Maths AI terms: A

A

Absolute erroralso absolute errors, size of the error

The size of the difference between an approximate value and the exact value, $|v_A - v_E|$, measured in the same units as the quantity.

Introduced in 1.6 Approximation and error

Absolute valuealso modulus of a real number, absolute values, magnitude of a number

The distance of a real number from zero on the number line, written $|x|$; it equals $x$ when $x \ge 0$ and $-x$ when $x < 0$

Introduced in 1.6 Approximation and error

Absorbing stateHL only · also absorbing states, absorbing Markov chain, absorbing chain

A state of a Markov chain that cannot be left once it is entered, so that the probability of moving from it to itself is 1.

Introduced in 4.19 Transition matrices and Markov chains

Academic integrityalso academic honesty, academically honest

The principle that work submitted for assessment is the student's own, with every idea, quotation, data set, image and piece of software output taken from someone else acknowledged where it is used.

AccelerationHL only · also a, dv/dt, accelerations, d²s/dt²

The rate of change of an object's velocity with respect to time, $a = \frac{\mathrm{d}v}{\mathrm{d}t} = \frac{\mathrm{d}^2s}{\mathrm{d}t^2}$

Acceptance regionHL only · also non-rejection region, region of acceptance

The set of values of the test statistic for which the null hypothesis is not rejected; it contains every possible value outside the critical region.

Introduced in 4.18 Further hypothesis testing

Accumulated errorHL only · also global error, truncation error of Euler's method, accumulated errors, cumulative error

The difference between a numerical estimate after many steps and the exact value of the solution, made up of the small error introduced at every step and carried forward through all later steps.

Introduced in 5.16 Euler’s method

Accuracy markalso answer mark, A mark, A1, accuracy marks

A mark, written A1 in a markscheme, awarded for a correct answer or a correct intermediate value, usually only when the method that produces it has also been credited.

Actual significance levelHL only · also size of a test, actual size, actual significance

The probability, assuming the null hypothesis is true, that the test statistic falls in the critical region; for a discrete test it is usually less than the nominal significance level.

Introduced in 4.18 Further hypothesis testing

Acute anglealso acute angles, acute

An angle greater than 0° and less than 90°.

Introduced in 3.2 Trigonometry in triangles

Additive property of the Poisson distributionHL only · also sum of independent Poisson variables, sum of Poisson distributions, additive property

If $X \sim \mathrm{Po}(m_1)$ and $Y \sim \mathrm{Po}(m_2)$

Adjacency matrixHL only · also adjacency matrices

The square matrix of a graph with $n$ vertices in which the entry in row $i$, column $j$ is the number of edges from vertex $i$ to vertex $j$.

Introduced in 3.15 Adjacency matrices

Adjacent edgesHL only

Two edges that share a common vertex.

Introduced in 3.14 Graph theory

Adjacent sidealso adj, adjacent sides

In a right-angled triangle, the side next to a given acute angle that is not the hypotenuse.

Introduced in 3.2 Trigonometry in triangles

Adjacent verticesHL only · also adjacent, neighbouring vertices

Two vertices that are joined by at least one edge.

Introduced in 3.14 Graph theory

Affine transformationHL only · also affine map, affine transformations, affine maps

A transformation of the form $\boldsymbol{r}' = A\boldsymbol{r} + \boldsymbol{b}$, where $A$ is a $2 \times 2$

Agreement between rankingsalso agreement, agreement between judges, agreement of rankings, rank agreement

The extent to which two rankings of the same items place them in the same order, measured by $r_s$, where 1 means identical orders and −1 means reversed orders.

Introduced in 4.10 Spearman’s rank correlation

Aimalso aims, research question, aim of the exploration, exploration aim

A precise statement of what an exploration sets out to find, model, test or decide, specific enough that the conclusion can say whether, and how well, it was achieved.

Algorithmalso algorithms

A finite sequence of precisely stated steps that solves a problem or carries out a task, and that can be followed mechanically.

Introduced in 3.6 Voronoi diagrams

Alternate anglesalso Z angles, alternate angle

A pair of equal angles formed on opposite sides of a line that crosses two parallel lines, each lying between the parallels.

Introduced in 3.3 Applications of trigonometry

Alternating currentHL only · also AC, alternating voltage, mains electricity, AC circuit

An electric current, or the voltage that drives it, that reverses direction periodically and is modelled by a sinusoidal function of time such as $V = A\cos(\omega t + \phi)$.

Introduced in 1.13 Polar and Euler form

Alternative hypothesisalso H1, H₁, alternative hypotheses

The statement, written $\mathrm{H}_1$, that is accepted if the null hypothesis is rejected; it describes a difference, an association or a departure from a model.

Introduced in 4.11 Hypothesis testing

Ambiguous case of the sine ruleHL only · also ambiguous case, SSA case, two possible triangles

The situation in which two sides of a triangle and an angle that is not between them are given, and the data fit two different triangles, one with an acute angle and one with the obtuse supplement of that angle.

Introduced in 3.8 The unit circle and trigonometric equations

Amortizationalso amortisation, amortize, amortise, amortizing a loan, amortised, amortized loan

The repayment of a loan by equal payments at regular intervals, each of which pays the interest due for that period and repays part of the principal, so that the debt is cleared at the end of the loan term.

Introduced in 1.7 Amortisation and annuities

Amortization schedulealso amortisation schedule, amortization table, amortisation table, repayment schedule, amortization schedules

A table showing, for each payment of an amortized loan, the payment, the interest charged, the part of the principal repaid and the outstanding balance after the payment.

Introduced in 1.7 Amortisation and annuities

Amplitudealso amplitudes

Half the vertical distance between the maximum and minimum values of a periodic function; for $a\sin(bx) + d$ and $a\cos(bx) + d$ it equals $|a|$.

Introduced in

Angle between a line and a planealso angle between line and plane

The angle between a line and its projection onto the plane, measured at the point where the line meets the plane.

Introduced in 3.1 Volume and surface area in three dimensions

Angle between two linesHL only · also acute angle between two lines, angle between lines

The acute angle (between 0° and 90°) formed by two lines, found from the angle between their direction vectors; if the angle between the direction vectors is obtuse, the angle between the lines is its supplement $180° - \theta$.

Introduced in 3.13 Scalar and vector products

Angle between two vectorsHL only · also angle between vectors, angle between two non-zero vectors

The angle $\theta$, with $0° \le \theta \le 180°$, between two non-zero vectors drawn from the same starting point; it satisfies $\cos\theta = \frac{\boldsymbol{v} \cdot \boldsymbol{w}}{|\boldsymbol{v}||\boldsymbol{w}|}$

Angle modealso degree mode, radian mode, DEG, angle setting

The GDC setting that fixes whether angles are entered and given in degrees or in radians.

Introduced in 3.2 Trigonometry in triangles

Angle of depressionalso depression, angles of depression

The angle measured downwards from the horizontal to the line of sight of an object below the observer.

Introduced in 3.3 Applications of trigonometry

Angle of elevationalso elevation, angles of elevation

The angle measured upwards from the horizontal to the line of sight of an object above the observer.

Introduced in 3.3 Applications of trigonometry

Angle of inclinationalso angle of slope, inclination, angle of a slope

The angle $\theta$ between a line or incline and the horizontal, measured upwards; it is related to the gradient $m$ by $\tan\theta = m$.

Introduced in 2.1 Equations of straight lines

Angular diameterHL only · also angular size, apparent size, angular diameters

The angle that an object's diameter subtends at the eye of an observer, which for a distant object is approximately its diameter divided by its distance, in radians.

Introduced in 3.7 Radian measure

Angular displacementHL only · also angle turned through, angular displacements

The angle through which an object rotates about a fixed point, usually measured in radians.

Introduced in 3.7 Radian measure

Angular frequencyHL only · also ω, omega, angular speed of a wave

The constant $\omega$ in a sinusoidal function $A\cos(\omega t + \phi)$, measured in radians per second, equal to $2\pi f$ where $f$

Angular speedHL only · also angular velocity, rad s⁻¹, radians per second

The angle turned through per unit time by a rotating object, usually measured in radians per second (rad s⁻¹) and written $\omega$.

Introduced in 3.7 Radian measure

Annual percentage rate (APR)also APR, annual percentage rate of charge, APRC

The yearly cost of a loan expressed as a single percentage that includes the interest and certain compulsory fees, published by lenders so that different loans can be compared.

Introduced in 1.7 Amortisation and annuities

Annuityalso annuities, savings plan, annuity fund, series of payments

A series of equal payments made at equal time intervals, either paid into a fund to build up savings or paid out of a fund to provide an income.

Introduced in 1.7 Amortisation and annuities

Annular sectoralso annular sectors, sector of an annulus, ring sector

The part of an annulus between two radii; for central angle $\theta$ degrees, outer radius $R$ and inner radius $r$ its area is $\frac{\theta}{360} \times \pi(R^2 - r^2)$

Annulusalso ring, annuli, annular region

The region between two concentric circles; for outer radius $R$ and inner radius $r$ its area is $\pi R^2 - \pi r^2 = \pi(R^2 - r^2)$

Answer given (AG)also AG, answer given

A label in a markscheme showing that the line is the result printed in the question, so no mark is awarded for writing it; the marks are for the working that reaches it.

Anti-derivativealso antiderivative, anti-differentiation, antidifferentiation, primitive, anti-derivatives

A function $F(x)$ whose derivative is a given function $f(x)$, so that $F'(x) = f(x)$

Approximate valuealso v_A, approximation, approximations

A value used in place of the exact value of a quantity, such as a rounded number, an estimate or a measurement, written $v_A$.

Introduced in 1.6 Approximation and error

Arcalso arcs, circular arc

A part of the circumference of a circle between two points on the circle.

Introduced in 3.4 Arcs and sectors

Arc lengthalso length of an arc, arc lengths

The distance along an arc of a circle; for radius $r$ and central angle $\theta$ degrees it is $l = \frac{\theta}{360} \times 2\pi r$

Arcsecondalso arc second, ″, second of arc, arcseconds, milliarcsecond

A unit of angle equal to $\frac{1}{3600}$ of a degree, written ″; a milliarcsecond is one thousandth of an arcsecond.

Introduced in 3.3 Applications of trigonometry

Area between two curvesalso area between a curve and a line, area between curves

The area of the region enclosed by two graphs between two values of $x$, found by subtracting the area under the lower graph from the area under the upper graph over the same interval.

Introduced in 5.5 Introduction to integration

Area of a triangle using sinealso ½ab sin C, half ab sin C, area formula ½ab sin C, area of a triangle formula

The area of any triangle equals $\frac{1}{2}ab\sin C$, half the product of two sides multiplied by the sine of the angle between them.

Introduced in 3.2 Trigonometry in triangles

Area scale factorHL only · also area of image, area factor, modulus of the determinant

The number by which a transformation multiplies every area; for the transformation $\boldsymbol{r}' = A\boldsymbol{r} + \boldsymbol{b}$ it equals $|\det A|$.

Introduced in 3.9 Matrix transformations

Area under a curvealso area under the graph, area under the curve, area beneath a curve

The area of the region bounded by a curve $y = f(x)$ with $f(x) > 0$, the $x$-axis and the vertical lines $x = a$

Argand diagramHL only · also complex plane, Argand plane

A diagram of the complex plane in which the complex number $a + b\mathrm{i}$ is represented by the point $(a, b)$, with real parts on the horizontal real axis and imaginary parts on the vertical imaginary axis.

Introduced in 1.12 Complex numbers

Argument of a complex numberHL only · also argument, arg z, arg

The angle $\theta$, measured anticlockwise in radians from the positive real axis, between that axis and the line joining the origin to the point representing $z$ on the Argand diagram; it is written $\arg z$.

Introduced in 1.12 Complex numbers

Argument of a logarithmHL only · also argument of a log, argument of log

The number or expression whose logarithm is taken, $x$ in $\log_a x$; it must be positive for the logarithm to be defined.

Introduced in 1.9 Laws of logarithms

Arithmetic sequencealso arithmetic progression, arithmetic sequences, AP

A sequence in which each term after the first is found by adding the same fixed number, the common difference, to the term before it.

Introduced in 1.2 Arithmetic sequences and series

Arithmetic series

The sum of the terms of an arithmetic sequence.

Introduced in 1.2 Arithmetic sequences and series

Associationalso associated, positive association, negative association

A tendency for the values of two variables to change together, so that knowing one gives information about the other; the pattern need not be linear.

Introduced in 4.10 Spearman’s rank correlation

AssociativityHL only · also associative, associative law, (AB)C = A(BC)

The property that $(AB)C = A(BC)$ for any matrices $A$, $B$ and $C$ whose products are defined, so a product of several matrices can be written

Assumptionalso assumptions, simplifying assumption, modelling assumption

A statement accepted as true, without proof, in order to simplify a real situation enough for it to be modelled mathematically.

Introduced in 2.6 The modelling process

Astronomical unitalso AU, au, astronomical units

A unit of length used for distances in the solar system, defined as exactly 149,597,870,700 m, about the mean distance from the Earth to the Sun.

Introduced in 1.1 Scientific notation

Asymptotealso asymptotes, asymptotic

A straight line that the graph of a function approaches more and more closely, getting as near to it as desired, as $x$ or $y$ becomes very large in size.

Introduced in 2.4 Key features of graphs

Autonomous differential equationHL only · also autonomous DE, autonomous equation, autonomous differential equations

A first-order differential equation $\frac{\mathrm{d}y}{\mathrm{d}x} = f(y)$ whose right-hand side depends only on the unknown $y$ and not on the independent variable.

Auxiliary equationHL only · also λ² + aλ + b = 0, auxiliary equations, characteristic equation of a second-order DE

For the differential equation $\ddot{x} + a\dot{x} + bx = 0$, the quadratic equation $\lambda^2 + a\lambda + b = 0$

Average rate of changealso average rate, mean rate of change

The change in a quantity divided by the change in the variable it depends on over an interval, $\frac{f(b) - f(a)}{b - a}$, which is the gradient of the secant between the two endpoints.

Introduced in 5.1 Limits and the derivative

Avogadro constantalso Avogadro's number, N_A, Avogadro number

The number of particles in one mole of a substance, fixed in the SI as exactly $6.022\,140\,76 \times 10^{23}$ per mole.

Introduced in 1.1 Scientific notation

Axis of rotationHL only · also axis of revolution, axis of symmetry of the solid, rotation axis

The straight line about which a region is rotated to form a solid of revolution; every cross-section of the solid perpendicular to this line is a circle centred on it.

Introduced in 5.12 Areas and volumes

Axis of symmetryalso line of symmetry, x = −b/2a, axis of symmetry of a parabola

The vertical line about which a graph is symmetrical; for the parabola $y = ax^2 + bx + c$ it is the line $x = -\frac{b}{2a}$