Math Glossary

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.

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).

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.

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.

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.

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.

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 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.

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.

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.

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.

An angle that is smaller than a right angle (90°). Acute means "sharp" so it may also be refered to as a "sharp" angle. A helpful way to help differenciate the different types of angles is to think of acute angles as "a cute" angle, meaning small and less than 90°. A triangle with three acute angles is known as a acute triangle.

A triangle that contains three acute angles. Which is, all three interior angles must be less than 90°. There are three major types of acute triangles. The first is equilateral triangle. It has three equal angles all measuring at 60° and three equal sides. The second is acute isocelese triangle. It has two equal angles and two equal sides. The third type is acute scalene triangle. It is when there are no angles and no equal sides.

Also known as the "sum rule." It is a rule for calculating the probability of two events A and B, that can be mutually exclusive or non-mutually exclusive. The formula P(A or B) = P(A) + P(B) is used for mutually exclusive events, and P(A or B) = P(A) + P(B) – P(A and B) for events that are non-mutually exclusive. For example, to calculate the probability of rolling a 1 or 2 on a 6 sided die we would simply add up the probability of each event as 1/6 + 1/6 = 1/3. This event is mutually exclusive because it is impossible to roll both numbers at the same time with one die. Example 2, calculating the probability of drawing a queen or daimond card from a 52 card deck. This event is non-mutually exclusive because there is a possibility of drawing a queen of diamonds which satisfies both events. So the second formula must be used to subtract the queen of diamonds from being counted twice.

Additive inverse rule applied to a matrix. The rule will change the sign of every matrix element from positive (+) to negative (-) or vice versa. The sum of the original matrix and its additive inverse matrix would result in a matrix full of zeros, or "zero matrix."

The opposite sign of a number. Flipping the sign of a number from positive (+) to negative (-) or vice versa. For example, the additive inverse of 10 and -5 is -10 and 5 respectively. When adding a number with its additive inverse, it will always result in a zero. A double additive inverse is the rule applied twice, and would have no effect as it cancels out each other.

The property states that if a = b then a + c = b + c. When solving equations, variables or terms that equal can be substituted in and out with each other. For equations with multiple variables and terms, this property can be used to substitute and collect like terms to solve for one variable.

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.

An arrangement of objects, pictures, or numbers in rows and columns is called an array. This array has 4 rows and 3 columns. It can also be described as a 4 by 3 array

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.

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

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.

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.

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.

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.

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.

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.

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 ↔.

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.

Numbers that The coefficients in the binomial equation. The coefficients must be a positive integer and when arranged in rows

The formula used to calculate the probability of a "Bernoulli trial" or an event with exactly two different possible outcomes, such as flipping a coin. The formula is represented as _______ where "n" is the number of trials, "k" is the number of successes, "n-k" is the number of failures, "p" is the probability of success in one trial, and "q=1-p" is the probability of failure in one trial.

Also known as "binomial expansion." It is used to describe or expand the binomial expression raised to a power. For example:\( (a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4\). Expanding this equation one by one would take very long, so a equation was made (as seen in the picture) to help simplify this process by plugging in numbers.

To split a geometric shape into two congruent parts or exactly in half of equal shape and sizes. The line used to split the congruent shapes is called a "bisector" and the object being split is known as the "bisected." It is also possible to bisect angles and lines or segments. When bisecting an angle, the bisector passes through the apex of the angle splitting it into two equal angles. In three dimentional objects, bisection is done through planes, known as "bisecting plane."

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.

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.

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.

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 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).

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.

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.

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.

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.

A stationary point in which all objects rotate about that point in a circular motion. For example, if an arrow is pointing towards the center of rotation. When rotated about that point, the arrow moves in an arc but remains the same distance throughout the rotation and the direction of the arrow remains pointing at the center of rotation. When the center of rotation is within the figure, the figure would stay in its spot and spin.

Triangles can have thousands of different centers. The four main ones are Centroid, Circumcenter, Incenter and Orthocenter. A centroid

An angle with a vertex on the midpoint of a circle. That is an angle ABC, the points A and C reside on the circles circumference and B is located at the center of the circle. The curve between points A and C is known as the arc A C.

One of the 4 main "centers of a traingle." Centroid refers to the center of mass of a figure. In a triangle, the centroid is located by drawing 3 medians (lines from the vertex to the midpoint of the opposite side). The point where the three lines intersect is the centroid of the triangle.

Formula used to find the coordinates of the centroid for a triangle or any sets of points on a X-Y plane. In a triangle, if we average the x and y coordinates of the verticies, it will result in the coordinates of the centroid.

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.

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.

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 \(1\over10\)th of the population.

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.

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.

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.

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.

\( Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 \)

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 \(1 \over 360\) of a revolution. Degrees are usually measured using a protractor.

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.

The exponent of a term. For example \(3x^6\), the degree will be 6. For multiple variables within the same term, the degree is the sum of all the variables exponents. For example \(3x^5y^4\), the degree will be 9. In the case of a polynomial with multiple terms, the degree of the polynomial is the highest degree of any term. For example \(4x^3 + 2x^2 + 5\), the degree of the polynomial is 3, because it is the highest.

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 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 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.

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.

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.

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.

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.

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.

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.

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.

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 "∅"

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 = π\(r^2\), which is the equation for the area of a circle.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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").

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.

A angle that measures greater than 90° but less than 180°. In other words it is an angle between a right angle and a straight line. It is the biggest out of the three main angle categories (obtuse angle, right angle, acute angle).

A triangle which contains one obtuse angle in its interior angles. In other words, it is a triangle with one angle that is greater than 90°. The sum of the interior angles of an obtuse triangle will equal 360°.

Steming from the greek word meaning 8. An octagon can be defined by a polygon with 8 angles and 8 sides. A regular octagon has 8 equal sides and 8 equal interal angles measuring 135° each. Think of it like a square but with 8 sides instead of 4. The internal angles of any octagon add up to 1080°.

An 8 faced polyhedron, a 3D shape with 8 faces. A regular octahedron will have 8 equal faces formed by equilateral triangles. Imagine it as two square pyramids stuck together from the bottom. It is one of the 5 platonic solids. The volume is defined as :V = \(\sqrt2 \over 3\)a³, and the surface area is defined as : \(A=2\sqrt3 a^3\)

\(1 \over 8\) of the 3D region divided up by 3 planes (X,Y,Z). Think about a rubik's cube with 8 individual cubes. 4 at the top and 4 at the bottom, forming a giant cube. It can also be defined as \(1 \over 8\) of a full circle. It would have an angle of 45° (360°/ 8 = 45)

Defined as an odd function only if f(–x) = –f(x). The graph of an odd function with respect from the origin will be identically symetrical.

An integer that cannot be factored by 2. Any number containing 1,3,5,7,9 in the ones place is a odd number. Some odd number examples include: 11, 23, 55, 67, 89, 111. Odd numbers go by the pattern 1+2X, with X being any integer.

A way of simplifying and grouping different functions. We can define trigonometry identities as either a odd or even function. For example, sin and tan are odd functions while cos is an even function.

Odds is short for "odds against" It is the chances of a event occuring in your favor. The value is calculated from the sum of all desired outcomes divided by the sum of all possible outcomes. An example is, what are the odds of rolling a 2 on a 6 sided die, the odds are 1/6. Higher odds means a greater chance of getting a desired outcome. While lower odds means a small likelyhood of the desired outcome.

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 \(\sum_{m=1}^{\infty } \frac{1}{m^p}\). Used in the comparison and limit comparison test.

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.

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.

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.

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.

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 ||.

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.

Also known as "Playfairs Axiom." In Geometry, the axiom states that if there is a point and a line on a 2 dimentional plane. There is only one possible line that can be drawn through the point and be parallel with the line. An equivalent property is called "Euclid's fifth postulate," a seperate property that can be used to prove each other.

A 2 dimentional shape made up of two sets of parallel lines. Each set of parallel lines are directly opposite across each other, and do not intercect. A parallelogram can be imagined as a slanted square. Its area is calculated as base x height, where the height is a vertical line perpendicular to the base and the top. An alternative formula for the area is (AB)(AD)sinA or (AB)(BC)sinB

In geometry, it is a polyhedron with 6 faces made up of parallelograms. Much like how a parallelogram looks like a slanted square, a parallelpiped is like a slanted cube. Its volume can be calculated by multiiplying the area of the base with the height. The formula is a · (b × c) where each letter desinates each edge on a different plane.

In algebra, a parameter is defined as the independant or dependant variables in a system of equations. For example, in the system of equations, X = 3 + Y, and Z = 4Y. Y is the parameter of the system of equations.

Formulas for the first derivative and second derivitive often used to find the equation of a tangent line to a parametric curve. The derivative of Y (a dependant variable) with respect to X (a independant variable) is calculated when both X and Y depend on T (a third independant variable).

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.

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.

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.

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

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.

From the greek origin meaning 4. In plane geometry quadrants refers to the 4 different sections of a graph divided by X and Y axis. Imagine a square being cut evenly into 4 pieces, 2 at the top and 2 at the bottom. The 4 sections are usually numbered from 1-4, with the top right being quadrant 1, and naming counterclockwise, quadrant 2 on the top left, quadrant three at bottom left and quadrant 4 on the bottom right. We can use a mnemonic to help us remember which of three trigonometry functions are positive in which quadrant. "All Science Teachers Crazy" is placed in order of the quadrants. All represents all three functions are positive, Science represents Sin being positive in its quadrant, Teachers represents Tan, and Crazy represents Cos.

From the Latin word "Quadratus" meaning square. In math terms that translates to a degree of 2, think about X squared is \(X^2\). A graph, expression or data that is to a degree of 2 can be defined as quadratic.

An equation that is to the second degree polynomial. A standard quadratic equation looks like this, \(ax^2+bx+c=0\). There can be two variables to the second degree such as \(3x^2-5y^2+1=0\). It is considered a quadratic equation as long as the highest degree of polynomial is two.

The most common formula to solve quadratic equations. The formula can be used to quicly determine how many real zeros the equation has.

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.

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.

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.

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.

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.

All the possible values specified within the highest and lowest number of a set. It is calculated by subtracting the highest value with the lowest value. In algebra, range refers to the Y - values on a graph, expression or function.

Written in the form "A : B" or "A to B." It may also be described as the quotient of "A and B" It compares the porportion of A and B relative to each other. For example, if there are 5 oranges and 10 apples. The ratio can be written as 5 : 10 or 1 : 2 (simplified). Like fractions, ratios are written in its simplist form.

Triganometry identities that define TAN and COT, in terms of SIN and COS. It is a means of simplifying equations by writing two trigonometry functions in terms of basic functions. TAN is a ratio of SIN and COS while COT is the ratio of COS and SIN.

A convergence test for a series when . It states that a series converges absolutely if L < 1. A series is divergent if L > 1. One of these two results must be met or the limit does not exist. If L = 1 the series may diverge or converge thus rendering the test inconclusive.

An equation that contains at least one rational expression on one or both sides of the equation. The rational expresion is a fraction where the denominator and numerator are polynomials. Rational equations can be solved by reducing the common denominator and then solve for the numerator.

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.

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}.

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.

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.

Any real number used in linear algebra. A quantity with a magnitude but no direction. Mass, height, temperature, distance are all examples of scalar quantities.

Also known as the dot product or inner product. It is the name given when vectors are multiplied and resulting in a scalar answer. The scalar product of two vectors at 90° (right angle) to each other will always be zero.

The ratio of 2 similar geometric shapes or quantities with similar unit of measurements. To find the scale factor of two similar geometric shapes. Write the lenghts of the corresponding sides of each shape to one another to get the ratio. For example, a scale of 1:2 represents the length of the second object being double of the first. Scale factors are commonly found in maps to translate the measurement of two points on a map to actual distance.

A triangle with three unequal lengths and angles. Scalene triangles can have a right angle with 2 acute angles, 3 acute angles, or an obtuse angle and 2 acute angles. The angles of any triangle must add up to 180°.

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.

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.

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.

A trigonometry function written as Tan or as Tan θ. Tanθ = Sin θ/Cos θ. In a right angle triangle, the tangent of angle θ is the ratio of the opposite side over the adjacent side of the angle θ. In plane geometry, a perpendicular line to the circles radius, that touches a circle at just one point but does not pass through is a tangent.

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 = \(opposite \over adjacent\). The memory device SOHCAHTOA can help you to remember this.

A straight line that touches one point on the function without crossing over. At the point of intersection, the slope of the tangent line equals the derivative of the fuction of that point. The derivitave is also known as the instantaneous rate of change.

Used to approximate the function using

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.

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.

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.

A slope that cannot be defined. Calculating the slope of a vertical line will always result in a undefined slope. This happens because the X values remains the same and thus the denominator would be zero when using the slope formula: \(m = \frac{y_2-y_1}{x_2- x_1}\).

An equation that consists of more variables than equations. Underdetermined equations either have no solution (inconsistent) or a multiple number of solutions (consistent). For example X + Y + Z = 1, X + Y + Z = 0 has 3 variables and 2 solutions. It does not have any solutions, therefore this underdetermined equation is inconsistent. X + Y + Z = 1, X + Y + 2Z = 3 would be a consistent equation because there can be multiple solutions to this equation.

A standard circle with a radius of 1 unit. It is commonly used in trigonometry to make solving angles and trigonomic functions easier to use and understand. By evaluating Sin and Cos angles in the unit circle, we are able to determine all of the 6 trigonometry function ratios as real numbers.

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.

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.

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.

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.

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.

A standard venn diagram is drawn by partially overlaping two circles over each other. Each circle represents a set and is used to compare differences and similarities between the two sets. The elements of each set are bounded within the non overlapped portion of the circle. Any common elements of the two sets are bounded within the overlapped portion of the corresponding circles. Venn diagrams can also be drawn with multiple circles used to compare multiple sets.

The process to prove the solution is true and correct. Often asked in a variable equation question, it requires the substitution of one or more variables to verify the equations or inequalities of the problem. For example: verify that x=2 is the solution of the equation X + 3 = 5.

Vertex refers to one point where two edges or lines meet. The plurl form is "vertices." In geometry, it is the corner points of the shape. In an angle, the vertex is the endpoint where two lines begin or meet. In three dimentional solids, the vertex refers to the point where three or more lines meet up. On a curve with no corners, the vertex refers to the point of maximum curvature (bends the most).

The vertices on a eclipse refers to the points of maximum curvature. On a eclipse there will always be two vertices directly across one another, and is always aligned with the line of symmetry as well as the X or Y axis

The vertices on a hyperbola refers to the point of maximum curvature. On a hyperbola, each curve will have one vertex, and is always aligned with the line of symmetry as well as the X axis

The vertices on a parabola refers to the point of maximum curvature. On a parabola there is one vertex located at the highest or lowest point of U bend. The vertex is the midpoint between the focus and directrix.

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.

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.

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.

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.

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.

The points where a curve intersects the x-axis (the horizontal axis on a cartesian plane). Also known as "zero of a function." When a curve intersects the x-axis the value of that point produced by the function is zero. The x-intercept must always be a real number.

Can also be refered to as the "cartesian plane." It is a 2 dimentional flat surface formed by the X-axis and the Z-axis.

Can also be refered to as the "Cartesian plane." It is a 2 dimentional flat surface formed by the horizontal X-axis and the vertical Y-axis. This plane extends indefinitely in all directions and is most commonly used for graphing coordinates and plotting data. The X and Y axis also divide the plane into four sections called "quadrants."

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.

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).

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.

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.

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.

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 equal to 0.

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.

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.

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.

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.

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.