AQA Level 2 Certificate Further Mathematics key terms

The signed change in the $y$-coordinate between two points, calculated as $y_2-y_1$.

A value of the variable that makes an expression equal to zero. Roots of a quadratic identify possible boundaries of its inequality solutions.

A turn through a specified angle and direction about a fixed centre.

The signed change in the $x$-coordinate between two points, calculated as $x_2-x_1$.

A number used to multiply every element of a matrix.

A matrix obtained by multiplying every entry of a matrix by the same number. For example, $kI=\begin{pmatrix}k&0\\0&k\end{pmatrix}$.

The multiplier applied to every length when enlarging or reducing a shape.

A triangle with three different side lengths and three different interior angles.

The derivative of the gradient function, written $\frac{d^2y}{dx^2}$. It measures the rate at which the gradient changes with respect to $x$.

A method for classifying a stationary point: $\frac{d^2y}{dx^2}>0$ gives a local minimum, while $\frac{d^2y}{dx^2}<0$ gives a local maximum. A value of zero is inconclusive.

The result of subtracting one first difference from the next first difference.

An equation whose highest total degree is two: it can contain terms such as $x^2$, $y^2$ or $xy$, but no higher-degree terms.

A region of a circle bounded by a chord and an arc.

An ordered list of values, called terms, which follow a rule.

The property of having the same shape: corresponding angles are equal and corresponding lengths are in a common ratio.

Triangles with equal corresponding angles and proportional corresponding side lengths.

A set of equations that must all be satisfied by the same values of the unknowns.

The $y$-coordinate of the point reached on the unit circle after rotating through an angle $\theta$: $\sin\theta=y$.

A relationship valid in any triangle: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$, where each lower-case side letter matches its opposite upper-case angle.

For a cone, the distance along its surface from the apex to the edge of its circular base.

A value of the unknown that makes an equation true when substituted into it.

A range of allowed values for the unknown angle. For example, $0^\circ\leq x\leq360^\circ$ includes both endpoints.

All values of the variable that make an equation or inequality true.

A factor that is a perfect square. For example, $16$ is a square factor of $48$, allowing $\sqrt{48}$ to simplify to $4\sqrt{3}$.

The equation $(x-a)^2+(y-b)^2=r^2$, which describes a circle with centre $(a,b)$ and radius $r$.

A point on a curve where the gradient is zero, so $\frac{dy}{dx}=0$ and the tangent is horizontal.

An inequality using $<$ or $>$, so equality is not allowed.