ENP Alger Access Contest key terms

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

The value a function or sequence approaches as its input or index approaches a specified point, regardless of whether the function actually attains that value there.

A quantity representing accumulated change, defined as the limit of sums of many small contributions; the definite integral gives signed area under a curve over an interval.

A differentiation rule for composite functions: the derivative of f(g(x)) equals f'(g(x)) multiplied by g'(x), allowing derivatives of nested expressions to be computed step by step.

A mathematical object having both magnitude and direction, often written as an ordered list of components; vectors can be added and scaled by numbers.

An operation on two vectors producing a number equal to the product of their magnitudes and the cosine of the angle between them; it is zero when the vectors are perpendicular.

An operation on two three-dimensional vectors producing a new vector perpendicular to both, with magnitude equal to the product of their magnitudes times the sine of the angle between them.

A rectangular array of numbers arranged in rows and columns, used to represent linear transformations and to solve systems of linear equations through operations such as row reduction.

A number computed from a square matrix that indicates whether the matrix is invertible; it is nonzero exactly when the associated linear system has a unique solution.

A number between zero and one expressing how likely an event is, defined for equally likely outcomes as the count of favorable outcomes divided by the total count of outcomes.

The probability that an event occurs given that another event is known to have occurred, computed as the probability of both events divided by the probability of the given event.

The long-run average of a random variable, obtained by multiplying each possible value by its probability and summing these products over all outcomes.

The net force acting on a body equals its mass multiplied by its acceleration, written F = ma; it links force, mass, and motion for bodies of constant mass.

The rate at which velocity changes with time, including changes in speed, direction, or both; its SI unit is the metre per second squared.

A vector quantity giving the rate of change of position with time; unlike speed, it carries direction, so a body moving in a circle at constant speed still changes velocity.

The product of a body's mass and its velocity, a vector quantity conserved in any isolated system where no external net force acts.

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

Energy stored in a system because of the relative positions of its parts, such as a raised mass in a gravitational field or a stretched spring.

Energy transferred to or from a body by a force acting through a displacement, computed as the product of force and displacement along the force direction; its unit is the joule.

A region in which a charged body experiences a force; the field at a point equals the force per unit positive charge placed there, and its direction points away from positive charge.

The electric potential energy per unit positive charge at a point in an electric field; the difference in this quantity between two points drives current through a conductor.

The electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance separating them.

The SI amount-of-substance unit, defined as containing exactly 6.02214076 × 10^23 elementary entities; it links the mass of a sample to the number of particles it contains.

The mass of one mole of a substance, expressed in grams per mole; numerically it equals the relative atomic or molecular mass of the substance.

The number of elementary entities in one mole, approximately 6.022 × 10^23 per mole, used to convert between particle counts and amounts of substance.

The calculation of quantities of reactants and products in a chemical reaction using the ratios given by the balanced equation and the mole concept.

The reactant that is completely consumed first in a reaction, thereby determining the maximum amount of product that can be formed from the given quantities.

A logarithmic scale of acidity defined as the negative base-ten logarithm of hydrogen ion concentration in mol/L; values below 7 are acidic and above 7 are basic at room temperature.

A substance that donates a proton to another species or accepts an electron pair; in water it increases the hydrogen ion concentration and lowers the pH.

A substance that accepts a proton from another species or donates an electron pair; in water it increases the hydroxide ion concentration and raises the pH.

The loss of electrons by a species during a redox reaction, accompanied by an increase in its oxidation number and occurring together with a reduction.

The gain of electrons by a species during a redox reaction, accompanied by a decrease in its oxidation number and occurring together with an oxidation.

A substance that increases the rate of a reaction by providing an alternative pathway of lower activation energy, without being consumed in the overall process.

The minimum energy that reacting particles must possess for a collision to lead to product formation; it appears as a barrier on a reaction energy profile.

The state of a reversible reaction in which forward and reverse rates are equal, so concentrations of reactants and products remain constant over time.

A protein that acts as a biological catalyst, speeding up a specific reaction by binding its substrate at an active site and lowering the activation energy.

A type of cell division producing two genetically identical daughter cells with the same chromosome number as the parent, used for growth and repair.

A reduction division producing four daughter cells each with half the chromosome number of the parent, generating genetic variation through crossing over and independent assortment.

A threadlike structure of DNA and associated proteins that carries genes; human body cells normally contain 46 chromosomes arranged in 23 pairs.

One of the alternative versions of a gene at a given locus; an individual inherits two alleles, one from each parent, which may be dominant or recessive.

The particular combination of alleles an organism carries for a gene or set of genes, which together with environmental effects determines the observable traits.

The observable characteristics of an organism, arising from the interaction between its genotype and the environment in which it develops.

The process by which green plants, algae, and some bacteria use light energy to convert carbon dioxide and water into organic compounds, releasing oxygen as a by-product.

The set of metabolic reactions in cells that release energy from organic molecules, typically using oxygen and producing carbon dioxide and water.

The maintenance of a stable internal environment within narrow limits despite changes in external conditions, achieved through feedback mechanisms such as temperature regulation.

A testable, falsifiable statement proposed as a possible explanation for an observation, which must be checked against evidence rather than accepted by assumption.

The factor that an experimenter deliberately changes or selects in an experiment, in order to observe whether and how the dependent variable responds.

The factor that is measured or observed in an experiment, expected to change in response to manipulation of the independent variable.

The comparison group in an experiment that does not receive the treatment being tested, allowing observed effects to be attributed to the treatment rather than other factors.

A statistical relationship in which two variables tend to vary together; it does not by itself establish that one variable causes the other.

A statistical judgement that an observed result is unlikely to have arisen by chance alone under the assumed null hypothesis, usually assessed against a chosen probability threshold.

Producing an approximate value for a quantity by rounding, using known reference values, or applying proportional reasoning, then checking the result for plausibility.

Changing a measured quantity from one unit to another by multiplying by a ratio equal to one, such as 1000 metres per kilometre, so the value is unchanged.

A rough scale of a quantity expressed as the nearest power of ten, useful for quick comparison and for judging whether a computed answer is reasonable.