50 of the Maths AI glossary’s terms, each with the part of the syllabus where you first meet it.
The angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle.
A sample chosen by a process in which every member of the population has a known, non-zero chance of being selected, decided by chance rather than by the person collecting the data.
A variable whose value is a number determined by the outcome of a random process, so that each possible value has a probability.
A process in which a walker moves from vertex to vertex along edges, at each step choosing one of the edges leaving the current vertex at random, all such edges being equally likely.
The set of all output values that a function takes when the input runs through the whole of its domain.
The difference between the largest and smallest values in a data set, maximum − minimum.
The position of a value when all the values of a variable are arranged in order, with 1 for the first value in the chosen order.
How fast one quantity changes in relation to another quantity on which it depends, measured in units of the first quantity per unit of the second.
An exponent that is a fraction , with and integers and
A number that can be written as a fraction , where and are integers and
Rewriting a fraction with a surd in its denominator as an equal fraction whose denominator is a rational number, by multiplying the numerator and denominator by a suitable expression.
The part of a line that starts at a point and continues without end in one direction; with the line , it is the set of points with .
The rate at which the buying power of an investment grows once inflation is taken into account; it is approximately the nominal interest rate minus the inflation rate.
Any number that can be represented as a point on the number line, rational or irrational; the set of real numbers is written .
For a complex number with , the real number , written
The value of a future amount of money measured in the prices of an earlier time (usually the start of the investment), so that it shows what the money can actually buy.
The set of input values for which a model makes sense in its real context, given by physical limits, by the meaning of the variables and by the range of the data used to build it.
A mark, written R1 in a markscheme, awarded for a clear, valid reason that supports a conclusion.
The reciprocal of a non-zero number is , the number that gives 1 when multiplied by .
A formula that defines each term of a sequence from the term or terms before it, so that the sequence is generated one term at a time from a starting value.
Rewriting a second-order differential equation as the coupled first-order equations
A transformation that maps every point to its mirror image in a fixed line, so that the line is the perpendicular bisector of the segment joining each point to its image.
Criterion D of the exploration, worth 3 marks, which assesses how the student reviews, analyses and evaluates the exploration, including its results, methods and limitations, throughout the report as well as in the conclusion.
The straight line that makes the sum of the squares of the vertical distances from the data points to the line as small as possible; it is used to predict values of from values of .
A Markov chain whose transition matrix has some power in which every entry is strictly positive.
The fixed amount paid at equal time intervals to repay a loan or to build up or draw from an annuity, written in the TVM solver.
The number of times an event occurs in a set of trials divided by the total number of trials; it is used as an estimate of the probability of the event.
The position of an object B from the viewpoint of an object A, given by the vector
The velocity of an object B from the viewpoint of an object A, given by ; it is the rate of change of the relative position
A variable that has a direct bearing on the research question being investigated, chosen from all the variables available because it measures the quantity of interest or a factor that could affect it.
The extent to which data can be trusted to be accurate and consistent, so that collecting them again in the same way would give similar results.
A root of a polynomial equation whose factor appears more than once in the factorised polynomial; a root that appears twice is called a double root.
Multiplying a vector by a positive scalar so that it has a required magnitude while keeping its direction; the vector of magnitude in the direction of is
The difference between an observed value of the dependent variable and the value predicted by a model, ; it is positive when the data point lies above the model's graph and negative when it lies below.
A scatter diagram of the residuals of a model, , plotted against the independent variable
The single vector equal to the sum of two or more vectors, which has the same effect as all of them acting together.
A function that gives the total income from selling items; at a fixed price per item, .
The result
A unit of rotation rate equal to the number of complete turns made in one minute.
A logarithmic scale of earthquake magnitude,
A solid with a circular base and a curved surface that rises to a point (the apex) directly above the centre of the base.
A solid with a polygonal base and triangular faces meeting at a point (the apex) that lies directly above the centre of the base.
The rule fixing the direction of ; if the fingers of the right hand curl from towards through the angle between them, the thumb points in the direction of
In the HL use of mathematics criterion, clarity of logic and language in mathematical arguments and calculations, with every mathematical claim that the exploration relies on justified or proved.
A summary statistic that changes little when a few extreme values or outliers are added, removed or changed; the median and the interquartile range are robust, while the mean, range and standard deviation are not.
A value of the unknown that makes an equation true; the roots of are its solutions.
A transformation that turns every point through the same angle, in a stated direction (clockwise or anticlockwise), about a fixed centre, keeping its distance from the centre the same.
Replacing a number by the closest value that has a stated accuracy, such as a given number of decimal places or significant figures.
A drawing made using only an unmarked straight edge and a pair of compasses, in which every length and point comes from circles and lines rather than from measurement.