MATH GLOSSARY

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AAS Congruence Angle-angle-side congruence between two (or more) triangles.
Congruent triangles have sides and angles of identical measure.
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Abscissa The horizontal axis, or the first coordinate in an ordered pair.
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Absolute Maximum The highest point on a graph, especially over a specified domain.
It is the greatest value of f(x) over a defined interval of x, provided y=f(x).
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Absolute Minimum The lowest point on a graph, especially over a specified domain.
It is the least value of f(x) over a defined interval of x, provided y=f(x).
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Absolute Value The distance on the real number line between an value and zero.
It applies best to things for which negative values have no meaning, such as mass or length.
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Accuracy The quality of approaching an exact value.
Distinct from precision, accuracy means to approach correctness, to tend toward an established value.
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Acute Angle An angle whose measure is less than 90 degrees. Play_video
Acute Triangle A triangle whose interior angles are each acute, that is, less than 90 degrees (or π/2 radians). Play_video
Addend Most simply a term.
More specifically a term to be added to other terms to find a sum.
Addends can have a negative value.
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Addition The process of finding a sum or determining a total by joining values together.
Values are summed in the process to result in a total.
Matrix addition adds elements of matrices of the same order (or dimension).
Vector addition results in the diagonal of a parallelogram (if in two dimensions).
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Additive Inverse for Arithmetic The opposite of a given number.
Change the sign of a number to have its additive inverse.
The sum of a number and its additive inverse is always zero.
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Additive Inverse for Matrices Mr. X takes the mystery out of Additive Inverse for Matrices, a matrix when added to another equals the Zero Matrix.
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Additive Property of Equality This property allows us to add equals to equals to stay equal.
Given two equal values, we may add the same quantity to both values and retain an equality.
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Adjacent Next to each other.
The idea is especially important in geometry, as with adjacent angles that share a common ray.
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Adjacent Angles Next to each other.
Adjacent angles share a common ray and subsequently have a common vertex.
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Algebra The branch of mathematics that allows manipulation of symbols and values to determine quantities that are not always fixed.
Variables are essential to algebra.
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Algorithm A sequence of steps to accomplish a familiar task; a recipe. Play_video
Alpha The first letter of the Greek alphabet. Play_video
Alternate Exterior Angles Given two parallel lines cut by a transversal, angles exterior to the parallel lines and on opposite (alternate) sides of the transversal are congruent. Play_video
Alternate Interior Angles Given two parallel lines cut by a transversal, angles interior to (between) the parallel lines and on opposite (alternate) sides of the transversal are congruent.
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Alternating Series A series in which successive terms have opposite signs.
Every other term is positive; every other term is negative.
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Altitude Height.
The perpendicular or orthogonal distance above a fixed reference, as height above mean sea level.
In geometry, the shortest distance from the base of an object to its apex (or top).
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Altitude of a Cone The shortest line segment from the apex (tip) of a cone to the plane of its base.
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Altitude of a Cylinder The distance between the planes containing the bases of a cylinder. Play_video
Altitude of a Parellelogram The distance between opposite sides of a parallelogram Play_video
Altitude of a Prism The length of the shortest line segment between the planes containing the bases of a prism. Play_video
Altitude of a Trapezoid The distance between bases of a trapezoid. Play_video
Altitude of a Triangle The shortest line segment between the vertex of a triangle and line containing the opposide of the triangle.
The three altitudes of a triangle are concurrent at the orthocenter.
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Amplitude Periodic functions have an amplitude that is half the range between the highest and lowest values.
The height a sinewave climbs from zero (if zero is its mean values) is its amplitude.
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Analytic Geometry Effectively coordinate geometry.
It is the use of coordinates (in two or more dimensions) to determine geometric relationships.
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Angle The separation of two rays measured as the rotation of one of the rays.
Usually measured in either degrees or radians, other systems of measuring rotation are also used to assign values to angles.
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Angle Bisector A ray (or line) that divides an angle into two congruent halves.
The three angle bisectors of a triangle are concurrent at the incenter.
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Angle of Depression The angle below a horizontal reference.
Typically it is the angle between a line-of-sight ray referenced to a horizontal line (or plane).
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Angle of Elevation The angle above a horizontal reference.
Typically it is the angle between a line-of-sight ray referenced to a horizontal line (or plane).
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Annulus The area, or region, between two concentric circles of different radii. Play_video
Antiderivative Given a function with a derivative, the antiderivative of that derivative function returns the original function. Play_video
Apex The top.
Most generally a singular situation as a point.
The vertex of a cone or pyramid is an apex.
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Apothem The apothem applies to a regular polygon; it is either the distance from the center to a midpoint of a side, or the radius of an inscribed circle in the polygon. Play_video
Arc A section of circumference.
An arc is measured either by its own length or with a central angle.
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Arc Length A curved length; it can be the distance around a portion of a circle, or around a different shape of curved figure. Play_video
Arccos The inverse cosine.
Given the number that represents the cosine of an angle, the arccosine of the number returns the angle whose cosine is the given number.
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Arccot The inverse cotangent.
Given the number that represents the cotangent of an angle, the arccotangent of the number returns the angle whose cotangent is the given number.
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Arccsc The inverse cosecant.
Given the number that represents the cosecant of an angle, the arccosecant of the number returns the angle whose cosecant is the given number.
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Arcsec The inverse secant.
Given the number that represents the secant of an angle, the arcsecant of the number returns the angle whose secant is the given number.
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Arcsin The inverse sine.
Given the number that represents the sine of an angle, the arcsine of the number returns the angle whose sine is the given number.
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Arctan The inverse tangent.
Given the number that represents the tangent of an angle, the arctangent of the number returns the angle whose tangent is the given number.
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Area The measure of a plane region defined to be within some boundary. Play_video
Area of a Circle The extent of surface contained within the circle; π times the square of the radius.
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Area of a Kite Half the product of the diagonals. Play_video
Area of a Parallelogram Akin to the area of a rectangle, the area of a parallelogram can be expressed as the product of length times width. Play_video
Area of a Rectangle The extent of surface contained within the rectangle; length times width.
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Area of a Regular Polygon One-half the product of perimeter times the apothem.
Remember that regular means equilateral and equiangular.
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Area of a Rhombus If s is the length of a side and h is the height, s-squared times the sine of the big interior angle; s-squared times the sine of the smaller interior angle; half the product of the diagonals.
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Area of a Sector of a Circle It is the surface area of a slice of pie.
We like arc length s=rΘ.
So area of a sector is r-squared times theta all over two (Θ in radians).
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Area of a Segment of a Circle Given central angle theta, area of the segment is one-half the square of the radius times the quantity (Θ minus sine Θ), provided Θ is in radians.
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Area of a Trapezoid One-half the (sum of the bases) times the height.
Or, the product of (median) and (altitude).
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Area of a Triangle One-half times the base times the height.
Also, given perimeter a+b+c, and semiperimeter s=half that sum, then area = the square root of [s times (s-a) times (s-b) times (s-c)].
(Heron).
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Area of an Ellipse If 2a and 2b are the lengths of the major and minor axes of the ellipse, then the area of the ellipse is simply πab. Play_video
Area of an Equilateral Triangle Given side of length s, the area of an equilateral triangle is s-squared times the-square-root-of-three over four.
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Area Under a Curve If we have limits of integration, it is most simply the definite integral of the function defined between those limits of integration. Play_video
Argument of a Function The term or expression upon which a function operates.
In y=f(x), the argument of the function is x.
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Argument of a Vector The angle at which a vector is directed.
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Arithmetic A branch of mathematics built upon the basic operations of addition, subtraction, division, and multiplication.
Powers, roots, and logarithms are often considered arithmetic in nature.
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Arithmetic Mean What we generally consider to be the average.
The sum of a set of values divided by the cardinal number of the set of values.
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Arithmetic Progression Also Arithmetic Sequence.
A series of terms where successive terms are obtained by addition of a constant.
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Arithmetic Sequence Also Arithmetic Sequence.
A series of terms where successive terms are obtained by addition of a constant.
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Arithmetic Series Akin to Arithmetic Progressions and Arithmetic Sequences, the series typically reflects an addition operator between terms, as a sum. Play_video
ASA Congruence Angle-side-angle congruence between two (or more) triangles.
Congruent triangles have sides and angles of identical measure.
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Associative Law of Addition Provides that addition of groups of terms or values is indifferent to the order of grouping.
We may add terms in any order, or group them in any order.
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Associative Law of Multiplication Provides that multiplication of groups of terms or factors is indifferent to the order of grouping.
We may multiply factors in any order, or group them in any order.
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ASTC Mnemonic device for remembering which trig functions are positive in the four Cartesian quadrants. Play_video
Asymptote A line (or curve) that a function approaches without actually reaching the line as the domain either grows unbounded or approaches a limit. Play_video
Augmented Matrix A matrix form for a linear system of equations where the number of columns is one greater than the number of rows, the final column typically coming from the constants in the linear equations.
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Average Most commonly, average means the arithmetic mean; we sum the values and divide that sum by the number of numbers.
The average between two real values is the midpoint between those values.
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Average Rate of Change The change in value divided by elapsed time. Play_video
Axes Most simply, the plural of axis.
More generally, the horizontal x-axis and the vertical y-axis that comprise the skeleton of Cartesian Coordinates.
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Axiom Accepted without proof (unlike a theorem), an axiom is readily understood and regarded as fact. Play_video
Axis In physics, a line about which a body rotates.
In mathematics, a line that divides a plane or space into two equal halves, typically demarcated in units.
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Axis of Rotation A line about which a body rotates. Play_video
Axis of Symmetry A line about which a graph or body is symmetrical, that is, a mirror image on one side of the axis from the body or graph on the other side.
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