Kumamoto Entrance Science key terms

The value a function or sequence approaches as its input or index gets arbitrarily close to a target. In Japanese Mathematics III it underpins differentiation and integration, and you must often distinguish one-sided limits.

The instantaneous rate of change of a function at one point, defined as the limit of the difference quotient. Geometrically it is the slope of the tangent line at that point.

A straight line touching a curve at a point with the same slope as the curve there. Its equation uses the derivative evaluated at that point, often written y minus f(a) equals f prime of a times x minus a.

The limit of a sum of rectangular areas over an interval, giving signed area under a curve. It is computed using an antiderivative evaluated at the upper and lower bounds and subtracted.

A function whose derivative equals a given function. Any two antiderivatives of the same function differ only by a constant, which is why indefinite integrals carry an arbitrary constant.

A technique that rewrites an integral in a new variable to simplify it. You must also transform the differential and, for definite integrals, change the limits of integration accordingly.

A rule derived from the product rule that integrates a product of two functions by trading one factor's derivative for the other's integral. Choosing which factor to differentiate is the key skill.

An equation expressing a sequence term in terms of earlier terms. Solving it means finding an explicit formula, often by guessing a shifted geometric form or using characteristic equations.

A proof method for statements about all natural numbers: verify the base case, assume the statement for n equals k, then prove it for k plus one. Both steps are required for full credit.

The number of ways an event can occur, computed with permutations when order matters and combinations when it does not. Distinguishing ordered from unordered selection is the central skill.

A number from zero to one measuring how likely an event is, often as favorable outcomes divided by total equally likely outcomes. Conditional probability and independence are frequently tested extensions.

A quantity with both magnitude and direction, represented by components or arrows. In Mathematics B you use dot products, position vectors, and vector equations of lines and planes.

A scalar formed from two vectors, equal to the product of their magnitudes and the cosine of the angle between them. It is zero exactly when the vectors are perpendicular.

A coordinate plane where a complex number a plus bi is plotted at point (a, b). Multiplication by i rotates a point ninety degrees, and modulus and argument describe polar position.

The rule that raising a complex number in polar form to a power multiplies its argument by that power and raises its modulus to that power. It simplifies powers and roots of complex numbers.

Newton's second law written as mass times acceleration equals net force. Solving mechanics problems usually begins by drawing a free-body diagram and resolving forces along chosen axes.

When only conservative forces do work, the sum of kinetic and potential energy stays constant. It converts otherwise difficult force-and-time problems into simple energy bookkeeping.

The total momentum of a system stays constant when no external force acts on it. It is essential for collisions and explosions, where internal forces cancel in pairs.

The ratio of relative separation speed to relative approach speed for two colliding bodies. A value of one means perfectly elastic, zero means perfectly inelastic, and between means partially elastic.

Oscillation where restoring force is proportional to displacement and directed toward equilibrium. Displacement follows a sine curve, and period depends on mass and the spring or restoring constant.

When two waves meet at a point, the resulting displacement is the sum of their individual displacements. This explains interference, standing waves, and beats between close frequencies.

The change in observed frequency when a wave source and observer move relative to each other. Approaching raises observed frequency, and receding lowers it, according to relative speed.

When light travels from a denser to a less dense medium beyond the critical angle, no light refracts out and all reflects internally. The critical angle satisfies sine of it equals the index ratio.

The force per unit positive charge at a point in space, a vector quantity. Field lines point away from positive charge and toward negative charge, and the field is uniform between parallel plates.

The electric potential energy per unit positive charge at a point, measured relative to a chosen zero. Charge moves spontaneously from higher to lower potential, and potential difference drives current.

Two rules for circuits: current into a junction equals current out, and the sum of potential changes around any closed loop is zero. They solve multi-loop circuits with several batteries.

A changing magnetic flux through a circuit induces an electromotive force. Lenz's law says the induced current opposes the change that produced it, which determines the current's direction.

The amount of substance containing Avogadro's number of particles, about 6.02 times ten to the twenty-third. It links mass, particle count, and gas volume in stoichiometric calculations.

The number of moles of solute per liter of solution, written mol/L. It is used in titration calculations and dilution problems, where moles of solute stay constant on dilution.

A procedure adding a solution of known concentration to a measured volume of unknown until neutralization. At the equivalence point, moles of hydrogen ion equal moles of hydroxide ion.

A logarithmic scale of hydrogen ion concentration, defined as the negative base-ten logarithm of that concentration. A change of one unit means a tenfold change in acidity.

A reaction in which electrons transfer between species: one is oxidized, losing electrons, and another is reduced, gaining them. Oxidation numbers track the electron shift.

Using an external voltage to drive a nonspontaneous redox reaction in an electrolyte. The amount of substance deposited or released is proportional to the charge passed, per Faraday's law.

A reversible reaction's state where forward and reverse rates are equal, so concentrations stay constant though reactions continue. The equilibrium constant expresses the ratio of product to reactant concentrations.

When a system at equilibrium is disturbed, it shifts in the direction that counteracts the disturbance. Changing concentration, pressure, or temperature shifts equilibrium predictably.

An atom or group of atoms that gives an organic molecule its characteristic reactions, such as hydroxyl, carboxyl, aldehyde, or amino groups. Identifying it predicts properties and reaction products.

Molecules with the same molecular formula but different arrangements of atoms, giving different properties. Structural, geometric, and optical isomerism are the main categories tested.

A membrane-bound or structurally distinct part of a cell with a specific function, such as mitochondrion, chloroplast, or ribosome. Comparing which organelles appear in plant and animal cells is a common question.

Prokaryotic cells lack a nucleus and membrane-bound organelles, while eukaryotic cells have both. Bacteria are prokaryotic; plants, animals, fungi, and protists are eukaryotic.

The process by which plants, algae, and some bacteria use light energy to convert carbon dioxide and water into organic matter and oxygen. It occurs in chloroplasts, in light and dark reactions.

The breakdown of organic molecules to release energy stored as ATP, using oxygen in aerobic forms. It occurs partly in the cytoplasm and partly in mitochondria, producing carbon dioxide and water.

Mendel's rules: traits are controlled by paired factors that separate during gamete formation and assort independently when on different chromosomes. These predict offspring ratios in crosses.

A cell division producing four haploid gametes from one diploid cell through two divisions. Crossing over and independent assortment during meiosis generate genetic variation.

Hormones are chemical messengers secreted into blood that act on target organs. Negative feedback keeps levels stable, as when rising thyroid hormone suppresses further stimulation from the pituitary.

The theory that Earth's rigid outer shell is divided into plates that move over the mantle. Their interactions at boundaries cause earthquakes, volcanoes, and mountain building.

P waves are longitudinal and travel fastest; S waves are transverse and slower, and cannot pass through liquids. The time gap between their arrivals locates an earthquake's epicenter.

Magnitude measures the energy released at an earthquake's source on a logarithmic scale. Seismic intensity measures shaking strength at a specific location, so one quake has one magnitude but many intensities.

The atmosphere is layered by temperature trend: troposphere cools with height, stratosphere warms because ozone absorbs ultraviolet, mesosphere cools, and thermosphere warms again. Weather occurs mainly in the troposphere.

The balance between incoming solar radiation absorbed and outgoing infrared radiation emitted by Earth. Greenhouse gases slow the outgoing radiation, raising surface temperature.

The verb must match its subject in number and person, even when phrases separate them. Inverted sentences and collective nouns are frequent traps in grammar questions.

A word such as who, which, or that that introduces a clause modifying a noun. Choosing it depends on whether the antecedent is a person or thing and on the clause's grammatical role.

A reduced clause using a present or past participle to express reason, time, condition, or result. The participle's subject normally matches the main clause's subject.

Verb forms expressing unreal or hypothetical situations, such as if I were you. Past forms refer to present unreality, and past perfect forms refer to unreal past situations.

The sentence stating a paragraph's main idea, usually placed first. In reading and composition tasks, locating it quickly reveals the paragraph's purpose and the writer's argument structure.

Correctly reading and writing the kanji designated for upper secondary study, including on and kun readings and radical composition. Common traps involve similar-looking characters and readings that change with context.

Inflecting suffixes attached to classical Japanese words that add meaning such as past, negation, conjecture, or politeness. Each has a required connection form, and identifying it is essential for translation.

Japanese polite language divides into respectful, humble, and polite forms. Choosing correctly depends on whether the action belongs to the speaker, the listener, or a third party being respected.

The way a Japanese expository essay develops its claim through examples, contrasts, and qualifications. Identifying the author's conclusion and the relation between paragraphs is central to comprehension questions.