Maharashtra HSC Education key terms

The instantaneous rate at which one quantity changes with respect to another, found as the limit of the difference quotient; it also gives the slope of the tangent to a curve at a point.

The value a function's output approaches as its input approaches a chosen point, whether or not the function is actually defined at that point.

A property of a function that has no breaks or jumps at a point: the limit exists there, the function is defined there, and the two are equal.

A differentiation rule for composite functions: differentiate the outer function, keep the inner function unchanged, then multiply by the derivative of the inner function.

A technique for integrating a product of two functions, based on reversing the product rule; the integral of u dv equals uv minus the integral of v du.

The limit of a sum of areas of thin rectangles under a curve between two limits; it yields a number that can represent signed area, displacement, or total accumulated change.

A function formed by applying one function to the output of another, written f(g(x)); its domain is restricted to inputs where g(x) lies in the domain of f.

A function that returns the angle whose sine, cosine, or tangent equals a given value, with a restricted principal range so that the result is unique.

A quantity having both magnitude and direction, represented by a directed line segment and often written in component form using unit vectors along the coordinate axes.

A scalar obtained from two vectors by multiplying corresponding components and adding the results; it equals the product of their magnitudes and the cosine of the angle between them.

A vector perpendicular to two given vectors, with magnitude equal to the product of their magnitudes and the sine of the angle between them; it is used for areas and moments.

The idea that one mole contains Avogadro's number of particles and has a mass in grams equal to the substance's relative molecular mass; it links particle counts to weighable amounts.

The number of moles of solute dissolved in one litre of solution, expressed in mol per litre; it changes slightly with temperature because solution volume expands.

The simplest whole-number ratio of atoms of each element in a compound, obtained from percentage composition data and distinct from the actual molecular formula.

When a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, it shifts in the direction that partially opposes the disturbance.

The ratio of product concentrations to reactant concentrations, each raised to its stoichiometric coefficient, at equilibrium; it depends on temperature and indicates the extent of reaction.

A logarithmic measure of hydrogen ion concentration in a solution, defined as the negative logarithm to base ten of that concentration; values below seven are acidic.

A solution that resists large changes in pH when small amounts of acid or base are added, usually made from a weak acid with its salt or a weak base with its salt.

A device converting chemical energy into electrical energy, or the reverse, through redox reactions at two electrodes dipped in electrolytes and joined by a conducting circuit.

A number assigned to an atom in a compound showing its apparent charge if bonding electrons were fully transferred; it helps balance redox equations and identify oxidising agents.

The existence of two or more compounds with the same molecular formula but different arrangements of atoms, giving different physical or chemical properties.

The systematic set of rules for naming organic compounds: choose the longest carbon chain, number it to give the lowest locants, and name substituents as prefixes.

An atom or group of atoms within an organic molecule that determines its characteristic reactions and properties, such as hydroxyl, carbonyl, carboxyl, or amino groups.

The production of an electromotive force in a conductor when the magnetic flux linked with it changes, whether by moving the conductor, the magnet, or altering the current nearby.

The induced electromotive force in a circuit equals the negative rate of change of magnetic flux linkage through it; more turns or faster flux change give a larger induced emf.

The induced current flows in a direction whose magnetic field opposes the change in flux that produced it, reflecting conservation of energy and explaining the minus sign in Faraday's law.

The emission of electrons from a metal surface when light of sufficiently high frequency falls on it; the emitted electrons' maximum kinetic energy depends on frequency, not intensity.

The minimum energy needed to remove an electron from the surface of a metal; it sets the threshold frequency below which no photoelectric emission occurs.

The wavelength associated with a moving particle, equal to Planck's constant divided by its momentum; it explains electron diffraction and the wave nature of matter.

The superposition of two or more coherent waves producing alternate regions of reinforcement and cancellation; sustained fringes require a constant phase difference between sources.

The spreading of waves around obstacles or through narrow slits, producing patterns of bright and dark bands whose spacing depends on wavelength and slit width.

Two rules for circuits: the sum of currents entering a junction equals the sum leaving, and the sum of potential differences around any closed loop is zero.

A semiconductor device formed by joining p-type and n-type material; it conducts easily under forward bias and blocks current under reverse bias, acting as a rectifier.

A type of cell division producing four haploid gametes from one diploid cell through two successive divisions, with crossing over and independent assortment creating genetic variation.

Patterns of trait transmission explained by segregation of alleles and independent assortment of genes, giving predictable ratios such as 3:1 in monohybrid crosses.

Genotype is the specific combination of alleles an organism carries for a gene; phenotype is the observable trait resulting from that genotype interacting with the environment.

The tendency of genes located close together on the same chromosome to be inherited together, so their alleles do not assort independently and recombinant types appear less often.

The synthesis of an RNA molecule from a DNA template strand, catalysed by RNA polymerase, producing messenger RNA that carries the code to the ribosome.

The process at the ribosome in which messenger RNA codons are read and matching amino acids are joined into a polypeptide chain, using transfer RNA molecules.

The correspondence between triplets of RNA bases and amino acids; it is degenerate, non-overlapping, and read in a fixed reading frame from a start codon.

The differential survival and reproduction of individuals carrying heritable variations better suited to their environment, leading to gradual change in population traits.