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Basic and Intermediate Algebra Terms
A comprehensive list of basic and Intermediate mathematics terms
224
Mathematics
Undergraduate 1
07/12/2009

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Term
Abscissa
Definition

The first number in an ordered pair.

It measures horizontal distance and

is also called the first cordinate.

Term
Absolute Value of A Number
Definition

The distance of the number

from zero on the number line.

Term
Acute Angle
Definition

An angle whose measure

is between 0° and 90°.

Term
Addend
Definition

In addition a number

being added.

Term
Addition
Definition

The process of finding the

total of two numbers.

Term
Addition Method
Definition

An algebraic method of finding an

exact solution of a system

of linear equations.

Term
Additive Inverses
Definition

Numbers that are the same distance

from zero on the number line,

but not opposite sides;

also called opposites.

Term
Adjacent Angles
Definition

Two angles that share

a common side.

Term
Alternate Interior Angles
Definition

Two nonadjacent angles that are on opposite sides

of the transversal and between parallel lines.

Term
Alternate Exterior Angles
Definition

Two nonadjacent angles that are

on opposite of the transversal and

opposite the parellel lines.

Term
Analytic Geometry
Definition

Geometry in which a coordinate

system is used to study the

relationships between variables.

Term
Angle
Definition

Figure formed when two rays

start from the same point.

Term
Arithmetic Mean of Values
Definition

The average determined by calculating

the sum of the values and then

dividing that result by the

number of values.

Term
Axes
Definition

The two number lines that form

a rectangular coordinate system;

also called coordinate axes.

Term
Base
Definition

In exponential notation the factor that is multiplied

the number of times shown by the exponent.

Term
Basic Percent Equation
Definition
Percent times base equals amount.
Term
Binomial
Definition
A polynomial of two terms.
Term
Binomial Factor
Definition
A factor that has two terms.
Term
Center of A Circle
Definition

The point from which all points

on the circle are equidistant.

Term
Circle
Definition

Plane figure in which all points

are the same distance from its center.

Term
Circumference
Definition
The perimeter of a circle.
Term
Clearing Denominators
Definition

Removing denominators from an equation

that contains fractions by multiplying each side

of the equation by the LCM of the denominators.

Term
Coefficient
Definition
The number part of a variable term.
Term
Combining Like Terms
Definition

Using the Distributive Property to add

the coefficients of like variable terms;

adding like terms of variable expressions.

Term
Complementary Angles
Definition
Two angles whose sum is 90°.
Term
Completing the Square
Definition

Adding to a binomial the constant term

that makes it a perfect-square trinomial.

Term
Complex Fraction
Definition
A fraction whose numerator or denominator contains one or more fractions.
Term
Complex Number
Definition

A natural number greater than 1

that is not a prime number.

Term
Conjugates
Definition

Binomial expressions that differ

only in the sign of a term.

The expressions a + b and a - b are conjugates.

Term
Consecutive Even Integers
Definition
Even integers that follow one another in order.
Term
Consecutive Integers
Definition
Integers that follow one another in order.
Term
Consecutive Odd Integers
Definition
Odd integers that follow one another in order.
Term
Constant Term
Definition

A term that includes no variable part;

also called a constant.

Term
Coordinate Axes
Definition

The two number lines that form

a rectangular coordinate system;

also simply called axes.

Term
Coordinates of A Point
Definition

The numbers in an ordered pair

that are associated with a point.

Term
Corresponding Angles
Definition

Two angles that are on the same side

of the transversal and are both acute angles

are both obtuse angles.

Term
Cost
Definition
The price that a business pays for a product.
Term
Decimal Notation
Definition

Notation in which a number

consists of a whole-number part,

a decimal point, and a decimal part.

Term
Degree
Definition
A unit used to measure angles.
Term
Degree of A Polynomial in One Variable
Definition
The largest exponent that appears on the variable.
Term
Dependent System
Definition

A system of equations that

has an insignificant amount of

number of solutions.

Term
Dependent Variable
Definition

In a funtion, the variable whose value depends on the value of another variable known

as the independent variable.

Term
Descending Order
Definition

The terms of the polynomial in one variable arranged so that the exponents on

the variable decrease from left to right.

Term
Diameter
Definition

Line segment across a circle that passes

through the circle's center.

Term
The Difference of Two Square
Definition
A polynomial of the form a2 - b2.
Term
Discount
Definition

The amount by which a retailer reduces

the regular price of a product

for a promotional sale.

Term
Discount Rate
Definition

The percent of the regular price

that the discount represents.

Term
Domain
Definition

The set of first coordinates of

the ordered pairs in a relation.

Term
Double Root
Definition

The two equal roots of a quadratic equation

which occurs when the discriminate b2 - 4ac

equals zero.

Term
Element of A Set
Definition
One of the objects in a set.
Term
Empty Set
Definition

The set that contains no elements;

also called the null set.

Term
Equation
Definition

A statement of the equality

of two mathematical expressions.

Term
Equilateral Triangle
Definition

A trangle in which all three

sides are of equal length.

Term
Equivalent Equations
Definition
Equations that have the same solution.
Term
Evaluating A Fraction
Definition

Replacing x in f(x) with some value

and then simplifying the

numerical expression that results.

Term
Evaluating A Variable Expression
Definition

Replacing each variable by its

value and then simplifying the

resulting numerical expression.

Term
Even Integer
Definition
An ingteger that is divisible by 2.
Term
Exponent
Definition

In exponential notation, the elavated number

that indicates how many times

the base occurs in the multiplication.

Term
Exponential Form
Definition
The expression 25 is in exponential form.
Term
Exterior Angle of A Triangle
Definition
Angle adjacent to an interior angle of a triangle.
Term
Factor By Grouping
Definition

Process of grouping and factoring terms

in a polynomial in such a way

that a common binomial factor is found.

Term
Factor Completely
Definition

Refers to writing a polynomial as a product

of factors that are nonfactorable over the intergers.

Term
Factor of A Number
Definition
In multiplication, a number being multiplied.
Term
Factor A Polynomial
Definition

To write the polynomial as a product

of other polynomials.

Term
Factor a trinomial of the form x2 + bx + c
Definition

To express the trinomials as the

product of two binomials.

Term
Factored Form
Definition
The expression 2 x 2 x 2 x 2 x 2 is in factored form.
Term
First Coordinate
Definition

The first number in an ordered pair.

It measures a horizontal distance

and is also called the abscissa.

Term
First-degree equation In Two Variables
Definition

An equation of the form y=mx+b, where m

is the coefficient and b is a constance;

also called a linear equation in two variables

Term
FOIL
Definition
A method of finding the product of two binomials; the letters stand for First, Outer, Inner, and Last.
Term
Formula
Definition

A literal equation

that states rules about measurements.

Term
Function
Definition

A relation in which no two ordered pairs

that have the same first coordinate

have different second coordinates.

Term
Functional Notation
Definition

A function designed by f(x),

which is the value of the funtion at x.

Term
Graph A Point In the Plane
Definition

To place a dot at the location given

by the ordered pair;

also called plotting a point in the plane.

Term
Graph Of A Relation
Definition

The graph of the ordered pairs

that belong to the relation.

Term
Graph An Equation In Two Variables
Definition

A graph of the ordered pairs

that belong to the relation.

Term
Graph of an Integer
Definition

A heavy dot directly above

that number on the number line.

Term
Graph of an Ordered Pair
Definition

The dot drawn at the coordinants

of the point in a plane.

Term
Greater Than
Definition
A number a is greater thananother number b, written a > b on the number line.
Term
Greater Than or Equal To
Definition
The symbol ≥ means "is greater than or equal to."
Term
Greatest Common Factor (GCF)
Definition

The greatest common factor of two or more integers is the GCF of the coefficients

and the common variable factors.

Term

Greatest Common Factor (GCF)

of Two or More Monomials

Definition

The product of the GCF of the coefficients

and the common variable factors.

Term
Half-plane
Definition
The solution set of an inequality in two variables.
Term
Hypotenuse
Definition
In a right triangle, the side opposite the 90° angle.
Term
Inconsistent System
Definition
A system of equations that has no solution.
Term
Independent System
Definition
A system of equations that has one solution.
Term
Independent Variable
Definition

In a function, the variable that varies independently and whose value determines the value

of the dependent variable.

Term
Inequality
Definition

An expression that contains the symbol

>, <, ≥ (is greater than or equal to),

or ≤ (is less than or equal to).

Term
Integers
Definition
The numbers {..., -3, -2, -1, 0, 1, 2 , 3, ...}
Term
Interior Angle of A Triangle
Definition
Angle within the region enclosed by a triangle.
Term
Intersecting Lines
Definition
Lines that cross at a point on a plane.
Term
Intersection of Sets A and B
Definition

The set that contains the elememts

that are common to both A and B.

Term
Irrational Number
Definition

The decimal representation of an irrational number never repeats or terminates

and can only be approximated.

Term
Isosceles Triangle
Definition

A triangle that has two equal angles

and two equal sides.

Term
Least Common Denominator (LCD)
Definition

The smallest number that is a multiple of each

denominator in question.

Term
Least Common Multiple (LCM)
Definition

The LCM of two or more numbers is the smallest

number that contains the prime factorizations of each number.

Term

Least Common Multiple

(LCM) of Two or More Polynomials

Definition

The polynomial of least degree that contains

all the factors of each polynomial.

Term
Legs
Definition

The sides opposite the hypotenuse

in a right triangle.

Term
Less Than
Definition

A number a is less than another number b,

written a < b on the number line.

Term
Less Than or Equal To
Definition
The symbol ≤ means "is less than or equal to."
Term
Like Terms
Definition

Terms of a variable expression

that have the same variable part.

Term
Line
Definition

Having no width, it extends indefinately

in two directions in a plane.

Term
Line of Best Fit
Definition

A line drawn to approximate data

that are graphed as points in a coordinate system.

Term
Line Segment
Definition
Part of a line that has two endpoints.
Term
Linear Equations in Two Variables
Definition

An equation of the form y=mx+b,

where m and b are constants;

also called a linear function

or a first-degree equation in two variables.

Term
Linear Function
Definition

An equation of the form y=mx+b,

where m and bare constants;

also called a linear equation in two variables

or a first-degree equation in two variables.

Term
Linear Model
Definition

A first degee equation that is used to describe

a relationship between quantities.

Term
Literal Equation
Definition
An equation that contains more than one variable.
Term
Markdown
Definition

The amount by which a retailer reduces

the regular price of a product

for a promotional sale.

Term
Markup
Definition
The difference between selling price and cost.
Term
Markup Rate
Definition

The percent of retailer's cost

that the markup represents.

Term
Monomial
Definition

A number, a variable, or a product of numbers

and variables; a polynomial of one term.

Term
Moving Average
Definition

The arithmetic mean of the changes

in the the value of a stock

for a given numer of days.

Term
Multiplicative Inverse
Definition
The reciprocal of a number.
Term
Natural Numbers
Definition
The numbers {1, 2, 3, ...}
Term
Negative Integers
Definition
The integers {..., -4. -3. -2. -1}.
Term
Negative Slope
Definition

A property of a line that

slants downward to the right.

Term
Nonfactorable Over the Intergers
Definition

A polynomial that does

not factor using only intergers.

Term
Null Set
Definition

The set that contains no

elements; also called the empty set.

Term
Numerical Coefficient
Definition

The numerical part of a

variable term. When the

numerical coefficient is 1

or -1, the 1 is usually not written.

Term
Obtuse Angle
Definition

An angle whose measure

is between is between 90° and 180°.

Term
Odd Interger
Definition

An interger that is

not divisible by 2.

Term
Opposite of A Polynomial
Definition

The polonomial created when

the sign of each term of the

original polynomial is changed.

Term
Opposites
Definition

Numbers that are the same

distance from zero on

the number line, but on

opposite sides; also called

additive inverses.

Term
Ordered Pair
Definition

Pair of numbers of the form

that can be used to identify

a point in the plane determined

by the axes ofa rectangular

coordinate system.

Term
Order of Operations Agreement
Definition

A set of rules that tell us in what order

to perform the operations

that occur in a numerical expression.

Term
Ordinate
Definition

The second number in an ordered pair.

It measures a vertical distance

and is also called the second coordinate.

Term
Origin
Definition
The point of intersection of the two coordinate axes that form a rectangular coordinate system.
Term
Parabola
Definition
The graph of a quadratic equation in two variables.
Term
Parallel Lines
Definition

Lines that never meet;

the distance between them is always the same.

Parallel lines have the same slope.

Term
Parallelogram
Definition
Four-sided plane figure with opposite sides parallel.
Term
Percent
Definition
Parts of 100.
Term
Perfect Square
Definition
The square of an integer.
Term
Perfect-Square Trinomial
Definition

A trinomial that is a product

of a binomial and itself.

Term
Perimeter
Definition
The distance around a plane geometric figure.
Term
Perpendicular Lines
Definition
Intersecting lines that form right angles.
Term
Plane
Definition
Flat surface that extends indefinately.
Term
Plane Figure
Definition
Figure that lies entirely in a plane.
Term
Plot a point in a plane
Definition

To place a dot at the location given

by an ordered pair;

to graph a point in the plane.

Term
Point-slope Formula
Definition

If (x1,y1) is a point on a line with slope m,

then y-y1=m(x-x1).

Term
Polynomial
Definition

A variable expression in which

the terms are monomials.

Term
Positive Integers
Definition
The intergers  {1, 2, 3, 4, ...}
Term
Positive Slope
Definition
A property of a line that slants upward to the right.
Term
Prime Factorization
Definition

Expressing a number as a product

of prime numbers.

Term
Prime Number
Definition
Number whose only factors are 1 and the number.
Term
Prime Polynomial
Definition

A polynomial that is nonfactorable

over the integers.

Term
Principle Square Root
Definition
The positive square root of a number.
Term
Product
Definition

In multiplication, the result of

multiplying two numbers.

Term
Proportion
Definition

An equation that states the equality

of two ratios or rates.

Term
Pythagorean Theorem
Definition

The square of the hypotenuse of a right triangle

is equal to the sum of the squares of the two legs.

Term
Quadrant
Definition

One of the four regions into which the two axes

of a rectangular coordinate system divide the plane.

Term
Quadratic Equation
Definition

An equation of the form ax2 + bx + c = 0,

where a, b, and c are constants

and a is not equal zero;

also called a second-degree equation.

Term
Quadratic Equation In Two Variables
Definition

An equation of the form y=ax2+bx+c,

where a is not equal to zero.

Term
Quadratic Function
Definition

A quadratic funtction is given f(x)=ax2+bx+c,

where a is not equal to zero.

Term
Radical Equation
Definition

An equation that contains a variable expression

in a radicand.

Term
Radical Sign
Definition
The symbol, which is used to indicate the positive, or principle, square root of a number.
Term
Radicand
Definition

In a radical expression, the expression

under the radical sign.

Term
Radius
Definition

Line segment from the center to a point

on the circle.

Term
Range
Definition
The set of second coordinates of the ordered pairs in a relation.
Term
Rate
Definition

The quotient of two quantities

that have different units.

Term
Rate of Work
Definition

That part of a task that is completed

in one unit of time.

Term
Ratio
Definition

The quotient of two quatities

that have the same unit.

Term
Rational Expression
Definition

A fraction in which the numerator

or denominator is a polynomial.

Term
Rational Number
Definition

A number that can be written in the form of a/b, where a and b are integers

and b is not equal to zero.

Term
Rationalizing the Denominator
Definition

The procedure used to remove a radical

from the denominator from a fraction.

Term
Ray
Definition
Line that starts at a point and extends indefinately in one direction.
Term
Real Numbers
Definition
The rational numbers and the irrational numbers.
Term
Reciprocal of A Fraction
Definition

Fraction that results when the numerator

and the denominator of a fraction are interchanged.

Term
Reciprocal of a rational expression
Definition
A rational expression in which the numerator and the denominator have been interchanged.
Term
Rectangle
Definition
Parallelogram that has four right angles.
Term
Rectangular Coordinate System
Definition

System formed by two number lines, one horizontal and one vertical, that intersect

at the zero point of each line.

Term
Relation
Definition
Any set of ordered pairs.
Term
Repeating Decimal
Definition

Decimal that is formed when dividing the numerator of its fractional counterpart by the denominator results in a decimal part

wherein a block of digits repeats infinitely.

Term
Right Angle
Definition
An angle whose measure is 90°.
Term
Right Triangle
Definition
A triangle that contains a 90° angle.
Term
Roster Method
Definition

Method of writing a set by enclosing a list

of the elements in braces.

Term
Scatter Diagram
Definition

A graph of collected data as points

in a coordinate system.

Term
Scientific Notation
Definition

Notation in which each number is expressed

as the product of two factors, one a number between 1 and 10 and the other a power of ten.

Term
Second Coordinate
Definition
The second number in an ordered pair. It measures a vertical distance and is also called the ordinate.
Term
Second-degee Equation
Definition

An equation of the form ax2 + bx + c = 0,

where a, b, and c are constants

and a is not equal to zero;

also called a quadratic equation.

Term
Selling Price
Definition

The price for which a business sells a product

to a customer.

Term
Set
Definition
A collection of objects.
Term
Set-builder Notation
Definition

A method of designating a set that makes use

of a variable and a certain property

that only elements of that set posess.

Term
Similar Objects
Definition

Similar objects have the have the same shape

but not necessarily the same size.

Term
Simplest form of a fraction
Definition
A fraction in which the numerator and the denominator have no common factors other than 1.
Term
Simplest form of a rational expressions
Definition

A rational expression is in simplest form

when the numerator and denominator

have no common factors.

Term
Slope
Definition

The measure of the slant of a line.

The symbol for slope is m.

Term
Slope-intercept Form
Definition

The slope-intercept form of an equation

of a straight line is y=mx+b.

Term
Solid
Definition
An object that exists in space.
Term
Solution of a system of equations in two variables
Definition

An ordered pair that is a solution

of each equation of the system.

Term
Solution of an equation
Definition
A number that, when substituted for the variable, results in a true equation.
Term
Solution of an equation in two variables
Definition
An ordered pair whose coordinates make the equation a true statement.
Term
Solution Set of an Inequality
Definition

A set of numbers, each element of which,

when substitued for the variable,

results in a true inequality.

Term
Solving an Equation
Definition
Finding a solution of the equation
Term
Square
Definition
Rectangle with four equal sides.
Term
Square Root
Definition

A square root of a positive number x

is a number a for a2=x.

Term
Standard Form
Definition

A quadratic equation is in standard form

when the polynomial is in descending order

and equal to zero.

ax2+bx+c=0 is in standard form.

Term
Standard Form of a linear equation in two variables
Definition
An equation in the form of Ax+By=C, where A and B are coefficients amd C is a constant.
Term
Straight Angle
Definition
An angle whose measure is 180°.
Term
Substitution Method
Definition

An algebraic method of finding an exact solution

of a system of equations.

Term
Sum
Definition
In addition, the total of two or more numbers.
Term
Supplementary Angles
Definition
Two angles whose sum is 180°.
Term
System of Equations
Definition
Equations that are considered together.
Term
Terminating Decimal
Definition
Decimal that is formed when dividing the numerator of its fractional counterpart by the denominator results in a remainder of zero.
Term
Terms of A Variable Expression
Definition
The addends of the expression.
Term
Transversal
Definition

A line intersecting two other lines

at two different points

Term
Triangle
Definition
A three-sided closed figure.
Term
Trinomial
Definition
A polynomial of three terms.
Term
Undefined Slope
Definition
A property of a vertical line.
Term
Uniform Motion
Definition

The motion of a moving object

whose speed and direction do not change.

Term
Union of sets A and B
Definition

The set that contains all the elements of A

and all the elements of B.

Term
Value of a Variable
Definition
The number assigned to the variable.
Term
Value of a Funtion at x
Definition
The result of evaluating a variable expression, represented by the symbol.
Term
Variable
Definition
A letter of the alphabet used to stand for a number that is unknown or that can change.
Term
Variable Expression
Definition
An expression that contains one or more variables.
Term
Variable Part
Definition

In a variable term, the variable or variables

and their exponents.

Term
Variable Term
Definition

A term composed of a numerical coefficient

and a variable part.

Term
Vertex
Definition
Point at which the rays that form an angle meet.
Term
Vertical Angles
Definition

Two angles that are on opposite

of the intersection of two lines.

Term
x-coordinate
Definition
The abscissa in an xy-coordinate system.
Term
x-intercept
Definition
The point at which a graph crosses the x-axis.
Term
xy-coordinate system
Definition

A rectangular coordinate system in which

the horizontal axis is labeled x

and the vertical axis is labeled y.

Term
y-coordinate
Definition
The ordinate in an xy-coordinate system.
Term
y-intercept
Definition
The point at which a graph crosses the y-axis.
Term
Zero Slope
Definition
A property of a horizontal line.
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