# Pre-Calculus Definitions

Browse our growing collection of pre-calculus definitions:

## 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-value (Δy) divided by the change in the x-value (Δx) for two distinct points on the graph.

## 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 some point.

## Area of an Ellipse

The area of an ellipse is calculated using a formula similar to that of a circle. For an ellipse with a semi-major and semi-minor axes the formula is: A = πxy where x represents the ellipses semi-major axes and y represents the semi-minor axis of the ellipse.

## 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 and the perpendicular imaginary axis.

## 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) divided by the change in the x-value (Δx) for two distinct points on the graph.

## 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 position of an element (a point).

## 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, usually euclidean vectors in which the resulting product is a scalar.

## 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 and the perpendicular imaginary 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 figure) or with respect to the axis of a graph (compression of a graph).

## 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 images are not necessarily equivalent for fixed objects.

## 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 alphabet, and was the first alphabetic script in history to have distinct letters for vowels as well as consonants.

## 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 discontinuity where the limits from the left and right both exist but are not equal to each other.

## 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, usually euclidean vectors in which the resulting product is a scalar.

## 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.

## 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).

## 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, usually euclidean vectors in which the resulting product is a scalar.

## 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 is used as an operator for summation.

## 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.

## 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, Pappus's harmonic theorem, and Pappus's hexagon theorem.

## 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, usually euclidean vectors in which the resulting product is a scalar.

## 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 the position of an element (a point).

## 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 direction, it is referred to as a scalar.

## 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 intersections of the curve with vertical lines.

## 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 the Cartesian coordinate system.

## 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 the Cartesian coordinate system.

## 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 cm^{3}, in^{3}, m^{3} km^{3}, 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.