Maths AI terms: V

V

Validity of a modelalso model validity, valid model, appropriateness, appropriateness of a model, reasonableness

The extent to which a model's assumptions, type of function and outputs match the real situation over the inputs where it is used, so that conclusions drawn from it can be trusted.

Introduced in 2.6 The modelling process

Validity of a testHL only · also validity, valid test, measurement validity, valid

The extent to which a test or other measuring instrument measures what it is intended to measure, so that conclusions drawn from its results are justified.

Introduced in 4.12 Data collection and reliability

Variable velocityHL only · also non-constant velocity, changing velocity

A velocity whose magnitude or direction (or both) changes with time, so that the velocity vector is a function $\boldsymbol{v}(t)$ and the path is in general curved.

Introduced in 3.12 Vectors in kinematics

Variancealso σ², population variance, variance of data

The mean of the squared deviations of the data values from their mean, $\sigma^2 = \frac{\sum f_i (x_i - \mu)^2}{n}$

Variance of a random variableHL only · also Var(X), variance of X, population variance of a random variable

The expected value of the squared deviation of a random variable from its mean, $\mathrm{Var}(X) = \mathrm{E}\big((X - \mu)^2\big)$, where $\mu = \mathrm{E}(X)$

VectorHL only · also vectors, vector quantity

A quantity that has both a size (magnitude) and a direction.

Introduced in 3.10 Vectors

Vector equation of a lineHL only · also r = a + λb, vector form of a line, equation of a line in vector form, vector equations of lines, vector equation

An equation $\boldsymbol{r} = \boldsymbol{a} + \lambda\boldsymbol{b}$ that gives the position vector $\boldsymbol{r}$ of every point on a line, where $\boldsymbol{a}$ is the position vector of a known point on the line, $\boldsymbol{b}$

Vector productHL only · also cross product, vector products, v × w

For two vectors in three dimensions, the vector $\boldsymbol{v} \times \boldsymbol{w} = \begin{pmatrix} v_2w_3 - v_3w_2 \\ v_3w_1 - v_1w_3 \\ v_1w_2 - v_2w_1 \end{pmatrix}$

VelocityHL only · also v, ds/dt, instantaneous velocity, velocities

The rate of change of an object's displacement with respect to time, $v = \frac{\mathrm{d}s}{\mathrm{d}t}$; its sign gives the direction of motion and its size gives how fast the object moves.

Introduced in 5.13 Kinematics

Velocity vectorHL only · also velocity as a vector, constant velocity vector, velocity vectors

The vector $\boldsymbol{v}$ whose components are the rates of change of the components of an object's position, so that its direction is the direction of motion and its magnitude is the speed.

Introduced in 3.12 Vectors in kinematics

Velocity–time graphHL only · also v–t graph, velocity-time graph, v-t graph, velocity–time graphs

A graph of an object's velocity against time, whose gradient at any point is the acceleration and whose signed area over an interval is the displacement.

Introduced in 5.13 Kinematics

Venn diagramalso Venn diagrams, Venn

A diagram in which a rectangle represents the universal set and closed curves (usually circles) inside it represent events or sets, with overlapping regions showing outcomes that belong to more than one event.

Introduced in 4.6 Combined events

Vertex (graph)HL only · also vertices

One of the objects of a graph, drawn as a point or a small dot; the plural is vertices.

Introduced in 3.14 Graph theory

Vertex (of a parabola)also vertex of a quadratic, vertices of parabolas

The turning point of a parabola, where it meets its axis of symmetry; it is the minimum point when $a > 0$ and the maximum point when $a < 0$.

Introduced in 2.5 Modelling with functions

Vertex (Voronoi diagram)also Voronoi vertex, Voronoi vertices, vertices of a Voronoi diagram

A point where three or more edges of a Voronoi diagram meet; it is equidistant from the three or more sites whose cells meet there.

Introduced in 3.6 Voronoi diagrams

Vertical asymptotealso vertical asymptotes

A vertical line $x = a$ that a graph approaches while its outputs grow without limit (positive or negative) as $x$ gets closer to $a$; the function is undefined at $x = a$.

Introduced in 2.4 Key features of graphs

Vertical line testalso vertical-line test, vertical line rule

A graph represents a function of $x$ if and only if no vertical line meets the graph more than once.

Introduced in 2.2 Functions, domain and range

Vertical stretchHL only · also stretch parallel to the y-axis, vertical stretches, stretch in the y-direction

A transformation that multiplies the $y$-coordinate of every point by a scale factor $p$, leaving the $x$-coordinate unchanged; the graph of $y = pf(x)$ is a vertical stretch of $y = f(x)$

Viewing windowalso window, GDC window, graph window, view window

The rectangular part of the coordinate plane displayed by a GDC or graphing software, set by the minimum and maximum $x$-values and the minimum and maximum $y$-values.

Introduced in 2.3 Graphing functions with technology

Volume

The amount of three-dimensional space occupied by a solid, measured in cubic units such as $\text{cm}^3$ or $\text{m}^3$.

Introduced in 3.1 Volume and surface area in three dimensions

Volume of revolutionHL only · also volumes of revolution, volume of a solid of revolution

The volume of a solid of revolution, given by $V = \int_a^b \pi y^2\,\mathrm{d}x$ for rotation about the $x$

Voronoi diagramalso Voronoi diagrams, Voronoi tessellation, Dirichlet tessellation, Voronoi partition

A division of a plane, or of a region of it, into cells, one for each of a given set of sites, in which every point of a cell is closer to that cell's site than to any other site.

Introduced in 3.6 Voronoi diagrams