TG POLYCET key terms

An equation of the form ax² + bx + c = 0 where a is not zero. Its solutions, called roots, are found using the quadratic formula or by factorisation.

The quantity b² − 4ac in a quadratic equation. Its sign tells whether the roots are real and distinct, real and equal, or not real.

The values of the variable that make an equation true. For a polynomial, a root makes the polynomial equal to zero when substituted.

A sequence in which each term after the first is obtained by adding a fixed number, the common difference, to the previous term.

The constant amount added to each term of an arithmetic progression to get the next term; it equals any term minus the one before it.

A sequence in which each term after the first is obtained by multiplying the previous term by a fixed non-zero number called the common ratio.

The fixed multiplier between consecutive terms of a geometric progression. It is found by dividing any term by the term just before it.

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.

Triangles that are exactly equal in shape and size, so all corresponding sides and angles match. Standard tests include SSS, SAS, ASA and RHS.

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It is used to find unknown side lengths.

Ratios of pairs of sides in a right-angled triangle, namely sine, cosine and tangent, defined relative to a chosen acute angle. Their reciprocals are cosecant, secant and cotangent.

A number from 0 to 1 giving the chance that an event occurs, calculated as the number of favourable outcomes divided by the total number of equally likely outcomes.

The event that a given event does not happen. The probabilities of an event and its complement always add up to one.

An average computed from class intervals by multiplying each class mark by its frequency, summing these products, and dividing by the total frequency.

The middle value of an ordered data set, found for grouped data using the cumulative frequency and a formula based on the median class.

The value or class interval that occurs most often in a data set. A data set may have one mode, several modes, or none.

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; commonly written F = ma.

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

The product of a body's mass and its velocity, a vector quantity measured in kilogram metre per second. Total momentum is conserved in an isolated system.

The net work done on a body equals the change in its kinetic energy. It links force and displacement with changes in speed.

Energy can neither be created nor destroyed, only converted from one form to another. In a closed system the total energy remains constant.

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

The opposition a conductor offers to the flow of electric current, measured in ohms. It depends on material, length, area of cross-section and temperature.

Ways of connecting components. In series the current is the same and resistances add; in parallel the voltage is the same and reciprocals of resistance add.

The bending of light as it passes from one transparent medium to another because its speed changes. It is governed by Snell's law.

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

A transparent refracting device with curved surfaces that converges or diverges light to form an image. Its power is the reciprocal of focal length in metres.

An arrangement of elements in order of increasing atomic number, grouped so that elements with similar chemical properties fall in the same vertical column.

The number of protons in the nucleus of an atom, which identifies the element and equals the number of electrons in a neutral atom.

One of two or more atoms of the same element that have the same number of protons but different numbers of neutrons, giving different mass numbers.

A regular variation in properties such as atomic radius, ionisation energy or electronegativity as one moves across a period or down a group of the periodic table.

A measure of how strongly an atom attracts the shared pair of electrons in a covalent bond. It generally increases across a period and decreases down a group.

A chemical bond formed when two atoms share one or more pairs of electrons. It is typical between non-metals and can be single, double or triple.

The strong electrostatic attraction between oppositely charged ions formed when one atom transfers electrons to another, typically between a metal and a non-metal.

A scale from 0 to 14 expressing the acidity or alkalinity of an aqueous solution, based on hydrogen ion concentration; 7 is neutral at room temperature.

A substance that releases hydrogen ions in water, turns blue litmus red, and reacts with bases to form salt and water.

A substance that accepts hydrogen ions or releases hydroxide ions in water, turns red litmus blue, and neutralises acids to form salt and water.

A family of organic compounds with the same general formula and similar chemical properties, where successive members differ by one CH₂ unit.

An atom or group of atoms within a molecule that determines its characteristic chemical reactions, such as the hydroxyl group in alcohols.

The process by which green plants use light energy, carbon dioxide and water to make glucose and release oxygen, mainly in chloroplasts containing chlorophyll.

The green pigment in chloroplasts that absorbs light energy for photosynthesis. It absorbs mainly red and blue light and reflects green light.

The breakdown of glucose in cells to release energy, with or without oxygen, producing carbon dioxide and water in aerobic respiration.

A type of cell division producing two daughter cells with the same chromosome number as the parent cell; it is used for growth and repair.

A reduction division that produces four cells, each with half the chromosome number of the parent cell, forming gametes and creating genetic variation.

The genetic makeup of an organism for a particular characteristic, described by the alleles it carries, such as homozygous or heterozygous combinations.

The observable characteristics of an organism resulting from its genotype interacting with the environment, such as flower colour or seed shape.

The movement of blood through the heart, arteries, capillaries and veins, delivering oxygen and nutrients to tissues and removing waste products.

The removal of metabolic waste products from the body, such as urea and carbon dioxide, mainly by the kidneys and lungs.