Maths AA terms: V

V

Variancealso σ²

The mean of the squared deviations from the mean, $\sigma^2 = \frac{\sum f(x - \mu)^2}{n}$. Its units are the square of the data's units.

Introduced in 4.3 Measures of central tendency and dispersion

Variance of a random variableHL only · also Var(X)

The expected squared distance of a random variable from its mean, $\operatorname{Var}(X) = E\left((X - \mu)^2\right) = E(X^2) - [E(X)]^2$

VectorHL only · also vectors

A quantity with both a size (magnitude) and a direction, such as a displacement, a velocity or a force. It is drawn as a directed line segment and written in bold, $\boldsymbol{v}$, or as $\overrightarrow{AB}$.

Introduced in 3.12 Vectors

Vector equation of a lineHL only · also parametric equations of a line

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

Vector equation of a planeHL only · also parametric equation of a plane

The equation $\boldsymbol{r} = \boldsymbol{a} + \lambda\boldsymbol{b} + \mu\boldsymbol{c}$, giving every point of a plane through the point with position vector $\boldsymbol{a}$, where $\boldsymbol{b}$

Vector productHL only · also cross product

The vector $\boldsymbol{v} \times \boldsymbol{w}$ perpendicular to both $\boldsymbol{v}$ and $\boldsymbol{w}$, with magnitude $|\boldsymbol{v}||\boldsymbol{w}|\sin\theta$

Vector projectionHL only · also projection of a vector

The vector along $\boldsymbol{w}$ whose length is the scalar projection of $\boldsymbol{v}$ on $\boldsymbol{w}$: $\frac{\boldsymbol{v} \cdot \boldsymbol{w}}{|\boldsymbol{w}|^2}\boldsymbol{w}$

Velocity

The rate of change of displacement with respect to time, $v = \frac{ds}{dt}$. Its sign shows the direction of motion; its size is the speed.

Introduced in 5.9 Kinematics

Venn diagram

A diagram in which a rectangle represents the sample space $U$ and circles inside it represent events; overlapping regions show outcomes that belong to more than one event.

Introduced in 4.6 Venn diagrams, tree diagrams and combined events

Vertex (of a parabola)also vertex of a parabola

The point where a parabola turns, lying on its axis of symmetry. It is the minimum point of the graph when $a > 0$ and the maximum point when $a < 0$.

Introduced in 2.6 Quadratic functions

Vertex formalso turning point form, completed square form

The form $f(x) = a(x - h)^2 + k$ of a quadratic function, in which $(h, k)$

Vertical asymptote

A vertical line $x = k$ that a graph approaches as $x$ gets closer to $k$, with $y$ increasing or decreasing without bound. The function is undefined at $x = k$

Vertical line test

A graph represents a function of $x$ when every vertical line meets it at most once.

Introduced in 2.2 Functions, domain, range and inverse

Viewing windowalso window

The part of the plane shown on a calculator or graphing app, set by the least and greatest values of $x$ and $y$ on the screen.

Introduced in 2.3 The graph of a function

Volume of revolutionHL only · also solid of revolution

The volume of the solid formed when a region is rotated through $2\pi$ radians (one full turn) about a line: $V = \int_a^b \pi y^2\,dx$