AEEE key terms

The instantaneous rate at which a function changes with respect to its variable, defined as the limit of the difference quotient; it gives the slope of the tangent line at a point.

The value a function approaches as its input approaches some point, even if the function is not defined there; the foundation on which derivatives and integrals are built.

A quantity representing accumulated change, computed as the limit of a sum of small products; the definite integral gives signed area under a curve and reverses differentiation.

A property of a function that has no breaks, jumps, or holes at a point: the function's value there equals its limit from both sides.

A single number computed from a square matrix that indicates whether the matrix is invertible and scales volumes under the associated linear transformation.

A rectangular array of numbers arranged in rows and columns, used to represent linear transformations and to solve systems of linear equations compactly.

A scalar by which an eigenvector is stretched when a linear transformation is applied; found by solving the characteristic equation det(A − λI) = 0.

An ordered arrangement of a set of items, where changing the order produces a different arrangement; counted as n! or nPr depending on how many are chosen.

A selection of items from a group in which order does not matter; counted by the binomial coefficient nCr = n!/[r!(n−r)!].

A number between 0 and 1 expressing how likely an event is, computed as favourable outcomes divided by total equally likely outcomes in simple settings.

A number of the form a + bi, where a and b are real and i² = −1; it extends the real line to a plane and appears in roots of polynomial equations.

For a complex number a + bi, the value a − bi; multiplying a number by its conjugate gives the real quantity a² + b², useful for division.

A sequence in which each term differs from the previous one by a fixed constant called the common difference, such as 3, 7, 11, 15.

A sequence in which each term is obtained by multiplying the previous term by a fixed constant ratio, such as 2, 6, 18, 54.

A vector quantity describing the rate of change of displacement with time, possessing both magnitude (speed) and direction.

The rate at which velocity changes with time; because velocity is a vector, acceleration arises from changes in speed, direction, or both.

The straight-line change in position from an initial point to a final point, including direction; it differs from distance, which is the total path length travelled.

The net force on a body equals the product of its mass and acceleration (F = ma); it links force to how motion changes.

The product of a body's mass and velocity, a vector quantity; in an isolated system the total momentum before and after a collision is conserved.

The energy a body possesses due to its motion, equal to one-half its mass times the square of its speed; it is a scalar measured in joules.

The energy transferred when a force moves a body through a displacement, computed as the force component along the displacement multiplied by that displacement.

The rate at which work is done or energy is transferred, equal to work divided by time and measured in watts.

For a conductor at constant temperature, the current through it is directly proportional to the potential difference across it; the constant of proportionality is resistance.

The opposition a component offers to the flow of electric current, equal to voltage divided by current and measured in ohms.

The rate of flow of electric charge past a point in a circuit, measured in amperes; conventionally taken in the direction of positive charge flow.

The ratio of the speed of light in vacuum to its speed in a medium, governing how much a light ray bends at the boundary between two media.

Complete reflection of light back into a denser medium when it strikes a boundary at an angle greater than the critical angle.

The amount of substance containing Avogadro's number (about 6.022 × 10²³) of particles; it connects particle counts to measurable masses.

The mass of one mole of a substance in grams per mole, numerically equal to its formula mass in atomic mass units.

The number of elementary particles in one mole of a substance, approximately 6.022 × 10²³ per mole.

A logarithmic scale from 0 to 14 measuring hydrogen-ion concentration: pH = −log[H⁺]; values below 7 are acidic and above 7 are basic.

A substance that donates protons (Brønsted–Lowry) or accepts electron pairs (Lewis); aqueous acids increase hydrogen-ion concentration and turn blue litmus red.

A solution that resists large pH changes when small amounts of acid or base are added, typically made from a weak acid and its conjugate base.

Loss of electrons by a species, accompanied by an increase in oxidation number; it always occurs together with reduction in a redox reaction.

Gain of electrons by a species, accompanied by a decrease in oxidation number; it always occurs together with oxidation.

One of two or more compounds with the same molecular formula but different arrangements of atoms, giving different physical or chemical properties.

A specific group of atoms within a molecule, such as hydroxyl or carboxyl, that determines the molecule's characteristic chemical reactions.

A fraction expressed out of one hundred, found by dividing the part by the whole and multiplying by 100; widely used in profit, loss, and data problems.

A comparison of two or more quantities showing how many times one contains another, written as a : b and often simplified to lowest whole numbers.

The sum of a set of values divided by the number of values; also called the arithmetic mean, it summarises a data set with one number.

A word whose meaning is opposite to that of another word, such as 'scarce' for 'abundant'; antonym questions test vocabulary range and precision.

A word that has the same or nearly the same meaning as another word, such as 'rapid' for 'swift'; synonym questions test vocabulary range.

The grammatical rule that a verb must match its subject in number and person, so a singular subject takes a singular verb form.

A word such as 'in', 'on', or 'between' that links a noun or pronoun to another part of the sentence, usually showing place, time, or direction.