Maths & Science Glossary

The area under a curve is the region between the graph and the x-axis, found exactly by definite integration or estimated using the trapezium rule.

The chain rule differentiates a composite function — a function inside another function — by multiplying the derivatives of the outer and inner parts.

Completing the square rewrites a quadratic in the form a(x + p)² + q, revealing the turning point and allowing exact solutions.

A definite integral evaluates an integral between two limits and returns a single numerical value, usually representing signed area.

Differentiation is the process of finding the rate at which one quantity changes with respect to another — the gradient of a curve at a point.

The discriminant, b² − 4ac, tells you how many real roots a quadratic equation has without solving it.

Exponential growth or decay describes a quantity that changes by a fixed percentage in each equal time interval.

Factorising rewrites an expression as a product of brackets or factors — the reverse of expanding.

The gradient of a line measures its steepness — the change in y divided by the change in x between two points.

Integration is the reverse of differentiation: it recovers a function from its rate of change and measures the area under a curve.

A logarithm answers the question 'what power do I raise this base to?' — it is the inverse of exponentiation.

The mean, median and mode are three averages: the arithmetic average, the middle value in order, and the most frequent value.

The normal distribution is a symmetric, bell-shaped continuous probability distribution defined by its mean and standard deviation.

Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain).

The product rule differentiates the product of two functions: differentiate the first times the second, plus the first times the derivative of the second.

Pythagoras' theorem states that in a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides.

The quadratic formula solves any equation of the form ax² + bx + c = 0, including those that will not factorise.

A radian is the angle subtended at the centre of a circle by an arc equal in length to the radius; 2π radians make a full turn.

The second derivative is the derivative of the derivative — it measures how fast the gradient itself is changing, and hence the concavity of a curve.

Standard deviation measures the average spread of data values about the mean — a small value means tightly clustered data.

A stationary point is a point on a curve where the gradient is zero — a maximum, a minimum or a point of inflection.

The trapezium rule estimates the area under a curve by dividing it into strips of equal width and treating each strip as a trapezium.

Trigonometry relates the angles of a triangle to the lengths of its sides using the sine, cosine and tangent ratios.

A vector is a quantity with both magnitude and direction, such as displacement, velocity or force.

Acceleration is the rate of change of velocity with time, measured in metres per second squared.

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred between stores.

Electric current is the rate of flow of electric charge, measured in amperes — one ampere is one coulomb per second.

Frequency is the number of complete waves or oscillations passing a point each second, measured in hertz.

Kinetic energy is the energy an object has because of its motion, equal to half its mass times its velocity squared.

The moment of a force is its turning effect about a pivot, equal to the force multiplied by the perpendicular distance to the pivot.

Momentum is the product of an object's mass and velocity, and it is conserved in any collision or explosion with no external force.

Newton's second law states that the resultant force on an object equals its mass multiplied by its acceleration.

Ohm's law states that the current through a metallic conductor is directly proportional to the potential difference across it, provided temperature stays constant.

Refraction is the change in direction of a wave as it crosses a boundary between media, caused by a change in its speed.

Resistance measures how strongly a component opposes the flow of electric current, and is defined as potential difference divided by current.

The resultant force is the single force that has the same effect as all the forces acting on an object combined.

Wave speed is how fast a wave transfers energy through a medium, equal to frequency multiplied by wavelength.

Work done is the energy transferred when a force moves an object through a distance in the direction of the force.

A catalyst speeds up a reaction by providing an alternative pathway with a lower activation energy, without being used up itself.

Concentration is the amount of solute dissolved in a given volume of solution, usually in moles per cubic decimetre.

A covalent bond is a shared pair of electrons between two non-metal atoms, held together by attraction to both nuclei.

A dynamic equilibrium is reached in a closed system when the forward and reverse reactions occur at the same rate, so concentrations stay constant.

Electronegativity is the ability of an atom to attract the shared pair of electrons in a covalent bond towards itself.

An ionic bond is the strong electrostatic attraction between oppositely charged ions formed when electrons transfer from a metal to a non-metal.

The limiting reagent is the reactant that is fully used up first and therefore determines the maximum yield of product.

Molar mass is the mass of one mole of a substance in grams, numerically equal to its relative formula mass.

A mole is the amount of substance containing 6.02 × 10²³ particles — the chemist's counting unit that links mass to number of particles.

Percentage yield compares the mass of product actually obtained with the theoretical maximum predicted by the balanced equation.

pH is a logarithmic measure of hydrogen ion concentration: the lower the pH, the more acidic the solution.

The rate of reaction is how quickly reactants are used up or products are formed, usually measured as a change in amount per unit time.

A titration is a quantitative technique that finds an unknown concentration by reacting it with a solution of known concentration until the end point.

Active transport moves substances against a concentration gradient using carrier proteins and energy from ATP.

Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration, down a concentration gradient.

DNA is the double-helix molecule that stores genetic information as a sequence of four bases along a sugar-phosphate backbone.

An enzyme is a biological catalyst — a protein that speeds up a specific reaction by lowering its activation energy.

Homeostasis is the maintenance of a constant internal environment despite changes in external conditions.

Mitosis is nuclear division that produces two genetically identical daughter cells, used for growth, repair and asexual reproduction.

Natural selection is the process by which organisms with advantageous inherited characteristics are more likely to survive, reproduce and pass those alleles on.

Osmosis is the net movement of water molecules from a dilute solution to a concentrated one through a partially permeable membrane.

Photosynthesis is the process by which plants use light energy to convert carbon dioxide and water into glucose and oxygen.

Respiration is the enzyme-controlled release of energy from glucose in every living cell, transferring it to ATP.