Iwate Entrance Science key terms

The expression b² − 4ac from a quadratic ax² + bx + c. Its sign tells how many real roots exist: positive gives two, zero gives one repeated root, negative gives none.

A rule giving the roots of ax² + bx + c = 0 as x = (−b ± √(b² − 4ac)) / 2a. It solves any quadratic, including ones that do not factor neatly.

Rewriting a quadratic as a perfect square plus a constant, for example x² + 6x + 1 = (x + 3)² − 8. It reveals the vertex of a parabola and derives the quadratic formula.

A list of numbers where each term differs from the previous one by a fixed amount called the common difference. The nth term equals the first term plus (n − 1) times that difference.

A list of numbers where each term is the previous term multiplied by a fixed ratio. Terms grow or shrink exponentially, and the nth term equals the first term times the ratio to the power n − 1.

The total obtained by adding the terms of a sequence. For an arithmetic series the sum is n/2 times the first plus last term; for a geometric series it is a(1 − rⁿ)/(1 − r).

The instantaneous rate at which a function changes, equal to the slope of its tangent line. It is defined as the limit of a difference quotient as the interval shrinks to zero.

The limit of a sum of thin rectangular areas under a curve between two limits. It measures accumulated change and is evaluated using an antiderivative at the endpoints.

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

The net force on an object equals its mass times its acceleration. It links cause (force) to effect (acceleration) and shows that heavier objects need more force for the same acceleration.

A sketch showing one object alone with every force acting on it drawn as an arrow from its centre. It is the standard first step in solving mechanics problems.

A contact force opposing relative sliding between surfaces. Static friction adjusts up to a maximum; kinetic friction stays roughly constant once sliding begins.

The product of an object's mass and velocity. In a closed system with no external net force, total momentum before a collision equals total momentum after it.

The principle that energy is never created or destroyed, only transferred or transformed. In mechanics, kinetic plus potential energy stays constant when only gravity does work.

The bending of a wave as it passes from one medium into another where its speed differs. The change in direction follows Snell's law and depends on the refractive indices.

The spreading of waves around obstacles and through gaps, most noticeable when the gap is comparable to the wavelength. It is evidence that light behaves as a wave.

The combining of two or more waves so their displacements add. In-phase waves reinforce (constructive); out-of-phase waves cancel (destructive), producing bright and dark bands.

The generation of an electromotive force in a conductor when the magnetic flux through it changes. Faraday's law states the induced emf is proportional to the rate of flux change.

A measure of how much magnetic field passes through a given area, equal to field strength times area times the cosine of the angle between field and area normal.

The induced current flows in a direction that opposes the change in flux that produced it. This follows from energy conservation and determines the sign of induced emf.

The energy needed to raise one kilogram of a substance by one kelvin. Water's high value explains why it heats slowly and moderates temperature in organisms and climates.

The relation PV = nRT linking pressure, volume, amount of gas and absolute temperature. It models gases whose particles have negligible volume and no intermolecular forces.

The electrostatic attraction between oppositely charged ions formed when one atom transfers electrons to another. It typically joins a metal to a non-metal and gives high melting points.

A bond formed when two atoms share one or more pairs of electrons. It is common between non-metals and can be polar or non-polar depending on electronegativity difference.

A measure of how strongly an atom attracts shared electrons in a bond. Large differences between bonded atoms produce polar or ionic character; small differences give non-polar bonds.

The amount of substance containing 6.02 × 10²³ particles. It converts between mass, number of particles and gas volume, making stoichiometric calculations possible.

The calculation of reactant and product quantities from a balanced equation. Coefficients give mole ratios, which are converted to masses or volumes using molar mass or gas laws.

The reactant that is used up first and therefore determines the maximum amount of product formed. Other reactants are said to be in excess.

The heat absorbed or released by a reaction at constant pressure, written ΔH. Negative values mean exothermic; positive values mean endothermic. It is measured by calorimetry.

The minimum energy colliding particles need for a reaction to occur. A catalyst lowers it, speeding the reaction without being consumed or changing the overall enthalpy change.

A substance that increases reaction rate by providing an alternative pathway with lower activation energy, while remaining chemically unchanged at the end of the reaction.

A specific cluster of atoms within an organic molecule that gives it characteristic reactions and properties, such as hydroxyl, carboxyl, amino or carbonyl groups.

One of two or more compounds with the same molecular formula but different arrangements of atoms. Structural isomers differ in connectivity; stereoisomers differ only in spatial arrangement.

A large molecule built from many repeating small units called monomers joined by covalent bonds. Examples include proteins, starch, polyethylene and DNA.

The net movement of water across a selectively permeable membrane from a region of higher water potential to lower water potential. It drives water uptake by plant roots.

The random net movement of particles from a region of higher concentration to lower concentration, driven by thermal motion. Rate rises with temperature and concentration gradient.

A protein that catalyses a specific biochemical reaction by binding its substrate at an active site. Activity depends on temperature and pH, which affect shape.

Cell division producing two genetically identical daughter cells with the same chromosome number as the parent. It underlies growth, repair and asexual reproduction.

A two-stage division producing four cells with half the parent's chromosome number. Crossing over and independent assortment generate genetic variation in gametes.

One of the alternative versions of a gene at a given locus. An organism inherits one allele from each parent, and their combination determines the observed trait.

The particular combination of alleles an organism carries for a gene or set of genes. It interacts with the environment to produce the observable phenotype.

The process by which individuals with inherited traits that improve survival and reproduction leave more offspring, so those traits become more common over generations.

A step in a food chain defined by how an organism obtains energy, such as producer, primary consumer or secondary consumer. Energy decreases at each higher level.

The maximum population size an environment can sustain indefinitely given available food, space and other resources. Growth slows as the population approaches it.

The group in an experiment that does not receive the treatment being tested. Comparing it with the treated group isolates the effect of the independent variable.

The factor deliberately changed by the experimenter to test its effect. All other variables should be held constant so the result can be attributed to it.

The consistency of measurements when an experiment is repeated. It improves with more repeats, careful technique and averaging, and is distinct from accuracy.

Selecting subjects or quadrats so every member of the population has an equal chance of being chosen. It reduces bias and supports valid generalisation from the sample.

The digits in a measured value that carry reliable information about precision. Results of calculations should be rounded to match the least precise input.

A procedure in which a solution of known concentration is added from a burette until a reaction endpoint is detected, allowing the unknown concentration to be calculated.

A separation technique in which components move at different rates through a stationary phase carried by a mobile phase. It identifies substances by comparing migration distances.

The factor by which an image is enlarged, calculated as image size divided by actual size. Total magnification of a compound microscope is the eyepiece times objective power.