Index

A

Abel, Neils Henrik

Absolute value:

definition of

as distance on the number line

equations

function

inequalities

properties of

Addition of matrices

Addition rule of probabilities

Additive identity:

for complex numbers

for m X n matrices

for real numbers

Additive inverse:

for complex numbers

for m X n matrices

for real numbers

Adjoint matrix

Age problems

Algebra, Fundamental Theorem of

Algebraic expression

Aphelion

Approximating zeros using Bisection Method

Archimedes' principle

Arithmetic sequence

Arithmetic series:

definition of

sum of

Associative law:

of addition

of multiplication

Asymptote(s):

of an exponential function

definition of

horizontal

of a hyperbola

of a logarithmic function

of a rational function

slant

vertical

Augmented matrix

Auxiliary rectangle of a hyperbola

Axis (axes):

conjugate axis of a hyperbola

major axis of an ellipse

minor axis of an ellipse

of a parabola

of a rectangular coordinate system

of symmetry

tangent to

transverse axis of a hyperbola

x-axis

y-axis

B

Back substitution

Balancing a chemical equation

Base:

change of base formula

e

of an exponential function

of a logarithmic function

ten

Beer-Lambert-Bouguer law

Binomial

Binomial coefficients

Binomial theorem:

proof of

statement of

Bisection method for approximating zeros

Branch of a tree diagram

Branches of a hyperbola

Briggs, Henry

C

Carbon dating

Carrying capacity

Cartesian coordinate system:

axes of

coordinates of a point in

definition of

origin in

quadrants

Catenary

Cayley, Arthur

Ceiling function

Center:

of a circle

of an ellipse

of a hyperbola

Certain event

Change in x

Change in y

Change of base formula for a logarithm

Chord, focal, of a parabola

Circle:

center of

definition of

equation of

radius of

Closed interval

Codes

Coefficient(s):

binomial

leading, of a polynomial

matrix

Cofactor

Combination

Combined variation

Combining:

fractions

functions

Common difference

Common logarithm

Common ratio

Commutative law:

of addition

of matrices

of multiplication

Complete factorization of a polynomial

Completing the square

Complement of an event

Complex number(s):

additive identity for

additive inverse of

conjugate of

definition of

difference of

division of

equality of

imaginary part of

multiplicative identity for

multiplicative inverse of

product of

properties of

pure imaginary

real part of

standard form of

subtraction of

sum of

Complex zero of function

Composition of functions:

definition of

domain of

Compound interest

Conditional equation

Conic sections:

definitions of

eccentricity

in rectangular coordinates

Conjugate axis of a hyperbola

Conjugate of a complex number

Conjugate solutions of a quadratic equation

Conjugate zeros theorem

Consistent system of equations

Constant function

Constant of proportionality

Constraint

Continuous compounding of interest

Continuous function

Convergent infinite series

Convergent sequence

Convex set in the plane:

definition of

vertex of

Coordinate(s):

of a point in the Cartesian coordinate system

of a point on the real number line

x-coordinate

y-coordinate

Coordinate plane

Coordinate system:

Cartesian

rectangular

Correspondence, rule of

Cosine(s), hyperbolic

Counting, principles of

Cramer, Gabriel

Cramer's rule

Cryptography

Cube of a binomial

Cube root

Cubic function

Curie, Pierre and Marie

Curve, Gompertz

D

Dantzig, George B.

Dead Sea scrolls

Decay:

carbon dating

constant

effective

half-life

radioactive

Decimal form of a real number

Decimals:

nonrepeating

repeating

terminating

Decoding matrix

Decreasing function

Degree(s), of a polynomial

Denominator:

of a fraction

least common

rationalization of

Dependent equations in a linear system

Dependent variable

Descartes, Rene

Determinant(s):

definition of

expansion by cofactors of first row

expansion theorem for

minor

of order n

properties of

solving systems of equations by

of a square matrix

Diagonal, main, of a matrix

Difference:

common

of complex numbers

of functions

of matrices

of two cubes

of two squares

Difference quotient

Difference trigonometric formulas:

for cosine

for sine

for tangent

Difference of two cubes

Difference of two squares

Dimension of a matrix

Diophantus

Direct proportion

Direct variation

Directrix of a parabola

Discontinuous function

Discriminant

Disjoint sets

Distance:

between points on the number line

formula

Distributive law

Divergent to infinity

Divergent infinite series

Divergent sequence

Dividend

Divides evenly

Divisible

Division:

of polynomials

synthetic

Division algorithm for polynomials

Divisor

Domain:

of a function

implicit

of a sequence

of a variable

Double-napped cone

E

e:

as base

definition of

Eccentricity

Echelon form of a matrix

Echo sounding

Effective half-life

Element of a set

Elementary row operations on an augmented matrix

Elimination, method of

Elimination operations symbols

Ellipse:

applications of

center of

with center (h, k)

definition of

eccentricity of

equations of

focal width of

foci of

major axis of

minor axis of

in rectangular coordinates

standard form for

vertices of

Ellipsis

Empty set

Encoding matrix

End behavior of a function

Entry of a matrix

Equality:

of complex numbers

of matrices

Equation(s):

absolute value

of a circle

conditional

dependent

of an ellipse

equivalent

exponential

extraneous solution of

first degree

graph of an

independent

identity

intercepts of an

of a hyperbola

of a line with slope

of a horizontal line

of a vertical line

linear

logarithmic

in one variable

of a parabola

quadratic

root of

satisfy

simultaneous

solution set of

solving

system(s) of

in two variables

Equivalent equations

Equivalent inequalities

Equivalent matrices, row

Equivalent systems of equations

Even function

Event:

certain

definition of

impossible

mutually exclusive

Expansion theorem for determinants

Exponent(s):

integer

irrational

laws of

rational

Exponential equations

Exponential function:

applications of

asymptote for

base of

definition of

domain of

graph of

natural

properties of

Extraneous solution

F

Factor completely

Factor a polynomial

Factorial function

Factorial notation

Factoring:

FOIL method

polynomials

quadratic polynomials

Factorization formulas

Factor theorem

Family of lines

Feasible solution

Ferrari, Lodovico

Fibonacci

Finite geometric series

Finite sequence

First-degree equation

Floor function

Focal chord of a parabola

Focal width:

of an ellipse

of a hyperbola

of a parabola

Focus (foci):

of an ellipse

of a hyperbola

of a parabola

Fontana, Niccolò (Tartaglia)

Function(s):

denominator of

improper

numerator of

partial

proper

Fractional expression

Function(s):

absolute value

asymptotes for

ceiling

combining

composition of

constant

continuous

cubic

decreasing

definition of

difference of

domain of

discontinuous

end behavior of

even

exponential

factorial

floor

global behavior of

graph of

greatest integer

horizontal-line test

hyperbolic

image of

implicit domain of

increasing

intercepts of

inverse of

inverse hyperbolic sine

linear

local behavior of

logarithmic

logistic

natural exponential

natural logarithmic

notation

objective

odd

one-to-one

piecewise-defined

polynomial

postage stamp

power

product of

quadratic

quartic

quintic

quotient of

range of

rational

reflected graphs of

shifted graphs of

square root

squaring

sum

sum of

symmetry of graphs of

of two variables

value of

vertical-line test for

zero

zeros of

Fundamental counting principle

Fundamental theorem of algebra

Future value

G

Galileo

Gauss, Carl Friedrich

Gaussian elimination

Gauss-Jordan elimination

General term of a sequence

Generation time

Geometric sequence

Geometric series:

definition of

finite

infinite

sum of

Global behavior of a function

Golden ratio

Gompertz curve

Gospel of Judas

Graph(s):

end behavior of

of an equation

of the exponential function

of a function

intercepts of

of linear inequalities in two variables

of the logarithmic function

points of intersection

of power functions

reflected

shifted

symmetry of

tangent to an axis

Greater than

Greater than or equal to

Greatest integer function

Grouping, factoring by

Growth, population

H

Half-life:

definition of

effective

of radium

Half-open interval

Half-plane

Hildago, asteroid

Hole in a graph

Homogeneous system of equations

Hookes law

Horizontal asymptote:

for exponential functions

definition of

for rational functions

Horizontal line, equation of

Horizontal shift of a graph

Horizontal-line test for a one-to-one function

Hypatia

Hyperbola(s):

applications

asymptotes of

auxiliary rectangle of

branches of

center of

conjugate axis of

definition of

eccentricity of

equations of

focal width of

foci of

in rectangular coordinates

standard form for

transverse axis of

vertices of

with center (h, k)

Hyperbolic functions:

definitions of

graphs of

I

i (imaginary unit)

Iceman (Otzi)

Identity

Identity element:

for addition

for multiplication

Identity matrix

Image of a function

Imaginary number

Imaginary part of a complex number

Imaginary unit

Implicit domain of a function

Impossible event

Improper fraction

Inconsistent system of equations

Increasing function

Independent equations in a linear system

Independent variable

Index of a radical

Index of summation

Induction, mathematical

Inequality (inequalities):

absolute values and

definition of

equivalent

linear

nonlinear

nonstrict inequality

polynomial

rational

simultaneous

solution of

solving

solving simultaneous

systems of

strict inequality

transitivity property of

triangle

involving two variables

Infinite geometric series

Infinite sequence

Infinity symbols

Inner product

Integer exponents

Integers

Intensity level of sound

Intercept(s):

of the graph of an equation

of the graph of a function

x-intercept

y-intercept

Interest:

compound

continuous compounding of

simple

Intermediate value theorem

Intersection of sets

Interval:

closed

endpoints of

graphs of

half-open

notation

open

unbounded

Inverse of a function:

definition of

finding the

properties of

Inverse hyperbolic sine

Inverse of a matrix:

definition of

methods for finding an

Inverse proportion

Inverse variation

Invertible matrix

Investment problems

Irrational exponents

Irrational number

Irreducible quadratic polynomial

J

Joint variation

K

Kepler, Johannes

Kepler's first law

Kepler's third law

L

Lascaux cave drawings

Law(s):

associative, of addition

associative, of multiplication

commutative, of addition

commutative, of multiplication

distributive

of integer exponents

of logarithms

of radicals

of rational exponents

of real exponents

Leading coefficient of a polynomial function

Least common denominator

Least squares line

Leibniz, Gottfried Wilhelm

Less than, definition of

Less than or equal to

Libby, Willard

Liber Abacci

Line(s):

of best fit

equations of

horizontal

least squares

parallel

perpendicular

point-slope equation of

segment, midpoint of

segment in the plane, midpoint of

slope

slope-intercept equation of

vertical

Linear equation:

in n variables

in two variables

Linear function:

of one variable

of two variables

Linear inequality in one variable

Linear inequality in two variables:

definition of

graphing of

half-plane

solution of

system of

Linear programming:

constraints

definition of

objective function

Linear system:

consistent

definition of

inconsistent

Local behavior of a function

Local extremum

Logarithm(s):

base e

base 10

change of base

definition of

laws of

Logarithmic differentiation

Logarithmic equations

Logarithmic function(s):

applications of

asymptote for

base of

common

definition of

domain of

graph of

natural

properties of

Logistic function

LORAN

M

Main diagonal of a matrix

Major axis of an ellipse:

definition of

length of

Malthus, Thomas, R.

Mathematical model

Mathematical induction

Matrix (matrices):

addition of

additive identity

additive inverse

adjoint

associative law of

augmented

coefficient

column (vector)

commutative law of

decoding

definition of

determinant of

difference of

dimension of

distributive law of

elementary row operations on

encoding

entry of

equality of

identity

inner product of

inverse

invertible

main diagonal of

multiplication of

multiplicative identity

multiplicative inverse

noninvertible

nonsingular

of order n

product

rectangular

reduced row echelon form

row echelon form

row equivalent

row operations

row reduction

row (vector)

scalar multiple of

singular

square

subtraction of

sum of

transpose of

zero

Maximum (minimum) of a quadratic function

Method of elimination

Method of factoring for solving quadratic equations

Method of substitution

Midpoint of a line segment:

in the plane

on the real number line

Minor

Minor axis of an ellipse

Mixture problems

Monomial

Multiplication:

of complex numbers

of matrices

Multiplicative identity:

for m X n matrices

for real numbers

Multiplicative inverse:

for complex numbers

for m X n matrices

for real numbers

Multiplicity of a zero

Mutually exclusive events

N

Napier, John

Nappes of a cone

Natural exponential function

Natural logarithmic function

Natural numbers

Negative integer power of x

Negative real numbers

Newton, Isaac

Newton's law of cooling/warming

Noninvertible matrix

Nonlinear equation

Nonlinear system

Nonnegative real numbers

Nonpositive real numbers

Nonrigid transformation of a graph

Nonsingular matrix

Nonstrict inequality

Notation:

factorial

function

interval

scientific

summation

NSAIDs, half-life of

n th-order determinant

Number(s):

complex

imaginary

integer

irrational

natural

negative

nonnegative

positive

rational

real

Number line, real

Number system:

complex

real

Numerator of a fraction

O

Objective function

Oblique asymptote

Odd function

One-to-one function:

definition of

horizontal-line test for

Open interval

Order of a matrix

Order relations:

greater than

greater than or equal to

less than

less than or equal to

Ordered n-tuple

Ordered triple

Origin:

in the rectangular coordinate system

on the real line

Outcomes

Overdetermined system of equations

P

Parabola:

applications of

axis of

definition of

directrix of

equations of

focal chord of

focal width of

focus of

in rectangular coordinates

standard form for

vertex of

Paraboloid

Parallel lines:

definition of

slope of

Partial fraction decomposition

Partial fractions

Pascal, Blaise

Pascal's triangle

Perfect square

Perihelion

Permutation

Perpendicular lines:

definition of

slope of

pH of a solution

Piecewise-defined function

Pisano, Leonardo (Fibonacci)

Plane:

coordinate

xy-plane

Plotting points

Point(s):

coordinate of, on the real number line

distance between, on the number line

plotting

rectangular coordinates of a

turning

Point-slope equation of a line

Polygon

Polynomial(s):

algebra of

binomial

complete linear factorization of

constant

constant term of

cubic

definition of

degree of

division algorithm for

end behavior of

equation

factoring of

factor theorem for

function

graph of

inequalities

in one variable

leading coefficient of

linear

local behavior of

monomial

product of

quadratic

quartic

quintic

rational zeros of

relative extremum of

remainder theorem for

single term

standard form of

synthetic division of

term of

in three variables

trinomial

turning point of

in two variables

zero of

Polynomial equation:

completing the square

of degree n

factoring

linear

quadratic

quadratic formula

rational roots of

square root method

Polynomial inequalities:

definition of

guidelines for solving

Population growth

Position vector

Positive integers

Positive integer power of x

Positive real numbers

Postage stamp function

Power function:

definition of

domain of

Present value

Principle of mathematical induction

Principle n th root of a real number

Principal square root

Probability of an event

Product:

of complex numbers

of functions

inner

of matrices

of polynomials

Programming, linear:

basic problem of

constraints

objective function

Proper fraction

Proper rational expression

Properties of determinants

Proportion:

direct

inverse

jointly

Proportionality, constant of

Psalms scroll

Pure imaginary number

Pythagoras

Pythagorean theorem, statement of

Q

Quadrants

Quadratic:

equation

formula

function

maximum (minimum) of

irreducible

polynomial

Quartic polymonial function

Quintic polymonial function

Quotient:

difference

of functions

Quotient trigonometric identities

R

Radical:

definition of

index of

laws of

radicand of

rationalizing

Radicand of a radical

Radioactive decay:

carbon dating

definition of

half-life

Radius of a circle

Range:

of a function

of a sequence

Rate problems

Ratio:

common

golden

Rational exponents, laws of

Rational expression:

definition of

domain of

Rational function:

asymptotes of

definition of

Rational inequalities

Rational numbers

Rational zero of a polynomial

Rational Zeros Theorem

Rationalizing radicals

Real number(s):

absolute value of

decimal form of

integers

irrational

negative

nonnegative

order relations for

positive

properties of

rational

root of

set R of

Real number line:

coordinate of a point on

description of

midpoint of a line segment on

origin on

Real number system

Real part of a complex number

Reciprocal

Rectangular coordinate system:

definition of

symmetry of a graph in

Rectangular matrices

Recursion formula

Reduced row echelon form

Reflections of a graph:

in the x-axis

in the y-axis

Relations, order

Relative extrema:

definition of

maximum

minimum

Remainder theorem

Repeated zero

Repeating decimals

Rhind, Alexander Henry

Rhind papyrus

Richter scale

Rigid transformation of a graph

Rise

Root(s):

cube

of an equation

extraneous

of multiplicity m

of a polynomial equation

principal rath

principal square

rational roots (zeros) of a polynomial

of real numbers

Row echelon form

Row matrix

Row vector

Rule of correspondence

Run

S

Sample space

Scientific notation

Secant line

Semicircle

Sequence:

arithmetic

convergent

definition of

divergent

finite

general term of

geometric

infinite

nth term of

of partial sums

recursively defined

Series:

arithmetic

sum of

geometric

infinite

partial sums of

sum of

Set builder notation

Set(s):

convex

definition of

disjoint

element of

empty

intersection of

of real numbers

subset of

union of

Shifted graphs, of a function

Shroud of Turin

Sigma notation

Sign chart method

Sign properties:

of a product

of a quotient

Significant digits

Simple interest

Simple zero

Simultaneous equations

Simultaneous inequalities

Sine, hyperbolic

Single-term polynomial

Singular matrix

Slant asymptote

Slope(s):

of a line

of parallel lines

of perpendicular lines

rise

run

undefined

Slope-intercept equation of a line

Solution:

of an equation

extraneous

feasible

of inequalities

of a system of inequalities

pH of

Solution set:

of an equation

of an inequality

of a system of equations

of a system of inequalities

Solving:

equations

simultaneous inequalities

systems of equations by determinants

S0rens0n, S0ren

Sound, intensity level of

Sounding, echo

Space, sample

Square of a binomial

Square error

Square matrix

Square root

Square root, principal

Square root method

Square of a sum

Standard forms for:

circles

complex numbers

ellipses

hyperbolas

parabolas

polynomials

Statuary hall

Strict inequality

Subset of a set

Substitution:

back

method of

Subtraction:

of complex numbers

of matrices

Sum:

of complex numbers

of functions

of a geometric series

of matrices

of square errors

of two cubes

Summation index

Summation notation:

definition

index of

properties of

Symmetry of a graph:

of a function

in rectangular coordinates

tests for

Sylvester, James Joseph

Synthetic division

System of equations:

consistent

elimination operations

equivalent

homogeneous

inconsistent

linear

method of elimination

method of substitution

nonlinear

solving, by determinants

solving, by matrices

Systems of inequalities:

linear

nonlinear

T

Tangent to an axis

Tangent line to a circle

Tangent line to an ellipse

Telescoping series

Term(s):

of a polynomial

of a sequence

Terminating decimals

Test point

Tests for symmetry of a graph

Train and fly problem

Transitivity property

Transpose of a matrix

Transverse axis of a hyperbola:

definition of

length of

Tree diagram

Triangle, Pascal's

Triangle inequality

Trichotomy law

Trinomial

Trivial solution

Turning point of a graph

2-space

U

Union of sets

Unit, imaginary

Unit vector

Universal gravitation constant

V

Value:

absolute

of a function

future

present

Variable:

definition of

dependent

domain of

independent

Variation:

combined

direct

inverse

joint

Verhulst, P.F.

Vertex (vertices):

of a convex set

of an ellipse

of a hyperbola

of a parabola

Vertical asymptotes:

definition of

for logarithmic functions

for rational functions

Vertical compression of a graph

Vertical line, equation of

Vertical shift of a graph

Vertical stretch of a graph

Vertical-line test for a function

Viete, Francois

W

Whispering gallery

Width, focal:

of an ellipse

of a hyperbola

of a parabola

Witch of Agnesi

Word problems:

age

investment

mixture

rate

work

X

x-axis:

definition of

tangent to

x-coordinate

x-intercept

x-y-plane

Y

y-axis

y-coordinate

y-intercept

Z

Zero(s):

bisection method for approximating

complex

of a function

of multiplicity m

of a polynomial

real

rational

repeated

simple

Zero factor property of real numbers

Zero matrix

Zero polynomial