Absolute Value
The number's distance from 0 on a number line. The absolute value of a number
x is denoted by 
x and

x =
xx > 0
 xx < 0
So with absolute value, we're not concerned with whether
x is positive or negative, we just want to know how far it is away from 0. Because 0 has had some problems with
x in the past, and has applied for a restraining order.
The value of a number when you strip it naked of any negative signs. It's also the distance the number is away from zero on the number line.
The distance a number is from 0. The absolute value is always positive.
Two bars that drop around an expression and force everything to be sunshine and rainbows: real positive stuff.
The magnitude of a number when sign is not considered. Or, the positive version of the story. It's like when you tell your friends you might have failed the driver's test, but at least you got some parallel parking practice out of it.
Any negative value inside an absolute value sign is changed to positive.
Acute Angles
angle less that 90°; not "the nice one"
Acute Triangle
a triangle with three acute angles (angles less than 90°) ; so adorable and petite
A triangle that's slightly less cute than asupercute triangle. For that to be true, all the angles in the triangle have to be less than 90°.
A triangle with all three interior angles less than 90°. It may or may not be attractive.
Adjacent
next to each other; you want to sit adjacent to the hot guy/gal
The conjoined twins of the geometry world. Adjacent angles always share a vertex and a side.
Adjacent Angles
angles that share a side
Two angles that share both a side and a vertex. They stick by each other through and through.
Alternate Exterior Angles
angles on opposite sides of the transversal and on the exterior of the parallel lines
The pair of angles on the outside of the two lines cut by the transversal and on alternate sides of the transversal. Alternate exterior angles are congruent if and only if the two lines crossed by the transversal are parallel.
Two angles that are on the outside of the parallel lines and opposite sides of the transversal. These types of angles are always congruent to one another.
Alternate Interior Angles
angles on the opposite sides of the transversal and on the interior of the parallel lines
The pair of angles in between the two lines cut by the transversal and on alternate sides of the transversal. Alternate interior angles are congruent if and only if the two lines crossed by the transversal are parallel.
Two angles that are on the inside of the parallel lines and opposite sides of the transversal. These types of angles are always congruent to one another.
Angle
the shape formed when two rays meet at a common point (aka "the corner")
The corner of empty space between two lines, rays, or segments that share a point. Usually, angles are measured in degrees (and most of them have at least a bachelor's degree).
The space in between two intersecting lines. We measure the "wideness" of this space in units called degrees.
Apothem
the distance from the center of a regular polygon to the midpoint of one side
The length from the center of a regular polygon to the center of one of its sides. If you look close, it is equivalent to the height of a triangle if you were to slice the polygon into the threesided shapes.
Area
The amount of space inside the boundary of a closed shape. As in, "there is
x room to fit all the aliens inside Area 51."
The amount of space within the boundaries of a twodimensional shape, reported in square units (like miles
^{2} or feet
^{2}). Area is essentially space, but don't go around saying things like, "areaships," "area cadets," or the areabar.
The twodimensional space contained by a particular region.
The amount of twodimensional space that is taken up within a shape's perimeter.
Arithmetic Patterns
numbers in a pattern that are separated by a common difference
Base Of A Polygon
the bottom side of a polygon
Base Of A Solid
the bottom surface of an object; its tush
Basic Counting Principle
to find the total number of possible combinations multiply the number of options
Biased Questions
questions that try to influence the interviewee
Binomial
an algebraic expression with two terms
A polynomial with two terms.
A polynomial with only two terms. The expression
x – 3 is a binomial, and so is 96
x^{2}y + 13,0278,543.
Box And Whisker Plot
a plot that displays data broken into four quartiles, where the box represents Q1 to Q3 and the whiskers represent the extreme values
A representation of data that displays the range and quartiles of the data set. Looks like a kitty cat when you squint and tilt your head to the left.
A plot that depicts the four quartiles of date. No cat necessary.
A plot that clearly shows all of the quartiles in a set of quantitative data.
Cartesian Coordinate System
a system that has perpendicular axes, usually the x and yaxis
Chord
a line segment connecting two points on a circle; not "do re mi"
A line segment whose endpoints are both on a circle. Not a collection of musical notes.
Any segment from one point on a circle to another. Despite what you might think, they aren't all that musical.
Circle
A closed plane figure wherein points on the boundary are equidistant from the fixed center. More importantly, it is the shape of a pizza pie.
The set of all points in a plane that are exactly
r units away from point
O, where
r is the radius and
O is the center. The basis for such artifacts as wheels, wedding rings, and many types of cookies. We write "⊙
O" to denote "the circle with center
O."
A perfectly round twodimensional shape. More technically, it's the set of all points that are the same distance away from another point (called the center).
A round conic defined by an eccentricity of 0. Also, a favorite shape for the terminally lost.
Common Denominator
the bottom part of fractions; in this case when more than one fraction has the same bottom as all the others
Commutative
when the order of the number doesn't matter; this works for addition and multiplication, but not subtraction nor division. 6 + 2 = 2 + 6 and 6 × 2 = 2 × 6
Complementary Angles
Angles that add up to 90°
Two wrongs don't make a right, but two complementary angles do. They're two angles that add up to 90° exactly.
Two angles that add up to 90°. Two wrongs don't make a right, but two complementary angles sure do.
Complementary Events
in probability, results that do not overlap with one another (when flipping a coin, if you get a tail, then the complementary event is getting a head)
Compound Events
in probability, when there is more than one outcome, which may (taking a second card after a first has been chosen) or may not (throwing two dice at the same time) affect the outcome of the other
These are when more than one event occurs. For instance, instead of picking one card from a deck, you pick two cards and find the likelihood of a King of Hearts and Queen of Diamonds being selected. Things are getting a bit more complicated with this one.
Compound Interest
adding interest earned before calculating the new interest
Cone
chocolate or brownie fudge? ; a solid with circular base and a curved side that ends in one point and has one vertex; a duncecap
A threedimensional solid with a circular base and one vertex. We prefer to think of it as the waffle thing that ice cream comes in.
A 3D solid with a circular base and a curved surface that meets at a point. Essentially, a pyramid with a circular base.
Congruent Angles
two or more angles that have the same measurement
Constant
A value that does not change. Like pride in one's football team. Exception: the entire Philadelphia Eagles fan base.
A value that does not change.
A value that does not change. Stay gold, Ponyconstant!
A number that doesn't change. Sometimes, we use this to mean a constant term, which is a number that isn't multiplied by any variables. In the expression 3
y + 6, the 6 is a constant term, but the 3 can also be thought of as a constant.
A number that doesn't change. Disproves the whole, "The only constant is change," idea, doesn't it?
A number that doesn't change in value. Like ½ or 7 or 38,501.
A value that does not change because it's oldfashioned and thinks everything is fine as is. When we look at an expression like 6
x + 2, the 2 is the constant.
Coplanar
on the same plane
Used to describe lines or points that are all on the same plane.
Correlation
how two variables relate to each other
The measure of the linear relationship between two variables. Is not causation.
If this is present, then there is an apparent trend in bivariate data. Correlation is generally positive or negative.
Corresponding Angles
when a transversal intersects two lines, these angles are in the same position on each line. When a transversal crosses two parallel lines, corresponding angles are congruent
Two angles that are in the same relative place compared to each of the two lines and the transversal that cuts them. Corresponding angles are congruent if and only if the two lines crossed by the transversal are parallel.
A pair of angles that are in the same place relative to the transversal and their respective parallel line. They're congruent, too.
Coterminal Angles
angles that share a terminal side
Angles that occupy the same position on the unit circle.
Angles that start and end at the same spots (usually start at θ = 0). They are different in the direction they travel or how many times they go around. (e.g. 270° and 90°, 30° and 360°).
CrossCanceling
reducing the numerator of one fraction with the denominator of another when multiplying fractions; wearing bright orange on top might cancel the orange pants your date has on
Cube
a prism with six congruent faces, all right angles and parallel opposite faces; it is a form of a rectangular prism
Cylinder
a solid with two parallel circular bases; if you "unwrap" the middle section and lay it flat, it is a rectangle
Two parallel congruent circles whose circumferences are connected by a curvy rectangle.
A 3D solid that has two parallel circles for bases and a curved surface that connects them. Essentially, a prism with circles for bases.
Denominator
the bottom number of a fraction
A fraction's bottom. The fraction will usually try to keep this part of him covered up, but his mother will usually produce some scandalous baby picture of him in the tub where his denominator is clearly visible.
A fraction's bottom. The fraction will usually try to keep this part of him covered up, but his mother will usually produce some scandalous baby picture of him in the tub where his denominator is clearly visible.
The polynomial in the bottom of the rational expression. Be sure to keep it nonzero. Bad things might happen if not. Not that we're superstitious or anything.
Diagonal
a line connecting two vertices of a polygon
A segment that connects the 2 pairs of opposite vertices in a quadrilateral. In polygons with more sides, a diagonal connects any two vertices that are not right next to each other.
Diameter
the distance across the center of a circle
A chord of a circle that contains the center of that circle. Or, you know, the length of such a chord.
A segment from one end of the circle to the other. It's a chord that contains the center of the circle, or the length of that chord (which also happens to be twice the radius).
Disperse
Spread or distribute over a wide area
to spread around
Distribute
to spread the term in front of the parentheses to each term inside the parentheses; share the wealth
Dividend
A number that is to be divided by another number. Apparently, this other number got hold of a butcher's knife.
The “thrown off” value from common equity. It’s not the same as interest on a bond, which is a fixed percentage and nondiscretionary. Dividends are discretionary and the company must decide from quarter to quarter whether or not pay one. There are a lot of reasons why companies want to be consistent in their dividend policies, but just know that a dividend on common stock is
not a legal requirement. The middle of the fairway definition of a dividend is rooted in equity investments in stocks. Heinz ketchup, ticker: HNZ, pays a $1.92 dividend per year. It is a roughly $50 stock. It’s “dividend yield” is $1.92 / $50 which is 3.84%.
Divisor
the number doing the dividing
The number which a dividend is divided by. Or, the number doing the dividing. Whichever way makes the most sense to you. Either way, there's going to be some good oldfashioned dividing going on.
Edge
the intersection of two faces on a solid object; this is a line; "Livin' on the Edge"
A line segment that represents the intersection of two faces on a 3D figure.
Equation
An expression that states the equation of two algebraic expressions. Equations: bringing expressions together since 1931.
An expression that states the equivalence of two algebraic expressions.
Two expressions that have the same value, separated by an equal sign. They can play tugofwar as much as they like, but the fact is they'll always be equal.
A mathematical statement that says two expressions are equal. Usually, the two expressions are separated by an equal sign.
A mathematical statement in which two different quantities have the same value. If it's got an equal sign (=) in it, it's an equation.
A complete math sentence. It connects two expressions using an equal sign.
Equiangular
a figure where all angles are equal in measure
Equilateral Triangle
a triangle with three congruent sides
A triangle that has three congruent sides. It should also be known that an equilateral triangle has three 60° congruent angles as well.
A triangle with all three side lengths that are equal. All three angles are also equal. If it has three of anything else, they're equal too.
Equivalent
equal to
Experimental Probability
probability calculated by the outcome of an experiment or trial
This is when we actually flip a coin, pull colored socks from the drawer, and so on, and record the results. This is real stuff.
Exponents
the power to which a number or expression is raised
Expression
a fragment of a mathematical sentence; it doesn't have a sign of equality
A collection of numbers, variables, and operations with no equal sign. Not the look on your face.
A mathematical quantity expressed in terms of constants and variables. No equal signs on these bad boys, since they represent a single value.
Extreme Values
the largest and smallest values in data set; think extremes  extreme sports are at the high end of danger
Values that are more than 3(IQR) away from the outer quartiles; shown as open circles on a box and whisker plot.
Face
a flat side of a 3dimensional object
The flat side of a 3D figure.
Factor
A number that divides evenly into another number. For example, 8 and 3 are factors of 24. Oh great—now we're really gonna hear it from 2, 4, 6 and 12. We said
for example. Sheesh.
A number that divides evenly into another number. For example, 8 and 3 are factors of 24. Oh great—now we're really gonna hear it from 2, 4, 6 and 12. We said for example. Sheesh.
Factorial
the product of all positive integers less than or equal to the given number; 5! = 5 × 4 × 3 × 2 × 1 = 120; a very excited number
n! =
n × (
n – 1) × (
n – 2) . . . × 2 × 1. The most excited of all key terms.
The product of a number and all the numbers before it, starting with 1, so 5! would be 5 times all the numbers before it down to one: 5 × 4 × 3 × 2 × 1
When you see the !, multiply the original number by one less than that number times one less than that number, until you get all the way to the number 1. For instance, 5! = 5 × 4 × 3 × 2 × 1.
Fauna
Animals of a particular habitat or time period
Finite Decimals
decimals that have an ending; unlike that dreadful movie from last weekend that seemed to never end
Frequency
the number of times an event occurs; Jim asked Danielle out with uncommon frequency
Geometric Patterns
numbers in a pattern that are separated by a common ratio (number being multiplied)
Golden Ratio
a ideal proportion that occurs regularly in nature, architecture, and art; approximately 1.618 (not 6'0", 185...)
The ratio that is seen in nature and art. It makes structures look proportional.
Greatest Common Factor (GCF)
The largest positive integer that divides evenly into two or more nonzero numbers. For example, the
GCF of 18 and 24 is 6.
It is also known as the
greatest common divisor or
highest common factor. It goes by many names, and has a different passport for each. How Jason Bourne is that?
The largest positive integer that evenly divides (with zero remainder) two or more nonzero numbers. It is also known as the
greatest common divisor or
highest common factor. For example, the
GCF of 18 and 24 is 6.
Hexagon
a sixsided figure
Hexagonal Prism
a prism with hexagons for bases; opposite faces are parallel
Hypotenuse
The longest side of a right triangle. It'll always be opposite the right angle.
Looks a little like the word hippo, so remember hippos are big and the "hypos" are the biggest side of the right triangle. It's the side opposite the right angle in a right triangle.
Improper Fraction
A fraction that tells bawdy jokes in mixed company.
Oh, all right. You're no fun. An improper fraction is one in which the numerator is larger than the denominator, like 13/5 or 25/4. These can be expressed as mixed numbers. Keeping with the examples, these fractions could be written as 2 3/5 and 6 1/4, respectively. There, now our fractions aren't so topheavy.
A fraction whose denominator is smaller than its numerator. It's a little topheavy. An example is
^{4}/
_{3}.
Inequality
A relation between two unequal algebraic expressions using the symbols <, >, ≤, and ≥.
A relation between two unequal algebraic expressions using the symbols <, >, ≤, and ≥.
A relation between two algebraic expressions that aren't equal. It uses the symbols >, <, ≤, and ≥.
A mathematical statement using the symbols <, >, ≤, ≥.
A mathematical statement using the symbols <, >, ≤, ≥.
A mathematical statement that says two expressions aren't equal in some way. Sometimes, it's a little more specific (like saying one expression is greater than or less than the other).
A mathematical statement in which two different quantities do not have the same value. We can use symbols like greater than (>), less than (<), or not equal to (≠) for inequalities.
A mathematical statement using the symbols <, >, ≤, ≥. Like not equal, man.
A relation between two algebraic expressions that are not equal, expressed using symbols like <, >, ≤, ≥. However, those expressions are currently marching on Washington, and hopefully, someday soon, there will be equality for all.
Similar to an equation, these have > or ≥ or < or ≤ instead of an equal sign.
A mathematical expression that uses ≤, ≥, <, or ˃ to define a relationship between two groups. It's not the opposite of an equality. It's like a more inclusive one.
Integers
natural numbers (1, 2, 3, 4,...), their negatives (..4, 3, 2, 1) , and zero; from the root "untouched"; simply virginal numbers
Intercept
the place where a line or curve crosses an axis
The point where the graph of a function crosses the
xaxis or
yaxis.
The point where the graph of a function crosses the
xaxis or
yaxis.
For all you sports nuts—think football. It's the point where a graph "takes," "seizes," or "crosses" an axis.
This is the place where a graphed equation hits the
x or
yaxis. It's also the point at which
x = 0 or
y = 0.
The point where the graph of a function crosses the
xaxis or
yaxis. Slow down line. The axis gets the rightofway.
A point on a graph where a line or plane crosses one of the axes.
The point where the line crosses the
x or
yaxis. Hope it looks both ways first.
Interquartile Range
the difference between the upper quartile and the lower quartile
The difference between the third and the first quartile.
The difference between the first quartile and the third quartile.
Isosceles Trapezoid
a trapezoid with only one set of congruent sides and two sets of congruent angles and has all the characteristics of a trapezoid (see trapezoid)
A trapezoid whose two nonparallel sides (legs) are congruent. Its two pairs of base angles are also congruent too, much like those of an isosceles triangle.
Kite
a quadrilateral with two sets of adjacent congruent sides and only one set of congruent angles
A quadrilateral with two distinct sets of congruent consecutive sides. (They share an angle.) It has perpendicular diagonals and is perfect for windy days.
A quadrilateral with two pairs of congruent consecutive sides and only one pair of congruent opposite angles. You'll recognize these guys because…well, they look like kites.
Least Common Multiple (LCM)
The smallest integer that is a multiple of two or more integers. For example, the
LCM of 4 and 6 is 12. If you take 36, on the other hand, it's a multiple of both numbers, but it is not the
least common multiple. Don't get down on yourself, 36. You'll have your day in the sun.
Like Terms
Two terms that have the same variables raised to the same exponent. Like terms may have different coefficients. We give them permission.
Two terms that have the same variables raised to the same exponent. Like terms may have different coefficients.
Two terms that have the same variables raised to the same exponent. Like terms may have different coefficients.
Two terms with the same variables raised to the same exponent. Like terms may have different coefficients.
Terms that have the same variables raised to the same exponents.
Terms that are made up of the same variables and the same exponents. They play nice together because they "like" each other.
Terms that can be added or subtracted together. They'll always have the exact same variables with the exact same exponents, like 8
x^{2}y and 3
x^{2}y. They go together like crunchy peanut butter and smooth peanut butter.
Line
a straight path passing through at least two points that extends in both directions; imagine the fifty yard line going on forever
A line is a unit of poetry that takes up—you guessed it—a line of text. It's not a unit of sense or meaning (although it can be if the lines are
endstopped). It's a unit of form.
And now, Shmoop will regale you with recitations of our top ten favorite lines of poetry. Ever.
She walks in beauty like the nightL'amor che move il sole e l'altre stelleThere is no Frigate like a BookJazz June. WeI am large . . . . I contain multitudes.The blackbird must be flying.Te amo sin saber cómo, ni cuándo, ni de dónde,Lose something every day. Accept the flusterWhat form my dreaming was about to take.Time's wingèd chariot hurrying near;
Okay, okay, eleven:
I have measured out my life with coffee spoons;A onedimensional segment that continues on forever in both directions. Timeconsuming to draw, so we use arrows on the ends to symbolize that it never ends.
A unit of poetry that goes in a straight...line.
See also line.
A unit of poetry that goes in a straight...line.
See also line.
An infinite length. We usually draw them as straight lines with arrows on either end to indicate that it goes on forever in both directions. Lines are onedimensional since they're only length without depth or width.
Line Segment
a portion of a line that has limits at each end; think football field  there is an outofbounds at each yard line
Sometimes just called a "segment." It's a finite piece of line between two endpoints.
A measurable piece of a line. Rather than continue on forever, line segments are onedimensional lengths caught between two endpoints.
Linear
in a straight line
An equation or graph whose rate of change is constant over time. They're on the straight and narrow path and they have no plans to switch things up anytime soon.
Mean
the sum of all numbers in a set divided by the number of data values
Also known as the average; found by adding all of the numbers up, then dividing by how many there are.
The average entered the witness protection program, and this is its new name. Although now that we've told someone, that kind of defeats the purpose of the whole thing. Whoops.
Median
the middle value in a data set
The middle value of a list of data points.
A segment parallel to the bases of a trapezoid that connects the midpoints of the nonparallel sides. A trapezoids median also has a length that's the average of the two bases.
The middle value in a data set when all of the values are lined up in order.
The line from a vertex of a triangle to the midpoint of the opposite side.
The middle value of a dataset. Like, even moreso than the mean.
Mixed Number
A number expressed as a whole number
and a fraction, like 2½ or 4¾. You'd never be able to bake a cake without these bad boys.
No only is there a fraction, but there's a whole number attached, too. An example is 4
^{1}/
_{3}.
Mode
the number that occurs the most in a data set
The data point with highest frequency.
The value that shows up the most in a set of data.
The most common value in a dataset. The mode of a beach is "sand," the mode of Alaska is "snow," and the mode of Shmoop is "fun."
Monomial
an algebraic expression with one term
A polynomial with one term.
A polynomial with one term.
An algebraic expression with only one term. That term could be
x or 7 or 18,942
x^{13}y^{8}.
Mutually Exclusive Events
in probability these are two or more outcomes that can't occur at the same time (like rolling a die and getting a 1 and a 3)
Events that cannot both occur at the same time.
Negative Correlation
as one variable increases, the other decreases; like hours spent on homework and the amount of time your parents nag you
No Correlation
the variables have no relation; like hours spent on homework and height
Nonagon
a ninesided figure
Numerator
The top part of a fraction.
"I'll be back... on top of the denominator." 
Numerator II: Judgment DayThe top part of a fraction. "I'll be back... on top of the denominator."  Numerator II: Judgment Day
This is the polynomial in the top of the denominator.
Obtuse Angle
an angle greater than 90°, but less than 180°; a notvery bright angle
An angle greater than 90°. Or just a really thickheaded angle.
Obtuse Triangle
a triangle with one obtuse angle (an angle greater than 90°)
A triangle that's a little slow on the uptake. Or one with an angle that's over 90°.
A triangle with one angle greater than 90°. It may or may not be intelligent.
Octagon
an eightsided figure
Order Of Operations
The rule that states which operation takes precedence over others. The correct order is given by the acronym "PEMDAS," which can be remembered by using the mnemonic "Please Excuse My Dear Aunt Sally." It stands for "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction." It's something like a ranking system or a chain of command. So an exponent had better never go over a parenthesis' head, or it might be cited for insubordination.
Outliers
a number that is far greater or smaller than the rest of the data; it is calculated as 1.5(IQR) > Q3 or 1.5(IQR) < Q1; hopefully not your math score on the low end
Data points that are numerically far away from the rest of the data set. The loners of the group, if you will.
Data points that don't go along with the trend. They like to stand out from the crowd.
Values that are more than 1.5(IQR) away from the outer quartiles (the edges of the box on a box and whisker plot); shown as asterisks on a box and whisker plot.
A data point that is very far away from most of the rest of the data. It gets a bit lonely sometimes.
Parallel Lines
lines that lie on the same plane and never intersect (Labeled as JK  LM )
Two lines that never ever intersect. They can continue on forever, but they'll always stay the same exact distance apart.
Lines that will never intersect, because they share the same slope.
Parallelogram
A foursided, closed shape with straight lines and two pairs of opposite sides that are parallel. You can send someone a parallelogram for his or her birthday, but it is not as entertaining as a singogram.
A quadrilateral in which both pairs of opposite sides are parallel. Consequently, they're also congruent. And their opposite angles are congruent. And their consecutive angles are supplementary. And their diagonals bisect each other. And they like long romantic walks on the beach and reading Danielle Steel novels.
A quadrilateral with two sets of parallel lines. It's not called a parallelogram for nothing, you know.
Percent
The portion of a number out of 100. We're sure you can grasp this concept if you just give it 110%.
A number that expresses a ratio out of 100. If you've ever been to a department store or taken a test, you've seen percents in their natural habitats. We're 100% sure of it.
Perimeter
The length of the boundary of a closed shape. If the boundary is a light, bluishpurple and you can only see it out of the corner of your eye, it is a peripheral periwinkle perimeter. Just in case that ever comes up.
The length of the boundary of a closed shape.
The total distance around a twodimensional figure. We can calculate the perimeter for any figure by adding up all the side lengths together.
Perpendicular Lines
lines that intersect at a 90° angle; a linebacker's path while running at the quarterback
Two lines that intersect at a right angle. Actually, they make
four right angles.
Pi
apple or cranberry? the ratio of the circumference of a circle to its diameter, 3.14159...; impress family and friends by memorizing to at least 10 digits
Place Value
each digit in a number has its own place; think Thanksgiving dinner; the ones place is to the left of Grandpa (or the decimal), tens place is far down from Aunt Gert
Plane
a flat surface without boundaries (Labeled by naming three nonlinear points on the plane,
A "slice" of threedimensional space. It has length and width, but no depth, like a sheet of paper that stretches out forever in all directions.
A twodimensional region that has length and width, but no depth. Think of a sheet of paper that's both infinitely thin and extends in all directions.
Point
a single location usually drawn as a dot; "dimensionless" (labeled as point P)
The smallest object…ever. It has no mass, no length, and no size. It describes only a location.
A single location in space. Even though we represent it using a dot, it technically has no dimensions and no size.
Polygon
a closed figure of three or more sides
A closed twodimensional shape that is made of only straight line segments. No curves allowed. Sorry, Beyoncé.
A closed 2D shape that is made up entirely of segments. No saucy curves on these guys. They're all lines and angles.
Positive Correlation
as one variable increases so does the other; like hours spent putting and accuracy (we hope)
Powers
math "shorthand" devices used to make writing long multiplication expressions easier and faster (also see exponents)
Prime
a number that is only divisible by one and itself; the first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 31
Prism
a solid object with two congruent and parallel faces
Two parallel congruent polyhedrons connected by lateral faces. Not "prison" in a French accent.
A 3D solid with two polygonal bases that are parallel and rectangular faces connecting them.
Probability
the likelihood of an event occurring
Likelihood or chance of the occurrence of an event.
This is the study of how likely an event is to happen.
How likely something is to occur;
Product
A molecule that is produced in a chemical reaction. Products are generated by reactants.
The chemical compounds resulting from a chemical reaction. In a chemical equation, the products are listed on the right hand side of the arrow.
In a chemical reaction, the product is the chemical outcome. It appears to the right of the arrow in a chemical equation.
The compounds that exist after the conclusion of a reaction. It's also the new molecules that are formed as a result of a chemical reaction.
Proportion
a comparison between one part and the whole
A mathematical statement that establishes equality between two ratios. By calling themselves proportional, ratios proclaim to all that they are equivalent and deserve a nice crusty baguette just as much as the next ratio. "Liberté, égalité, geometré," as Victor Hugo so wisely wrote.
A single ratio comparing a part to a whole or two equivalent ratios. In the first case, the "part" is always the first number (the numerator in the fraction) and the "whole" is the second number (the denominator). When referring to equivalent ratios, it's most commonly written as two equal fractions.
This means there is some relationship between two things, as compared to the whole.
Proportional
having a constant ratio; similar figures are proportional
Pyramid
a solid object with a polygon for a base and triangles for sides
Those huge stone buildings that the Egyptians built. It's basically a solid (definitely not liquids or gases) with a noncurvy shape for the base and one tip at the top.
A 3D solid with a single polygonal base and several triangular faces that meet at a single vertex.
Q1
quartile 1; the median of the lower half of the data set
Q2
quartile 2; the median of the entire data set
Q3
quartile 3; the median of the upper half of the data set
Quadrilateral
foursided shapes
A polygon with four sides. We can remember this easily because "quad" means "four" and "lateral" means "side."
A twodimensional figure with four sides.
Quartile
one of three values that divide a data set into four equal sections
A measure of spread in a data set.
Numbers that divide a dataset into 4 equal quarters. We mostly use them to ride the mechanical horses outside the grocery store.
Quotient
The number obtained by dividing one number by another. (Did you know that I.Q. stands for Intelligence Quotient? That's because we can tell how smart you are by dividing your brain up into pieces. Sounds rough, but it's a relatively painless procedure.)
Radius
the distance from the center of a circle to a point on the circle
A line segment with one endpoint at the center of a circle and the other endpoint on the circle itself. Alternatively, the length of such a segment. (The plural is
radii, pronounced "raidy eye.")
A segment from the center of a circle to any point on that circle. Sometimes it just describes the length of that segment.
Range
the difference between the highest and the lowest data value; on a golf driving range, the difference between your ball and that of Tiger's might be large
The set of all possible output values of the function.
The geographical area an organism lives in. The range is the extent of land (or water) that a species occupies. Species periodically expand their ranges, just naturally or because of changes in habitat and climate. Before 1850, the Rio Grande was the northern range limit for armadillos. Since then, armadillos have moved further north into the US, but no one knows why. Many species ranges are expected to shift because of climate change.
The output values of a function or relation.
This is the set of all possible outputs of a function. It's generally the possible
y values. It has very little to do with the Lone Ranger or free range chickens.
The difference between the highest value and the lowest value in a data set.
The set of
y values for which a function is defined. It's anything that comes out the other end when we put in one of our domain values.
Ratio
a comparison between two or more quantities; the ratio the distance Drew Brees throws the football over the distance you throw it is probably a high number
A comparison of two quantities, written as a fraction (½), with the word "to" in between (3 to 5), or with a colon (9:2). Not to be confused with
CSI: Miami's Horatio. Yeah!
Two numbers compared to each other. We can represent ratios as fractions or two numbers with either a colon or the word "to" in between them. The order of the numbers is important!
The amount of times one value occurs in relation to another value.
Ray
a straight path with one terminal point and extending indefinitely in the other direction; think sunshine
A hybrid of a line and a segment. It has one endpoint, but then goes off forever in the other direction. It's like a ray of sunshine that starts at the sun and then continues on forever.
A segment that has one endpoint but extends forever in a single direction. Think "ray of sunshine," and not "stingray."
Rectangle
A parallelogram with all angles equal to 90°. More importantly, it is the shape of a rectangular pizza.
A parallelogram with all angles equal to 90°.
A parallelogram with four right angles. Also known as "The Equiangulizer" because any equiangular quadrilateral is automatically a rectangle.
A quadrilateral with four right angles.
Regular Polygon
an equilateral, equiangular polygon
A shape whose sides are all equal in length and whose angles are all equal in measure.
These are polygons that have all equal sides and angles. A stop sign is an example of a regular octagon.
Regular Prism
a prism with rectangular bases, six faces, all right angles and parallel opposite faces
A prism or pyramid whose base has edges that are all congruent. Also, a prism or pyramid that has daily scheduled trips to the potty.
Rhombus
a quadrilateral with parallel opposite sides, congruent opposite angles, supplementary adjacent angles and four congruent sides; a square after running a marathon might tilt like a rhombus
A quadrilateral whose four sides are all equilateral. Rhombi (that's the plural of rhombus) have all the properties of parallelograms, too.
A quadrilateral with four sides of equal length. So actually, rhombi are a girl's best friend.
Right Angle
an angle that is exactly 90°; often seen with a small box in the corner
An angle that's exactly 90°. Naturally, that means any angle that isn't 90° is wrong.
A 90° angle. Of course, that makes any angle that doesn't have a 90° angle wrong.
Right Triangle
a triangle with one right angle (a 90° angle); can also be on the left side
A triangle that has an angle that's exactly 90°. Or possibly a triangle that's just never wrong about anything.
A triangle with one angle of exactly 90°. You can't argue with it, because it's always right. (Groan.)
Roots
opposites of powers; trees have roots as do numbers; in this case it can be the square (the number that multiplied by itself twice equals), the cube (multipled three times), or the nth (you get the picture)
The organs responsible for getting nutrients from the soil, among other things. Dig in the ground a little bit, and you’ll probably come across one of these pretty soon. You may even see some aboveground, if there are large trees growing near any of your sidewalks. Did you know that tree roots are the main cause of water pipe damage? Roots are surprisingly strong, and they don’t always grow underground, either.
Scalene Triangle
a triangle with all sides of different lengths
A triangle whose three sides are all different lengths. He's probably just going through a growth spurt.
A triangle with none of the side lengths being equal. It's every side for himself. Or herself—maybe you have a female scalene triangle.
Scatter Plots
a type of plot that shows individual data values; dog doing its business outside on a windy day might do this to the snow
Scientific Notation
an operation using exponents to write very large and very small numbers. For example, the scientific notation for .00004 is 4 X 10^5
Secant
a line intersecting a circle at two points
A line that intersects a circle at two points. Really, line, how intrusive can you get?
A line that intersects a circle at two points.
We get this when cosine goes topsyturvy. The reciprocal of the cosine function or just the cosine function flipped over.
Septagon
a sevensided figure
Side
the straight edge of a polygon
Significant Digit
all nonzero digits in a number
Similar Figures
two figures that have the same shape, but not the same size; siblings  one exercises and one eats doughnuts
Figures that are proportional to one another and have the same angles. The only difference is their relative sizes.
Slope
The steepness of a line, calculated as rise over run; think skiing (the bunny slope is less steep than the triple black diamond).
The measure of a line's steepness.
The measure of a line's steepness.
The "steepness" of a line. On the coordinate plane, it's calculated as "rise over run," or the vertical difference between two points divided by the horizontal difference between those same points.
The steepness of the line as you move along from left to right.
How steep a line is. It's measured as rise over run. Think ski slopes.
The difference between black diamond and the bunny hill. The measure of a line's steepness.
Measures the steepness of a line. Constantly rises to the occasion and runs over the competition.
A number that summarizes the rate of change of a line (also known as rise over run). It tells us whether the ski hill made by our line would be a green circle or a black diamond.
SlopeIntercept Form
a representation of a line in y = mx + b form, where m is the slope and b is the yintercept
The special way true mathematicians communicate linear equations to each other. The format is
y =
mx +
b, where
m is the slope and
b is the
yintercept of the line.
Sloth
Laziness; inactivity; sluggishness
Sphere
a solid figure where all points are an equal distance from the center point; a ball
A ball. It's a central point that includes all the points a certain distance away from it in space. It's like a circle—but in 3D.
A solid in which all points are an equal distance from a central point. In other words, a ball.
No, you haven't stumbled into a geometry course. A sphere is a planet controlled by an angelic intelligence. In metaphors, "sphere" can also refer to the human body.
Square
A parallelogram with all angles equal to 90° and all sides equal. Read: glorified rectangle.
A parallelogram with all angles equal to 90° and all sides equal in length.
A number raised to the power of two.
A rectangle with four congruent sides. It's also got that 90° angles thing going on, plus the bisected congruent perpendicular diagonals. It's also the quadrilateral worthy of the title "regular."
A quadrilateral with four right angles and four sides of equal length.
Square Pyramid
a pyramid with a square base; all sides on the bottom are the same and the top looks like a place in Egypt
Standard Form Of A Line
a representation of a line in Ax + By = C form, where A, B, and C are all integers and A is also positive
Statistics
the branch of math that deals with collecting and analyzing data; you can justify almost anything with the right stats
Straight Angle
180° angle; basically a straight line
An angle that measures 180°. The title a straight line gives itself when it wants to seem more impressive.
A 180° angle. Or a straight line with an identity crisis.
Supplementary Angles
angles that add up to 180°; think a flat line when the angles are put together
Two angles that add up to 180°. It doesn't matter if they're adjacent or on different planets.
Two angles that add up to 180°.
Surface Area
the total area of all faces of a 3dimensional object
The amount of the giftwrapping paper it takes to cover all of particular shape. You can use newspaper instead of giftwrapping paper; it's a lot cheaper.
The twodimensional area needed to cover the entire figure perfectly with no gaps or overlaps.
The area of all of the space figure's surfaces combined.
Tangent
a line intersecting a circle at exactly one point
A line that intersects a circle at exactly one point (the point of tangency). The word "tangent" literally means "touching." So a line tangent to a circle is "just touching" the circle.
A line that intersects the circle at exactly one point. Or a polite man who's been in the sun for a while.
The ratio of the side opposite the reference angle to the side adjacent to it in a right triangle.
In a right triangle, tangent equals an angle's opposite side over its adjacent side.
Term
each part of an expression separated by addition or subtraction
A collection of numbers and variables in an expression separated by a plus or minus sign. They can be as simple as 3 or as complicated as 934
a^{7}b^{3}.
The smallest mathematical unit separated by + or – signs. If the expression 7
x + 2
y – 17 +
z was a family, then 7
x, 2
y, 17, and
z would be the terms.
Tetrahedron
a pyramid with a triangular base
Theoretical Probability
the probability of an event determined by favorable outcomes ÷ possible outcomes; what math predicts, not necessarily what really happens
This is the numbercrunching side of probability. Statisticians attempt to predict what might happen in the real world using math theories and numbers.
Three Dimensional Solid Objects
objects with width, length and height; not just flat, think
AvatarTransversal
a line that intersects two or more lines
A line that intersects two other lines, forming a total of eight angles. If the other two lines are parallel (and they usually are), then all these angles are special in some way.
A line that cuts across two other lines.
Trapezoid
A foursided, closed shape with straight lines and only one pair of opposite sides equal. The best of all shapes, because of how much fun it is to say "zoid."
A foursided closed shape with straight lines and only one pair of opposite sides equal in length.
A quadrilateral with
only one set of parallel sides (called the "bases"). Trapezoids absolutely cannot have two sets of parallel sides. That's a big fat nono.
A quadrilateral with only one pair of parallel sides. These guys look a little funky compared to the fancy shmancy parallelograms.
Triangular Prism
a prism with triangle bases; only the bases are parallel
Triangular Pyramid (aka Tetrahedron)
a pyramid with triangular base; a tetrahedron made up of four equilateral triangles is called a regular tetrahedron
Trinomial
an algebraic expression with three terms
A polynomial with three terms.
A polynomial with three terms.
Twodimensional
flat objects and shapes; think of a piece of paper; these objects only have two of the following: width, length, or height
Unit Rate
price per unit; written as a ratio (same as unit cost)
A ratio that compares two different units in which the second number is 1. Whacking 144 moles in 3 minutes is a ratio, but whacking 48 moles per minute is a unit rate (the ratio was reduced from 144:3 to 48:1).
Vertex
The point where two rays meet; the corner of a polygon (plural is vertices).
The single maximum or minimum value of a parabola.
A point on a 3D figure where two or more edges meet.
The point at an intersection of two lines. It usually refers to a specific point within a larger figure (like an angle or a shape).
The sharp, pointy bit of an absolute value graph.
The point at which a parabola changes from increasing to decreasing or vice versa. Also where the slope is equal to zero. It's where things start looking up (or down). It's located at (
h,
k) if the equation is in vertex form.
A point on a curve where the slope goes from negative to positive. We mostly see them as minima and maxima of parabolas. They're the highest high and lowest low.
Vertical Angles
when two lines intersect, opposite angles are called "vertical angles", these angles are congruent
Angles that are opposite each other resulting from two intersecting lines. Vertical angles are
always congruent.
A pair of angles opposite one another formed by the intersection of two lines. Oh, and they're congruent, too.
Volume
the amount of space inside a 3dimensional object.
The amount of threedimensional space that an object takes up. Or what your mom asks you turn down when you're listening to "that noise you kids call music nowadays."
The amount of 1 × 1 × 1 unit cubes that would fit inside a solid. In other words, it's a measure of how much 3D space a solid takes up.
The amount of space a space figure takes up. It's also how much soda fits inside a soda can.
A measurement of the amount of space contained within a threedimensional shape.
X Axis
the horizontal axis on a coordinate graph
Y Axis
the vertical axis on a coordinate graph