AQA Level 2 Certificate Further Mathematics key terms

An answer without rounding, such as $\frac{7+\sqrt{73}}{4}$.

A value given without rounding, for example as an integer, fraction or surd.

A value written without rounding or approximation, for example $\frac{\sqrt{3}}{2}$ rather than $0.866$.

Rewriting a product involving brackets as a sum or difference by multiplying out the brackets.

Rewriting a product containing brackets as a sum of terms by multiplying out the brackets.

A function in which the variable appears in the exponent, such as $y=ab^x$, where $b>0$.

An angle between a side of a polygon and the extension of an adjacent side. It adds to $180^\circ$ with the adjacent interior angle.

An expression that multiplies another expression to form a product. For example, $x-2$ is a factor of $(x-2)(x+3)$.

The product of all positive integers from a given positive integer down to 1, written using an exclamation mark: for example, $4! = 4 \times 3 \times 2 \times 1 = 24$.

Writing an expression as a product of factors.

Factorising pairs or groups of terms separately so that a shared factor, often a whole bracket, can then be extracted.

Rewriting an expression as a product of factors; this reverses expanding.

For a polynomial $f(x)$, $f(r)=0$ if and only if $x-r$ is a factor of $f(x)$.

The result of subtracting a term in a sequence from the next term.

An equation expressing a relationship between quantities, usually represented by letters.

A power written as a fraction. For a positive base, $a^{m/n}=(\sqrt[n]{a})^m$: the denominator gives the root and the numerator gives the power.

A rule that assigns exactly one output to each allowed input. In $y=f(x)$, $x$ is the input and $f(x)$ is the output.

A way of naming a function and showing its input: $f(x)$ means the output of function $f$ when the input is $x$.

A logical argument establishing a geometrical statement from given information and known mathematical facts, with a reason for each deduction.

The change in $y$ divided by the corresponding change in $x$, measuring the steepness and direction of a straight line.

A function that gives the gradient of a curve at each value of $x$, written $\frac{dy}{dx}$.

The greatest numerical factor together with all variable factors shared by every term, each taken to its smallest shared power.

The longest side of a right-angled triangle, opposite its right angle.

A statement that two expressions are equal for every value of their variable, written using $\equiv$.

A square matrix that leaves a matrix unchanged when multiplied by it. In this course, $I=\begin{pmatrix}1&0\\0&1\end{pmatrix}$.

The symbol $\equiv$, meaning ‘identically equal to’: two expressions have the same value throughout their common domain.

The shape or point produced by a transformation.

The angle between the two sides being used in a triangle calculation.