Basic Operations
Basic Operations Terms
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| = x
x > 0 - x
x < 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 (or 0 if we have | 0 |).
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.
The magnitude of a number, irrespective of sign. It works great when we talk about distance, but not so great when we talk about temperature.
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 petiteA triangle that's slightly less cute than a-super-cute 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.
A triangle whose angles are all less than 90 degrees. They have to shop in the petites section.
Adjacent
next to each other; you want to sit adjacent to the hot guy/galThe conjoined twins of the geometry world. Adjacent angles always share a vertex and a side.
Adjacent Angles
angles that share a sideTwo 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 linesThe 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.
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.
Alternate Interior Angles
angles on the opposite sides of the transversal and on the interior of the parallel linesThe 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.
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.
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.
The separation in degrees of two lines with a common vertex. Any time lines cross, an angle is made. And when an angle is made, a math problem is born.
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).
Apothem
the distance from the center of a regular polygon to the midpoint of one sideThe 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 three-sided 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 two-dimensional shape, reported in square units (like miles^{2} or feet^{2}). Area is essentially space, but don't go around saying things like, "area-ships," "area cadets," or the area-bar.
The two-dimensional space contained by a particular region.
The amount of two-dimensional space that is taken up within a shape's perimeter.
A measurement of surface. It's like the amount of ground a piece of sod will cover, or exactly how much carpet we have to clean after spilling an entire crockpot of chili (oops).
The measure of the amount of space inside a polygon.
The amount of "stuff" inside of a figure. Very technical, we know.
Arithmetic Patterns
numbers in a pattern that are separated by a common differenceBase Of A Polygon
the bottom side of a polygonBase Of A Solid
the bottom surface of an object; its tushBasic Counting Principle
to find the total number of possible combinations multiply the number of optionsBiased Questions
questions that try to influence the intervieweeBinomial
an algebraic expression with two termsA polynomial with two terms.
A polynomial with only two terms. The expression x – 3 is a binomial, and so is 96x^{2}y + 13,0278,543.
A polynomial with two terms. You can probably guess what trinomial means.
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 valuesA 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 data. 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 y-axis.The flat grid we use to plot out functions. It has an x-axis, a y-axis, and a very big name.
A grid made up of two perpendicular number lines.
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 two-dimensional 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 othersCommutative
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 × 6Complementary 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)A pair of mutually exclusive events where the occurrence of one implies the non-occurrence of the other; this is represented by the fact that the respective Venn diagrams for these events do not overlap, and that the two events themselves comprise the entire sample space.
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 otherThese 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.
When more than one event happens at once. The lions, tigers, and bears all arrive at the same time? We think you know how that one ends.
Compound Interest
adding interest earned before calculating the new interestA type of interest in which the money you acquire through interest also acquires interest, which increases your money exponentially. Those two words should be music to your ears.
Cone
chocolate or brownie fudge? ; a solid with circular base and a curved side that ends in one point and has one vertex; a duncecapA three-dimensional 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.
An object that tapers from a circular base to a point. Just like a birthday hat (and sorry again about forgetting your birthday).
Congruent Angles
two or more angles that have the same measurementConstant
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 3y + 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 old-fashioned and thinks everything is fine as is. When we look at an expression like 6x + 2, the 2 is the constant.
A number whose value doesn't change. We call any freestanding numbers in an expression constants, because their values are fixed (in contrast to those shifty variables). In the expression 3x + 7, 7 is a constant.
A number that is in a term all by itself. In the expression y = 2x – 16, 16 is a constant.
A term that is just a number, not multiplied by a variable or anything else. It's just along for the ride.
Coplanar
on the same planeUsed to describe lines or points that are all on the same plane.
Used to describe lines or points that are all on the same plane.
Correlation
how two variables relate to each otherThe 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.
A relationship between two variables. They can be low or high, negative or positive, but if two things are correlated, they are more than just casual acquaintances.
When two variables we've measured have some kind of association or relationship between them. It can be positive, negative, or not exist. The last one is the most depressing, naturally.
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 congruentTwo 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.
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.
Coterminal Angles
angles that share a terminal sideAngles 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°).
Cross-Canceling
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 onCube
a prism with six congruent faces, all right angles and parallel opposite faces; it is a form of a rectangular prismA polyhedron made from six equal square faces. Also, the standard unit for ice.
Cylinder
a solid with two parallel circular bases; if you "unwrap" the middle section and lay it flat, it is a rectangleTwo 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.
A figure with parallel sides and circular bases. Picture a toilet paper tube. And for Pete's sake, if you finish the roll, replace it.
Denominator
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 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.
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.
The bottom half, or quotient, of a fraction. It's the ground level, supporting the rest of the fraction house on its shoulders.
In a fraction, the number on the bottom.
The bottom number in a fraction. It represents how many pieces the whole has been divided into.
The bottom number, or divisor, of a fraction.
Diagonal
a line connecting two vertices of a polygonA 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 circleA 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).
The distance across a circle, going through its center point. Also two times the radius. If you walk from one side of a crop circle to the other, you've walked the diameter. (But you'll probably be sucked into a UFO before you get there.)
Disperse
Spread or distribute over a wide areato spread around
Distribute
to spread the term in front of the parentheses to each term inside the parentheses; share the wealthDividend
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 non-discretionary. Dividends are discretionary, which means 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.
Example
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%.In division, a number that is being divided by another number called the divisor.
The amount to be divided up in a division problem.
Divisor
the number doing the dividingThe 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 old-fashioned dividing going on.
In division, a number that divides another number called the dividend.
a number that another number will divide.
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 tug-of-war 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.
A statement that two expressions separate by an equal sign are equal to one another. Get comfy with them, because pretty much all the math from here on out will be centered on them.
An equals sign with equivalent expressions on either side of it. Equations are the mathematical equivalents of a complete sentence.
When two expressions are just made for each other, they're exactly alike, they are equal.
A mathematical statement that says two expressions or values are equal to one another. You can tell a mathematical statement is an equation by the telltale equal sign.
A statement that says two expressions are equal to each other.
Equiangular
a figure where all angles are equal in measureEquilateral Triangle
a triangle with three congruent sidesA 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 (all are 60°). If it has three of anything else, they're equal too.
Equivalent
equal toExperimental Probability
probability calculated by the outcome of an experiment or trialThis is when we actually flip a coin, pull colored socks from the drawer, and so on, and record the results. This is real stuff.
A probability calculated from data over many trials of an experiment, and which represents the probability a given event in the sample space has of occurring.
Exponents
the power to which a number or expression is raisedExpression
a fragment of a mathematical sentence; it doesn't have a sign of equalityA 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.
A mathematical phrase containing numbers and operators, but no equal sign. For you English buffs out there, they're a clause, but not a sentence.
A series of terms representing a quantity. Speaks only in emoticons.
Extreme Values
the largest and smallest values in data set; think extremes - extreme sports are at the high end of dangerValues 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 3-dimensional objectThe flat side of a 3D figure.
One of the surface shapes that forms a 3D solid, or what your Dad shaves every morning…or most mornings.
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.
Any number or variable that is multiplied by something else. Since 1 counts as a factor even when it's not written out, every term (see below) in an expression has at least two factors.
A factor is any integer that you can multiply by another number to get a specific product n. If a set of numbers (two or more) has a product equal to n, we say they are all factors of n.
A thing that's multiplied by another thing. For instance, 3x has two factors: 3 and x. They're partners in crime, and the crime is making a larger number.
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 numbern! = 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.
A number multiplied by every positive integer less than itself. n! = n × (n – 1) × (n – 2) × … × 2 × 1.
Fauna
Animals of a particular habitat or time periodFinite Decimals
decimals that have an ending; unlike that dreadful movie from last weekend that seemed to never endFrequency
the number of times an event occurs; Jim asked Danielle out with uncommon frequencyGeometric 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 non-zero 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.
The GCF is the largest factor that two numbers share.
Hexagon
a six-sided figureHexagonal Prism
a prism with hexagons for bases; opposite faces are parallelHypotenuse
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.
The longest side of a right triangle, or the one directly across from the right angle. It's the star of the show, and the triangle legs are its backup singers.
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 top-heavy.
A fraction whose denominator is smaller than its numerator. It's a little top-heavy. An example is ^{4}/_{3}.
A fraction where the numerator is greater than the denominator. They usually have really poor table manners, too.
Inequality
A relation between two 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.
An expression showing the way in which two things are not equal. Symbols are used to demonstrate the relationship between the quantities. Sorry if they cause flashbacks to the time your sister got more ice cream than you did.
A mathematical statement comparing two quantities
The inequality signs < and > tell us that one number is less than or greater than another, respectively. They could be hungry mouths, or accusing arrows. Or maybe something even scarier.
A statement that compares two expressions and says that one expression is greater than the other, using less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥) signs.
Integers
natural numbers (1, 2, 3, 4,...), their negatives (..-4, -3, -2, -1) , and zero; from the root "untouched"; simply virginal numbersIntegers are positive or negative whole numbers, including 0. They have a big "No Fractions Allowed" posted on their clubhouse.
The inequality signs < and > tell us that one number is less than or greater than another, respectively. They could be hungry mouths, or accusing arrows. Or maybe something even scarier.
Intercept
the place where a line or curve crosses an axisThe point where the graph of a function crosses the x-axis or y-axis.
The point where the graph of a function crosses the x-axis or y-axis.
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 y-axis. It's also the point at which x = 0 or y = 0.
The point where the graph of a function crosses the x-axis or y-axis. Slow down line. The axis gets the right-of-way.
A point on a graph where a line or plane crosses one of the axes.
The point where the line crosses the x- or y-axis. Hope it looks both ways first.
The place on an axis where the graph intersects it. A spot where the graph crosses the x-axis is called an x-intercept; anywhere it crosses the y-axis is a y-intercept.
Interquartile Range
the difference between the upper quartile and the lower quartileThe difference between the third and the first quartile.
The difference between the first quartile and the third quartile.
The middle 50% of a data set, located between Q1 and Q3. It's a club with a 50/50 acceptance rate, you could say.
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 non-parallel 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 anglesA 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.The LCM is the least common multiple that two numbers share.
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 8x^{2}y and -3x^{2}y. They go together like crunchy peanut butter and smooth peanut butter.
Any terms that have the exact same variable, raised to the exact same power. Accept no substitutions. Thanks to their identical variables, like terms can be added to and subtracted from one another: 2x^{2} + 5x^{2} = 7x^{2}.
We do like "terms," but that's not what this term means. "Like terms" refers to all the terms that contain the same variables and so can be added together.
Terms in a polynomial that exactly match their variables and the exponents for each variable. The coefficients may be different.
Line
a straight path passing through at least two points that extends in both directions; imagine the fifty yard line going on foreverA 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 end-stopped). 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 night
L'amor che move il sole e l'altre stelle
There is no Frigate like a Book
Jazz June. We
I 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 fluster
What 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 one-dimensional segment that continues on forever in both directions. Time-consuming 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 one-dimensional since they're only length without depth or width.
A perfectly straight connection between any two points, extending out to infinity in both directions, with no thickness. It sounds weird spelled out like that, but it's just the mark you make with a ruler.
A one-dimensional bar that continues on forever in both directions. Time-consuming 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.
Line Segment
a portion of a line that has limits at each end; think football field - there is an out-of-bounds at each yard lineSometimes 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 one-dimensional lengths caught between two endpoints.
A measurable piece of a line. Rather than continue on forever, line segments are one-dimensional lengths caught between two endpoints.
Linear
in a straight lineAn 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.
A function that changes at a constant rate. They found something that works for them and they see no reason to change things up.
Something to do with equations, maybe? Yes, if you're talking math, but not so much in literature. A linear plot is one that goes from one event to the next in the order they happen—no flashbacks or flashforwards, and probably not a lot of subplots. It's linear because if you diagrammed the plot, it would look like a straight line. (Sadly, there are no geometric plots—except maybe in Flatland.)
Mean
the sum of all numbers in a set divided by the number of data valuesAlso 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.
The average of all your data points, or the sum of their values divided by the number of values.
The average value of the data, or all the points added up, then divided by the number of points there are. Contrary to the name, it's very agreeable.
The opposite of nice.
In finance, it's basically a fancy word for "average."
Median
the middle value in a data setThe middle value of a list of data points.
A segment parallel to the bases of a trapezoid that connects the midpoints of the non-parallel sides. A trapezoid's 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.
The value of the middlemost data point. If you arrange all your data points in increasing order, it'll be the one smack-dab in the middle.
The center value in the data, or one with an equal number of points smaller than and greater than it. It's the bullseye on the graph dartboard.
Here's a series of numbers: 2, 3, 5, 5, 5, 7, 7, 8.
The median is 5.
Why? Click here.
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}.
A number that's written as the combination of a whole number and a proper fraction.
Mode
the number that occurs the most in a data setThe 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."
The most common response. If your data set were a graduating class, the mode would be the student voted Most Popular.
Monomial
an algebraic expression with one termA polynomial with one term.
A polynomial with one term.
An algebraic expression with only one term. That term could be x or 7 or 18,942x^{13}y^{8}.
A polynomial with one term.
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.
Two or more events that can never occur at the same time; this is represented by the fact that their respective Venn diagrams do not overlap.
Two events A and B are mutually exclusive if they share no outcomes. Never the twain shall meet.
Negative Correlation
as one variable increases, the other decreases; like hours spent on homework and the amount of time your parents nag youNo Correlation
the variables have no relation; like hours spent on homework and heightNonagon
a nine-sided figureNumerator
The top part of a fraction."I'll be back... on top of the denominator." - Numerator II: Judgment Day
The 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.
The top number in a fraction, or the dividend. It's the attic space holding the group of things we need to divide. And a lot of spiders.
In a fraction, the number on the top.
The top number in a fraction. It represents the number of parts included in the fraction.
The top number, or dividend, of a fraction.
Obtuse Angle
an angle greater than 90°, but less than 180°; a not-very bright angleAn angle greater than 90°. Or just a really thickheaded 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.
A triangle in which one of the angles is more than 90 degrees. It's like a normal triangle someone sat on and squished a little.
Octagon
an eight-sided figureOrder 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.All bow before mighty PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Execute your operations in this order, or else PEMDAS will have a stern word or a thousand for you.
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 endData 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.
Two lines that are on the same plane but never intersect. They're always in sight, but never touch…sort of sad, ain't it?
Parallelogram
A four-sided, 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 sing-o-gram.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.
A specified amount for every hundred. It's what happens when the denominator of every fraction is converted to 100. It's like they're all wearing matching pants.
Means "out of a hundred." The value of a percent can be expressed as a fraction with a numerator out of 100. Percents can also be converted to decimals by moving the decimal place two spaces to the left.
Percents represent part-to-whole relationships that have been converted into a ratio where the whole is equal to 100. They can be written as fractions with 100 in the denominator, as percents, or as decimals.
Perimeter
The length of the boundary of a closed shape. If the boundary is a light, bluish-purple 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 two-dimensional figure. We can calculate the perimeter for any figure by adding up all the side lengths together.
The distance around the edge of any shape (or the sum of its side lengths). "Patrolling the perimeter" just means walking around the edge. We've been doing it wrong this whole time.
The measure of the total distance around a polygon.
Perpendicular Lines
lines that intersect at a 90° angle; a linebacker's path while running at the quarterbackTwo lines that intersect at a right angle. Actually, they make four right angles.
Two lines that create a 90° angle when they intersect. Well, actually they create four 90° angles, but who's counting?
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 digitsPlace 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 GertPlane
a flat surface without boundaries (Labeled by naming three nonlinear points on the plane,A "slice" of three-dimensional space. It has length and width, but no depth, like a sheet of paper that stretches out forever in all directions.
A two-dimensional 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.
A "slice" of three-dimensional space. It has length and width, but no depth, like a sheet of paper that stretches out forever 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.
An exact position on a plane, like a zit on a chin. It has no size or dimensions (unlike that zit).
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 sidesA closed two-dimensional 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.
A closed 2-D shape that is made up entirely of segments. No saucy curves on these guys. They're all lines and angles.
A flat, closed 2D shape made of straight lines.
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 31Prism
a solid object with two congruent and parallel facesTwo 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 occurringLikelihood 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.
The result of multiplication. For example, the product of 3 and a number is 3x. It's what gets made at the end.
Proportion
a comparison between one part and the wholeA 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.
The relationship between two equivalent ratios. When doubling a recipe, it's important that the new ingredient amounts be in proportion to the original amounts.
Proportional
having a constant ratio; similar figures are proportionalCorresponding in size or amount to something else. It's like how our model trains are all in scale with the real deal (but have many fewer delays and unruly passengers).
Two things are proportional if their ratio is constant. Those things can be parts of shapes, like side lengths, which makes the shapes similar.
A relationship where a number either increases at the same rate that another increases or decreases at the same rate as another decreases.
Pyramid
a solid object with a polygon for a base and triangles for sidesThose huge stone buildings that the Egyptians built. It's basically a solid (definitely not liquids or gases) with a non-curvy 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.
A figure with a polygon base and triangular sides that meet at an apex. Generally full of old organs in jars.
Q1
quartile 1; the median of the lower half of the data setQ2
quartile 2; the median of the entire data setQ3
quartile 3; the median of the upper half of the data setQuadrilateral
four-sided shapesA polygon with four sides. We can remember this easily because "quad" means "four" and "lateral" means "side."
A two-dimensional figure with four sides.
Quartile
one of three values that divide a data set into four equal sectionsOne of three values that divide a data set into four equal sections.
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.)The divisor in a division problem, or the number of groups the problem creates. If we are dividing the episodes of a TV show into seasons, it's the number of seasons we have.
The result of dividing a dividend by a divisor. For example, 2 is the quotient of 8 divided by 4.
The answer of a division problem. It's what we get out when a fraction goes through a simplifying steamroller.
Radius
the distance from the center of a circle to a point on the circleA 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.
The length from the center of a circle to any point on its edge. It's the distance from the cheesy tip of a pizza slice to the crust. (And if you're not planning to eat that, slide it our way.)
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 largeThe 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.
The set of all possible outputs, y, for a given function. The impossible outputs are in the don'trange. Wait, nevermind, that joke doesn't work.
The set of values that the dependent (y) variable can have.
The possible outputs of a function. It's like all the possible meals you can make with what's in the pantry. (We've got tuna, peanut butter, and lentils and we are taking suggestions.)
All the values f(x) can take, based on the domain. Just how high and low does it go?
Home, home on the...yeah.
The term also refers to the prices in which, say, an IPO is expected to be priced. That is, you'll find on the cover of the Red Herring IPO marketing document an "expected range of $12-14," for example.
The term can also apply to, say, the 52-week trading range in which Stock X has traded between $15 and $24 a share.
The term also means the difference between the highest and lowest numbers in a group.
The term also refers to the thing you cook on...
Actually, the term means too many things. It should stop hogging all the definitions.
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 numberA comparison of two quantities, written as a fraction (), 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.
Relative sizes of two or more values. Usually presented looking like a fraction. But don't let them fool you! Their bottoms don't represent the whole.
The relationship between the sizes of two groups. A ratio may compare groups of two different things (two mushrooms to every anchovy on a pizza), two groups of the same type of thing (for every kitten Jim has, Marv has two kittens), or the size of a subgroup compared to the size of the whole group (the number of green M&Ms in a bag relative to the total number of M&Ms in the bag).
Ray
a straight path with one terminal point and extending indefinitely in the other direction; think sunshineA 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."
A line with one endpoint, shooting infinitely in one direction. It's like a ray of sunshine shooting off from its endpoint on the sun and giving you tan lines.
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 polygonA 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.
A shape whose sides are all equal in length and whose angles are all equal in measure.
Polygons where all the angles and sides are equal. Squares, equilateral triangles, and stop signs are all regular polygons we've met a time or two before.
Regular Prism
a prism with rectangular bases, six faces, all right angles and parallel opposite facesA 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 rhombusA 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 cornerAn angle that measures exactly 90°. Naturally, that means any angle that doesn't measure 90° is wrong.
A 90° angle. Of course, that makes any angle that doesn't have a 90° angle wrong.
An angle that measures exactly 90°. Naturally, that means any angle that doesn't measure 90° is wrong.
Right Triangle
a triangle with one right angle (a 90° angle); can also be on the left sideA 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.)
A triangle with one right angle. Super important when trigonometry rolls around, but kind of just a really specific definition for now.
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.
The points where the whole polynomial is equal to zero. If a root is real (i.e. not an imaginary or complex number), it also tells us what the function's x-intercepts are. When graphing a polynomial function, these things are the root of our solution.
Much like the support system of a mighty tree, the roots of words are the base on which affixes can be added to alter the word and make it anew. What once was a mere "agree" can transform into "disagree" with a prefix and a "disagreement" with an additional suffix. Beautiful.
Scalene Triangle
a triangle with all sides of different lengthsA 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 snowScientific Notation
an operation using exponents to write very large and very small numbers. For example, the scientific notation for .00004 is 4 X 10^-5A coefficient, a 10, and an exponent walk into a lab, and say "Let's make some science."
Secant
a line intersecting a circle at two pointsA 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 topsy-turvy. The reciprocal of the cosine function or just the cosine function flipped over.
Septagon
a seven-sided figureSide
the straight edge of a polygonSignificant Digit
all non-zero digits in a numberSimilar Figures
two figures that have the same shape, but not the same size; siblings - one exercises and one eats doughnutsFigures that are proportional to one another and have the same angles. The only difference is their relative sizes.
Figures that share the same angle measures, and their sides lengths are all proportional. A fake mustache won't really disguise the fact that they are so similar.
Figures that are proportional to one another and have the same angles. The only difference is their relative sizes, and their taste in bolivian orchestras.
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.
The steepness of the line as it moves along from left to right. Try not to fall off of it. It's a long way down.
The change in the y-axis over the change in the x-axis, or (y_{2} – y_{1})/(x_{2} – x_{1}).
The steepness of the graph at a given point. Slope is defined as the vertical change between two ordered pairs divided by the horizontal change between those pairs.
The ratio of a line's changes in y over its changes in x.
Slope-Intercept Form
a representation of the equation of line in y = mx + b form, where m is the slope and b is the y-interceptThe 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 y-intercept of the line.
The equation of a linear function in the form y = mx + b, where m is the slope and b is the y-intercept of the line. Some mathematicians play favorites and like this form the best.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
For a line with slope m and y-intercept b, the line's slope-intercept form is: y = mx + b.
Sloth
Laziness; inactivity; sluggishnessSphere
a solid figure where all points are an equal distance from the center point; a ballA 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.
A ball-shaped figure in which every surface point is equidistant from a center. A keystone of sports everywhere.
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 EgyptStandard 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 positiveStatistics
the branch of math that deals with collecting and analyzing data; you can justify almost anything with the right statsThe math of taking a bunch of data and turning it into values that allow us to conclude something about that data.
Straight Angle
180° angle; basically a straight lineAn 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.
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 togetherTwo 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 3-dimensional objectThe amount of the gift-wrapping paper it takes to cover all of particular shape. You can use newspaper instead of gift-wrapping paper; it's a lot cheaper.
The two-dimensional area needed to cover the entire figure perfectly with no gaps or overlaps.
The area of all of the space figure's surfaces combined.
The total exterior surface of a solid. If we took our shape to the beach, it's everywhere it would get sand.
A measure of the amount of 2D space it takes to cover a 3D figure without gaps or overlaps.
The measure of the total area of all of a 3D shape's faces.
Tangent
a line intersecting a circle at exactly one pointA 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 subtractionA 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 -934a^{7}b^{3}.
The smallest mathematical unit separated by + or – signs. If the expression 7x + 2y – 17 + z was a family, then 7x, 2y, -17, and z would be the terms.
A piece of an expression that is added or subtracted. A term can be a variable, a constant, or the product of constants and/or variables.
One piece of an expression, separated by the other pieces by a + or – sign. A term can be a number, a variable, or a combination of numbers and/or variables.
Parts of algebraic expressions that are separated by an addition or subtraction sign. 3 + x + 5x^{2} has three terms. They are all those "Terms and Conditions" you agreed to without reading them coming back to haunt you.
The amount of time you have to repay a loan.
The longer the term, the less you will pay each month but the more you'll pay overall in interest on your loan.
Example
John takes out a 3-year, $50,000 car loan to help him pay for his new BMW. The term of his loan is 3 years.Tetrahedron
a pyramid with a triangular baseTheoretical Probability
The probability of an event determined by favorable outcomes ÷ possible outcomes; what math predicts, not necessarily what really happens.This is the number-crunching 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 linesA 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.
A line that crosses two or more parallel lines.
A line which crosses over a pair of parallel lines to create eight angles. It's a classic third-wheel scenario.
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 so
Trapezoid
A four-sided, 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 four-sided 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 no-no.
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 parallelA prism with a triangular base.
Triangular Pyramid (aka Tetrahedron)
a pyramid with triangular base; a tetrahedron made up of four equilateral triangles is called a regular tetrahedronTrinomial
an algebraic expression with three termsA polynomial with three terms.
A polynomial with three terms.
Two-dimensional
flat objects and shapes; think of a piece of paper; these objects only have two of the following: width, length, or heightUnit 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).
A simplified ratio of two numbers with (usually different) units. Speed, density, and price per weight are common examples. If you say it, "something per something," it's probably a rate.
In a given situation, the ratio between the value of y and x. Looks a lot like the slope if you squint at it.
A ratio relating things of two different types. Unit rate tells us how much of Thing A corresponds to one unit of Thing B—such as how many miles our Hummer gets per gallon of gasoline.
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.
In conic sections, the point (or points) on a curve where the graph changes direction; sometimes a maximum or minimum.
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 corner where two sides of a polygon meet, or where 3 or more faces of a 3D object meet.
Vertical Angles
when two lines intersect, opposite angles are called "vertical angles", these angles are congruentAngles 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.
Angles formed when two lines cross. They lie across the vertex from one another and are always congruent. It's like a pair of twins sitting across from one another in a booth and sharing a milkshake.
Volume
the amount of space inside a 3-dimensional object.The amount of three-dimensional space that an object takes up. Or what your mom asks you to 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 three-dimensional shape.
The amount of space that an object occupies or encloses. If the object was our pants pocket, its volume is how much candy we can smuggle into the movie theatre.
The space inside a 3D object, like a cereal bowl or your brother's head. Insert your own joke here.
The measure of the amount of space inside a 3D shape.
The amount of space a solid takes up. It's also how much soda fits inside a soda can.