CG PET key terms

The shortest straight-line distance from an initial position to a final position, together with its direction. It is a vector quantity and may be smaller than the total path length travelled.

The rate of change of displacement with respect to time. Because displacement is a vector, velocity has both magnitude and direction, and average velocity differs from average speed.

The rate at which velocity changes with time, including changes in direction. For motion under gravity near Earth's surface it is approximately constant at about 9.8 metres per second squared downward.

Two-dimensional motion of an object launched into the air and then acted on only by gravity. Horizontal and vertical motions are treated independently; the horizontal velocity stays constant while the vertical velocity changes uniformly.

The net force on a body equals its mass multiplied by its acceleration, expressed as F = ma. Force and acceleration point in the same direction, and the law links cause (force) with effect (acceleration).

The tendency of a body to resist any change in its state of rest or uniform motion. It depends only on mass, so a more massive object needs a larger net force to produce the same acceleration.

A contact force opposing relative sliding or the tendency to slide between surfaces. Static friction adjusts up to a maximum value, while kinetic friction is roughly constant and slightly smaller.

The product of a body's mass and its velocity, a vector quantity measured in kilogram metres per second. In an isolated system the total momentum before and after a collision remains constant.

The energy transferred to or from an object when a force acts through a displacement. It equals the product of force, displacement and the cosine of the angle between them, and is measured in joules.

The energy a body possesses because of its motion, equal to one half of its mass times the square of its speed. It is a scalar quantity and is always zero for a body at rest.

The principle that energy cannot be created or destroyed, only converted between forms or transferred between bodies. In mechanical systems without friction, the sum of kinetic and potential energy stays constant.

The rate at which work is done or energy is transferred, measured in watts, where one watt equals one joule per second. Average power is total work divided by the time taken.

Oscillation in which the restoring force is directly proportional to displacement from equilibrium and directed toward it. The motion is sinusoidal, and the period is independent of amplitude.

The number of complete oscillations or wave cycles passing a point each second, measured in hertz. It equals the reciprocal of the period and is set by the source, not by the medium.

The distance between two consecutive points in phase on a wave, such as two adjacent crests. For a wave travelling at constant speed, wavelength equals speed divided by frequency.

The change in direction of a wave as it passes from one medium into another where its speed differs. Light bending toward the normal on entering a denser medium is a familiar example.

A scalar is fully described by magnitude alone, such as mass or temperature. A vector also requires direction, such as force or velocity, and vectors add by geometric rules rather than simple arithmetic.

The amount of substance containing exactly 6.022 times ten to the twenty-third elementary entities, whether atoms, molecules or ions. It links the microscopic count of particles to measurable macroscopic mass.

The number of constituent particles in one mole of a substance, approximately 6.022 times ten to the twenty-third per mole. It allows conversion between particle count and amount in moles.

The mass of one mole of a substance, expressed in grams per mole and numerically equal to its relative molecular mass. It converts between mass in grams and amount in moles.

The calculation of reactant and product quantities from a balanced chemical equation using mole ratios. Coefficients in the equation give the proportions in which substances react and are formed.

The reactant that is completely consumed first and therefore determines the maximum amount of product formed. Other reactants are present in excess and remain partly unreacted.

The concentration of a solution expressed as moles of solute per litre of solution, with units mol per litre. It changes slightly with temperature because solution volume expands on heating.

A logarithmic scale from 0 to 14 measuring hydrogen ion concentration, defined as the negative logarithm to base ten of that concentration in moles per litre. Values below 7 are acidic and above 7 are basic.

An acid donates protons or accepts electron pairs, while a base accepts protons or donates electron pairs. In water, acids raise hydrogen ion concentration and bases raise hydroxide ion concentration.

The reaction between an acid and a base producing a salt and usually water. The hydrogen ions of the acid combine with the hydroxide ions of the base in a proton transfer.

Oxidation is loss of electrons and reduction is gain of electrons; the two always occur together. Changes in oxidation number reveal which species is oxidised and which is reduced in a reaction.

The decomposition of a compound by passing direct electric current through it in molten or dissolved form. Positive ions migrate to the cathode and negative ions to the anode, where discharge occurs.

An arrangement of elements in order of increasing atomic number, organised into groups with similar chemical properties and periods across which properties change gradually. Position predicts reactivity and bonding behaviour.

A measure of how strongly an atom attracts the shared electrons of a covalent bond. It generally increases across a period and decreases down a group, and large differences favour ionic bonding.

The electrostatic attraction between oppositely charged ions formed when one atom transfers electrons to another. Such compounds usually have high melting points and conduct electricity when molten or dissolved.

A bond formed when two atoms share one or more pairs of electrons. It is typically strong and directional, giving molecules definite shapes, and is common between non-metal atoms.

One of two or more compounds with the same molecular formula but different arrangements of atoms and therefore different properties. Structural isomers differ in connectivity; stereoisomers differ only in spatial arrangement.

A specific group of atoms within a molecule that gives the compound its characteristic chemical reactions. Examples include hydroxyl, carboxyl, carbonyl and amino groups in organic molecules.

A family of organic compounds with the same functional group and general formula, in which successive members differ by one carbon atom and two hydrogen atoms. Members show gradually changing physical properties.

The instantaneous rate of change of a function with respect to a variable, interpreted as the slope of the tangent to its graph. It is defined as a limit of difference quotients.

The value a function approaches as its input approaches a specified point, whether or not the function is defined there. Limits underpin the definitions of continuity, derivative and integral.

A property of a function whose value at a point equals the limit approached there, with no jumps, holes or breaks. A function continuous on a closed interval attains maximum and minimum values there.

The accumulated total of a function over an interval, interpreted as signed area under its graph. The definite integral is defined as a limit of sums and is evaluated using antiderivatives.

A rectangular array of numbers arranged in rows and columns, written with brackets. Matrices can be added, multiplied by scalars, and multiplied together when their dimensions are compatible.

A single number computed from a square matrix that indicates whether the matrix is invertible. A zero determinant means the matrix has no inverse and its rows are linearly dependent.

The matrix which, when multiplied by a given square matrix, yields the identity matrix. It exists only when the determinant is nonzero and is used to solve systems of linear equations.

A permutation counts ordered arrangements of selected items, while a combination counts unordered selections. The choice depends on whether the order of chosen items matters.

A number between zero and one expressing how likely an event is, computed for equally likely outcomes as favourable outcomes divided by total outcomes. Probabilities of mutually exclusive events add.

A formula expanding a binomial raised to a positive integer power as a sum of terms involving binomial coefficients. Each term contains powers of both parts whose exponents sum to the power.

A sequence in which each term after the first is obtained by adding a fixed constant called the common difference. The nth term is linear in n and the sum of terms is quadratic in n.

A sequence in which each term after the first is obtained by multiplying by a fixed nonzero constant called the common ratio. An infinite progression converges in sum only when that ratio is smaller than one in magnitude.

The sum of the terms of a sequence, written with sigma notation when a general term is known. Finite series have a definite total, while infinite series may converge to a limit or diverge.

A number of the form a plus bi, where a and b are real and i squared equals minus one. It can be represented as a point in a plane and written in modulus-argument form.

The modulus of a complex number is its distance from the origin in the complex plane, and the argument is the angle its position vector makes with the positive real axis.

An equation of the form ax squared plus bx plus c equals zero with a nonzero. Its roots are found by factorising or the quadratic formula, and the discriminant reveals their nature.

The quantity b squared minus four ac in a quadratic equation. Its sign shows whether the roots are real and distinct, real and equal, or a complex conjugate pair.

A ratio of two sides of a right-angled triangle, such as sine, cosine or tangent, defined relative to a chosen acute angle. These ratios extend to all angles through the unit circle.

An equation involving trigonometric functions that holds for every value of the variable where both sides are defined. Familiar examples relate sine and cosine or express double angles.

The manipulation of quantities having magnitude and direction, using addition, scalar multiplication, dot products and cross products. Dot products give a scalar; cross products of two vectors give another vector.