Kyoto Entrance Science key terms

The instantaneous rate at which a function's value changes with respect to its input, defined as the limit of the difference quotient. Geometrically it gives the slope of the tangent line at a point.

The accumulation of a function's values over an interval, computed as a limit of sums of small rectangles. The definite integral measures signed area and reverses differentiation via the fundamental theorem.

The value a function or sequence approaches as its input approaches a specified point or grows without bound. Limits underpin continuity, derivatives, and integrals in calculus.

A function whose value at each point equals the limit of its values nearby, so its graph has no breaks or jumps. Continuity on a closed interval guarantees extreme values and intermediate values.

If a function is continuous on a closed interval, it takes every value between its endpoint values at least once. Used to prove existence of roots and solutions without finding them explicitly.

A sequence in which each term equals the previous term multiplied by a fixed nonzero constant called the common ratio. Its general term is a*r^(n-1), and its partial sums have a closed formula.

A sequence in which each term differs from the previous one by a fixed constant called the common difference. Its general term is linear in the index, and partial sums form a quadratic.

The total of the first n terms of a geometric sequence, a(1-r^n)/(1-r) when r is not 1. When the absolute ratio is below one, the infinite sum converges to a/(1-r).

A number of the form a+bi where a and b are real and i squared equals negative one. Complex numbers add componentwise and multiply by distributing, and can be drawn as points in a plane.

For a complex number written in polar form r(cos θ + i sin θ), raising it to the nth power gives r^n(cos nθ + i sin nθ). Also used to extract roots of complex numbers.

A quantity with both magnitude and direction, represented by an arrow or by components along coordinate axes. Vectors add tip to tail, and their dot product measures alignment.

A scalar obtained from two vectors by multiplying corresponding components and summing, equal to the product of magnitudes times the cosine of the included angle. Zero dot product means perpendicular vectors.

A vector drawn from the origin to a point, whose components are that point's coordinates. Differences of position vectors give displacement vectors between points.

An assignment of probabilities to the possible values of a random variable, described by a table, formula, or graph. Probabilities are nonnegative and sum to one across all outcomes.

The probability-weighted average of a random variable's values, obtained by multiplying each value by its probability and summing. It estimates the long-run mean over many repetitions.

The probability distribution of the number of successes in n independent trials, each succeeding with the same probability p. Its probability mass function involves binomial coefficients.

The net force on an object equals its mass times its acceleration, F=ma. It links force, motion, and mass and is applied along chosen axes, often after drawing a free-body diagram.

A sketch showing one object isolated with arrows for every external force acting on it, such as gravity, normal force, tension, and friction. It is the starting point for writing force equations.

When only conservative forces do work, the sum of kinetic and potential energy stays constant. This lets speed at one height be found from speed at another without tracking forces over time.

A contact force that opposes impending sliding between surfaces at rest, adjusting up to a maximum of the coefficient times the normal force. It prevents motion rather than slowing it.

For a dilute gas, pressure times volume equals the number of moles times the gas constant times absolute temperature, PV=nRT. It relates the macroscopic state variables of a gas.

The amount of substance containing Avogadro's number of particles, about 6.02 times ten to the twenty-third. It converts between particle counts and measurable masses using molar mass.

A bookkeeping charge assigned to an atom in a compound by assuming electrons go to the more electronegative atom. Changes in oxidation number reveal oxidation and reduction in a reaction.

When a system at equilibrium is disturbed by changes in concentration, pressure, or temperature, it shifts in the direction that partly offsets the disturbance. Used to predict how yields respond.

A logarithmic measure of hydrogen ion concentration in a solution, equal to the negative base-ten logarithm of that concentration. Values below seven are acidic and above seven basic at room temperature.

A protein, or occasionally RNA, that speeds a biochemical reaction by lowering its activation energy. Each enzyme typically acts on specific substrates at a region called the active site.

The process by which plants and algae use light energy to convert carbon dioxide and water into organic compounds, releasing oxygen. It occurs in chloroplasts and drives most food chains.

The breakdown of organic molecules, such as glucose, to release usable energy stored in ATP, with oxygen as the final electron acceptor in aerobic cells. It occurs partly in mitochondria.

Division of a cell nucleus producing two daughter nuclei with the same chromosome number as the parent. It supports growth and repair and is distinct from the reduction division of meiosis.

Two successive nuclear divisions that halve the chromosome number and generate genetically varied gametes through crossing over and independent assortment. Fusion of such cells restores the full number.

The theory that Earth's rigid outer shell is divided into plates that move over the underlying mantle, driven by convection and slab pull. Their interactions cause earthquakes, volcanoes, and mountain belts.

Elastic energy traveling through Earth from an earthquake source, including fast compressional P waves and slower shear S waves. Their arrival times reveal the structure of Earth's interior.

The rate at which temperature rises with depth inside Earth, typically about 25 degrees Celsius per kilometer in the crust. It drives heat flow and metamorphism and varies with tectonic setting.

The apparent deflection of moving air or water caused by Earth's rotation, to the right in the Northern Hemisphere and left in the Southern. It shapes global wind belts and ocean currents.

A sentence construction in which the subject receives the action, formed with a form of be plus a past participle, often with by introducing the agent. Common in scientific writing to focus on processes.

A subordinate clause beginning with a relative pronoun such as who, which, or that, modifying a preceding noun. It adds identifying or extra information within a sentence.

A reduced clause built from a present or past participle, such as having finished or written in English, used to compress reason, time, or condition into a phrase rather than a full clause.

A verb form expressing hypothetical, wished, or demanded situations, as in if I were or it is essential that he be present. English marks it mainly in fixed forms and after certain verbs.