42 of the Maths AI glossary’s terms, each with the part of the syllabus where you first meet it.
The length of a vector, written ; for it equals .
The longer of the two arcs joining two points on a circle; its central angle is greater than 180°.
The number in a number written in standard form , with
A function in which at least one output comes from two or more different inputs.
A pairing of the elements of one set (the inputs) with elements of another set (the outputs), often shown as a diagram of arrows from each input to its output.
Half the width of a confidence interval, the distance from the point estimate to either confidence limit; for a z-interval it equals
The derivative of a cost function with respect to the number of items produced, which gives the rate of increase of total cost per extra item and approximates the cost of producing one more item; marginal revenue and marginal profit
The price and quantity at which the quantity buyers want to buy equals the quantity sellers want to sell; graphically, the point of intersection of the demand and supply curves.
A sequence of random states, observed at equal steps, in which the probability of moving to each state at the next step depends only on the current state, and these probabilities stay the same at every step.
The property that the probability of the next state depends only on the current state, and not on the states that came before it.
The document examiners use to mark a question, listing each available mark, the work or answer that earns it, accepted alternative methods and notes on what is not accepted.
Data in which each value in one sample is linked to exactly one value in the other, because both come from the same individual or from two individuals deliberately matched on relevant characteristics.
Criterion B of the exploration, worth 4 marks, which assesses the use of correct notation, symbols and terminology, the definition of key terms and variables, the use of suitable forms of representation and the logical setting out of arguments.
The internally assessed component of an IB mathematics course, a written report of about 12 to 20 double-spaced pages in which a student investigates an area of mathematics or a real situation of their own choice, marked by the teacher against five criteria and moderated by the IB.
A function, equation or graph that represents a real situation in mathematical form, so that it can be analysed and used to make predictions.
A rectangular array of numbers arranged in rows and columns, enclosed in brackets and treated as a single object.
A system of linear equations written as , where is the matrix of coefficients, is the column of unknowns and is the column of constants.
The product of an matrix and an matrix
The sum of all the values in a data set divided by the number of values; written , or when the data are a whole population.
The point whose coordinates are the mean of the -values and the mean of the -values of a set of bivariate data.
The mean number of times an event occurs per unit of time or space, which gives the parameter of a Poisson distribution once it is multiplied by the size of the interval.
A single value that represents the centre or typical value of a data set; the mean, the median and the mode are the three standard measures.
A single value that describes how spread out the values of a data set are; the range, interquartile range, variance and standard deviation are measures of dispersion.
The difference between a measured value and the true value of a quantity, caused by the limited precision of the measuring instrument, rounding of the reading, or the way the measurement is made.
The middle value of a data set arranged in order of size, so that half of the values are less than or equal to it and half are greater than or equal to it.
A mark, written M1 in a markscheme, awarded for an attempt to use a correct method, whether or not the final answer is correct.
The value halfway between the lower and upper boundaries of a class interval, used to represent every value in that class when estimating with grouped data.
The point on a line segment that is the same distance from both endpoints; for endpoints and
A spanning tree of a weighted graph whose total weight is as small as possible.
The shorter of the two arcs joining two points on a circle; its central angle is less than 180°.
The fixed line in which a reflection takes place; every point on it is unmoved, and each other point is mapped to the point the same distance away on the other side, along a perpendicular to the line.
Values that should be in a data set but were not recorded or cannot be used.
The class interval with the highest frequency in a grouped frequency table whose classes all have equal width.
The value that occurs most often in a data set; a data set can have more than one mode, or none if every value occurs equally often.
The repeated process of stating assumptions about a real situation, choosing and fitting a model, testing it against reality, reflecting on and adapting it, and finally using it to explain, predict or inform decisions.
The process by which the IB re-marks a sample of a school's internally assessed work and, if the teacher's marks differ from the IB's standard, adjusts the marks of every student in the school's group so that all schools are marked to the same standard.
The distance of the point representing from the origin of the Argand diagram, written and equal to
A relationship between two variables in which one variable always increases, or always decreases, as the other increases, at a rate that may change.
A long-term loan used to buy property, in which the property is security for the loan and can be repossessed by the lender if the payments are not made.
Two or more edges that join the same pair of vertices.
Carrying out many hypothesis tests on the same data, which greatly increases the probability that at least one test gives a significant result by chance even when every null hypothesis is true.
Events that cannot occur at the same time, so that contains no outcomes and .