummies (Sterling), 4
midpoint, determining, 120
money story problems, 109
multiplying and multiplication
about, 41
answers to practice problems, 198–209
binomials using distributing, 42
binomials using FOIL, 43
distributing binomials over trinomials, 43
distributing one term over sums and differences, 42
distributing over addition and subtraction, 15
distributing using division, 42
exponentials with same base, 24
factors, 36
finding special products of binomials and trinomials, 45
fractions, 18
multiplying binomials using distributing, 42
multiplying binomials using FOIL, 43
raising binomials to third power, 44
squaring binomials, 44
• N •
natural numbers, adding, 94–95
nonlinear inequalities, finding solutions of, 90
nontraditional grouping symbols, 14
notation. See properties and notation, algebraic
number line, placing real numbers on, 8
numbers, as roots, 80
• O •
objects, height of, 103
1001 Algebra II Practice Problems For Dummies (Sterling), 4
operating
with factorials, 39
on factors with fractional exponents, 33
operations
changing base to perform, 26
combining on exponentials, 25
performing on inequalities, 88
solving linear equations using basic, 70–71
• P •
parabolas, creating graphs of, 123
plotting points on coordinate system, 112
polynomials
about, 79
answers to practice problems, 294–304
applying Descartes's Rule of Sign, 80
applying Rational Root Theorem, 80
determining whether numbers are roots, 80
powers, raising to a power, 24–25, 44
practice problems. See specific topics
prime factorizations, 54
properties and notation, algebraic
about, 13
answers to practice problems, 135–142
applying properties to expressions, 16
applying traditional grouping symbols, 14
associative property, 15
commutative property, 16
distributing multiplication over addition and subtraction, 15
nontraditional grouping symbols, 14
• Q •
quadrants, determining, 113
quadratic equations
about, 73
answers to practice problems, 278–293
applying quadratic formula to, 75–76
applying square root rule, 74
completing the square to solve, 76
finding complex solutions using quadratic formula, 77
solving using factoring, 74–75
writing complex numbers in standard a + bi form, 76–77
quadratic inequalities, solving, 89–90
quadratic trinomials. See factoring quadratic trinomials
quadratic-like expressions, factoring, 63
quality and quantity story problems, 108
• R •
radians, changing to/from degrees, 102
radical and absolute value equations
about, 83
answers to practice problems, 304–323
checking for extraneous roots, 84
handling absolute value equations with no solution, 86
solving absolute value equations, 85
solving basic radical equations, 84
solving radicals with roots, 85
squaring both sides of equations twice, 84–85
radicals
about, 29
answers to practice problems, 169–184
fractional exponents for, 31–32
operating on factors with fractional exponents, 33
rationalizing denominators, 30–31
simplifying radical expressions, 30
raising
binomials to third power, 44
Rational Root Theorem, 80
rationalizing denominators, 30–31
real numbers, placing on number line, 8
real roots, counting, 80
rectangles, area and perimeter of, 100, 101
reducing fractions with a common GCF, 56
roots
checking for extraneous, 84
numbers as, 80
solving for roots of polynomials, 81–82
solving radicals with, 85
Rule of Sign (Descartes), 80
rules of divisibility, 54
• S •
signed numbers
about, 7
absolute value operation, 8
adding, 9
answers to practice problems, 127–135
placing real numbers on number line, 8
simple interest formula, 94
simplifying
complex fractions, 19
expressions using order of operations, 37–38
radical expressions, 30
sketching
graphs of circles, 122
graphs of lines from its equation, 115
graphs of parabolas, 123
lines using two points, 116
slope-intercept form, 117
slopes of lines
calculating from two points, 114–115
parallel and perpendicular lines, 119
solving
absolute value equations, 85
absolute value inequalities, 90–91
basic radical equations, 84
linear inequalities, 89
quadratic equations using factoring, 74–75
radicals with roots, 85
for roots of polynomials, 81–82
square root rule, applying to quadratic equations, 74
squares, area and perimeter of, 100
squaring
binomials, 44
both sides of equations twice, 84–85
standard form, 117
Sterling, Mary Jane (author)
Algebra I Essentials For Dummies, 3
Algebra I For Dummies, 3
Algebra II For Dummies, 4
Business Math For Dummies, 4
Math Word Problems For Dummies, 4
1001 Algebra II Practice Problems For Dummies, 4
story problems
about, 105
age problems, 106
answers to practice problems, 368–386
formulas in. See formulas
money problems, 109
quality and quantity problems, 108
subtracting and subtraction
decimals, 19
distributing multiplication over addition and, 15
fractions, 18
like terms, 36
sum of first n cubes formula, 97
sum of n squares formula, 96
sums of interior angles, 96
synthetic division, dividing with binomials using, 50
• T •
temperature formulas, 94
terms of a sequence, 97
third power, raising binomials to, 44
traditional grouping symbols, 14
trapezoids, area of, 100
triangles, area and perimeter of, 101–103
trinomials
distributing binomials over, 43
factoring into products of binomials, 62–63
finding special products of, 45
trinomials, quadratic. See factoring quadratic trinomials
• V •
volume of boxes formula, 102
volume of cylinders formula, 102
• W •
writing
complex numbers in standard a + bi form, 76–77
inequalities using interval notation, 88
prime factorizations, 54