AP EAMCET key terms

A single number calculated from a square array of numbers using fixed expansion rules along a row or column. It indicates whether a linear system has a unique solution and measures how areas or volumes scale.

The number of linearly independent rows, which equals the number of linearly independent columns. It equals the size of the largest minor with non-zero determinant and reveals how many independent equations a system really contains.

A function is continuous at a point when the two-sided limit exists there, the function is defined there, and the limit equals the function value. Graphically, the curve has no break or hole at that point.

If a function is continuous on a closed interval, differentiable inside it, and takes equal values at the two endpoints, then its derivative is zero at some interior point. It guarantees a horizontal tangent somewhere between.

A rule for integrating a product, written as the integral of u dv equals uv minus the integral of v du. Choose u as the factor that becomes simpler when differentiated, often guided by the ILATE order.

The order is the highest derivative that appears in the equation. The degree is the power of that highest derivative once the equation is written as a polynomial in derivatives with integer powers.

A number measuring how far a conic departs from being a circle, equal to the distance from centre to focus divided by the semi-major axis. A circle has zero and an ellipse less than one, while a hyperbola exceeds one.

The dot product of one vector with the cross product of two others. Its absolute value gives the volume of the parallelepiped formed by the three vectors, and it is zero when they lie in one plane.

The probability that an event occurs when it is already known that another event occurred. It equals the probability of both events divided by the probability of the known event, provided that is not zero.

A formula that reverses a conditional probability: the probability of A given B equals the probability of B given A times the probability of A, divided by the probability of B. It updates a prior guess using new evidence.

The distribution of the count of successes in a fixed number of independent trials, each with the same success probability. Its mean is the number of trials times that probability, and its variance is smaller than the mean.

The cosines of the angles that a directed line makes with the positive x, y and z axes. Their squares add up to one, and together they fix the orientation of the line in space.

Points where a function takes a locally largest or smallest value compared with nearby points. They are located where the first derivative is zero or undefined, then classified by the sign change of the derivative.

An expression showing which base quantities build a physical quantity and with what powers, for example force as mass times length divided by time squared. It is used to check equations and convert units.

The motion of an object launched into the air, analysed as a horizontal motion at constant velocity combined with a vertical motion at constant acceleration due to gravity. Ignoring air resistance, the path is a parabola.

The smallest speed an object needs at a planet's surface to move away forever without further thrust. It equals the square root of twice the gravitational parameter divided by the radius, and does not depend on the object's mass.

A measure of how strongly an object resists angular acceleration about a particular axis. It depends on the total mass and on how far that mass lies from the axis.

Oscillation in which the restoring force is proportional to the displacement and always points back toward equilibrium. The displacement varies sinusoidally with time, and the period stays the same for all amplitudes.

For steady, incompressible, non-viscous flow along a streamline, pressure plus kinetic energy per unit volume plus potential energy per unit volume remains constant. It explains why faster-moving fluid exerts lower pressure.

The highest efficiency any heat engine can reach while working between two fixed reservoir temperatures. It equals one minus the cold temperature divided by the hot temperature, both measured in kelvin.

Two circuit rules. The junction rule states that total current entering a node equals total current leaving it. The loop rule states that potential changes around any closed loop add up to zero.

A relation giving the magnetic field created at a point by a short current element. The field is proportional to the current, the element length and the sine of the angle, and inversely proportional to the distance squared.

The complete bouncing back of light at a boundary when it travels from a denser to a rarer medium and strikes at an angle larger than the critical angle. No refracted ray leaves the denser medium.

The ejection of electrons from a metal surface when light above a threshold frequency falls on it. Emission begins almost instantly, and the maximum electron energy rises with frequency, not with brightness.

The wavelength attributed to a moving particle, equal to Planck's constant divided by the particle's momentum. It becomes significant for electrons and other light particles, explaining their diffraction patterns.

The time needed for half of the radioactive nuclei in a sample to decay. It is fixed for a given isotope, is independent of the starting amount, and equals about 0.693 divided by the decay constant.

A way of counting particles in bulk matter. One mole contains Avogadro's number of entities, about 6.022 times ten to the twenty-third, and its mass in grams equals the substance's formula mass in atomic mass units.

The reactant that is used up first in a chemical reaction, so it decides the maximum amount of product that can form. The other reactants remain partly unreacted and are said to be in excess.

The number of moles of solute dissolved in one litre of solution. Because solution volume expands when heated, molarity changes slightly with temperature, unlike molality, which uses mass of solvent.

For an ideal solution, the partial vapour pressure of each volatile component equals its mole fraction in the liquid multiplied by the vapour pressure of the pure component. It underpins distillation and vapour pressure calculations.

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

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

A thermodynamic quantity equal to internal energy plus pressure multiplied by volume. At constant pressure, the heat absorbed or released by a process equals the change in enthalpy.

A quantity defined as enthalpy minus temperature times entropy. A negative change at constant temperature and pressure means the process can occur spontaneously; zero means the system is at equilibrium.

A relation between the actual potential of a cell and its standard potential, corrected for the reaction quotient. At 298 kelvin it is written as standard potential minus 0.059 divided by n times log Q.

The sum of the powers of concentration terms in the experimentally measured rate law. It need not match the balanced equation's coefficients, and it can be zero or fractional.

The mixing of atomic orbitals of similar energy to produce new equivalent orbitals pointing in the directions needed to match the observed molecular shape and bond angles.

When a hydrogen halide adds to an unsymmetrical alkene, the hydrogen attaches to the carbon that already has more hydrogen atoms, giving the more stable carbocation intermediate. Peroxides can reverse this preference.

In a complex ion, the number of donor atoms bonded directly to the central metal. In a crystal, it is the number of nearest neighbouring ions surrounding a given ion.