AP POLYCET key terms

An equation of the form ax² + bx + c = 0, where a is not zero. Its highest power of the variable is two, and it has at most two real roots.

The quantity b² − 4ac computed from the quadratic ax² + bx + c = 0. Its sign tells whether the roots are real and distinct, real and equal, or not real.

A list of numbers in which each term after the first is obtained by adding a fixed constant, called the common difference, to the previous term, for example 3, 7, 11, 15.

A sequence in which each term after the first is found by multiplying the previous term by a fixed non-zero number called the common ratio, such as 2, 6, 18, 54.

For an acute angle in a right triangle, the ratio of two of its sides, named sine, cosine, tangent, cosecant, secant and cotangent, each fixed for that angle whatever the triangle size.

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides; conversely, this relation proves that a triangle is right-angled.

A straight line that meets a circle at exactly one point, called the point of contact, and is perpendicular to the radius drawn to that point.

Triangles whose corresponding angles are equal and whose corresponding sides are in the same ratio; their areas are in the ratio of the squares of corresponding sides.

The middle value of a data set arranged in ascending or descending order; if the number of observations is even, it is the average of the two middle values.

The number of outcomes favourable to the event divided by the total number of equally likely outcomes in the sample space; it always lies between zero and one.

For a non-vertical straight line, the rise in y divided by the run in x between any two points on it; it measures steepness and equals the tangent of the angle with the x-axis.

The space occupied by a cylinder, found by multiplying the area of its circular base by its height, that is πr²h, where r is the radius of the base.

The tendency of a body to resist any change in its state of rest or of uniform motion in a straight line; it depends on the mass of the body.

The rate of change of momentum of a body is directly proportional to the applied net force and takes place in the direction of that force; for constant mass it gives F = ma.

The rate at which velocity changes with time, measured in metres per second squared; it is positive when speed increases along the direction of motion and negative when speed decreases.

Work is done when a force moves a body through a distance; it is the product of the force and the displacement along the force, measured in joules.

The rate at which work is done or energy is transferred, equal to work divided by time and measured in watts, where one watt is one joule per second.

The energy a body possesses because of its motion, equal to half its mass multiplied by the square of its speed, and measured in joules.

At constant temperature, the current through a metallic conductor is directly proportional to the potential difference across its ends, so V = IR, where R is the resistance.

The rate at which electrical energy is consumed or delivered in a circuit, equal to voltage times current and also to I²R or V²/R, measured in watts.

The ratio of the speed of light in vacuum to its speed in a medium, or equivalently the sine of the angle of incidence divided by the sine of the angle of refraction.

The distance between the pole of a spherical mirror, or the optical centre of a lens, and its principal focus, measured along the principal axis.

A sound heard again after reflection from a distant hard surface; it is heard separately only when the reflected sound reaches the listener at least one-tenth of a second after the original.

A body wholly or partly immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.

A rule for the direction of force on a current-carrying conductor in a magnetic field: with forefinger along the field, middle finger along the current, the stretched thumb gives the force direction.

The number of protons in the nucleus of an atom, denoted by Z; it fixes the identity of the element and equals the number of electrons in a neutral atom.

The total number of protons and neutrons present in the nucleus of an atom, denoted by A; it is a whole number and is close to the atomic mass.

Atoms of the same element that have the same atomic number but different mass numbers because they contain different numbers of neutrons, for example chlorine-35 and chlorine-37.

The combining capacity of an element, equal to the number of hydrogen atoms or twice the number of oxygen atoms with which one atom of it combines, or the electrons lost, gained or shared.

The amount of a substance that contains as many particles as there are atoms in exactly 12 grams of carbon-12, that is 6.022 × 10²³ particles.

The number of particles present in one mole of any substance, approximately 6.022 × 10²³ per mole, used to convert between particle counts and amounts of substance.

A number from 0 to 14 measuring the acidity or alkalinity of an aqueous solution; below 7 is acidic, 7 is neutral and above 7 is basic. It equals minus log of hydrogen ion concentration.

The reaction between an acid and a base that produces a salt and water, for example hydrochloric acid with sodium hydroxide giving sodium chloride and water.

A process in which a substance loses electrons, or gains oxygen, or loses hydrogen; the substance that brings it about is called an oxidising agent.

The electrostatic attraction that holds oppositely charged ions together in a compound, formed when a metal transfers electrons to a non-metal, as in sodium chloride.

A family of organic compounds with the same general formula and similar chemical properties, in which successive members differ by one CH₂ unit, such as the alkanes.

An atom or group of atoms attached to a carbon chain that gives an organic compound its characteristic chemical properties, for example the hydroxyl or carboxyl group.

The decomposition of an electrolyte by passing direct electric current through its solution or melt, with oxidation occurring at the anode and reduction at the cathode.