Maths AA terms: A

A

Absolute valueHL only · also modulus function, modulus of a real number

The size of a real number without its sign: $|x| = x$ when $x \ge 0$ and $|x| = -x$ when $x < 0$. $|a - b|$ is the distance between $a$ and $b$ on the number line.

Introduced in 2.16 Modulus graphs and transformations

Acceleration

The rate of change of velocity with respect to time, $a = \frac{dv}{dt} = \frac{d^2s}{dt^2}$

Addition principleHL only · also rule of sum

If a task can be done in one of several separate cases that cannot happen together, with $m$ ways in one case and $n$ ways in the other, then the task can be done in $m + n$ ways.

Introduced in 1.10 Counting principles and the extended binomial theorem

Ambiguous casealso ambiguous case of the sine rule

The situation in which two sides and a non-included acute angle of a triangle fit two different triangles, so the sine rule gives two possible values (acute and obtuse) for an angle.

Introduced in 3.5 The unit circle

Amplitude

Half the distance between the maximum and minimum values of a sinusoidal function; for $y = a\sin(b(x + c)) + d$ it is $|a|$.

Introduced in 3.7 Circular functions

Analytic solutionalso algebraic solution, exact solution

A solution found by algebraic manipulation, which gives the exact value, such as $x = \ln 3$ or $x = \frac{1 + \sqrt{5}}{2}$

Angle between a line and a plane

The angle between the line and its projection onto the plane (the shadow it casts straight down onto the plane). It always lies between $0°$ and $90°$.

Introduced in 3.1 Distance, midpoint, volume and surface area

Angle between two planesHL only

The acute angle between two intersecting planes, equal to the acute angle between their normal vectors.

Introduced in 3.18 Intersections of lines and planes

Angle of depression

The angle between the horizontal and the line of sight from an observer down to an object below them.

Introduced in 3.3 Applications of trigonometry

Angle of elevation

The angle between the horizontal and the line of sight from an observer up to an object above them.

Introduced in 3.3 Applications of trigonometry

Antiderivativealso anti-differentiation, integration

A function $F$ whose derivative is a given function $f$, so that $F'(x) = f(x)$. Every continuous function has infinitely many antiderivatives, which differ only by a constant.

Introduced in 5.5 Introduction to integration

Arcalso arc length, minor arc, major arc

Part of the circumference of a circle between two points on it. Its length is $l = r\theta$ when the angle $\theta$ at the centre is in radians.

Introduced in 3.4 Radians, arcs and sectors

Area between curves

The area of the region enclosed by two curves $y = f(x)$ and $y = g(x)$ between $x = a$ and $x = b$

Argand diagramHL only · also complex plane

A plane with a horizontal real axis (Re) and a vertical imaginary axis (Im), on which the complex number $a + b\mathrm{i}$ is shown as the point $(a, b)$ or as the vector from the origin to that point.

Introduced in 1.12 Complex numbers in Cartesian form

Argument (of a complex number)HL only · also arg z, principal argument

The angle $\arg z$, in radians, from the positive real axis anticlockwise to the line joining the origin to $z$. The principal argument satisfies $-\pi < \arg z \le \pi$; $\arg 0$

Arithmetic sequencealso arithmetic progression

A sequence in which each term after the first is found by adding the same number, the common difference $d$, to the previous term.

Introduced in 1.2 Arithmetic sequences and series

Arithmetic series

The sum of the terms of an arithmetic sequence. The sum of the first $n$ terms is $S_n = \frac{n}{2}(u_1 + u_n)$

Asymptotealso asymptotes

A line that a graph approaches more and more closely, without reaching it, as $x$ or $y$ grows without bound, such as $x = 0$ and $y = 0$ for $y = \frac{1}{x}$

Average rate of change

The change in a function divided by the change in its input over an interval, $\frac{f(b) - f(a)}{b - a}$: the gradient of the chord joining the two points on the graph.

Introduced in 5.1 Limits and the derivative

Axis of rotationHL only

The fixed line about which a region is turned to form a solid of revolution. Every cross-section of the solid perpendicular to it is a circle or a ring.

Introduced in 5.17 Areas and volumes of revolution

Axis of symmetry

The vertical line through the vertex about which a parabola is symmetric. For $y = ax^2 + bx + c$ it is the line $x = -\frac{b}{2a}$