GLOSSARY

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acknowledgement

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Absolute Value the absolute value of a number is the distance the number is from the zero point on the number line.  The absolute value of a number or an expression is always greater than or equal to zero (i.e. nonnegative). see lesson
Addition a mathematical process to to combine numbers and/or variables into an equivalent quantity, number or algebraic expression
Adding integers To ADD integers with the same sign, add their absolute values.  Give the result the same sign as the integers.

To ADD integers with different signs, SUBTRACT the lesser absolute value from the greater absolute value.  Give the result the same sign as the integer with the greater absolute value.

Addition (and Subtraction) Property for Inequality

For all numbers a, b, and c, the following are true:

1.  If a > b, then a + c > b + c
                    and a - c > b - c

2.  If a < b, then a + c < b + c
                    and a - c < b - c

In words, if the same number or expression is added or subtracted from both sides of a true inequality, the new inequality is also true.
see lesson

Additive
Identity Property

For any number a,

a + 0 = 0 + a  

In words, adding zero to a number leaves the number unchanged, hence the "identical" number.

Additive Inverse Property

For every number a, a + (-a) = 0

e.g.

5 + ? = 0     5 + (-5) = 0

-17 + ? = 0    -17 + 17 = 0

In words, if the opposite of a number is added to the original number, the sum is equal to zero.

Algebra a language that helps translate real-life situations into mathematical form so that we can analyze change and answer the question "What if?" 
Algebraic Expression an expression consisting of one or more numbers and variables along with one or more arithmetic operations
Arithmetic Operation a mathematical process of addition, subtraction, multiplication or division.
Axes Two perpendicular number lines that are used to locate points in a coordinate plane.  By convention, the x-axis is the horizontal line and the y-axis is the vertical line.
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Best-Fit Line

A line drawn so it is close to most or all of the data points in a graph.

A best-fit line is described as strong or weak depending on how close the data points are on average.
see lesson

Binomial The sum of two monomials.
Boundary A boundary line of an inequality is a line that separates the coordinate plane into half-planes.
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Coefficient The numerical factor in a term. In the term 4x, 4 is the coefficient.  In the term 4x/5 ; 4/5 is the coefficient.  Note that 4x/5 can also be written as ( 4/5 )x.
Complex fraction A fraction that has one or more fractions in the numerator or denominator.
Compound Event A compound event consists of two or more simple events (i.e. the tossing of two or more coins).
Compound Inequality Two inequalities connected by AND or OR.
Consistent A system of equations is said to be consistent when it has at least one ordered pair that satisfies both equations.
Constants A monomial term that lacks a variable component.

Coordinate Plane  

the plane containing the x- and y- axes.
Counting Numbers The set of counting (aka "natural") numbers can be expressed as {1,2,3,...}.  This set is identical to the set of whole numbers, less the number zero. Counting numbers are not negative.
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Degree of a monomial The degree of a monomial is the sum of the exponents of its variables.
Degree of a polynomial The degree of a polynomial is the degree of the term of the greatest monomial degree.
Dependent (equations) A system of equations that has an infinite number of solutions
Dependent Event An occurrence or outcome that is affected by previous occurrences or outcomes.  The probability of drawing a red or black card from a deck of cards is affected by the colors of cards previously drawn. see independent event
Dependent Variable When solving an equation for a given variable, that variable becomes the dependent variable. That is, its value depends upon the domain values chosen for the other variable. The dependent variable represents the range and is graphed on the y-axis (see independent variable).
Difference The result of a subtraction operation.  Order matters!  The difference of 6 and 3 equals 3.  The difference of 3 and 6 equals -3.
Difference of Squares Two perfect squares separated by a subtraction sign: a2 - b2 & x2 - 49 are both examples of the difference of squares. 

The difference of squares can easily be factored as follows:

a2 - b2 = (a + b)(a - b)
x2 - 49 = (x + 7)(x - 7)

Division Property for Inequality

See Multiplication Property for Inequality

Domain the set of all first (x-) coordinates from the ordered pairs in a relation.
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Element A member of a set.
Elimination The elimination method of solving a system of equations is a method that uses addition or subtraction to eliminate one of the variables to solve for the other variable.
Equal
(also Equivalent)
a term used to indicate that two or more quantities are of the same value.
Equation a mathematical sentence that compares two expressions linked by an equals sign (=).
Evaluate To find the value of an expression when the value of the variables are known.
Exponent In an expression of the form xn, the exponent is n.  The exponent represents the number of times the base (in this case, x) is multiplied by itself.  The expression xn is called a power.
Expression see Algebraic Expression
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Factors In a multiplication expression, the quantities being multiplied are called factors.

In the monomial term 3bc, there are three factors: 3, b and c.

In the algebraic expression 3(m+5) there are two factors: 3 and (m+5). 

FOIL Method To multiply two binomials, find the sum of the products of:

F  the first terms,
O  the outside terms,
I    the inside terms, and... 
L   the last terms

Formula an equation that states a rule for the relationship between certain quantities. The formula for distance-rate-time problems is d=rt.
Function

(see vertical line test)

a function is a relation in which each element of the domain is paired with exactly one element of the range
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Graph To draw or plot the points named by:
1)  certain numbers on a number line or
2)  certain ordered pairs on a coordinate plane.
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Half-Plane The region on a graph on one side of a boundary is called a half-plane.
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Inconsistent A system of equations is said to be inconsistent when it has no ordered pair that satisfies both equations.
Independent (equations) A system of equations is said to be independent if the system has exactly one solution.
Independent Event An occurrence or outcome that is not affected by previous occurrences or outcomes.  The probability of tossing a coin heads or tails is an independent event.  see dependent event
Independent Variable  The domain contains values represented by the independent variable. The domain values are graphed on the x-axis (see dependent variable).
Inequality A mathematical sentence comparing two expressions that are linked by one of the following: <, <, >, or >.
Integer The set of numbers represented as {..., -3, -2, -1, 0, 1, 2, 3,...}.
Intersection (of sets) The intersection of two sets A and B is the set of elements common to both A and B.
Inverse of a Relation Relation Q is the inverse of Relation S if and only if for every ordered pair (a,b) in S, there is an ordered pair (b,a) in Q.  For example, the inverse of (2, 5) is (5, 2).
Irrational number A number that cannot be expressed in the form (a/b) where a and b are integers and b <> 0.
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Like Terms terms that contain the same variables, where the corresponding variables also are of the same power (exponent).
Linear Equation An equation whose graph is a line.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Mathematical Sentence see Open Sentence
Monomial A monomial is a number, a variable, or a product of a number and one or more variables.
Multiplication (and Division) Property for Inequality

For all numbers a, b, and c, the following are true:

IF c is POSITIVE:

1.  If a > b, then ac > bc
2.  If a < b, then ac < bc

the same holds true for DIVISION where c is not equal to zero.

+ + + + + + + + + + + + 

For all numbers a, b, and c, the following are true:

IF c is NEGATIVE:

1.  If a > b, then ac < bc
2.  If a < b, then ac > bc

the same holds true for DIVISION where c is not equal to zero.

Multiplicative
Identity Property
For any number a,

a . 1 = 1 . a = a

Multiplicative
Inverse Property
For every nonzero number a/b, there is exactly one number b/a such that (a/b) . (b/a) = 1  

In words, a number multiplied by its reciprocal will always equal zero.

Multiplicative
Property of Zero   
For any number a,

a . 0 = 0 . a = 0  

In words, any number or expression multiplied by zero will equal zero.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Natural Numbers see counting numbers.
Negative Correlation There is a negative correlation between x and y if the values are related in an opposite way - i.e. as x increases, y decreases or as x decreases, y increases.
see lesson
Negative Exponent For any non-zero number a and any integer n:
a-n = 1/an
Negative Number Any number that is less than zero.
Number an element of a mathematical system used to represent known quantities, both standalone and in mathematical sentences.
Number Line A line with equal distances marked off to represent numbers.
Numerical Expression an expression consisting of one or more numbers along with one or more arithmetic operations
   
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Odds a ratio of the number of ways a certain event can occur to the number of ways it cannot occur. see lesson
Open Sentence a statement in which numbers, variables, arithmetic operations and other symbols (i.e. =, <, %) are used to calculate or compare various quantities.
Ordered Pair a pair of numbers used to locate points in the coordinate plane.
Organize data Organizing data is useful before solving a problem.  Some ways to organize data are to use tables, charts, different types of graphs, or diagrams.
Origin the  point of intersection of the two axes in the coordinate plane.
Outcomes Outcomes are all possible combinations of a counting problem.  Positive and negative outcomes are the basis of many probability problems. see lesson
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Percent A percent is a ratio that compares a number to 100. see lesson
Percent of Decrease The ratio of an amount of decrease to a previous amount, expressed as a percent.
Percent of Increase The ratio of an amount of increase to a previous amount, expressed as a percent.
Perfect square A rational number whose square root is a rational number.
Point-slope form of a linear equation

For a given point (x1, y1) on a non-vertical line having slope m, the point-slope form is: 

y - y1 = m(x - x1)  

see lesson

Polynomial A polynomial is a monomial or a sum of monomials.
Positive Correlation There is a positive correlation between x and y if the values are related in the same way - i.e. as x increases, y also increases or as x decreases, y decreases. see lesson
Power of a Monomial

For any numbers a and b and any integers m, n, and p:

(ambn)p = ampanp

Power of a Power For any number a, and all integers m and n:

(am)n = amn

Power of a Product

For any numbers a and b and any integers m:

(ab)m = ambm

 

Principal square root The nonnegative square root of an expression.
Probability a ratio of the number of ways a certain event can occur to the number of possible outcomes. see lesson
Product The result of a multiplication operation.  Order does NOT matter.  The product of 6 and 3 equals 18.  The product of 3 and 6 also equals 18.
Product of Powers For any number a, and all integers m and n:

aman = am+n

Proportion an equation stating that two ratios, rates or fractions are equivalent.
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Quadrant One of the four regions into which the x- and y- axes separate the coordinate plane.  
Quantity the way in which a person, place or thing is measurable for purposes of assignment or comparison.  For example, a person could be measured in height, weight or intelligence.  A town could be measured in population, square miles, or tax revenue.  A building could be measured in height, floor space or storage capacity. Each measurement can be represented as a quantity.
Quotient The result of a division operation.  Order matters!  The quotient of 6 and 3 equals 2.  The quotient of 3 and 6 equals 1/2 (or 0.5).
Quotient of powers For any non-zero number a, and all integers m and n:

am/an = am-n

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Radical sign The symbol , indicating the principal square root of an expression.
Range the set of all second (y-) coordinates from the ordered pairs in a relation.
Rate

The relationship a/b of two quantities a and b that are measured in different units.  For example, a car that travels 100 miles in 2 hours has a unit RATE of speed of 50 miles per hour, or  50 miles/1 hour

Ratio a comparison of two quantities or numbers that are measured in the same units.  A ratio can be expressed as:
1)  a/b
2)  a:b    
3)  a to b

Recipe ingredients are often expressed as ratios to a unit of measure such as a cup or tablespoon.
see lesson
Rational Number a number that can be expressed as a ratio of two integers, except that the denominator cannot be equal to zero.
Real number The set of rational numbers and irrational numbers together form the set of real numbers.
Reflexive
Property of Equality
For any number a,

a = a

Relation a set of ordered pairs.
Replacement Set A set of numbers from which replacements for a number may be chosen.
Rise The vertical (up and down) change in a line graphed in the coordinate plane.
Run The horizontal (left and right) change in a line graphed in the coordinate plane.
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Scatter Plot In a scatter plot, two sets of data are plotted as ordered pairs in the coordinate plane. see lesson
Scientific Notation A number is expressed in scientific notation when it is in the form:
 
a 10n, where  1 < a < 10 and n is an integer.
Sequence A set of numbers in a specific order.
Set A collection of objects or numbers.
Set-builder Notation A notation used to describe the members of a set.  For example { y | y< 17 } represents the set of all numbers y such that y is less than 17. see lesson
Simple Events A single event in a probability problem (i.e. the tossing of one coin).
Simplest Form an algebraic expression is in simplest form when it contains no parentheses or like terms.
Slope The slope m of a line is the ratio of the change in the y-coordinates to the corresponding change in the x-coordinates.  Also described as "rise over run" or "the change in y over the change in x". see lesson
Slope-intercept form

Given the slope m and the
y-intercept b of a line, the equation of the line is:

y = mx + b  

Solution A replacement for the variable(s) in an open sentence that results in a true sentence.
Solution Set The set of all replacements for the variable(s) in an open sentence that result in a true sentence.
Square root One of two identical factors of a number.
Standard Form

The Standard Form of a linear equation is:

Ax + By = C

where A, B, and C are integers, A > 0 and A and B are both not equal to 0.
see
lesson

 

Substitution The substitution method of solving a system of equations is a method that uses substitution of one equation into the other equation to solve for the other variable.
Substitution
Property of Equality
Given that a and b are numbers or expressions, if a = b, then a may be replaced by b in any expression.
Subtracting Integers

To subtract a number, add its additive inverse. For any numbers a and b;

a - b = a + (-b) 

Subtraction (and Addition) Property for Inequality

See Addition Property for Inequality

Sum The result of an addition operation.  Order does not matter.  The sum of 6 and 3 equals 9.  The sum of 3 and 6 also equals 9.
Symmetric
Property of Equality
For any numbers a and b,

if a = b, then b = a

System of equations A set of equations (two or more) with the same variables.

With respect to a system of two linear equations, we can say the system has either:
a) one solution (intersecting lines)
b) infinite solutions (same line)
c) no solution (parallel lines).

System of inequalities A set of inequalities (two or more) with the same variables.
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Term (of an algebraic expression) a number, a variable, or a product of numbers and variables.
Term (2) (of a sequence) a number in a sequence.
Transitive
Property of Equality
For any numbers a, b, and c,

if a = b and b = c, then a = c

Tree Diagram A diagram used to show the total number of all possible outcomes for two or more independent events.
Trinomial A trinomial is the sum of three monomials, assuming that like terms have been combined.
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Uniform Motion When an object moves at a constant speed (or rate) it is said to be in uniform motion.  The formula distance = rate * time ( d = rt ) is used to solve uniform motion problems. see lesson
Union The union of two sets A and B is the set of elements contained in both A and B.
Unit Cost The cost of one unit of something.  For example if 12 bagels cost $3.60, the unit cost for one bagel is $0.30 or 30 cents, which is the quotient of (3.60)/(12).
Unit Rate A rate where the denominator is expressed as a single whole unit, i.e. miles per (one) hour, price per (one) pound, words per (one) minute, etc..  A rate can be converted to unit rate by using a proportion
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Value a numerical quantity that is assigned or is determined by calculation or measurement.
Variable a symbol, typically a lower case letter, that is used to represent an unspecified number.
Vertical Line Test for a Function if any vertical line passes through no more than one point of the graph of a relation, then the relation is a function.
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Whole numbers The set of whole numbers can be expressed as {0,1,2,3,...}.  This is the set of counting (aka "natural") numbers and zero. Whole numbers are not negative.
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x-coordinate the first number of an ordered pair. It corresponds to the numbers on the x-axis.
x-intercept The coordinate at which a graph intersects the x-axis.
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y-coordinate the second number of an ordered pair. It corresponds to the numbers on the y-axis.
y-intercept The coordinate at which a graph intersects the y-axis.
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Zero Product Property For all numbers a and b, if ab=0 then either a=0, b=0 or both a and b equal 0.
Zero exponent For any non-zero number  a:

a0 = 1