European Baccalaureate Mathematics (3-period course) key terms

A timed, invigilated paper sat in the June session under the European Schools' central subject panels; scripts are marked externally against a published marking scheme and weighted according to the subject's coefficient in the final Baccalaureate mark.

A short face-to-face assessment, typically around twenty minutes, in which the candidate prepares a topic for a fixed time and then defends or develops it before two examiners, one of whom may be external to the school.

The school-based component of the final result, combining A marks from S7 coursework and B marks from the Pre-Baccalaureate examinations, calculated before the June session and reported to the examining board.

A formative assessment mark awarded during the S7 year for classwork, tests, practical work or projects; it reflects sustained performance and is aggregated with B marks to give the preliminary mark.

The mark from the Pre-Baccalaureate examination sat in school during S7, set and marked internally but moderated against common standards; it carries more weight than A marks in the preliminary mark.

A formal S7 mock examination taken before the June session, written under exam conditions in the school; its result supplies the B mark and predicts likely performance in the written paper.

A weighting factor attached to each subject that determines how much its mark contributes to the overall Baccalaureate percentage; a three-period course carries a lower coefficient than a four- or five-period course.

A subject taught for three periods per week, usually taken as a complementary option; Mathematics as a three-period course is examined by one written paper and has a smaller coefficient than the five-period course.

A subject every candidate must take and be examined in, namely Language 1, Language 2 and Mathematics; failure or absence in a compulsory subject can prevent award of the Baccalaureate.

The candidate's first language, taught and examined at native-speaker level; the written paper tests literary analysis and composition, and an oral may also be taken in it.

The candidate's second language, examined at a defined level with written and oral components; it may also serve as the language of instruction for a non-linguistic subject such as History or Geography.

The language in which a content subject is taught and examined; candidates may study History or Geography through their Language 2 and be examined orally in that language.

The official grid of criteria and point allocations used by examiners to score scripts, specifying what earns marks and how partial credit is awarded; candidates should practise answering against it.

The process by which internally awarded marks, especially B marks and oral marks, are reviewed against common standards so that results are comparable across schools and language sections.

The pair or group of examiners conducting an oral examination, usually one internal teacher and one examiner from outside the school, who jointly agree the final mark after the candidate withdraws.

The supervised period, commonly fifteen to twenty minutes, during which a candidate studies the material drawn for the oral and plans a structured response before entering the examination room.

The text, document, data set or image supplied for an oral or written task, on which the candidate's analysis and argument must be based rather than on memorised content alone.

A rule assigning to each element of a domain exactly one value in the codomain; the central object of the three-period course, studied through notation, graphs, composition and inverses.

The set of inputs for which a function is defined and the set of values it actually takes; identifying them is essential before sketching, differentiating or inverting a function.

The limit of the difference quotient, interpreted as the instantaneous rate of change or gradient of the tangent; used for curve sketching, optimisation and kinematics.

The signed area under a curve between limits, computed as an antiderivative evaluated at the bounds; applied to areas between curves and to accumulated change.

A function whose derivative is the given function; because it is determined only up to an additive constant, a boundary condition is needed to fix a particular solution.

A point where the first derivative is zero; classified as maximum, minimum or inflection by the sign change of the derivative or the sign of the second derivative.

The straight line touching a curve at a point with gradient equal to the derivative there; its equation is written using point-slope form with the coordinates of that point.

The line perpendicular to the tangent at a point on a curve, so its gradient is the negative reciprocal of the derivative at that point.

A line that a curve approaches arbitrarily closely without meeting at finite distance; vertical asymptotes arise from undefined points and horizontal ones from limits at infinity.

The value a function's output approaches as the input approaches a specified point or infinity; the foundation of both the derivative and the study of asymptotic behaviour.

A quantity with magnitude and direction, represented by components or by an arrow; in the three-period course it is used for lines, planes and geometric proof in space.

The operation combining two vectors to give a number, equal to the product of their magnitudes and the cosine of the angle between them; zero for perpendicular vectors.

A description of a line or curve using a parameter, such as a fixed point plus a multiple of a direction vector; convenient for intersections and for describing motion.

A number between zero and one expressing the likelihood of an event, computed from equally likely outcomes or from relative frequency, and manipulated with addition and multiplication rules.

The probability of an event given that another has occurred, written as the joint probability divided by the probability of the condition; the basis of independence tests.

The probability-weighted mean of a discrete random variable, obtained by summing each value multiplied by its probability; used to compare strategies and fair games.

The square root of the variance, measuring the typical spread of data about the mean in the original units; reported alongside the mean when summarising a distribution.

A symmetric bell-shaped continuous distribution defined by its mean and standard deviation; probabilities are found by standardising to a z-score and reading cumulative tables or using technology.

A procedure comparing sample data with a null hypothesis by computing a test statistic and its probability, then deciding whether the evidence warrants rejection at a chosen significance level.

A range of plausible values for a population parameter, constructed from a sample estimate plus or minus a margin determined by the standard error and the chosen confidence level.

The oral or written skill of interrogating a document for origin, purpose, value and limitations, and of using its content as evidence within a reasoned argument rather than merely summarising it.

The planned organisation of an answer into introduction with a clear thesis, body paragraphs each making one supported point, and conclusion weighing the argument against the question asked.

A single sentence in the introduction stating the position the answer will defend; it must answer the question directly and be sustained by every subsequent paragraph.