Index
ALPHABETICAL LIST OF CONCEPTS WITH
PROBLEM NUMBERS
This comprehensive index organizes the concepts and skills discussed within the book alphabetically. Each
entry is accompanied by one or more problem numbers, in which the topics are most prominently featured.
A–B
abscissa: 15.1–15.4
absolute value
functions: 15.4–15.5, 16.3–16.4, 16.12–16.14,
16.28, 16.40–16.44
linear equations: 4.29–4.26, 5.40–5.44, 7.35
(of) signed numbers: 1.17–1.21, 1.27–1.30
additive identity: 1.36, 1.40, 10.3
age word problems: 23.6–23.8
area: 23.17–23.20
associative property: 1.32, 1.35, 1.43
asymptotes
horizontal: 20.35, 20.37, 20.40, 20.42
(of) hyperbolas: 22.36, 22.38–22.39, 22.42
oblique: 20.43
vertical: 20.35–20.36, 20.39, 20.42
augmented matrices: 10.1–10.2, 10.19, 10.23,
10.25–10.26, 10.32, 10.34, 10.36, 10.38, 10.40
axioms of algebra: see properties of algebra
axis of symmetry: 22.2, 22.6
base (of a triangle): 23.19
All of these numbers refer to problems, not pages, in the book. For example, 8.2 is the
second problem in Chapter 8.
C
carbon dating: 19.40–19.43
center
(of a) circle: 22.12, 22.15, 22.17, 22.20
(of an) ellipse: 22.22–22.24, 22.26, 22.29
(of a) hyperbola: 22.33, 22.38, 22.40, 22.42–
22.43
change of base formula: 18.25–18.33
circle: 22.12–22.21, 23.16, 23.18
circumference: 23.16
cofactor: 9.32–9.33
cofactor expansion: 9.34–9.37
coin word problems: 23.34–23.36
combination word problems: 23.30–23.33
common logarithms: 18.17–18.20
commutative property: 1.34–1.35
completing the square: 14.12–14.19, 14.27, 22.1,
22.4, 22.7, 22.10, 22.14–22.15, 22.17, 22.25,
22.28, 22.37, 22.41
complex fractions: 2.41–2.43, 20.30–20.34, 22.31
complex numbers: 1.7–1.10, 13.37–13.44, 14.19,
14.26, 14.31
composite numbers: 1.4
Index — Alphabetical List of Concepts with Problem Numbers
The Humongous Book of Algebra Problems
556
composition of functions: 15.18–15.27, 15.32,
15.34, 19.10–19.11
compound interest: 23.11–23.13, 23.15
conic sections
circle: 22.12–22.21
ellipse: 22.22–22.32
hyperbola: 22.33–22.43
parabola: 22.1–22.11
conjugate (of a complex number): 13.42, 13.44
conjugate axis: 22.34–22.35, 22.38, 22.42
consecutive integer word problems: 23.1–23.5
constant: 11.6, 11.8
constant of proportionality: 21.21–21.25
constant of variation: 21.21–21.30
continuously compounding interest: 23.14–23.15
coordinate plane: 5.1, 5.4–5.6
counting numbers: see natural numbers
Cramer’s Rule: 9.38, 9.40–9.44
critical numbers: 14.35, 14.38, 14.40, 14.42, 21.31,
21.34, 21.38, 21.42
cross multiplication: 21.1–21.8, 21.10–21.11, 23.26
cylinder: 23.21
D
diameter: 22.21
decimals
converting to/from fractions: 2.3, 2.5, 2.18–2.21,
4.26–4.28
converting to/from percentages: 2.1–2.2
Descartes’ rule of signs: 17.21–17.27, 17.35, 17.38,
17.41–17.42
determinant
(
of a) 2 × 2 matrix: 9.26–9.28
(of a) 3 × 3 matrix: 9.29–9.30, 9.34–9.36
(of a) 4 × 4 matrix: 9.37
diameter: 23.18
difference of perfect cubes: 12.31, 12.33–12.34,
20.6
difference of perfect squares: 12.26–12.30, 12.34,
14.5, 17.39, 20.4, 20.6, 20.13, 20.17, 20.22,
20.26–20.27, 20.33
direct variation: 21.21–21.25
directrix: 22.9–22.11
discriminant: 3.43, 14.29–14.34
distance formula: 22.18, 22.21
distance word problems: 23.23–23.29
distributive property: 1.38–1.39, 3.23–3.29
domain: 16.10, 16.13, 16.15–16.20, 16.26–16.30,
18.13, 19.3
double root: 14.9, 14.33–14.34, 14.38
E
eccentricity: 22.30
elements (of a matrix): 9.2–9.3, 9.5–9.6
elimination technique: 8.19–8.28, 23.6, 23.8
ellipse: 22.22–22.32
end behavior: see leading coefficient test
equations
absolute value: 5.40–5.44
exponential: 13.20, 19.19–19.24, 19.37, 19.39–
19.41, 23.13
linear: 5.7–5.9, 5.11, 5.13–5.14, 5.21, 5.23,
5.25, 5.39, 6.21–6.22, 6.24, 6.26, 6.32,
6.38, 6.41, 6.43, 8.1–8.7
logarithmic: 18.2–18.10, 18.19, 18.31–18.33,
19.25–19.35
matrix: 10.37, 10.39–10.41
quadratic: 14.1–14.42
radical: 13.32–13.36, 14.28
rational: 4.13–4.14, 4.19, 4.23, 21.2–21.20,
23.37–23.43
systems of: 8.1–8.28, 9.39–9.44, 10.19–10.24,
10.26, 10.33, 23.5–23.6, 23.8
Euler’s number: 18.21
even functions: 16.25
even numbers: 1.3
expressions
evaluating: 3.40–3.44
writing: 3.1–3.7
exponential growth and decay: 19.36–19.43,
23.14–23.15
exponentiation: 19.25–19.29, 19.31–19.33, 19.35
exponents
basic: 3.8–3.18, 3.35
equations involving: 13.20, 19.19–19.24, 19.37,
19.39–19.41, 23.13
expressions involving: 19.13, 19.18
Index — Alphabetical List of Concepts with Problem Numbers
The Humongous Book of Algebra Problems
557
F
factoring
(by) decomposition: 12.42–12.44, 14.8–14.9,
14.42, 17.10, 17.32
difference of perfect cubes: 12.31, 12.33–12.34,
20.6
difference of perfect squares: 12.26–12.30, 12.34,
14.5, 17.39, 20.4, 20.6, 20.13, 20.17, 20.22,
20.26–20.27, 20.33
(by) grouping: 12.20–12.25, 14.11
integers: 2.30, 2.32, 12.1–12.8, 12.10, 12.15
polynomials: 12.14, 12.16–12.44, 17.7–17.8,
17.10, 17.12, 17.30, 17.32, 17.34, 17.39
sum of perfect cubes: 12.31–12.32, 12.34, 20.26
trinomials 12.35–12.44, 14.6–14.9, 14.35, 14.38
focus
(of an) ellipse: 22.29
(of a) hyperbola: 22.40, 22.43
(of a) parabola: 22.8, 22.10
FOIL method: 11.19–11.25
fractions
adding and subtracting: 2.25, 2.27–2.29, 2.31–
2.32
complex: 2.41–2.43
expressed as decimals: 2.3, 2.5, 2.18–2.21
expressed as percentages: 2.4, 2.6
improper: 2.8–2.10
multiplying and dividing: 2.33–2.43
reducing to lowest terms: 2.11, 2.13, 2.15–2.18
functions
absolute value functions: 16.3–16.4, 16.12–
16.14, 16.28, 16.40–16.44
composition: 15.18–15.27, 15.32, 15.34, 19.10–
19.11
domain of: 16.10, 16.13, 16.15–16.20, 16.26–
16.30
evaluating: 15.1, 15.3, 15.5, 15.7, 15.10–15.12,
15.14–15.18, 15.21–15.23, 15.26, 15.40,
15.42, 17.3–17.6
even: 16.25
identifying: 15.1–15.8, 15.43
inverse: 15.27–15.37, 19.4, 19.10–19.11
logarithmic: 18.11–18.12, 18.14–18.16
odd: 16.24
operations on: 15.9–15.17
piecewise-defined: 15.38–15.43
range of: 16.11, 16.14, 16.20, 16.26–16.30
rational functions: 16.7–16.8, 16.15, 16.17,
16.30, 16.33–16.34
square root functions: 16.9–16.11, 16.16, 16.29,
16.35, 16.37, 16.39
symmetry: 16.21–16.30
Fundamental Theorem of Algebra: 17.1, 17.37
Fundamental Theorem of Arithmetic: 12.1
G
Gauss-Jordan elimination: see reduced-row
echelon form
Gaussian elimination: see row echelon form
geometric word problems: 23.16–23.22
graphing
absolute value functions: 16.3–16.4, 16.12–
16.14, 16.28, 16.40–16.44
circles: 22.12, 22.16
ellipses: 22.23, 22.26
exponential functions: 19.1–19.2, 19.4–19.9
hyperbolas: 22.38, 22.42
linear absolute value equations: 5.40–5.44
linear equations: 5.7–5.9, 5.11, 5.13–5.14, 5.21,
5.23, 5.25, 5.39, 6.21–6.22, 6.24, 6.26, 6.32,
6.38, 6.41, 6.43, 8.1–8.7
linear inequalities: 7.5–7.43, 8.29–8.36, 8.40
logarithms: 18.11–18.12, 18.14–18.16
parabolas: 16.1–16.2, 16.26, 16.31, 16.38,
17.16, 17.40, 22.3, 22.6
quadratic functions: 16.1–16.2, 16.26, 16.31,
16.38
quadratic inequalities: 14.37, 14.39, 14.41, 14.43
rational functions: 16.7–16.8, 16.15, 16.17,
16.30, 16.33–16.34, 20.38, 20.41, 20.44
rational inequalities: 21.33, 21.36, 21.40, 21.44
square roots: 16.9–16.11, 16.16, 16.29, 16.35,
16.37, 16.39
(using a) table of values: 16.1–16.9, 16.12,
16.26–16.30, 18.11–18.12, 18.15, 20.41,
20.44
(using) transformations: 16.31–16.40, 17.15–
17.16, 17.20, 17.40, 18.14, 18.16, 19.5, 19.9,
20.38
Index — Alphabetical List of Concepts with Problem Numbers
The Humongous Book of Algebra Problems
558
greatest common factor: 2.12, 2.14, 2.16–2.17,
12.9, 12.11–12.16, 12.29–12.30, 12.33
grouping symbols: 1.22–1.31
H
half-life: 19.40–19.43
horizontal asymptotes: 20.35, 20.37, 20.40, 20.42
horizontal line test: 15.29–15.30, 15.35
hyperbola: 22.33–22.43
I–J–K
i: see complex numbers
identity matrix: 10.4–10.7, 10.34–10.38, 10.40–
10.41
identity properties: 1.36
improper fractions: 2.8–2.10, 2.19
index (of a radical): 13.3–13.4
indirect variation: see inverse variation
inequalities
compound: 7.21–7.30, 7.36
containing absolute values: 7.27–7.34, 7.36–7.39
graphing in the coordinate plane: 7.40–7.43
graphing on a number line: 7.13–7.17, 7.22,
7.24, 7.26, 7.28–7.30, 7.32–7.34
linear, in one variable: 7.5–7.12, 7.17–7.20,
7.23, 7.25
linear, in two variables: 7.40–7.43
rational: 21.31–21.44
inequality symbols: 7.1–7.4
integer word problems: 23.1–23.5
integers: 1.2, 1.8–1.9
intercepts: 5.18–5.25, 5.37, 6.9, 6.17, 6.44, 18.13,
19.3
interest
compound: 23.11–23.13, 23.15
continuously compounding: 23.14–23.15
simple: 23.9–23.11
inverse functions: 15.27–15.37, 19.4, 19.10–19.11
inverse matrix: 10.34–10.41
inverse properties: 1.40–1.41
inverse variation: 21.26–21.30
irrational numbers: 1.6, 1.8
L
leading coefficient: 11.6, 11.8, 20.36
leading coefficient test: 17.14–17.20, 17.40
least common denominator: 2.22–2.24, 2.26,
2.28–2.30, 3.6, 20.9–20.18, 21.9, 21.12–21.20,
21.31, 21.41
like radicals: 13.21–13.24, 15.15
like terms: 3.6, 11.9
linear equations
graphing: 5.7–5.9, 5.11, 5.13–5.14, 5.21, 5.23,
5.25, 5.39, 6.21–6.22, 6.24, 6.26, 6.32,
6.38, 6.41, 6.43
in one variable: 4.1–4.28, 4.37–4.43
point-slope form of: 6.1–6.10, 6.20, 6.37, 6.43
slope of: 5.26–5.39, 6.28, 6.30–6.31, 6.37, 6.40,
6.43–6.44
slope-intercept form of: 6.11–6.20, 6.21–6.26,
6.32, 6.38, 6.41, 6.32, 22.36, 22.39
standard form of: 5.37–5.38, 6.29–6.36, 6.39,
6.42, 6.44
linear programming: 8.36–8.43
logarithms
change of base formula: 18.25–18.33
common logarithms: 18.17–18.20
equations: 18.1–18.10, 18.19, 18.31–18.33,
19.25–19.35
expressions: 19.12, 19.14–19.18
graphing: 18.11–18.12, 18.14–18.16
natural logarithms: 18.21–18.24
properties: 18.34–18.44, 19.14, 19.16–19.18,
19.28, 19.31–19.32, 19.35
long division: 11.29–11.36
M–N
major axis: 22.22–22.24, 22.26, 22.29, 22.31–
22.32
matrices
adding and subtracting: 9.7–9.15, 10.3
augmented: 10.1–10.2, 10.19, 10.23, 10.25–
10.26, 10.32, 10.34, 10.36, 10.38, 10.40
cofactors: 9.32–9.33
determinants: 9.26–9.30, 9.34–9.37
elements: 9.2–9.3, 9.5–9.6
Index — Alphabetical List of Concepts with Problem Numbers
The Humongous Book of Algebra Problems
559
equations: 10.37, 10.39–10.41
identity: 10.4–10.7, 10.34–10.38, 10.40–10.41
inverse: 10.34–10.41
minors: 9.31–9.33
multiplying: 9.16–9.25, 10.4, 10.7, 10.35, 10.37,
10.41
order: 9.1, 9.4
reduced-row echelon form: 10.18–10.34, 10.36,
10.38, 10.40
row echelon form: 10.18–10.21, 10.23, 10.25–
10.29, 10.32
row operations: 10.8–10.17
scalar multiplication: 9.10–9.15
midpoint formula: 22.20, 22.33
minor (of a matrix): 9.31–9.33
minor axis: 22.23–22.24, 22.26
mixed numbers: 2.7–2.10
mixture word problems: 23.30–23.33
multiplicative identity: 1.36, 1.41, 10.4, 10.6
natural logarithms: 18.21–18.24
natural numbers: 1.1–1.2, 1.8–1.9
number line: 5.1–5.3
O
oblique asymptotes: 20.43
odd functions: 16.24
odd numbers: 1.3, 1.9, 23.3
optimizing expressions: 8.36–8.43
order (of a matrix): 9.1, 9.4
order of operations: 1.22–1.30, 1.39, 3.30–3.39
ordinate: 15.1–15.4
P
parabolas: 16.1–16.2, 16.26, 16.31, 16.38, 17.16,
17.20, 17.40, 22.1–22.11
parallel lines: 5.33–5.34, 6.37, 8.7
percentages: 2.2, 2.4, 2.6
perimeter: 23.17, 23.20
perpendicular lines: 5.35–5.36, 6.40
pi (p): 1.6
piecewise-defined functions: 15.38–15.43
point-slope form of a line: 6.1–6.10, 6.20, 6.37,
6.43
polynomials
adding and subtracting: 11.9–11.18
classifying: 11.1–11.8
leading coefficient of: 11.6, 11.8
long division of: 11.29–11.36
multiplying: 11.19–11.28, 11.31
synthetic division of: 11.37–11.45
population modeling: 19.36–19.39
prime factorization: 2.30, 2.32, 12.1–12.8, 12.10,
12.15, 20.3, 20.5, 20.11
prime numbers: 1.4, 1.9, 12.1
principal: 23.9–23.15
prism: 23.22
p
roperties of algebra: 1.31–1.44
proportional variation: see direct variation
proportions: 21.1–21.11
Q
quadratic equations:
(solving by) completing the square: 14.14–14.19,
14.27
(solving by) factoring: 14.1–14.3, 14.5–14.9,
14.11, 14.35, 14.38, 14.42
(solving using the) quadratic formula: 14.20–
14.28, 14.30–14.34, 14.40, 23.5, 23.22
(solving using) radicals: 14.4, 14.10
quadratic formula: 14.20–14.28, 14.30–14.34,
14.40, 17.13, 17.37, 21.7, 21.17, 21.20, 23.5, 23.22
quadratic inequalities
graphing: 14.37, 14.39, 14.41, 14.43
solving: 14.35–14.36, 14.38, 14.40, 14.42
R
radical equations: 13.32–13.36, 14.28
radical expressions
adding/subtracting: 13.21–13.24, 15.15
classifying: 13.1, 13.3
dividing: 13.29–13.31
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