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Pre-Calculus Definitions

Browse our growing collection of pre-calculus definitions:

ARC =_ΔyΔx

ARC

ARC an abbreviation of average rate of change is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y…

Algorithm

An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at …

Argand Plane

The argand plane otherwise known as the complex plane, z-plane or gauss plane is a geometric representation of the complex numbers established by the real axis…

ARC =_ΔyΔx

Average Rate of Change

Average rate of change or ARC is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value (Δy)…

Bidimensional Space

Bidimensional space otherwise referred to as two dimensional space is a geometric setting in which two values (called parameters) are required to determine the…

Box Product

Box product otherwise referred to as scalar triple product, mixed product and triple scalar product is a method of multiplying three 3-dimensional vectors, usu…

Complex Plane

The complex plane otherwise known as the argand plane, z-plane or gauss plane is a geometric representation of the complex numbers established by the real axis…

Compression

A compression or contraction is a transformation in which a figure grows smaller. Compressions may be with respect to a point (compression of a geometric figur…

Δ δ

Delta (Δ, δ)

Delta (Δ, δ) is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4.

Fixed

Fixed means that the object is regarded as fixed in the plane so that it may not be picked up and flipped if referring to a planar object. As a result, mirror …

Greek Alphabet

The Greek alphabet has been used to write the Greek language since the late ninth or early eighth century BC. It is derived from the earlier Phoenician alphabe…

Horizontal Dilation

A horizontal dilation or stretch is a stretch in which a plane figure is distorted horizontally.

Horizontal Stretch

A horizontal stretch or dilation is a stretch in which a plane figure is distorted horizontally.

Jump Discontinuity

A jump discontinuity or step discontinuity is a discontinuity where the graph steps or jumps from one connected piece of the graph to another. It is a disconti…

Lemniscate

A lemniscate is a curve usually expressed in polar coordinates and is in the form of any of the various figure eight shaped curves.

Mixed Product

Mixed product otherwise referred to as scalar triple product, triple scalar product and box product is a method of multiplying three 3-dimensional vectors, usu…

Ω ω

Omega (Ω, ω)

Omega (Ω, ω) is the 24th and last letter of the Greek alphabet. In the system of Greek numerals it has a value of 800.

Φ φ

Phi (Φ, φ)

Phi (Φ, φ) is the 21st letter of the Greek alphabet. In the system of traditional Greek numerals, phi has a value of 500 (φʹ) or 500,000 (͵φ).

Ρ ρ

Rho (Ρ, ρ)

Rho (Ρ, ρ) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res.

Scalar Triple Product

Scalar triple product otherwise referred to as triple scalar product, mixed product and box product is a method of multiplying three 3-dimensional vectors, usu…

Σ σ

Sigma (Σ, σ)

Sigma (Σ, σ) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ i…

Step Discontinuity

A step discontinuity or jump discontinuity is a discontinuity where the graph steps or jumps from one connected piece of the graph to another.

Τ τ

Tau (Τ, τ)

Tau (Τ, τ) is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300.

Theorem of Pappus

The theorem of Pappus or Pappus's theorem generally refer to several different theorems. They include Pappus's centroid theorem, the Pappus chain, Pa…

Triple Scalar Product

Triple scalar product otherwise referred to as scalar triple product, mixed product and box product is a method of multiplying three 3-dimensional vectors, usu…

Two Dimensional

Two dimensional or two dimensions is the property of a plane that indicates that motion can take place in two perpendicular directions.

Two Dimensional Space

Two dimensional space otherwise referred to as bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine th…

Two Dimensions

Two dimensions or two dimensional is the property of a plane that indicates that motion can take place in two perpendicular directions.

Unit Vector

A unit vector is a vector with a length or magnitude of 1. Sometimes, the unit vector is also called a direction vector.

Vector

Vectors are a quantity, drawn as an arrow, with both direction and magnitude. For example, force and velocity are vectors. If a quantity has a magnitude but no…

Velocity

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

Vertical Compression

A vertical compression or shrink is a compression in which a plane figure is distorted vertically.

Vertical Dilation

A vertical dilation or stretch is a stretch in which a plane figure is distorted vertically.

Vertical Line Test

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of…

Vertical Shift

In geometry, a vertical shift otherwise known as vertical translation, is a translation of a geometric object in a direction parallel to the vertical axis of t…

Vertical Shrink

A vertical shrink or compression is a shrink in which a plane figure is distorted vertically.

Vertical Stretch

A vertical stretch or dilation is a stretch in which a plane figure is distorted vertically.

Vertical Translation

In geometry, a vertical translation otherwise known as vertical shift, is a translation of a geometric object in a direction parallel to the vertical axis of t…

Volume

Volume is the total amount of space enclosed or occupied in a solid. Volume generally has units of length and distance cubed (such as cm3, in3, m3 km3, etc.)

X-Y Plane

A plane formed by the x-axis and the y-axis.

X-Z Plane

A plane formed by the x-axis and the z-axis.

Y-Z Plane

A plane formed by the y-axis and the z-axis.

Zero Matrix

A zero matrix is an m x n matrix where all of its elements are equal to zero and denoted by 0. Zero matrices are sometimes also referred to as null matrices.

Zero Vector

A vector with a magnitude of zero. Denoted 0, it is a vector of length 0, and thus has all components equal to zero.

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