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

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