Glossary

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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).
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 see lesson
Additive Identity Property	For any number a, a + 0 = 0 + a
Additive Inverse Property	For every number a, a + (-a) = 0 e.g. 5 + ? = 0 5 + (-5) = 0 -17 + ? = 0 -17 + 17 = 0
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. 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/₅can 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	Monomials that are real numbers.
Coordinate Plane	the plane containing the x- and y- axes.
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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 of Squares	Two perfect squares separated by a subtraction sign, i.e. a² - b² = (a + b)(a - b)
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 contains 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 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 expression 3bc, there are three factors: 3, b and c. In the 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 containing the symbols <, <, >, 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.
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Mathematical Sentence	a statement in which numbers, variables, arithmetic operations and other symbols (i.e. =, <, %) are used to calculate or compare various quantities.
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
Multiplicative Property of Zero	For any number a, a ^.0 = 0 ^.a = 0
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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.
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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
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: (a^mbⁿ)^p = a^mpa^np
Power of a Power	For any number a, and all integers m and n: (a^m)ⁿ = a^mn
Power of a Product	For any numbers a and b and any integers m: (ab)^m = a^mb^m
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 multiplication.
Product of Powers	For any number a, and all integers m and n: a^maⁿ = a^m+n
Proportion	an equation stating that two ratios 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 of powers	For any non-zero number a, and all integers m and n: a^m/aⁿ = a^m-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.
Ratio	a comparison of two numbers by division. see lesson
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 x 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 in an open sentence that results in a true sentence.
Solution Set	The set of all replacements for the variable 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	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.
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 (1) (of an algebraic expression)	a number, a variable, or a product or quotient 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.
Trinomial	A trinomial is the sum of three monomials (after 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.
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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,...}. Whole number 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