Math Glossary of Terms

  • AAS Congruence

    AAS is an abreviation of Angle-angle-side congurence and sometimes written as SAA congruence. This theorem states that two triangles are congruent when two pairs of corresponding angles and a pair of opposite sides are the congruent.
  • Abscissa

    The perpendicular distance of a point in an ordered pair from the vertical axis as an absolute value. It is usually the horizontal coordinate when you are working with a point on a Cartesian plane—also known as the x-coordinate. When you have an ordered pair, you have two terms: the abscissa (usually the x coordinate in the pair), and the ordinate (usually the vertical y coordinate).
  • Absolute Convergence

    Also known as absolutely convergent, this refers to an infinite series that converges when its terms are changed to their absolute values. This is done by changing any subtraction signs in the series to additions, then checking if the new series converges.
  • Absolute Maximum

    The largest value of a function over its entire curve. There is only one absolute maximum, but the maximum can happen in more than one place over the curve. The absolute maximum is also sometimes known as the global maximum.
  • Absolute Minimum

    The smallest value of a function over its entire curve. There is only one absolute minimum, but this minimum can happen in more than one place over the curve. The absolute minimum is also sometimes known as the global minimum.
  • Absolute Value

    When a negative number is made positive. In other words, absolute values depicts the distance between the number and the origin. For 0 and numbers that are already positive, there is no need to do anything to them in order to get their absolute values.
  • Absolute Value of a Complex Number

    Also known as the modulus of a complex number in the form of a+bi. It tells you the distance between the origin and a point (a,b) that's on a complex plane. It is a measure of distance from 0 measured on the complex number plane, rather than using a number line as per usual absolute values.
  • Absolute Value Rules

    Absolute value rules tell you how you should go about taking the absolute value of a number. Absolute values always leave you with a postive number, whether or not the output is positive or negative. You will turn any negative numbers into positive ones for absolute values.
  • Absolutely Convergent

    Also known as absolute convergence, this refers to an infinite series that converges when its terms are changed to their absolute values. This is done by changing any subtraction signs in the series to additions, then checking if the new series converges.
  • Acceleration

    Can be thought of as the increase of something's speed. Acceleration tells you the rate of change in veolicty of an object in relation to time. A positive acceleration means there is an increase in acceleration (speed) and a negative acceleration means there is a decrease in speed.
  • Accuracy

    Tells you how close an estimation or an approximation is to its real value. Commonly compared against precision, which tells you how much information is conveyed by a number, accuracy reflects correctness. An example is the number of pi. 3.14 is accurate, but not precise.
  • Angle-angle Similarity

    Angle-angle similarity can also be called AA similarity. This is a postulate that says two triangles are similar when their corresponding angles are congruent.
  • Back Substitution

    When the agument matrix (a matrix that lists out the coefficients and constants in a system) is coverted to Row Echelon Form and then the free variables is made to equal an arbitrary value so that a general solution can be found for a linear system of equations. To do this, the last equation is solved first, and then we work backwards and proceed to the second last, third last, and so on.
  • Base (in Exponents)

    In exponential expressions, the base is the number that is being multiplied by the exponent or power. For example, in 232^3, 2 is the base while 3 is the exponent or power.
  • Base (in Geometry)

    Base is a term used in both plane geometry and solid geometry. A base can refer to the surface a 3-dimensional object that sits on or the bottom side of a shape. If the top is parallel to or the same as the bottom, both the top and bottom are called bases.
  • Base (Isosceles Triangle)

    An isosceles triangle's base is the side that is not congruent to the other. Remember that an isosceles triangle has two equal sides (called legs) and its last remaining side is called the base. Another way to phrase this is that the base of an isosceles triangle is the side that is not the legs of the triangle.
  • Base (Trapezoid)

    A trapezoid's base is either one of the parallel sides in a trapezoid. A trapezoid has two parallel sides (the top and bottom sides), and the other two sides have no special requirements. These two other sides are called the legs of a trapezoid. In other words, the base of a trapezoid are the sides that are not the legs.
  • Base (Triangle)

    In a triangle, any side of it can be a base. However, the base and the height of the triangle must be perpendicular to one another. The height of a triangle is the line from the vertex to the opposite side of the triangle that is perpendicular.
  • Bearing

    Helps to tell the direction. There is the true bearing and the conventional bearing. The true bearing measures in degrees starting from the north line in a clockwise manner. The conventional bearing tells the direction based on the number of degrees east or west of the north and south line.
  • Bernoulli Trials

    A trial in probability in which a random experiment with precisely two possible outcomes are repeated and it consistently gives the same probabilty of success. The binomial probability formula can help you find probabilites for Bernoulli trials.
  • Beta (β)

    The second letter in the Greek alphabet. In math, the beta function helps to reduce complex integrals into exprsesions. The beta function is also known as Euler's integral of the first time and is closely connected to the gamma function.
  • Between

    When you have a line with endpoints X and Z, a point Y is between points X and Z if it is on the XZ line segment. The idea of a number being between two other numbers is used in Euclid's proofs.
  • Biconditional

    When two conditionals (a conditional and its converse) are written both at once. Also known as the if and only if condition. In order for two propositions to be true, they must both be simultaneously true. The same goes for it being false. The symbol for biconditionals is ↔.
  • Binomial

    A polynomial that is made up of two terms. It is an algebraic expression that is made up of the sum or differences of two seperate terms. Therefore, each of the seperate terms can be seen as monomials when they are alone. An example of this would be 2x + y.
  • Calculus

    Is the mathamatical study of change. Calculus can be split into differential calculus and integral calculus. Differential calculus studies derivatives, which is the rate of change of functions. Integrals are the inverse of derivatives, and lets you find the area and volume of things.
  • Cardinal Numbers

    Numbers that are used for counting. Examples of this includes one, two, three and four. It deals with "how many" there are of something. Cardinal numbers do not have decimals or fractions. They are simple numbers that allows us to carry out counting. Its counterpart is ordinal numbers, which are used to identify the position of something.
  • Cardinality

    This is the number of elements that you have in a set. In a finite set, there is a value for cardinality which helps you determine the set's size. Cardinality is denoted by |A|. You can say that |A| = 4 for a set that has four elements in it.
  • Cardioid

    Describes a curve that is heart-like in shape. It is created when a circle rolls around a fixed circle that has the same radius. A cardioid has 3 parallel tangents and a cusp (the intersection of two branches of a curve). Named after the Latin word for heart, cordis.
  • Cartesian Coordinates

    Cartesian coordinates are also called rectangular coordinates. Part of the Cartesian Coordinates System where points are on a plane signified by a pair of numerical coordinates. There are two perpendicular lines that make up the axis of the plane and they meet at the origin, usually with the coordinates of (0,0).
  • Cartesian Form

    Also known as rectagular form. The cartesian form is used to indicate a position of a point on a two-dimensional or three-dimensional space. The cartesian coordinates were first used by René Descartes and therefore named after him.
  • Cartesian Plane

    Named after René Descartes who first used the plane formally in mathematics. Points can be located on a Cartesian plane by using the x-axis and y-axis to give you its horizontal and vertical locations. The x-axis and y-axis intersects at the origin in a Cartesian plane.
  • Catenary

    In geometry, it is a curve that looks like a slack hanging rope that is held up at its ends on two sides and pulled down by gravity. Its name cames from the latin word for "chain". Be cautious that a cartenary is not a parabola.
  • Cavalieri's Principle

    This principle tells us that if there are two solids with the same altitude, the section that come about from the planes that are parallel and the same distance from the two solids' bases are always equal. The volumes of the solids are also the same.
  • Ceiling Function

    The ceiling function maps out x's smallest integer that is greater than or equal to x. The ceiling has a domain of all real numbers and the set of all integers is its range. Sometimes, the ceiling function is also called the least integer function.
  • De Moivre’s Theorem

    Named after Abraham de Moivre, this theorem gives us a relatively simple formula that can help us find the powers and roots of complex numbers. Complex numbers that are in polar form can be raised to certain powers easily. Complex numbers are made of both real and imaginary parts.
  • Decagon

    A ten sided polygon. A regular decagon will have sides that are all congruent with the same interior angles. The sum of its angles measures 1,440 degrees when seen from above, meaning each angle equals 144 degrees. Its central angle totals to 360 degrees.
  • Deciles

    Refers to a way to split up percentile in a data set—similar to quartiles but rather than dividing up the data into four quarters, it divides it up equally into ten parts. For example, the first decile is the 10th percentile, whereas the third decile is the 30th percentile. Each part will then represent 1/10th of the population.
  • Decreasing Function

    Tells you the behaviour of a function. When the y-value of a function decreases as its x-value increases. This means that the graph is moving downwards as you go from left to right. Decreasing functions have negative slopes because of this.
  • Definite Integral

    An integral that has start and end values. You can find the definite integral by finding the indefinite integral at the two points specified in the interval and then subtract them. You can then find the area that is between a functions' graph and the x-axis.
  • Definite Integral Rules

    Defnite integrals are integrals that have start and end values. The definite integral rules tell you how to treat definite integrals in different situations. Keep in mind that these rules only apply when the integrals exist.
  • Degenerate

    When an object's nature is so changed that it should be classifed as another class. It is qualitatively different from the rest of its original class. An example of a degenerate form is a point being the degenerate form of a circle. Degenerate objects are used to test if certain formulas can be applied to objects that have been stretched from its original definition.
  • Degenerate Conic Sections

    Made up of a point, a line, and intersecting lines. Degenerate conic sections refer to plane figures that you get from the intersection of a double cone that has a plane passing through its apex.

    These sections can be expressed in an equation:
    Ax2+Bxy+Cy2+Dx+Ey+F=0 Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0
  • Degree (angle measure)

    Indicated in math by the ° symbol. It is a unit for measuring angles (not to be confused with the degree that measures temperature and also uses the same symbol). It takes 360 degrees to make a full rotation in a circle. Each degree is equal to 1/360 of a revolution. Degrees are usually measured using a protractor.
  • Degree of a Polynomial

    Refers to the highest degree in a polynomial. The degree in an expression tells us the order of an equation. They are represented by small numbers above and slightly beside a variable telling you that variable is raised to a certain degree.
  • Denominator

    Denominator is the number in the bottom part of a fraction. Denominator tells us how many equal parts the numerator is divided into.
  • Dependent Variable

    Dependent variable is a variable that its value is to be determined by the value(s) of independent variable(s). For example, in y = 2x + 7, y is the dependent variable and its values depend on the values of x.
  • e

    e in mathematics is the base of the natural logarithm. Its has an approximate value that is equal to 2.71828 and is one of the most important constants since it appears in a wide variety of problems. Most commonly, e is seen when dealing with exponential models and exponential functions.
  • Eccentricit

    Denoted by e or ε, eccentricity tells you how drawn out a conic section is. In other words, it shows how far the conic section is from being circular. When you have a circle, its eccentricity is 0. The eccentricity of a line, on the other hand, is infinite.
  • Echelon Form of a Matrix

    Comes in two forms: row echelon form and reduced row echelon form. The row echelon form has nonzero rows that are above any rows of all zeroes. The leading coefficient of a nonzero row is to the right of the leading coefficient of the row that's above it. For a reduced row echelon form matrix, it must be in row echelon form, but every leading coefficient is 1 and it has to be the only nonzero entry in that column.
  • Edge of a Polyhedron

    Where the faces of a polyhedron intersect with one another. These edges join together the polyhedron. The number of edges can be found using Euler's polyhedral formula which tells us that V + F - E = 2. V stands for vertices, F is for faces, and E is for edges.
  • Element of a Matrix

    A matrix is made up of rows and columns that have numbers or symbols amongst it. An entry in a matrix is also called the element of a matrix. An element can be referenced by first listing the row number followed by its column number.
  • Element of a Set

    The objects that make up a set. A set is usually made up of numbers or objects which individually, are each different entities. Elements can be, for example, letters, numbers or points. In the set {1, 2, 3}, the elements of the set would be 1, 2, and 3.
  • Ellipse

    A shape that looks like a stretched circle, giving it the appearance of an oval (keep in mind though that in mathematics, an ellipse is not an oval). It is a curve that is surrounded by two focal points of which the sum of the distances of the two foci are constant no matter which point you are at on the curve.
  • Ellipsoid

    A deformed sphere whose cross sections (no matter where you cut it) is either an ellipse, empty, or just a single point. It has three pairwise perpendicular axes of symmetry that intersect at a center of symmetry. A prominent object that is an ellipsoid is the earth, as it resembles a slightly flattened sphere more than a perfect sphere.
  • Elliptic Geometry

    Also known as Riemannian Geometry. An elliptic geometry is a non-Euclidean geometry that has a positive curvature of which Euclid's parallel postulate does not apply to. This geometry happens on the surface of a sphere where all the lines are great circles (circles on the surface of a sphere) and points are pairs of points that are directly opposite of one another. Therefore, all lines intersect.
  • Empty Set

    Sometimes known as a null set. It is a set that does not contain any elements within it. Therefore it has a size and cardinality of zero. The notation for empty sets are written as: "{ }" or "∅"
  • Equilateral Triangle

    It is a special case of an isosceles triangle which do not only have two but three sides equal to each other. Since all three sides of an equilateral triangle are congruent, the three angles are the same that each of them is 60?.
  • Even Numbers

    Even numbers are integers that are divisible by 2. In other words, they are multiples of 2. Some of the examples are ? 6, ? 4, ? 2, 0, 2, 4, 6.
  • Face of a Polyhedron

    A flat surface of a polyhedron. All of the faces of a polyhedron are polygons. The number of faces on a polyhedron can be found using Euler's polyhedral formula which tells us that V + F - E = 2. V stands for vertices, F is for faces, and E is for edges.
  • Factor of a Polynomial

    A polynomial divides into other polynomials. The process of factoring a polynomials breaks the polynomial into products of smaller polynomials. By multiplying these products together, you'd be able to return to the original polynomial.
  • Factor of an Integer

    When you have a number the divides evenly into another one, and in this case, these numbers are integers. Integers are whole numbers and fractions do not count as integers. As an example, the factors of 25 equals to 1, 5, and 25. 1, 5, and 25 are all whole numbers and not fractional ones.
  • Factor Theorem

    Helps to show the connection between the factors and zeroes of a polynomial. The factor theorem tells us that f(x) has a factor of (x - k) if f(k) = 0, meaning that k is a root of the polynomial.
  • Factor Tree

    One of the methods of carrying out prime factorization to identify prime factors of an integer. Prime factors are prime numbers that when multiplied, give you a number. In the factor tree method, each number branches off into into two numbers that will achieve the original number when multiplied (these are the factors). These two numbers will then each have their own branches. This is done until the original number is broken down into its prime factors.
  • Factorial

    It is the product of an integer with the rest of its smaller positive integers. A factorial is represented by a "!" sign after a number. It indicates that you should multiply a series of descending numbers. For example, 5! (read as "5 factorial") means you should carry out: 5 x 4 x 3 x 2 x 1 = 120.
  • Factoring Rules

    Rules that tell you how to properly handle different types of formulas when you're carrying out factoring. Examples of factoring rules include difference of squares, difference of cubes, and sum of squares. By observing the question you're dealing with, you can refer to the below rules to see how you can factor your formula.
  • Falling Bodies

    Also known as projectile motion. It is a formula that helps to find the vertical motion of an object that is throwing straight up or down, or simply dropped under gravitational force on Earth. The formula contains the variables of height, time, acceleration (due to gravity), initial veolocity and initial height.
  • Gambling Odds

    The payoff received from events dealing with gambling uses the odds against method. A bet of an amount n gives out a payout of m if the bettor wins the gamble. This is written as m:n. A note is that odds in gambling are not probabilities.
  • Gamma (Γ, γ)

    Gamma is the Greek alphabet’s third letter. In mathematics, the gamma function (which is represented by Γ) is an extension to the factorial function that allows you to deal with real and complex values.
  • Gauss-Jordan Elimination

    It is also known as Gaussian elimination. A way to solve linear systems of equations. It takes an equation's augmented matrix and turns it into a reduced row echelon form through row operations. The reduced row echelon form has zeroes on its lower diagonal and the first nonzero number in each of the rows is 1.
  • Gaussian Elimination

    It is also called Gauss-Jordan elimination. A way to solve linear systems of equations. It takes an equation's augmented matrix and turns it into a reduced row echelon form through row operations. The reduced row echelon form has zeroes on its lower diagonal and the first nonzero number in each of the rows is 1.
  • Gaussian Integer

    A complex number (x + yi) whose real and imaginary parts (both x and y) are both integers. Gaussian integers were originally introduced by Carl Friedrich Gauss.
  • General Form for the Equation of a Line

    An equation for a line in the form of Ax + By = C. Within this form, either A or B can be 0, but not both. There are several equations for a line and the general form is one of the ways that a line can be expressed. Its advantage is that it works well with vertical lines.
  • Greatest Common Factors (GCF)

    A greatest common factor is the largest integer that can completely divide a set of numbers. In other words, GCF is the largest common factor that these numbers share. This can be done by listing out the common factors for a set of numbers and then identifying the number with the highest value amongst them.
  • Half Number Identities

    Also known as half angle identities. They are identities that uses sine, cosine, and tangent for half a given angle in trigonometry. They help you to solve trig functions of angles that aren't on a unit circle by using one that is. You won't be able to get all the angles on a unit circle, but it does help you get a closer answer than without half angle identities.
  • Half-Life

    How long it takes an entity that's decaying exponentially to diminish by half. Half-life is usually used in physics to look at the stability of atoms or radioactive decay. It is constant over an exponentially decaying entity's lifetime.
  • Half-Open Interval

    An interval that only has one endpoint. It is represented as [a, b) or (a, b] with the square bracket [] on the end that is closed and the parentheses () on the end that isn't. It is also sometimes called a half-open interval.
  • Harmonic Mean

    It is an average. Sometimes known as the subcontrary mean. In order to identify the harmonic mean in a set of numbers, you'll have to add the reciprocals of each of the numbers then divide it by n. Lastly, take the reciprocal of the results.
  • Harmonic Progression

    Also known as a harmonic sequence. It is a progression that takes the reciprocals of an arithmetic progression. Harmonic progressions cannot be added up to an integer. This is due to there being at least one denominator that will be divisible by a prime number that doesn't divide any of the other denominators.
  • i

    An italicized i is used to represent an imaginary number. Imaginary numbers give you a negative result when squared. Usually, any number you square should come out positive. Therefore i is used to help us imagine that we would be able to get a negative outcome.
  • Icosahedron

    An icosahedron is a solid polyhedron that consists of 20 faces, 30 sides, and 12 vertices. It is a platonic solid. Its name comes from the Greek word "icos-", which means twenty, and "-hedron", an Indo-European word that means seat.
  • Identity (Equation)

    An identity is an equation that stays true no matter what values are substituted for any of its variables. It is an equality between functions that are defined differently. An example of this is tan θ = sin θ/cos θ. Both sides of this equation will produce the same values regardless of what θ¸ ends up becoming.
  • Identity Function

    A function that always gives you the same value as its argument. That means you're working with a function that looks like f(x) = x, where every real number x that is inputted gives you that same number x as the output. The graphs of identity functions all looks like a straight diagonal line that rises upwards from left to right.
  • Identity Matrix

    Sometimes known as a unit matrix. The n x n identity matrix has n rows and n columns. The upper left and bottom right diagonal consists of 1s, and the other entries in the matrix are all 0s. By multiplying another matrix by an identity matrix, it'll leave the original matrix the same.
  • Identity of an Operation

    A number where if you combine it with another quantity via an operation allows that quanity to remain the same. For addition, you have the additive identity of 0 since adding 0 to anything does not alter it. In multiplication, it is 1 since multiplying anything by 1 allows it to remain the same.
  • if and only if

    Also known as biconditional or shortened to iff. It means that a statement being true requires another statement to also be true. The inverse is true too. If one statement is false, it requires that the other statement is too. It plays on the fact that there is a neccessary and a sufficient condition for the statements.
  • Joint Variation

    A variable z that varies jointly with x and y means that you will be dealing with an equation in the form of z = kxy, where k stands for a constant. Sometimes, this is also referred to as jointly proportional. A example of this would be A = πr2r^2, which is the equation for the area of a circle.
  • Jump Discontinuity

    Also known as step discontinuity, this refers to a discontinuity that happens when a graph jumps from a connect section of a graph to another. It is also known as a discontinuity whose limits from both the left and right exists but don’t equal one another.
  • Kappa (Κ, κ)

    The tenth letter of the Greek alphabet. The Kappa curve in geometry borrows this letter since that curve resembles how Kappa is written in Greek. Algebraic curves that are Kappa curves have two vertical asymptotes.
  • Kite

    This refers to a quadrilateral with two congruent pairs of adjacent sides. This is the cause of difference between a kite and a parallelogram, whose pairs of congruents sides are opposite to each other rather than being adjacent. A kite's diagonals are perpendicular. It very much does look like a kite that one can fly at the beach, and that's what it was named after.
  • L'Hospital's Rule

    It is also known as L'Hôpital's Rule. Used to evaluate factions’ limits to indeterminate expressions of 0/0 and ±∞/±∞. This is carried out through finding limit of the derivatives of the numerator and the denominator. Then we are able to take its limit.
  • Lambda (Λ, λ)

    The eleventh letter of the Greek alphabet. In mathematics and physics, the lowercase version of Lambda is used for wavelengths of any wave. Wavelength tells you the distance between two crests of a wave. The formula to find wavelength is λ = v / ƒ, where "v" stands for velocity and "ƒ" stands for frequency.
  • Lateral Surface Area

    The surface area of 3D objects without its top and bottom base. The surface area is found by finding the area of the individual faces of an object and then summing it together to find the total surface area. In order to find just the lateral area, do not sum up the areas of the top and bottom base when totalling up the surface area.
  • Lateral Surface/Face

    A solid's surface that can be considered a face. This excludes the bases of the solid. In the case of a cylinder, for example, its lateral surface is the side of the cylinder. The top and bottom circles would not be considered a part of its lateral face.
  • Latus Rectum

    It is a segment of a line that perpendicular to the principal axis of a parabola, hyperbola, or ellipse. It starts and ends on the curve, so its endpoints sit on the curve. Different conics have different ways of determining its latus rectum.
  • Law of Cosines

    Also known as the cosine rule. The law of cosines relates the cosine of an interior angle in a triangle to its sides. It helps us find aspects to a triangle such as its third side when we know two sides and the angle between them, or we can even find the angles inside a triangle if we have all three sides of the triangle.
  • Maclaurin Series

    The name for a power series in x for a function in the form of f(x). It helps provide an approximation near the origin for this function and allows you to calculate a sum that's usually uncomputable. A Maclaurin Series is a special case of a Taylor series.
  • Magnitude of a Vector

    A magnitude in mathematics refers to the size of some quantity or object. It helps you compare if something is larger or smaller to another object. For the magnitude of a vector, it tells you the length of the vector. Along with telling you a magnitude, vectors also have a direction.
  • Main Diagonal of a Matrix

    Refers to a diagonal set of elements in a matrix. The main diagonal can be found by going from the upper left corner of a matrix and then diagonally going down and to the right.
  • Major Arc

    In situations where you have two arcs in a circle, the larger arc is referred to as the major arc. It is an arc that measures to or is greater than 180 degrees, which is also π in radians. Summing up the major arc and the minor arc (the arc that is smaller) gives you 360 degrees or 2π radians.
  • Major Axis of a Hyperbola

    The principle axis of symmetry in a hyperbola that seperates it into two mirrored halves. It is a line that passes through the vertices, center, and the foci of a hyperbola that ends at the widest points of a hyperbola's perimeter.
  • Major Axis of an Ellipse

    The principle axis of symmetry in an ellipse. It is a line that passes through the vertices, center, and the foci of an ellipse. It can also be considered the longest diameter that can be measured in an ellipse. One half of a major axis is called a the semi-major axis.
  • n Dimensions

    Indicates that n mutually perpendicular directions of motions are possible in a space. This means that in a space, you can find n vectors that are not a linear combination of the others. It helps go beyond the regular notion of three dimensions.
  • Natural Domain

    Is the maximum set of plausible values in a defined function which does not have an imposed domain. Each value in the set, when used with the function, will output a real value. An imposed domain on a function would cause it to have an unnatural domain.
  • Natural Logarithm

    A logarithm to the special base of base e (e = 2.7182818...). You may see it being written as ln(x) or logₑ(x). Natural logarithm functions are the inverse functions of exponential functions, which allows you to rewrite a natural logarithm in exponential form by converting back and forth.
  • Natural Numbers

    Positive whole numbers that are commonly used for counting and putting things in order. Natural numbers contains no negative numbers or numbers that are in fractions. The numbers 1, 2, 3, 4, 5 demonstrates this. 0 is a number that cannot be universally agreed on whether it is a natural number or not.
  • Negative Direction

    A descriptor of data on a plot. Negative direction is usually describing a downward slope on a plot, where one value is decreasing and the other value is increasing or vice versa.
  • Negative Exponents

    Another way to display reciprocals. Negative exponents allow you to write powers without having to use decimals or fractions. When you have a negative exponent, flipping it to the other side of the division line allows you to rewrite it as a number with a positive exponent.
  • Oblate Spheroid

    A name for a flattened sphere. It is obtained when you revolve an ellipse about its minor axis. A popular example for an oblate spheroid is the Earth. Due to earth's rotation, Earth has been flattened from its poles creating a shape that resembles an oblate.
  • Oblique

    When something is tilted at an angle. It is not horizontal or vertical. Alternatively, an oblique angle refers to an angle that is not 90 degrees or a multiple of 90 degrees. This means any other angle such as acute or obtuse angles can also be called oblique angles.
  • Oblique Asymptote

    An asymptote that is not not horizontal or vertical. It is a slanted line where a function approaches when x approaches infinity. A function is able to have a maximum of two oblique asymptotes. Some rational functions have oblique asymptotes if the degree in the numerator is one degree more than the degree in the denominator, an oblique asymptote will exist.
  • Oblique Cone

    A cone whose altitude does not intersect with the center of the cone's base. Its altitude is still perpendicular to the base, but it is not in the center. A oblique cone can be summarized as a 3D figure that has a lateral surface with altitude, a base that is circular, and a vertex.
  • Oblique Cylinder

    A cylinder that has two end planes that are parallel to one another. However, unlike a right cylinder, its lateral surface is not perpendicular to these end planes. These end planes (also known as its bases) don't align perfectly on top of one another.
  • Oblique Prism

    A prism whose end planes are parallel but not aligned on top of one another perfectly. An oblique prism's lateral faces (its sides) are parallelograms. Since its bases don't align perfectly, the prism looks like it is slanted (oblique means "slanting").
  • Oblique Pyramid

    A pyramid whose apex is not above the center of the pyramid's base. The pyramid looks as if it is tilted to one side (oblique means "slanting"). In order to calculate a oblique pyramid's surface area, you cannot use the regular formula anymore and must instead cauculate each of the faces seperately.
  • p-series

    You've got a p-series when you see that a series converges when p > 1 and diverges when p < 1. It is an infinite series in the form of m=11mp\sum_{m=1}^{\infty } \frac{1}{m^p}. Used in the comparison and limit comparison test.
  • Paired Data

    A name for data that exists in ordered pairs. The paired data can have a relationship of both data set having the same number of data points, or each data point on one set of data relates to another data point in the other set of data.
  • Pappus's Theorem

    A geometry theorem that helps you identify the surface area and volume of surfaces of a solid of revolution. It uses the distance travelled by the centroids of a curve and the region that experiences revolution. Named after Pappus of Alexandria who is attributed to this theorem.
  • Parabola

    A two-dimensional u-shaped curve. A parabola is made up of the focus (a point) and a directrix (a line). The focus does not lie on the directrix and the locus of points in the plane is such that the distance to the focus is the same as the distance to the directrix.
  • Parallel Cross Sections

    Cross sections that are parallel with the base of a solid. Cross sections can be thought of as slices of a shape - imagine slicing through a loaf of bread. The other orientation for cross sections is that they can be perpendicular to the base.
  • Parallel Lines

    Two lines that are always an equal distance apart and never touches each other. These two lines lie on the same plane and must lie on a perfectly flat surface. Note that lines that are parallel have the same slope. The symbol to signify that lines are "parallel to" one another is ||.
  • Parallel Planes

    Two planes in the same three-dimensional space that do not intersect and are parallel to the same line. The symbol to show that a plane is "parallel to" another is ||. There are proofs for you to find out if two planes are parallel to one another.
  • Q1

    In statistics, Q1 is known as the first quartile or lower quartile. Quartiles divide up a data set into four equal sections. Q1 is the middle value in the first half of the data set. It is also known as the first 25% of a data set. Remember that the data has to be sorted first before quartiles can be found.
  • Q3

    In statistics, Q3 is known as the third quartile or higher quartile. Quartiles divide up a data set into four equal sections. Q3 is also known as the 75th percentile of a data set. Remember that the data has to be sorted first before quartiles can be found.
  • QED

    An abbreviation of the latin phrase quod erat demonstrandum ("that which was to be demonstrated"). It signifies that we have come to the end of a proof. This is especially useful when it's not obvious that a proof has been completed.
  • Quadrangle

    Another name for a quadrilateral. This is a two dimensional shape that has four sides. Examples of quadrangles include parallelograms, rectangles, and squares.
  • Quadrantal Angle

    Angle in the standard position with a terminal side that lies on the x-axis or y-axis. This means that the angle will be multiples of 90°. Examples include 0°, 270°, -90° and so forth.
  • Radian

    A way to measure angles, as opposed to using degrees. You can equate radians to degrees as ½π radians equals 90°. This means that 360° is the same as 2π. Radians measure angles using the number of radii required to measure an arc that is described by that angle.
  • Radical

    What is referred to when you see the square root sign (√). Radical expressions have at least one number under a radical. The sign can mean square root, but it can also mean some other root. Radicals that aren't square roots will have a smaller number (a subscript) that allows you to identify which root you're dealing with.
  • Radical Rules

    Rules that tell you how to carry out operations on radicals. Keep in mind that radicals can be rewritten with exponents, so some of the rules you'll encounter will move the radicals into a number's exponent.
  • Radicand

    A number under the radical symbol (sometimes known as the square root symbol). It is the number that is having its root taken. It could be a square root, but you likely will encounter cube roots and more. A subscript outside the radical sign will allow you to identify which root you're dealing with.
  • Radius of a Circle or Sphere

    The line that connects the center of a circle to the circumference of the circle or sphere. Its plural form is radii. Two radii will give you the diameter of a circle, since the diameter is a line that touches two points on a circle's circumference that passes through the center.
  • SAA Congruence

    Stands for side-angle-angle congruence. Sometimes also known as AAS congruence (angle-angle-side). If two triangles have two angles and a non-included side that are the same, SAA can prove that the two are congruent.
  • Sample Space

    All the possible outcomes or results for an experiment. Sample space is usually written as a set where the possible results are listed out as elements. As an example, if you're rolling a die, you have 6 possible outcomes and you will get a sample space of {1, 2, 3, 4, 5, 6}.
  • SAS Congruence

    Stands for side-angle-side congruence. If two of a pair of triangles' corresponding sides and one of their included angles are the same, you can use SAS to prove that the two are congruent.
  • SAS Similarity

    Stands for side-angle-side similarity. If two triangles have a corresponding angle that is equal and two sides are the same proportion to the other triangle's corresponding sides, you can use SAS to prove that the two are similar.
  • Squeeze Theorem

    Also known as the Pinching or Sandwich Theorem. It tells you that if a function that is between two functions that approach the same limit, it too must also approach that limit. In other words, a function is "sandwich"-ed between two other ones.
  • Table of Integrals

    Helps with integration in calculus. The table of integrals lists out common antiderivatives so that you can carry out calculations that involve integrations. It also lists out the integrals in different categories to make it easier for you to find the ones you'll need.
  • Takeout Angle

    The angle you would cut out from a piece of paper so that it will turn into a right circular cone. Depending on how large the angle is, it can affect how spread out your cone is or how narrow its base is.
  • tan-1

    Tangent's inverse function. It can help you calculate angles when certain information is given to you. When you know the sides of a right triangle, but not the angle, inverse tangent comes into use. The inverse tangent performs the opposite of the tangent function.
  • Tangent (in Trigonometry)

    Known as tan, and usually written as tan θ¸ in trigonometry. Tangent can be represented as sine and cosine, since tan θ = sin θ/cos θ. Simplifying down sin θ¸ divided by cos θ, you will be left with tan = opposite/adjacent. The memory device SOHCAHTOA can help you to remember this.
  • u-Substitution

    An integration technique that can help make integration easier to carry out. It is used when an integral contains a function and it derivative. It involves using the chain rule in reverse.
  • Unbounded Set of Numbers

    Set of numbers that do not have either a lower or upper bound. Bounded sets are finite, whereas unbounded sets can be considered not. To demonstrate this, the sequence of 1, 2, 3, 4, 5... does not have an upper bound to it and is therefore an unbounded set of numbers.
  • Uncountably Infinite

    An infinite set that has too many elements in it that it is considered uncountable. This happens if a set's cardinal number is bigger than the set of all natural numbers. The best known example of a set of uncountable numbers is the set of all real numbers.
  • Undecagon

    A polygon that has 11 sides. It is more commonly known as a hendecagon. Hendecagons that have 11 equal number of angles are regular hendecagons. It will have internal angles of 147.27 degrees each.
  • Variable

    An alphabetical character in mathematics that can take on different number values. It also can mean a quantity that is subject to change or can be regarded as different quantities.
  • Varignon Parallelogram of a Quadrilateral

    The shape that you get when you take the midpoints of the sides of a quadrilateral and join them together to make a new four sided shape. Varignon's theorem tells us that this shape that ends up being formed is a parallelogram.
  • Vector

    A line with an arrowhead at its end in mathematics that has both a direction and a magnitude (a size) associated with it. The length of the arrow can tell you the magnitude and the arrowhead shows you the direction.
  • Vector Calculus

    Also known as multivariable calculus. Multivariable calculus has to do with functions whose outputs and inputs exist in two or more dimensions. Therefore, it will have two (or more) independent variables and dependent variables.
  • Velocity

    Tells you the rate of change of position of an object. It is speed with a direction attached to it. Commonly used to define how fast an object is moving, such as calculations that involve a car driving down a road. To make the car's speed a velocity, it should also specify which direction it is heading.
  • Washer

    A washer, or an annulus (in latin, this means little ring), is a ring shaped object. Its area is bounded by two concentric circles that has different radii. Both of the circles has the same center point. You are able to find the area of the annulus by subtracting the hole in the middle from the total area of the bigger circle.
  • Washer Method

    If you wanted to find the volume of a round shape with a hole in the center, the washer method can be used. This technique makes use of the disk method. A shape is cut into thin pieces (or disks) and then you can find the volume of the slices by subtracting out the hole in the middle.
  • Wavelength

    It is the period of a sine wave. A period can be thought of the amount of distance over which a shape repeats its own shape. It is usually found by calculating the distance between corresponding points of the wave going through a certain phase—for example, at the troughs at of the waves.
  • Weighted Average

    A method to find the mean in a set of numbers. The weighted average takes into consideration that some components in the set of numbers are more important than others. The average is calculated by multiplying each number with its assigned weight before adding them together and dividing it to find the average.
  • Whole Numbers

    Numbers such as 1, 2, 3. These do not have decimals and are not fractions. There are also no negative in whole numbers. 0 is also considered a whole number.
  • Work

    Tells you the amount of energy transer that occurs when something is moved over a certain distance by an external force. In mathematics, work can be found by finding the integral of the force over the distance that the object is displaced.
  • x-intercept

    In graphing, it is a point where the graph intersects with the x-axis (the horizontal axis on a Cartesian plane).To find the x-intercept in a linear equation for example, substitute in 0 for the y value in your linear equation and you can then solve for x.
  • x-y Plane

    Also known as the Cartesian plane. It is a plane that has its x and y axes defined. The values of x is called the x-coordinates (also known as the abscissae) and the values of y is called the y-coordinates (also known as the ordinates).
  • x-z Plane

    Can be found in a 3 dimensional coordinate system. It is the plane formed by the x-axis and the z-axis. It has the standard equation of y = 0.
  • Xi (Ξ)

    Xi is the Greek alphabet's fourteenth letter. Ξ or ξ represents the original Riemann Xi function. This function was named after B.G. Riemann, he wanted to estimate the number of primes less than a given number.
  • y-intercept

    In graphing, it is a point where the graph intersects with the y-axis (the vertical axis on a Cartesian plane).To find the y-intercept in a linear equation for example, substitute in 0 for the x value in your linear equation and you can then solve for y.
  • y-z Plane

    A part of the three dimensional coordinate system. It is the plane formed by the y-axis and the z-axis. It has the standard equation of x = 0.
  • z-intercept

    In graphing, it is a point where the graph crosses the z-axis on a three dimensional coordinate system in a Cartesian grid.To find the z-intercept you will need to figure out where the x and y coordinates are equalled to 0.
  • Zero

    A number that expresses something that has no size, quantity, or magnitude. If you see that something has the value of zero, it essentially means there is no amount. It is represented with the figure 0. It is regarded as being neither positive or negative.
  • Zero Dimensions

    Also known as zero dimensional. A topological space that has zero dimensions. An example of something with zero dimensions is a point. In order to indentify a point on a line, you'll need one coordinate to find that point and therefore it has a dimension. But for a point of a point, you don't need to use any coordinates to identify where it is.
  • Zero Matrix

    When you come across a matrix that has all 0's as its elements. They are also sometimes known as null matrices. "O" is used to denote a zero matrix and a small subscript next to it (i.e. 2x4) can depict the dimensions of the matrix if needed.
  • Zero of a Function

    Refers to the x-value that makes the function equal to 0. In other words, what input to a function can produce the output of zero? In polynomial functions, the zero is known as the root. The Zero of a function can be a real or a complex number.
  • Zero Slope

    Also known as the slope of a horizontal line. A horizontal line has all the same y-coordinates and therefore, when you attempt to find the slope of it usuing the slope formula, you'll get 0 no matter what. This is due to the "rise" of the line is always zero.
  • Zero Vector

    Also known as a null vector. A vector that has the length of 0. This means that all its components are also equal to 0. Since it doesn't have a length, its magnitude is not pointing in any direction and therefore has an undefined direction.
  • Zeta (Ζ)

    Zeta is the Greek alphabet's sixth letter. It is used in math in the Riemann zeta function that helps investigate the properties of prime numbers. This function is named after mathematician Bernhard Riemann.