Maths AA terms: F

F

Factor theoremHL only

For a polynomial $P(x)$, $(x - a)$ is a factor of $P(x)$ if and only if $P(a) = 0$. More generally, $(ax - b)$ is a factor if and only if $P\left(\frac{b}{a}\right) = 0$.

Introduced in 2.12 Polynomial functions

Factorialalso n!

The product of all positive integers from 1 up to $n$: $n! = n(n-1)(n-2)\cdots 2 \times 1$ for $n \in \mathbb{Z}^+$

Factorised formalso intercept form, factored form

The form $f(x) = a(x - p)(x - q)$ of a quadratic function, in which $p$ and $q$

Fair game

A game in which a player's expected gain is zero, so that $E(\text{gain}) = 0$: on average the player neither wins nor loses money over many plays.

Introduced in 4.7 Discrete random variables

False positiveHL only · also false negative

A positive test result for someone who does not have the condition. A false negative is a negative result for someone who does.

Introduced in 4.13 Bayes’ theorem

First derivative testalso sign test

A way to classify a stationary point at $x = a$ from the sign of $f'(x)$ just before and just after $a$: positive then negative gives a maximum, negative then positive a minimum, no change of sign a stationary point of inflexion.

Introduced in 5.8 Stationary points, optimisation and inflexion

Foot of the perpendicularHL only · also perpendicular foot

The point on a line or plane closest to a given point, where the segment from the given point meets the line or plane at a right angle.

Introduced in 3.15 Coincident, parallel, intersecting and skew lines

Fractalalso self-similar shape

A shape built by repeating the same construction at smaller and smaller scales, so that parts of it look like the whole. The Koch snowflake is an example.

Introduced in 1.8 Infinite geometric series

Frequency distributionalso frequency table

A table listing each value or class of values in a data set together with its frequency, the number of times it occurs.

Introduced in 4.2 Presenting data

Functionalso mapping

A relation that assigns to each input in its domain exactly one output. It is written $f(x)$ or $f: x \mapsto \ldots$, where $x$ is the input.

Introduced in 2.2 Functions, domain, range and inverse

Fundamental theorem of calculusalso FTC

The result linking differentiation and integration: if $F'(x) = f(x)$, then $\int_a^b f(x)\,dx = F(b) - F(a)$

Future valuealso FV

The value that an amount of money will have at a later date after interest has been added, written $FV$.

Introduced in 1.4 Financial applications of geometric sequences