Glossary

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The NROC Project

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Glossary Entries
Word(s)	Definition	Image	Caption	Link	Source
digit	One of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
place value	The value of a digit based on its position within a number.
place-value chart	A chart that shows the value of each digit in a number.
standard form	A way to write a number using digits. For example, thirty-two is written in standard form as 32.
periods	Each group of three digits in a number separated by a comma.
expanded form	A way to write a number as a sum of the value of its digits. For example, thirty-two is written in expanded form as 30+2, or 3 tens +2 ones, or (3^.10)+(2^.1).
rounding	Finding a number that’s close to a given number, but is easier to think about.
whole numbers	Any of the numbers 0, 1, 2, 3, and so on.
inequality	A mathematical sentence that compares two numbers that are not equal.
sum	The result when two or more numbers are added; the quantity that results from addition.
addends	A number added to one or more numbers to form a sum.
regroup	Rewriting a number so you can subtract a greater digit from a lesser digit.
polygon	A closed plane figure bounded by three or more line segments.
perimeter	The distance around a two-dimensional shape.
minuend	The number from which another number is subtracted.
subtrahend	The number that is subtracted from another number.
difference	The quantity that results from subtracting one number from another, or from subtracting the subtrahend from the minuend.
estimate	An answer to a problem that is close to the exact number, but not necessarily exact.
factors	A number that is multiplied by another number or numbers to get a product. For example, in the equation 4^.5=20, 4 and 5 are factors.
product	The result when two numbers are multiplied. For example, the product of 4^.5 is 20.
inverse operation	A mathematical operation that can reverse or “undo” another operation. Addition and subtraction are inverse operations. Multiplication and division are inverse operations.
dividend	The number to be divided up in a division problem. In the problem 8÷2=4, 8 is the dividend.
divisor	The number that is being divided into the dividend in a division problem. In the problem 8÷2=4, 2 is the divisor.
quotient	The result of a division problem. In the problem 8÷2=4, 4 is the quotient.
addition property of 0	The sum of any number and 0 is equal to that number. The number 0 is often called the additive identity.
multiplication property of 1	The product of any number and 1 is equal to that number. The number 1 is often called the multiplicative identity.
commutative law of addition	Two numbers can be added in any order without changing the sum. For example: 6+4=4+6
commutative law of multiplication	Two numbers can be multiplied in any order without changing the product. For example, 8^.9=9^.8
associative law of addition	For three or more numbers, the sum is the same regardless of how you group the numbers. For example, (6+2)+1=6+(2+1).
associative law of multiplication	For three or more numbers, the product is the same regardless of how you group the numbers. For example, (3^.5)^.7=3^.(5^.7)
distributive property of multiplication over addition	The product of a number and a sum is the same as the sum of the product of the number and each of the addends making up the sum. For example, 3(4+2)=3(4)+3(2).
distributing	To rewrite the product of the number and a sum or difference using the distributive property.
distributive property of multiplication over subtraction	The product of a number and a difference is the same as the difference of the product of the number and each of the numbers being subtracted. For example, 8(10-2)=8(10)-8(2).
operation	A mathematical process; the four basic operations are addition, subtraction, multiplication, and division.
Exponential notation	A notation that represents repeated multiplication using a base and an exponent. For example, 2² is notation that means 2^.2^.2^.2. This notation tells you that 2 is used as a factor 4 times. 2⁴=16. (Also called exponential form.)
base	In a percent problem, the base represents how much should be considered 100% (the whole); in exponents, the base is the value that is raised to a power when a number is written in exponential notation. In the example of 5³, 5 is the base.
exponent	The number that indicates how many times the base is used as a factor. In the example of 5³, 3 is the exponent and means that 5 is used three times as a factor: 5^.5^.5
factor	A number that is multiplied by another number or numbers to get a product. For example, in the equation 4^.5=20, 4 and 5 are factors.
squaring	Multiplying a number by itself, or raising the number to a power of 2. 8² can be read as "8 to the second power,” “8 to a power of 2,” or “8 squared.”
cubing	Raising a number to a power of 3. 2³ is read “2 to the third power” or “2 cubed,” and means use 2 as a factor three times in the multiplication. 2³= 2^.2^.2=8.
perfect square	A whole number that can be expressed as a whole number raised to a power of 2. For example, 25 is a perfect square because 25=5^.5=5²
raised to the power	When a base has an exponent, it can be said that the base is “raised to the power” of the exponent. For example, 3⁵ is read as “3 raised to the fifth power.”
inverse operation	A mathematical operation that can reverse or “undo” another operation. Addition and subtraction are inverse operations. Multiplication and division are inverse operations.
square root	A value that can be multiplied by itself to give the original number. For example if the original number is 9, then 3 is its square root because 3 multiplied by itself (3², pronounced "3 squared") equals 9. The symbol used for a square root is called a radical sign and goes on top of the number. The square root of 9 is written as: \(\ \sqrt{9}\)
radical sign	The symbol used for square root and other roots. It looks like \(\ \sqrt{}\) and the number is written under it. For example, the square root of nine is written with the radical sign: \(\ \sqrt{9}\)
order of operations	The rules that determine the sequence of calculations in an expression with more than one type of computation.
expression	A mathematical phrase. For example, \(\ 8\cdot2+3\) is an expression. It represents the quantity 19.
Grouping symbols	Symbols such as parentheses, braces, brackets, and fraction bars that indicate the numbers to be grouped together.
exponents	The number that indicates how many times the base is used as a factor. In the example of 5³, 3 is the exponent and means that 5 is used three times as a factor: \(\ 5\cdot 5\cdot5\)
square roots	A value that can be multiplied by itself to give the original number. For example if the original number is 9, then 3 multiplied by itself (3² pronounced "3 squared") equals 9. The symbol used for a square root is called a radical sign and goes on top of the number. The square root of 9 is written as: \(\ \sqrt{9}\)
Fractions	An expression used to refer to a part of a whole.
Natural numbers	The numbers 1, 2, 3, 4 and so on. Also called counting numbers.
numerator	The top number of a fraction that tells how many parts of a whole are being represented.
denominator	The bottom number of a fraction that tells how many equal parts are in the whole.
divisible	Can be divided by a number without leaving a remainder. For example, 20 is divisible by 4 because \(\ 20 \div 4=5\) (no remainder).
multiple	Any number that has a given number as a factor. For example, 4, 8, 16, and 200 are multiples of 4, because 4 is a factor of each of these numbers.
Divisibility tests	A rule that tells quickly whether dividing a number by another number can be done without leaving a remainder.
even number	A whole number that is divisible by 2.
divisor	The number that is being divided into the dividend in a division problem. In the problem \(\ 8\div2=4\), 2 is the divisor.
actor pair	A pair of numbers whose product is a given number. For example, 2 and 15 are a factor pair of of 30 because 2^.15=30. Both 2 and 15 are factors of 30.
prime number	A natural number with exactly two factors: 1 and the number itself.
composite number	A natural number that has at least one factor other than 1 and itself.
prime factorization	A number written as the product of its prime factors.
factor tree	A diagram showing how a number can be written as factors, and those factors written as a product of factors, and so on until only prime numbers are used.
equivalent fractions	Two or more fractions that name the same part of the whole.
simplest form	A fraction is in simplest form if the numerator and denominator have no common factors other than 1.
lowest terms	A fraction is in lowest terms if the numerator and denominator have no common factors other than 1.
prime factorization	A number written as the product of its prime factors.
common denominator	A number that is a multiple of all of the denominators in a group of fractions.
mixed numbers	An expression in which a whole number is combined with a proper fraction. For example \(\ 5\frac{2}{3}\) is a mixed number.
improper fraction	A fraction in which the numerator is equal to or greater than the denominator.
reciprocals	A number that when multiplied by a given number gives a product of 1. For example, \(\ \frac{2}{7}\) and \(\ \frac{7}{2}\) are reciprocals of each other.
mixed number	An expression in which a whole number is combined with a proper fraction. For example \(\ 5 \frac{2}{3}\) is a mixed number.
like denominators	Denominators that are the same.
unlike denominators	Denominators that are different from each other. For example the fractions \(\ \frac{1}{4}\) and \(\ \frac{1}{8}\) have different denominators, one denominator being 4 and the other denominator being 8.
least common multiple	(LCM) The least, or smallest, number that is a multiple of two or more numbers.
prime factorization	A number written as the product of its prime factors.
least common denominator	(LCD) The least, or smallest, number that is a multiple of all the denominators in a group of fractions.
Decimal numbers	Decimal numbers are numbers whose place value is based on 10s, including whole numbers and decimal fractions, which have decimal points and digits to the right of the decimal point. The numbers 18, 4.12 and 0.008 are all decimal numbers.
decimal fractions	A fraction written as a decimal point and digits to the right of the decimal point.
trailing zeros	A placeholder 0 that occurs after the final non-0 digit in a decimal number. In the number 22.0900, the 0s in the thousandths and ten-thousandths places are trailing zeros.
Ratios	A comparison of two numbers by division. For example, the ratio of 15 boys in a class to 14 girls in the same class is 15:14.
Rates	A ratio that compares quantities measured in different units. For example, a speed compares the distance traveled to a length of time.
unit rate	A rate in which the second quantity is one unit. If a bird flaps its wings 240 times in 3 minutes, the unit rate of wing flapping is 80 flaps per 1 minute.
unit price	A rate in which the quantity is expressed as one unit. If 12 candy bars cost 4, the unit price is per 1 candy bar.
proportion	An equation that states that two ratios are equal.
percent	A ratio that compares a number to 100. “Per cent” means “per 100,” or “how many out of 100.”
amount	In a percent problem, the portion of the whole corresponding to the percent.
Measurement	The use of standard units to find out the size or quantity of items such as length, width, height, mass, weight, volume, temperature or time.
metric system	A widely used system of measurement that is based on the decimal system and multiples of 10.
U.S. customary measurement system	The most common system of measurement used in the United States. It is based on English measurement systems of the 18th century.
units of measurement	A standard amount or quantity. For example, an inch is a unit of measurement.
Length	The distance from one end to the other or the distance from one point to another.
inch	A unit for measuring length in the U.S. customary measurement system. 1 foot = 12 inches
foot	A unit for measuring length in the U.S. customary measurement system. 1 foot = 12 inches
yard	A unit for measuring length in the U.S. customary measurement system. 1 = 3 feet or 36 inches
mile	A unit for measuring length in the U.S. customary measurement system. 1 mile = 5,280 feet or 1,760 yards.
factor label method	One method of converting a measurement from one unit of measurement to another unit of measurement. In this method, you multiply the original measurement by unit fractions containing different units of measurement to obtain the new unit of measurement.
weight	A mathematical description of how heavy an object is.
ounce	A unit for measuring weight in the U.S. customary measurement system. 16 ounces = 1 pound.
pound	A unit for measuring weight in the U.S. customary measurement system. 16 ounces = 1 pound.
ton	A unit for measuring the weight of heavier items in the U.S. customary measurement system. 1 ton = 2,000 pounds
Capacity	The amount of liquid (or other pourable substance) that an object can hold when it's full.
fluid ounce	A unit of capacity equal to \(\ \frac{1}{8}\) of a cup. One fluid ounce of water at 62^oF weighs about one ounce.
cup	A unit of capacity equal to 8 fluid ounces.
pint	A unit of capacity equal to 16 fluid ounces, or 2 cups.
quart	A unit of capacity equal to 32 fluid ounces, or 4 cups.
gallon	A unit equal to 4 quarts, or 128 fluid ounces.
meter	The base unit of length in the Metric system.
liter	The base unit of volume in the Metric system.
gram	The base unit of mass in the Metric system.
prefix	A short set of letters that denote the size of measurement units in the Metric System. Metric prefixes include centi-, milli-, kilo-, and hecto-.
unit equivalents	Statements of equivalence between measurement units within a system or in comparison to another system of units. For example 1 foot = 12 inches or 1 inch = 2.54 centimeters are both examples of unit equivalents.
unit fractions	A fraction where the numerator and denominator are equal amounts. For example: \(\ \frac{1 \text{ kg}}{1000 \text{ g}}\) or \(\ \frac{12 \text{ inches}}{1 \text{ foot}}\). Unit fractions serve to help with conversions in the Factor Label method.
Fahrenheit	A measure of temperature commonly used in the United States. On the Fahrenheit scale, water freezes at 32^o Fahrenheit and boils at 212^o Fahrenheit.
Celsius	A measure of temperature commonly used in countries that use the metric system. On the Celsius scale, water freezes at 0^o Celsius and boils at 100^o Celsius.
plane	In geometry, a two-dimensional surface that continues infinitely. Any three individual points that don't lie on the same line will lie on exactly one plane.
point	A zero-dimensional object that defines a specific location on a plane. It is represented by a small dot.
line	A line is a one-dimensional figure, which extends without end in two directions.
line segment	A finite section of a line between any two points that lie on the line.
ray	A half-line that begins at one point and goes on forever in one direction.
angle	A figure formed by the joining of two rays with a common endpoint.
vertex	A turning point in a graph. Also the endpoint of the two rays that form an angle.
right angle	An angle measuring exactly 90^o.
acute angles	An angle measuring less than 90^o.
obtuse angles	An angle measuring more than 90^o and less than 180^o.
straight angle	An angle measuring exactly 180^o.
Parallel lines	Two or more lines that lie in the same plane but which never intersect.
Perpendicular lines	Two lines that lie in the same plane and intersect at a angle.
supplementary angles	Two angles whose measurements add up to 180^o.
complementary angles	Two angles whose measurements add up to 90^o.
triangle	A polygon with three sides.
polygons	A closed plane figure with three or more straight sides.
congruent	Having the same size and shape.
Acute Triangle	A triangle with three angles that each measure between 0^o and 90^o.
Obtuse Triangle	A triangle with one angle that measures between 90^o and 180^o.
Right Triangle	A triangle containing a right angle.
Equilateral Triangle	A triangle with 3 equal sides.
Isosceles Triangle	A triangle with 2 equal sides.
Scalene Triangle	A triangle in which all three sides are a different length.
corresponding angles	Angles of separate figures that are in the same position within each figure.
corresponding sides	Sides of separate figures that are opposite corresponding angles.
similar	Having the same shape but not necessarily the same size.
Pythagoras	A Greek philosopher and mathematician who lived in the 6th Century B.C.
right triangles	A triangle containing a right angle.
legs	In a right triangle, one of the two sides creating a right angle.
hypotenuse	The side opposite the right angle in any right triangle. The hypotenuse is the longest side of any right triangle.
Pythagorean Theorem	The formula that relates the lengths of the sides of any right triangle: a²+b²=c², where c is the hypotenuse, and a and b are the legs of the right triangle.
Quadrilaterals	A four-sided polygon.
polygon	A closed plane figure with three or more straight sides.
rectangle	A quadrilateral with two pairs of parallel sides and four right angles.
square	A quadrilateral whose sides are all congruent and which has four right angles.
rhombus	A quadrilateral with four congruent sides.
trapezoid	A quadrilateral with one pair of parallel sides.
isosceles trapezoid	A trapezoid with one pair of parallel sides and another pair of opposite sides that are congruent.
area	The amount of space inside a two-dimensional shape, measured in square units.
polygon	A closed plane figure with three or more straight sides.
radius	The distance from the center of a circle to any point on the circle.
diameter	The length across a circle, passing through the center of the circle. A diameter is equal to the length of two radii.
pi	The ratio of a circle’s circumference to its diameter. Pi is denoted by the Greek letter \(\ \pi\). It is often approximated as 3.14 or \(\ \frac{22}{7}\).
face	The flat surface of a solid figure.
Polyhedrons	A solid whose faces are polygons.
cube	A six-sided polyhedron that has congruent squares as faces.
rectangular prism	A polyhedron that has three pairs of congruent, rectangular, parallel faces.
pyramids	A polyhedron with a polygonal base and a collection of triangular faces that meet at a point.
cone	A solid figure with a single circular base and a round, smooth face that diminishes to a single point.
sphere	A solid, round figure where every point on the surface is the same distance from the center.
volume	A measurement of how much it takes to fill up a three-dimensional figure. Volume is measured in cubic units.
cylinder	A solid figure with a pair of circular, parallel bases and a round, smooth face between them.
data	Mathematical term for information such as values or measurements.
pictograph	A graph that uses small icons or pictures to represent data.
Bar graphs	A graph that uses horizontal or vertical bars to represent data.
y-axis	The vertical axis of a coordinate plane. Also the vertical axis of a bar graph or histogram.
x-axis	The horizontal axis of a coordinate plane. Also the horizontal axis of a bar graph or histogram.
categorical data	Data that details non-numerical features of an object. Examples of categorical data include eye color, blood type, and types of computers.
histogram	A graph using bars to show continuous quantitative data over a series of similar-sized intervals. The height of the bar shows the frequency of the data, and the width of the bar represents the interval for the data.
circle graph	Also called a pie chart, a type of graph where categorical data is represented as sections of a whole circle.
line graphs	Used to show continuous data, a graph where individual data points are connected with line segments. Line graphs are typically used for data sets that track a quantity over time.
stem-and-leaf plot	A type of graph used to visualize quantitative data. In a stem-and-leaf plot the digits of each number are organized separately to display a set of data.
Mean	The sum of all the data values in a data set divided by the number of items in the data set; also called the average.
median	The middle number or the mean of the two middle numbers of a set of ordered data.
mode	The number that appears most often in a data set.
range	The set of all possible outputs in a function. Also the difference between the greatest value of a data set and the least value.
midrange	The mean of the greatest and least values of a data set.
box-and-whisker plot	A graph that uses a number line to show the distribution of a set of data.
quartiles	The name of quarter sections of an ordered set of data.
bar graphs	A graph that uses horizontal or vertical bars to represent data.
histograms	A graph using bars to show continuous quantitative data over a series of similar-sized intervals. The height of the bar shows the frequency of the data, and the width of the bar represents the interval for the data.
circle graphs	Also called a pie chart, a type of graph where categorical data is represented as sections of a whole circle.
Probability	A measure of how likely it is that something will occur.
trial	A random action or series of actions.
outcome	A result of a trial.
event	A collection of possible outcomes, often describable using a common characteristic, such as rolling an even number with a die or picking a card from a specific suit.
simple event	An event with only one outcome.
compound event	An event with more than one outcome.
equally likely	Having the same likelihood of occurring, such that in a large number of trials, two equally likely outcomes would happen roughly the same number of times.
event space	The set of possible outcomes in an event: for example, the event “rolling an even number” on a die has the event space of 2, 4, and 6.
sample space	The set of all possible outcomes.
tree diagram	A diagram that shows the choices or random outcomes from multiple trials, using branches for each new outcomes.
Fundamental Counting Principle	If one event has \(\ p\) possible outcomes, and another event has \(\ m\) possible outcomes, then there are a total of \(\ p \cdot m\) possible outcomes for the two events.
variable	A letter or symbol used to represent a quantity that can change.
constant	A symbol that represents a quantity that cannot change. It can be a number, letter or a symbol.
expression	A mathematical phrase that can contain a combination of numbers, variables, or operations.
evaluate	To find the value of an expression.
substitute	The replacement of a variable with a number.
sets	A collection or group of things such as numbers.
natural numbers	Also called counting numbers, the numbers 1, 2, 3, 4, ...
counting numbers	Also called natural numbers, the numbers 1, 2, 3, 4, ...
whole numbers	The numbers 0, 1, 2, 3, ..., or all natural numbers plus 0.
negative numbers	Numbers less than 0.
positive numbers	Numbers greater than 0.
Integers	The numbers …, -3, -2, -1, 0, 1, 2, 3...
absolute value	The absolute value of a number is its distance from 0 on a number line.
rational numbers	Numbers that can be written as the ratio of two integers, where the denominator is not zero.
whole numbers	The numbers 0, 1, 2, 3, ..., or all natural numbers plus 0.
Irrational numbers	Numbers that cannot be written as the ratio of two integers—the decimal representation of an irrational number is nonrepeating and nonterminating.
terminating decimals	Numbers whose decimal parts do not continue indefinitely but end eventually—these are all rational numbers.
nonterminating decimals	Numbers whose decimal parts continue forever (without ending in an infinite sequence of zeros)—these decimals can be rational (if they repeat) or irrational (if they are nonrepeating).
repeating decimals	Numbers whose decimal parts repeat a pattern of one or more digits—these are all rational numbers.
nonrepeating decimal	Numbers whose decimal parts continue without repeating—these are irrational numbers.
set	A collection or group of things such as numbers.
real numbers	All rational or irrational numbers.
addends	A number added to one or more other numbers to form a sum.
integers	The numbers ..., -3, -2, -1, 0, 1, 2, 3 ...
rational numbers	Numbers that can be written as the ratio of two integers, where the denominator is not zero.
additive identity	The number 0 is called the additive identity because when you add it to a number, the result you get is the same number. For example, 4+0=4.
identity property of 0	When you add 0 to any number, the sum is the same as the original number. For example, 55+0=55.
inverse operations	A mathematical operation that can reverse or “undo” another operation. Addition and subtraction are inverse operations. Multiplication and division are inverse operations.
opposite	An opposite of a number is the number with the opposite sign, but same absolute value. For example, the opposite of 72 is -72. A number plus its opposite is always 0.
additive inverses	Any two numbers whose sum is zero, such as 3 and -3, because 3+(-3)=0.
real numbers	All rational or irrational numbers.
identity property of 1	When you multiply any number by 1, the product is the same as the original number. For example, 9(1)=9.
multiplicative inverses	Two numbers are multiplicative inverses if their product is 1. For example, \(\ \frac{3}{1}\cdot\frac{1}{3}=\frac{3}{3}=1\).
reciprocal	A number that when multiplied by a given number gives a product of 1. For example, \(\ \frac{2}{7}\) and \(\ \frac{7}{2}\) are reciprocals of each other.
commutative property of addition	Two real numbers can be added in any order without changing the sum. For example, 6+4=4+6.
commutative property of multiplication	Two real numbers can be multiplied in any order without changing the product. For example, \(\ 8\cdot9=9\cdot8\).
associative property of addition	For three or more real numbers, the sum is the same regardless of how you group the numbers. For example, \(\ (6+2)+1=6+(2+1)\).
associative property of multiplication	For three or more real numbers, the product is the same regardless of how you group the numbers. For example, \(\ (3\cdot5)\cdot7=3\cdot(5\cdot7)\).
distributive property of multiplication	The product of a sum (or a difference) and a number is the same as the sum (or difference) of the product of each addend (or each number being subtracted) and the number. For example, \(\ 3(4+2)=3(4)+3(2)\), and \(\ 3(4-2)=3(4)-3(2)\).
order of operations	The rules that determine the sequence of calculations in an expression with more than one type of computation.
arithmetic operations	The operations of addition, subtraction, multiplication and division.
exponential notation	A shorter way to write repeated multiplication. For example, \(\ 2^4\) means \(\ 2\cdot2\cdot2\cdot2\). Two is used as a factor 4 times.
base	The expression that is being raised to a power when using exponential notation. In \(\ 5^3\), 5 is the base, which is the number that is repeatedly multiplied. \(\ 5^3=5\cdot5\cdot5\) In \(\ a^b\), \(\ a\) is the base.
exponent	When a number is expressed in the form \(\ a^b\), \(\ b\) is the exponent. The exponent indicates how many times the base is used as a factor. Power and exponent mean the same thing.
power	In an exponent \(\ a^b\), the power is represented by \(\ b\)
equation	A mathematical statement that two expressions are equal.
Expressions	A mathematical phrase that can contain a combination of numbers, variables, or operations.
terms	A number or product of a number and variables raised to powers. \(\ 4x, -5y^2, 6\), and \(\ x^3y^4\) are all examples of terms.
variables	A letter or symbol used to represent a quantity that can change.
coefficient	A number that multiplies a variable.
isolate the variable	A method for solving an equation that involves rewriting an equivalent equation in which the variable is on one side of the equation and everything else is on the other side of the equation.
addition property of equality	For all real numbers \(\ a\), \(\ b\), and \(\ c\), if \(\ a=b\) then \(\ a+c=b+c\). If two expressions are equal to each other and you add the same value to both sides of the equation, the equation will remain equal.
one-step equations	An equation that requires only one step to solve.
multiplication property of equality	For all real numbers \(\ a\), \(\ b\), and \(\ c\), \(\ c \neq 0\): If \(\ a=b\), then \(\ ac=bc\). If two expressions are equal to each other and you multiply both sides of the equation by the same non-zero number, the equation will remain equal.
multi-step equation	An equation that requires more than one step to solve.
like terms	Terms that contain the same variables raised to the same powers. For example, \(\ 3x\) and \(\ -8x\) are like terms, as are \(\ 8xy^2\) and \(\ 0.5xy^2\).
like terms	Terms that contain the same variables raised to the same powers. For example, \(\ 3x\) and \(\ -8x\) are like terms, as are \(\ 8xy^2\) and \(\ 0.5xy^2\)
constants	A symbol that represents a quantity that cannot change. It can be a number, letter or a symbol.
equations	A mathematical statement that two expressions are equal.
formulas	An equation or an expression that states a rule for a relationship among quantities. For example, the formula for finding the area of a rectangle can be represented as \(\ A=l\cdot w\), or simply \(\ l\cdot w\)
inequalities	A mathematical statement that shows the relationship between two expressions where one expression can be greater than or less than the other expression. An inequality is written by using an inequality sign (>, <, ≤, ≥, ≠).
inequality	A mathematical statement that shows the relationship between two expressions where one expression can be greater than or less than the other expression. An inequality is written by using an inequality sign (>, <, ≤, ≥, ≠).
compound inequality	A statement including two inequality statements joined either by the word “or” or “and.” For example, \(\ 2x-3<5\) and \(\ x+14>11\).
base	The expression that is being raised to a power when using exponential notation. In 5³, 5 is the base (which is the number that is repeatedly multiplied). \(\ 5^3=5\cdot5\cdot5\) And in \(\ a^b\), the base is \(\ a\).
exponent	When a number is expressed in the form \(\ a^b\), \(\ b\) is the exponent. The exponent indicates how many times the base is used as a factor. Power and exponent mean the same thing.
Exponential notation	A shorter way to write repeated multiplication. For example, \(\ 2^4\) means \(\ 2\cdot2\cdot2\cdot2\). Two is used as a factor 4 times.
Product Rule for Exponents	To multiply two exponential terms with the same base, add their exponents. \(\ (x^a)(x^b)=x^{a+b}\)
Power Rule for Exponents	To raise a power to a power, multiply the exponents. \(\ (x^a)^b=x^{a\cdot b}
Quotient Rule for Exponents	For any non-zero number \(\ x\) and any integers \(\ a\) and \(\ b\): \(\ \frac{x^a}{x^b}=x^{a-b}\)
exponents	When a number is expressed in the form \(\ a^b\), \(\ b\) is the exponent. The exponent indicates how many times the base is used as a factor. Power and exponent mean the same thing.
Product Raised to a Power	The product of two or more non-zero numbers raised to a power equals the product of each number raised to the same power: \(\ (ab)^x=a^x\cdot b^x\)
scientific notation	A positive number is written in scientific notation if it is written as \(\ a\times10^n\) where the coefficient \(\ a\) has a value such that \(\ 1\leq a\leq10\) and \(\ n\) is an integer.
exponent	When a number is expressed in the form \(\ a^b\), \(\ b\) is the exponent. The exponent indicates how many times the base is used as a factor. Power and exponent mean the same thing.
polynomial	A monomial or the sum or difference of two or more monomials.
monomial	A polynomial with exactly one term. \(\ 4x\), \(\ -5y^2\), and 6 are all examples of monomials.
coefficient	A number that multiplies a variable.
degree	The value of an exponent.
term	A number or product of a number and variables raised to powers. \(\ 4x\), \(\ -5y^2\), \(\ 6\), and \(\ x^3y^4\) are all examples of terms.
monomial	A polynomial with exactly one term. \(\ 4x\), \(\ -5y^2\), and \(\ 6\) are all examples of monomials.
binomial	A polynomial with exactly two terms, such as \(\ 5y^2-4^x\) and \(\ x^5+6\).
trinomial	A polynomial with exactly three terms, such as \(\ 5y^2-4y+4\) and \(\ x^2+2xy+y^2\).
like terms	Terms that contain the same variables raised to the same powers. For example, \(\ 3x\) and \(\ -8x\) are like terms, as are \(\ 8xy^2\) and \(\ 0.5xy^2\).
polynomials	A monomial or the sum or difference of two or more monomials.
monomials	A polynomial with exactly one term. \(\ 4x\), \(\ -5y^2\), and 6 are all examples of monomials.
binomials	A polynomial with exactly two terms, such as \(\ 5y^2-4x\) and \(\ x^5+6\).
degree of a monomial	The degree of a monomial is the power to which the variable is raised. For example, the monomial \(\ 5y^2\) has a degree of 2. If the monomial contains several variables then the degree of the monomial is the sum of the degree of all the variables. For example, the monomial \(\ 7x^2y^3\) has a degree of 5.
degree of a polynomial	The highest exponent or sum of exponents of a term in a polynomial. For example, \(\ 7x^2y^3+3x^2y-8\) is a 5th degree polynomial because the highest sum of exponents in a term is \(\ 2+3=5\).
Factoring	The process of breaking a number down into its multiplicative factors.
prime factor	A factor that only has itself and as factors.
prime number	A prime number is a natural number with exactly two distinct factors, 1 and itself. The number 1 is not a prime number because it does not have two distinct factors.
prime factorization	The process of breaking down a number (or expression) into its prime multiplicative factors. For example, the prime factorization of \(\ 12xy\) is \(\ 2\cdot2\cdot3\cdot x\cdot y\).
greatest common factor (GCF)	The product of the prime factors that two or more terms have in common. The greatest common factor of \(\ xyz\) and \(\ 3xy\) is \(\ xy\).
Perfect squares	A square of a whole number. Since \(\ 1^2=1\), \(\ 2^2=4\), \(\ 3^2=9\), etc., 1, 4, and 9 are perfect squares.
perfect square trinomial	A trinomial that is the product of a binomial times itself, such as \(\ a^2+2ab+b^2\) (from \(\ (a+b)^2\)), and \(\ a^2-2ab+b^2\) (from \(\ (a-b)^2\)).
quadratic equation	An equation that can be written in the form \(\ ax^2+bx+c=0\), where \(\ x\) is a variable, and \(\ a\), \(\ b\), and \(\ c\) are constants with \(\ a\neq0\).
Principle of Zero Products	If \(\ ab=0\), then either \(\ a=0\) or \(\ b=0\), or both \(\ a\) and \(\ b\) are 0.
coordinate plane	A plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis.
axis	One of two perpendicular lines of a coordinate place that intersect at the origin. The plural form of axis is axes.
x-axis	The horizontal axis of a coordinate plane. Also the horizontal axis of a bar graph or histogram.
y-axis	The vertical axis of a coordinate plane. Also the vertical axis of a bar graph or histogram.
origin	The point where the x-axis and the y-axis intersect on the coordinate plane (0, 0).
quadrants	The x- and y-axes divide the coordinate plane into four regions. These regions are called quadrants.
ordered pairs	A pair of numbers that indicates a point on a coordinate plane.
x-coordinate	The first number in an ordered pair, which tells the distance to the right or left from the origin when graphing in a coordinate plane.
y-coordinate	The second number in an ordered pair, which tells the distance to move up or down from the origin when graphing in a coordinate plane.
linear relationships	A linear relationship exists between two variables if, when you plot their values on a coordinate system, you get a straight line.
ordered pairs	A pair of numbers that indicates a point on a coordinate plane.
linear equation	An equation in two variables whose ordered pairs graph as a straight line.
x-intercept	The point where the graph of a linear equation intersects the x-axis (x, 0).
y-intercept	The point where the graph of a linear equation intersects the y-axis (0, y).
slope	The ratio of the vertical change to the horizontal change of two points on a line. \(\ \text{Slope }=\frac{\text{rise}}{\text{run}}\)
rise	The vertical change between two points on a line.
run	The horizontal change between two points on a line.
slope-intercept form	A linear equation written in the form \(\ y=mx+b\), where \(\ m\) represents the slope of the line, and \(\ b\) represents the y-value of the y-intercept, \(\ (0, b)\).
parallel lines	Two or more lines that lie in the same plane but which never intersect.
perpendicular lines	Two lines that lie in the same plane and intersect at a 90^o angle.
boundary line	A line that divides the coordinate plane into two regions. If points along the boundary line are included in the solution set, then a solid line is used; if points along the boundary line are not included then a dotted line is used.
linear inequality	A mathematical statement in two variables using the inequality symbols <, >, ≤, or ≥ to show the relationship between two expressions. When the inequality symbol is replaced by an equal sign, the resulting related equation will graph as a straight line.
system of linear equations	Two or more linear equations with the same variables.
consistent system of linear equations	A system of linear equations that has at least one solution.
inconsistent system of linear equations	A system of linear equations that has no solutions.
independent linear equations	Equations that graph as different straight lines.
dependent linear equations	Equations that graph as the same straight line.
system of linear inequalities	Two or more linear inequalities with the same variables.
substitution method	A method of solving a system of equations. Given a system, the substitution method allows you to create a simpler, one-variable equation by substituting one quantity in for an equivalent quantity.
elimination method	A method of solving a system of equations. Given a system, the elimination method allows you to add the two equations in order to eliminate a common variable.
Rational expressions	A fraction that contains a polynomial as the numerator, denominator, or both.
domain	The set of all possible input values for the variable in a function.
excluded values	A value for the variable that is not included in the domain because it would cause the function to be undefined.
greatest common factor	The largest number (or expression) that is a factor of a set of two or more numbers (or expressions).
least common denominator	The smallest number (or expression) that is a multiple of all the denominators in a group of fractions (or rational expressions).
least common multiple	The smallest number (or expression) that is a multiple of a set of two or more numbers (or expressions).
prime factorization	The process of breaking down a number (or expression) into its prime multiplicative factors. For example, the prime factorization of \(\ 12xy\) is \(\ 2\cdot 2\cdot 3\cdot x\cdot y\).
complex fraction	A quotient of two fractions.
complex rational expression	A quotient of two rational expressions.
rational equations	An equation that contains one or more rational expressions.
extraneous solutions	A solution of the simplified form of an equation that does not satisfy the original equation and must be discarded.
Rational formulas	A formula expressed as a rational equation.
constant of variation	Represented by the variable \(\ k\) in variation problems, the constant of variation is a number that relates the input and the output.
direct variation	A type of variation where the output varies directly with the input. Direct variation is represented by the formula \(\ y=kx\).
inverse variation	A type of variation where the output varies inversely with the input. Inverse variation is represented by the formula \(\ y=\frac{k}{x}\).
joint variation	A type of variation where the output varies jointly with multiple inputs. Joint variation is represented by the formula \(\ y=kxz\).
exponential functions	A function of the form \(f(x)=b^x\) where \(b > 0\) and \(b \neq 1\).
square root	A number that when multiplied by itself gives the original nonnegative number. For example, \(\ 6\cdot6=36\) and \(\ -6\cdot-6=36\) so 6 is the positive square of 36 and -6 is the negative square root of 36.
radical symbol	The symbol, \(\ \sqrt{ \quad}\), used to denote the process of taking a root of a quantity.
radicand	The number or value under the radical symbol.
principal root	The positive square root of a number, as in \(\ \sqrt{16}=4\). By definition, the radical symbol always means to find the principal root. Note that zero has only one square root, itself (since \(\ 0\cdot 0=0\)).
Product Raised to a Power Rule	The product of two or more non-zero numbers raised to a power equals the product of each number raised to the same power: \(\ (ab)^x=a^x\cdot b^x\)
Radical expressions	An expression that contains a radical.
principal root	The positive square root of a number, as in \(\ \sqrt{16}=4\). By definition, the radical symbol always means to find the principal root. Note that zero has only one square root, itself (since \(\ 0\cdot0=0\)).
cube root	The number which, when multiplied together three times yields the original number. For example, the cube root of 64 is 4 because \(\ 4\cdot 4\cdot 4=64\).
index	The small positive integer just outside and above the radical symbol that denotes the root. For example, \(\ \sqrt[3]{ }\) denotes the cube root.
perfect cube	A number whose cube root is an integer.
half-life	The amount of time it takes a substance to decrease to half its original amount.
principal	In finance, the amount of money on which interest is calculated.
exponential decay	An exponential function of the form \(f(x) = b^x\), where \(0 < b < 1\). The function decreases as \(x\) increases.
exponential growth	An exponential function of the form \(f(x) = b^x\), where \(b > 1\) and \(b \neq 0\). The function increases as \(x\) increases.
rational exponent	An exponent that is a fraction.
Quotient Raised to a Power Rule	For any real numbers \(\ a\) and \(\ b\) \(\ (b\neq0)\) and any positive integer \(\ x\): \(\ (\frac{a}{b})^\frac{1}{x}=\frac{a^\frac{1}{x}}{b^\frac{1}{x}}\). For any real numbers a and b \(\ (b\neq0)\) and any positive integer \(\ x\): \(\ \sqrt[x]{\frac{a}{b}}=\frac{\sqrt[x]{a}}{\sqrt[x]{b}}\).
rationalizing a denominator	The process by which a fraction containing radicals in the denominator is rewritten to have only rational numbers in the denominator.
conjugate	One binomial in a conjugate pair. Given the binomial \(\ a+b\), the conjugate is \(\ a-b\); given \(\ a-b\) the conjugate is \(\ a+b\).
conjugate pair	A pair of binomials that, when multiplied, follow the pattern: \(\ (a+b)(a-b)=a^2-b^2\). The product of a pair of binomials that are conjugates is the difference of two squares.
radical expression	An expression that contains a radical.
radical equation	An equation that contains a radical expression.
imaginary number	A number in the form \(\ bi\), where \(\ b\) is a real number and \(\ i\) is the square root of -1.
complex number	A number in the form \(\ a+bi\), where \(\ a\) and \(\ b\) are real numbers and \(\ i\) is the square root of -1.
real part	The real term, \(\ a\), in a complex number \(\ a+bi\).
imaginary part	The imaginary term, \(\ bi\), in a complex number \(\ a+bi\).
complex numbers	A number in the form \(\ a+bi\), where \(\ a\) and \(\ b\) are real numbers and \(\ i\) is the square root of -1.
Square Root Property	If \(\ x^2=a^2\), then \(\ x=a\) or \(\ x=-a\).
completing the square	A method for solving quadratic equations by rewriting one side of the equation as a squared binomial.
Square Root Property	If \(\ x^2=a^2\), then \(\ x=a\) or \(\ x=-a\).
discriminant	In the Quadratic Formula, the expression underneath the radical symbol: \(\ b^2-4ac\). The discriminant can be used to determine the number and type of solutions the formula will reveal.
relation	A correspondence between sets of values or information.
function	A relation that assigns to each x-value exactly one y-value.
domain of the function	The set of all input values or x-coordinates of the function.
range of the function	The set of all output values or y-coordinates of the function.
function notation	An equation that takes the form \(\ f(x)=\), and is read "\(\ f\) of \(\ x\) is..." For example, \(\ f(x)=3x+7\).
parabola	A u-shaped graph which is produced by a quadratic function.
line of reflection	The line that cuts a parabola into two halves (which are mirror images of each other).
common logarithm	A logarithm using 10 as the base, such as log₁₀.
Natural logarithms	A logarithm that uses e as the base (log_e).
e	An irrational number, approximately 2.718281828459; sometimes called Euler’s number.
logarithms	A calculation in which the exponent \(\ y\) in \(\ x=b^y\) is found when given \(\ x\) and \(\ b\); the corresponding notation is \(\ \log_bx=y\).
common log	A logarithm using 10 as the base (\(\ \log_{10}\)).
natural log	A logarithm using \(\ e\) as the base, written as \(\ \log_e\).
amplitude	The distance between the highest point and the rest position (zero position) in a wave.
adjacent side	For a given acute angle in a right triangle, the adjacent side to that angle is the side that, along with the hypotenuse, forms that acute angle.
opposite side	For a given acute angle in a right triangle, the opposite side to that angle is the side that is not one of the two sides that form that acute angle.
sine	If \(A\) is an acute angle of a right triangle, then the sine of angle \(A\) is the ratio of the length of the side opposite angle \(A\) over the length of the hypotenuse.
cosine	If \(A\) is an acute angle of a right triangle, then the cosine of angle \(A\) is the ratio of the length of the side adjacent to angle \(A\) over the length of the hypotenuse.
tangent	If \(A\) is an acute angle of a right triangle, then the tangent of angle \(A\) is the ratio of the length of the side opposite angle \(A\) over the length of the side adjacent to .
trigonometric functions	A function of an angle expressed as the ratio of two of the sides of a right triangle that contains that angle; the sine, cosine, tangent, cotangent, secant, cosecant.
identity	An equation that is true for any possible value of the variable.
cofunctions	Two trigonometric functions, such as sine and cosine, for which the value of the first function at an acute angle equals the value of the second function at the complement of that angle.
inverse function	If you take a function and reverse its inputs and outputs, then you get its inverse function.
initial side	The stationary ray that forms an angle in standard position and lies on the positive \(x\)-axis.
terminal side	The ray that has been rotated around the origin to form an angle with the stationary ray that is the initial side of the angle.
standard position	The placement of an angle upon a set of coordinate axes with its vertex at the origin, its initial side placed along the positive \(x\)-axis, and a directional arrow pointing to the angle’s terminal side.
coterminal angles	The description of two angles drawn in standard position that share their terminal side.
reference angle	The angle formed by the terminal side of an angle in standard position and the \(x\)-axis, whose measure is between 0° and 90°.
unit circle	A circle centered at the origin that has radius 1.
radian measure	A measure of a central angle given by the ratio of the arc length to the radius.
central angle	An angle whose vertex is at the center of a circle.
symmetric about the y-axis	The left and right halves of the graph are mirror images of each other over the \(y\)-axis.
periodic function	A function whose graph has a pattern that repeats forever in both directions.
period	The length of the smallest interval that contains exactly one copy of the repeating pattern of a periodic function.
cycle	Any part of a graph of a periodic function that is one period long.
logarithmic functions	A function using a logarithm, of the form \(f(x) = \log_{b}x\), \(b > 0\) and \(b \neq 1\). A calculation in which the exponent \(y\) in \(x = b^y\) is found when given \(x\) and \(b\); the corresponding notation is \(\log_{b}x = y\).
logarithm	A calculation in which the exponent \(y\) in \(x = b^y\) is found when given \(x\) and \(b\); the corresponding notation is \(\log_{b}x = y\).