AQA Level 2 Certificate Further Mathematics key terms

A fraction whose numerator, denominator or both contain an algebraic expression, such as $\frac{x+1}{x-2}$.

A logical argument using general algebraic expressions to establish that a statement is true for every value covered by its conditions.

Angles between two lines on opposite sides of a transversal. They are equal when the two lines are parallel.

The theorem stating that the angle between a tangent and a chord equals the angle subtended by that chord at the circumference in the alternate segment.

A situation in which the given sides and angle allow two different triangles, because an acute angle and its obtuse supplement have the same sine.

The maximum distance from a wave's centre line to a peak or trough. The standard sine and cosine graphs have amplitude $1$.

A part of the circumference between two points.

The amount of two-dimensional space inside a shape, measured in square units.

An operation is associative if changing the grouping, without changing the order, leaves the result unchanged. Matrix multiplication satisfies $(AB)C=A(BC)$.

The rule that changing the grouping of addition or multiplication does not change the result: $(a+b)+c=a+(b+c)$ and $(ab)c=a(bc)$.

A line that a curve approaches. Tangent has vertical asymptotes at $x=90^\circ+180^\circ n$, where $n$ is any integer.

The number or algebraic expression being raised to a power. In $x^3$, the base is $x$.

An algebraic expression consisting of two unlike terms added or subtracted, such as $3+2x$ or $a-b$.

Writing a power of a two-term expression as a sum of terms by multiplying out its repeated brackets.

To divide a line segment or angle into two equal parts.

A diagonal joining opposite vertices through the interior of a solid, rather than across one face.

The fixed point from which every point on a circle is the same distance.

A straight line segment joining two points on the circumference of a circle.

The set of all points in a plane at a fixed distance from a fixed point called the centre.

The boundary of a circle.

The constant multiplier of a variable or power of a variable. In $5x^3$, the coefficient is 5.

Angles between two lines on the same side of a transversal. They add to $180^\circ$ when the two lines are parallel.

Combining like terms by adding or subtracting their coefficients, while keeping their variable part unchanged.

A matrix with one column. A two-dimensional coordinate can be written as the column vector $\begin{pmatrix}x\\y\end{pmatrix}$.

A single transformation equivalent to applying two or more transformations in a specified order.

The amount added to each term to obtain the next term, calculated as next term minus previous term. It can be negative.

An operation is commutative if reversing the order leaves the result unchanged. Matrix multiplication is not commutative in general: $AB$ and $BA$ can differ.

The rule that changing the order of addition or multiplication does not change the result: $a+b=b+a$ and $ab=ba$.