AQA Level 2 Certificate Further Mathematics key terms

The point where a tangent touches a circle.

A point shared by two graphs. Its coordinates satisfy both equations.

A closed plane shape made from straight sides.

An expression made from a finite sum of constant multiples of non-negative whole-number powers of a variable, such as $2x^3-x+6$.

An angle measured by an anticlockwise rotation. In the unit-circle definitions, the rotation starts from the positive $x$-axis.

The rule $\frac{dy}{dx}=knx^{n-1}$ for differentiating $y=kx^n$, where $k$ is constant.

A three-dimensional solid with identical polygonal cross-sections throughout its length.

A counting method that multiplies the numbers of choices at successive stages, provided each earlier choice allows the stated number of choices at the next stage.

A solid with a polygonal base and triangular faces meeting at one point, called the apex.

For a right-angled triangle with perpendicular sides of lengths $a$ and $b$ and hypotenuse of length $c$, $a^2+b^2=c^2$.

The relationship $a^2+b^2=c^2$ in a right-angled triangle, where $c$ is the hypotenuse.

The relationship $\sin^2\theta+\cos^2\theta=1$, connecting the squared sine and cosine of the same angle.

A set of three positive integers $a$, $b$ and $c$ satisfying $a^2+b^2=c^2$. They can be the side lengths of a right-angled triangle.

One of the four regions into which the coordinate axes divide the plane, numbered I to IV anticlockwise from the top-right region.

An equation that can be written as $ax^2+bx+c=0$, where $a\ne0$.

An algebraic expression whose highest power of the variable is 2, such as $2x^2+6x+7$.

An inequality in which the variable has highest power two, such as $x^2-9<0$.

An ordered list of numbers whose nth term can be written as $an^2+bn+c$, where $a\ne0$. Its second differences are constant and non-zero.

A polygon with four sides.

A line segment from the centre of a circle to its circumference, or the length of that segment.

The set of possible output values of a function. Sine and cosine both have range $-1\leq y\leq1$.

How quickly $y$ changes as $x$ changes. At a particular point on a curve, this is measured by $\frac{dy}{dx}$.

A comparison of quantities. If $AP:PB=m:n$, the lengths $AP$ and $PB$ contain $m$ and $n$ equal parts respectively.

A quotient of two polynomials, such as $\frac{x^2-4}{x+3}$, defined only where its denominator is non-zero.

Rewriting a fraction as an equivalent fraction with no surd in its denominator.

A number that can be written as $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne0$. Integers are also rational numbers.

A number on the number line, including integers, fractions and irrational numbers such as $\sqrt{2}$ and $\pi$.

The multiplicative inverse of a non-zero number or expression. The reciprocal of $a$ is $\frac{1}{a}$.

The acute angle between the final arm of an angle and the $x$-axis.