Kagawa Entrance Science key terms

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

The value a sequence or function approaches as its input approaches a specified point or grows without bound. Existence requires the values to become arbitrarily close to one single number.

A straight line touching a curve at one point that matches the curve's instantaneous direction there. Its slope equals the derivative of the function at that point.

The accumulation of a quantity over an interval, computed as a limit of sums of small pieces. The definite integral gives signed area under a curve and is linked to antiderivatives by the fundamental theorem.

The integral of a function between two fixed limits, equal to the difference of an antiderivative evaluated at the upper and lower limits. It yields a number representing net signed area.

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

An ordered list of numbers indexed by the natural numbers. Questions often ask for the general term, partial sums, or limiting behaviour of arithmetic and geometric sequences.

An equation expressing each term of a sequence in terms of earlier terms. Solving it means finding an explicit formula for the general term, often by guessing a closed form or using characteristic equations.

A quantity with both magnitude and direction, represented by components or by an arrow. Addition, scalar multiplication, dot product, and position vectors are core tools in geometry and physics.

A scalar formed from two vectors by multiplying corresponding components and summing, or equivalently by the product of their magnitudes and the cosine of the angle between them. Zero dot product means perpendicular.

A number of the form a + bi where a and b are real and i satisfies i squared equals minus one. Complex numbers support addition, multiplication, conjugation, and polar representation.

Writing a complex number as r(cos θ + i sin θ), where r is its modulus and θ its argument. This form makes multiplication, division, and powers easy via De Moivre's theorem.

The number obtained by flipping the sign of the imaginary part, so a + bi becomes a − bi. Multiplying a complex number by its conjugate gives the squared modulus, a real number.

A proof technique for statements about all natural numbers: prove the base case, then show that assuming the statement for n implies it for n+1. This chain establishes every case at once.

A proof method that assumes the negation of the desired conclusion and derives an impossibility. Since the negation cannot hold, the original statement must be true.

A number between 0 and 1 expressing how likely an event is, often as favourable outcomes divided by total equally likely outcomes. Conditional probability and independence are common exam topics.

The probability-weighted average of all possible values of a random variable. It is computed by summing each value multiplied by its probability.

The relation that the net force on an object equals its mass times acceleration, F = ma. It connects forces to changes in motion and underlies most mechanics problems.

When only conservative forces do work, the sum of kinetic and potential energy stays constant. This lets you relate speeds and heights without tracking forces at every instant.

If no external force acts on a system, its total momentum remains constant. This governs collisions and explosions, including elastic and inelastic cases.

The ratio of relative separation speed to relative approach speed for two colliding bodies. A value of 1 means a perfectly elastic collision; 0 means they stick together.

The force per unit positive charge at a point in space, a vector quantity. Field lines point away from positive charges and toward negative ones.

The electric potential energy per unit charge at a point, measured in volts relative to a chosen reference. Charges naturally move from high to low potential.

For a resistor at constant temperature, the current through it is proportional to the voltage across it, V = IR. Resistance is the constant of proportionality.

Two circuit rules: current into a junction equals current out, and the sum of voltage changes around any closed loop is zero. They solve multi-loop circuits.

The amount of substance containing 6.02 × 10²³ particles. It links the mass of a sample to the number of atoms or molecules through molar mass.

The number of particles in one mole, approximately 6.02 × 10²³ per mole. It converts between particle counts and amounts of substance.

The number of moles of solute dissolved per litre of solution, in mol/L. It is used for dilution calculations and stoichiometry in solution.

The reaction between an acid and a base producing water and a salt. At equivalence the moles of hydrogen ions equal the moles of hydroxide ions.

A reaction in which electrons are transferred, one species losing electrons (oxidation) and another gaining them (reduction). Oxidation numbers track the electron exchange.

Driving a non-spontaneous redox reaction with an external voltage. Oxidation occurs at the anode and reduction at the cathode, depositing or dissolving material.

The state in a reversible reaction where forward and reverse rates are equal, so concentrations stop changing. The equilibrium constant expresses the ratio of product to reactant concentrations.

When a system at equilibrium is disturbed, it shifts to counteract the change. Changes in concentration, pressure, or temperature therefore alter the equilibrium position.

Genotype is the pair of alleles an organism carries for a gene; phenotype is the observable trait. Dominant alleles mask recessive ones in heterozygotes.

Cell division producing four haploid gametes from one diploid cell. Crossing over and independent assortment during it generate genetic variation.

The process by which plants use light energy to convert carbon dioxide and water into glucose and oxygen. It occurs in chloroplasts and underpins most food chains.

The breakdown of organic molecules such as glucose to release usable energy stored as ATP. Aerobic respiration uses oxygen and yields far more ATP than anaerobic routes.

A protein catalyst that speeds up biochemical reactions by lowering activation energy. Each enzyme has an active site whose shape determines its substrate specificity.

The theory that Earth's lithosphere is divided into plates that move over the asthenosphere. Their interactions cause earthquakes, volcanoes, and mountain building.

Ground shaking caused by the sudden release of accumulated stress along a fault. Energy radiates as seismic waves detected by seismographs.

The focus is the point inside Earth where an earthquake originates; seismic intensity measures shaking strength at a location. Intensity generally decreases with distance from the focus.

The ratio of light speed in one medium to its speed in another, determining how much a ray bends at the boundary. Snell's law relates it to the incidence and refraction angles.

When light travelling in a denser medium strikes a boundary beyond the critical angle, it reflects entirely back inside. No refracted ray escapes into the less dense medium.

Correlation means two variables change together; causation means one actually produces the other. A strong correlation alone does not prove a causal link, since confounders may exist.

An experiment comparing a treatment group with a control group that differs in only one variable. Keeping other conditions constant lets researchers attribute effects to the manipulated factor.

The digits in a measurement that carry meaningful information about its precision. Results should be reported to the appropriate number of figures given the inputs and operations used.