100 of the Maths AI glossary’s terms, each with the part of the syllabus where you first meet it.
The way a calculator or computer displays a number in standard form, with the letter E (or a small ×10) standing for "times ten to the power", as in 2.88E4 for .
The volume of liquid or other material that a hollow container can hold, often measured in litres or millilitres.
The limiting value of a logistic model , which is the horizontal asymptote that the output approaches but does not reach; in a population model it is the largest population the environment can support.
An equation connecting and only, found by eliminating from the parametric equations and
The form of a complex number, with , in which the number is written as a real part plus a real multiple of .
A relationship in which a change in one variable directly produces a change in the other variable.
The region of a Voronoi diagram that contains one site and every point that is closer to that site than to any other site.
A collection of data from every member of a population.
The angle between two radii of a circle, with its vertex at the centre; it is the angle that an arc or chord subtends at the centre.
For a random sample of independent observations from any population with mean and finite variance , the distribution of the sample mean approaches the normal distribution
An equilibrium point of a linear system whose eigenvalues are purely imaginary, ; the trajectories around it are closed curves (ellipses or circles), so solutions repeat periodically without approaching or leaving it.
The fixed point from which distances are multiplied by the scale factor in an enlargement; it is the only point that an enlargement with scale factor leaves unmoved.
The fixed point about which a rotation turns the plane; it is the only point that a rotation through an angle that is not a multiple of 360° leaves unmoved.
The rule for differentiating a composite function: if where , then
An instant at which an object's velocity changes sign, so that it reverses its direction of motion along the line.
The equation , whose solutions are the eigenvalues of the square matrix .
For a square matrix , the polynomial in given by ; for a 2 × 2 matrix it is a quadratic.
The continuous probability distribution, taking only non-negative values, that the chi-squared statistic follows when the null hypothesis is true; its shape is set by the number of degrees of freedom.
A test of whether observed frequencies in a set of categories are consistent with the frequencies predicted by a stated distribution.
A test of whether two categorical variables are independent in a population, using the observed frequencies in a contingency table.
The problem of finding the route of least total weight that travels along every edge of a connected weighted graph at least once and returns to its starting vertex.
A straight line segment joining two points on a circle.
A trail that starts and finishes at the same vertex, so it has no repeated edges.
Motion along a circle; for uniform circular motion about the origin, the position is
The point that is equidistant from the three vertices of a triangle; it is where the perpendicular bisectors of the three sides meet.
The circle that passes through all three vertices of a triangle; its centre is the circumcentre and its radius is the distance from the circumcentre to any vertex.
The distance around a circle, equal to for a circle of radius .
The abbreviation , so that a complex number in polar form is written .
A short reference placed in the text at the point where a source is used, identifying that source so that the reader can find its full details in the bibliography.
A range of values grouped together as one class in a frequency distribution, written as an inequality such as .
An instrument for measuring an angle of elevation or depression, by sighting an object along it and reading the angle from the horizontal.
A walk that starts and finishes at the same vertex.
The moment at which the distance between two moving objects, or between a moving object and a fixed point, is smallest, together with that smallest distance.
Two angles between a pair of parallel lines on the same side of a line crossing them; they add up to 180°.
The constant that multiplies a variable, or a power of a variable, in a term of an expression or equation.
A measure of how well a regression model fits bivariate data, equal to the proportion of the variation in the dependent variable that is explained by the model; it lies between 0 and 1 for a least squares model, with values close to 1 showing a close fit.
Lines that have every point in common, so that two different equations describe the same line.
Lying on the same straight line; points , and are collinear when
The event of two moving objects being at the same position at the same time, so that for one value of
A vector written as a vertical list of its components in brackets, with the -component at the top, then the -component and, in three dimensions, the -component.
An event formed from two or more events using union ("or"), intersection ("and") or complement ("not").
Merging adjacent categories of a chi-squared table, adding their observed frequencies and their expected frequencies, so that every expected frequency is greater than 5.
A word or phrase at the start of an exam question part that tells the candidate what kind of answer to give and how much working to show.
The fixed amount by which each term of an arithmetic sequence differs from the term before it; it can be positive, negative or zero.
The logarithm with base 10, written or simply ; it is the power to which 10 must be raised to give .
The constant by which each term of a geometric sequence is multiplied to give the next term, so that
A pair of coupled differential equations for two populations that use the same resources, in which each population grows logistically on its own and the presence of the other species reduces its growth rate.
The event that does not occur, written and read "not "; it contains every outcome in the sample space that is not in .
A simple graph in which every pair of distinct vertices is joined by exactly one edge; the complete graph on vertices is written .
For a complex number with , the number
A number of the form , where and are real numbers and
The signed amount by which a vector moves in the direction of one of the coordinate axes; a vector in two dimensions has an -component and a -component, and one in three dimensions also has a -component.
The function obtained by applying one function to the output of another; the composite is defined by , so
A transformation made by applying two or more transformations one after another, in a stated order.
Interest that is added to the balance at the end of each compounding period, so that in later periods interest is earned on the original amount and on the interest already added.
A solid formed by joining two or more simpler solids, or by removing one solid from another.
The length of time between the moments when interest is added to a balance; the number of compounding periods in a year is written .
Describes a curve, or a part of one, that bends downwards, so that its gradient decreases as increases and every chord joining two of its points lies below the curve.
Describes a curve, or a part of one, that bends upwards, so that its gradient increases as increases and every chord joining two of its points lies above the curve.
The direction in which a curve bends on an interval, either concave up, where and the gradient increases, or concave down, where
The probability that an event occurs given that an event has occurred, written ; it is found by treating as the new sample space.
The flat shape that folds to make the curved surface of a cone, a sector whose radius is the cone's slant height and whose arc length equals the circumference of the cone's base.
A range of values, calculated from a sample, constructed by a method that captures the true value of a population parameter in a stated proportion of all possible samples.
The percentage of all possible samples for which the method used to construct a confidence interval would produce an interval containing the true value of the parameter.
The lower and upper end points of a confidence interval.
A variable, not included in the analysis, that affects both of the variables being studied and so creates or strengthens a correlation between them.
Two complex numbers of the form and , with real and
A graph in which every vertex can be reached from every other vertex by travelling along a sequence of edges.
If a function is multiplied by a constant , its derivative is multiplied by the same constant, so the derivative of is .
The arbitrary constant added to an anti-derivative in an indefinite integral, because a constant term disappears on differentiation and so cannot be recovered from the derivative alone.
The constant in a variation relationship , equal to
The term of a polynomial that does not contain the variable, equal to the value of the polynomial when the variable is 0.
Motion in which the velocity vector does not change, so the object travels in a straight line at constant speed and its position at time is .
A fixed condition in an optimisation problem, such as a given amount of material, volume, perimeter or length, that links the variables and so allows all but one of them to be eliminated.
The extent to which a test covers all the aspects of the quantity it is intended to measure, in the right proportions; it is judged by experts who compare the content of the test with a full description of what should be measured.
A table of observed frequencies that classifies each member of a sample by two categorical variables, one for the rows and one for the columns.
The limiting case of compound interest in which interest is added at every instant, so that an amount at a nominal annual rate grows to after
Quantitative data that can take any value within an interval, usually obtained by measuring.
A function whose graph can be drawn without lifting the pen from the paper; a piecewise function is continuous at a boundary when the formulae on either side give the same value there.
A random variable that can take any value in an interval of real numbers, so that its probabilities are given by areas under a curve rather than by a list of separate values.
A method in which the sample consists of members of the population who are easy to reach or who volunteer, with no random selection and no fixed numbers from each category.
An infinite series whose partial sums approach a finite limit as increases without bound; that limit is the sum of the series.
A relationship between two variables in which one tends to change as the other changes, described by its direction (positive or negative) and its strength.
The function whose value is the -coordinate of the point where the arm of the angle , in standard position, meets the unit circle.
For an acute angle in a right-angled triangle, .
In any triangle ,
A function that gives the total cost of producing or buying a quantity of goods, usually a fixed cost plus a cost for each unit.
A set of differential equations in which the rate of change of each variable depends on the other variables as well as its own, so that the equations must be solved together.
The set of values of the test statistic for which the null hypothesis is rejected at a given significance level.
The boundary value of a test statistic for a given significance level; a test statistic beyond the critical value leads to rejecting the null hypothesis.
A polynomial equation of degree 3, which can be written as with
A model of the form , where
Fitting a model of the form to bivariate data by least squares.
The running total of the frequencies up to and including a given class, which gives the number of data values below that class's upper class boundary.
A graph of cumulative frequency (vertical axis) against the upper class boundaries (horizontal axis), with the points joined by a smooth increasing curve or by straight line segments.
The probability that a random variable takes a value less than or equal to a given value, , for a discrete random variable it is found by adding the probabilities of all values up to and including .
The area of the curved part of the surface of a solid such as a cylinder, cone or sphere, not including any flat faces.
A walk that starts and finishes at the same vertex and repeats no other vertex, so it also repeats no edge.
A solid with two identical, parallel circular ends joined by a curved surface, so that every cross-section parallel to the ends is the same circle.