AQA Level 2 Certificate Further Mathematics key terms

The power to which a base is raised. For a positive integer index, it counts repeated factors: $x^3=x\times x\times x$. Also called an exponent.

A mathematical statement comparing expressions using $<$, $>$, $\leq$ or $\geq$.

The function applied first in a nested expression. In $f(g(x))$, the inner function is $g$.

The value put into a function; in $f(x)$, the input is $x$.

A whole number, including negative whole numbers and zero: for example, $-3$, $0$ and $7$.

A point where a graph meets a coordinate axis. At an $x$-intercept, $y=0$; at a $y$-intercept, $x=0$.

An angle inside a polygon, between two sides meeting at a vertex.

A continuous range of values, such as $0<x<1$.

A function that reverses another function, returning each output to its original input. The inverse of $f$ is written $f^{-1}$.

An operation that reverses another operation, such as division reversing multiplication.

A relationship in which the product of two quantities is constant: $xy=k$, or $y=\frac{k}{x}$.

A function used to find an angle from a trigonometric value, such as $\sin^{-1}(0.5)=30^\circ$. The notation $\sin^{-1}$ does not mean $1/\sin$.

Terms with the same surd part after simplification, such as $3\sqrt{5}$ and $8\sqrt{5}$.

Terms with exactly the same variables raised to exactly the same powers, such as $3x^2y$ and $-7x^2y$.

A number that the terms of a sequence approach arbitrarily closely and remain close to as the term number increases without bound.

An equation in which each unknown appears only to the first power, with no products of unknowns; for example, $2x-5y+4z=22$.

A degree-one expression, such as $x-2$ or $2x-3$, which multiplies another polynomial to give the original polynomial exactly.

An inequality in which the variable has highest power one, such as $3x+4\geq7$.

A sequence with a constant difference between consecutive terms; also called an arithmetic sequence.

The part of a straight line between two endpoints.

A point whose y-coordinate is greater than those of nearby points on either side.

A point whose y-coordinate is smaller than those of nearby points on either side.

The simplest common multiple of the denominators, containing each required factor to its highest power.

A rectangular array of numbers or letters arranged in rows and columns.

The greatest value a function actually reaches over the domain being considered.

The point halfway along a line segment, at equal distances from its endpoints. It divides the segment in the ratio $1:1$.

The least value a function actually reaches over the domain being considered.

A number that can be written as $kq$, where $q$ is an integer. For example, $20$ is a multiple of $4$ because $20=4\times5$.

A power representing a reciprocal: for example, $x^{-3}=\frac{1}{x^3}$, with $x\ne0$.