UB Concours d'Entrée key terms

Function giving the instantaneous rate of change of another function at each point, computed as the limit of a difference quotient; it measures slope of the tangent line and underlies optimization and motion problems.

Value that a sequence or function approaches as its input approaches a given point or grows without bound; the foundation on which continuity, derivatives and integrals are formally defined.

Accumulated total of a function over an interval, interpreted as signed area under its curve; computed exactly using antiderivatives via the fundamental theorem of calculus.

A function whose derivative equals a given function; every continuous function has infinitely many primitives differing by an additive constant, used to evaluate definite integrals.

Sequence in which each term is obtained by adding a fixed constant to the previous one; its general term is linear in the index and its partial sums grow quadratically.

Sequence in which each term equals the previous term multiplied by a fixed ratio; its behaviour depends on whether that ratio has absolute value below, equal to, or above one.

Probability that an event occurs given that another event is known to have occurred, defined as the joint probability divided by the probability of the conditioning event when that is nonzero.

Weighted average value of a random variable, each outcome weighted by its probability; it describes the long-run mean of repeated independent trials of the same experiment.

Numerical function defined on the outcomes of a random experiment, assigning a real number to each possible result so that probabilities of numerical events can be computed.

Probability distribution counting the number of successes in a fixed number of independent trials, each with the same success probability; specified by two parameters, trial count and success probability.

Property of two events where the occurrence of one does not change the probability of the other, equivalently their joint probability equals the product of their individual probabilities.

Property of a function whose value at each point equals its limit there, so its graph has no breaks; on a closed interval it guarantees bounds and intermediate values.

Result stating that a continuous function on a closed interval attains every value between its endpoint values; used to prove existence of solutions to equations.

Number written in the form a + bi where a and b are real and i squared equals minus one; it can be represented as a point in the plane with modulus and argument.

Non-negative distance from the origin to the point representing a complex number in the plane; it equals the square root of the sum of squares of real and imaginary parts.

Angle, measured from the positive real axis, locating the point that represents a complex number in the plane; it is defined up to addition of full turns.

Rectangular array of numbers arranged in rows and columns, supporting addition and multiplication under dimension constraints; used to encode linear systems and linear transformations compactly.

Scalar assigned to a square matrix that indicates whether the matrix is invertible and measures how the associated linear transformation scales areas or volumes.

Collection of linear equations in several unknowns solved simultaneously; its solution set is described using matrix row reduction and depends on rank and consistency conditions.

Deliberate deviation from ordinary expression used for expressive effect, such as comparison, metaphor, hyperbole or anaphora; identified and interpreted in literary commentary and text analysis.

Figure of speech that transfers meaning by asserting an implicit resemblance between two things without a comparative word, unlike a simile which uses an explicit comparison marker.

Set of words in a text sharing a common semantic theme, such as terms of seafaring or of grief; its identification supports interpretation of tone and subject matter.

Level of language used in a text or utterance, such as formal, standard or familiar, determined by vocabulary, syntax and social context; it shapes tone and characterization.

Voice that tells a narrative, distinct from the author; its position, knowledge and reliability determine focalization and how the reader receives the story's events.

Perspective from which a narrative is presented, ranging from omniscient narration to restricted or external viewpoint; it controls what information the reader can access.

Central claim that a philosophical or argumentative text defends, supported by premises and reasoning; identifying it is the first step in analysing an argument.

Set of premises offered as reasons supporting a conclusion; assessed for validity, meaning the conclusion follows from the premises, and for soundness of those premises.

Reasoning that appears persuasive but is logically flawed, such as attacking a person instead of the claim or begging the question; recognized and named in critical analysis.

Descartes' argument that the very act of doubting proves the existence of a thinking subject; it serves as a first indubitable foundation for knowledge.

Philosophical position holding that knowledge derives from sensory experience rather than innate ideas; associated with thinkers who treat the mind as receiving impressions from observation.

Economic principle stating that, other things equal, quantity demanded of a good falls as its price rises; it explains the downward slope of a demand curve.

Total market value of final goods and services produced within a country's borders during a period; a standard measure of economic output, though it omits unpaid work and inequality.

Sustained rise in the general price level, reducing the purchasing power of money; measured by changes in a consumer price index and often targeted by central banks.

Relation stating that voltage across a conductor equals current through it multiplied by its resistance; valid for ohmic materials at constant temperature.

Electrical arrangement in which components are connected one after another so the same current flows through each, while voltages add across the components.

Electrical arrangement in which components are connected across the same two nodes, so each experiences the same voltage while currents divide among the branches.

Rate at which electrical energy is transferred or dissipated by a component, equal to voltage multiplied by current; measured in watts in the international system.

Process by which green plants, algae and some bacteria use light energy to convert carbon dioxide and water into organic compounds, releasing oxygen as a by-product.

Series of metabolic reactions in which cells break down organic molecules, typically glucose, to release usable energy stored in ATP, consuming oxygen in aerobic forms.

Double-stranded molecule carrying genetic instructions in the sequence of its nucleotide bases; it is replicated before cell division and transcribed into RNA for protein synthesis.

Type of cell division producing two genetically identical daughter cells, used for growth and repair; it proceeds through prophase, metaphase, anaphase and telophase stages.

Green pigment in chloroplasts that absorbs light, mainly in red and blue wavelengths, and transfers the captured energy to the reactions of photosynthesis.

Sentence, usually first in a paragraph, stating the paragraph's main idea and controlling its content; it guides the supporting details that follow and improves coherence.

Concise sentence near the start of an essay that presents the central claim the essay will defend; it should be specific, arguable and preview the line of reasoning.

Quality of a text whose sentences and paragraphs are linked smoothly through connectors, pronouns and consistent terminology, so the reader follows the argument without confusion.

Word in a second language that resembles a word in one's own language but differs in meaning, such as a term that looks familiar yet translates differently; a common source of error.

Constitutional principle dividing state authority among legislative, executive and judicial branches so that each limits the others and no single body holds unchecked power.

Political system in which public authority is itself bound by law, with independent courts able to review official acts and protect individual rights against arbitrary power.

Supreme authority within a state to make and enforce law over its territory, and the corresponding independence of that state from external control in international affairs.

Model of development meeting present needs without compromising the ability of future generations to meet theirs, balancing economic, social and environmental concerns.