Vestibular Seriado UFMG key terms

A polynomial function of degree two, written f(x) = ax² + bx + c with a ≠ 0, whose graph is a parabola opening upward when a is positive and downward when a is negative.

The highest or lowest point of a parabola, located at x = -b/(2a) for f(x) = ax² + bx + c; it marks the maximum or minimum value of the function.

The expression Δ = b² - 4ac in a quadratic equation; its sign tells how many real roots exist: positive gives two, zero gives one, negative gives none.

The values of the unknown that make an equation true. For a polynomial, they are the x-values where the graph crosses or touches the horizontal axis.

A number sequence in which each term after the first is obtained by adding a fixed constant called the common difference, as in 3, 7, 11, 15.

A number sequence in which each term after the first is obtained by multiplying the previous term by a fixed nonzero constant called the common ratio, as in 2, 6, 18, 54.

A formula that expresses any term of a sequence directly in terms of its position n, allowing a distant term to be calculated without listing all previous ones.

A function of the form f(x) = aˣ with a positive base different from 1; it grows or decays by a constant factor and models phenomena such as compound interest and population change.

The exponent to which a fixed base must be raised to produce a given number; log base b of x equals y exactly when b raised to y equals x.

The study of ratios between sides of a right triangle: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.

A relation extending Pythagoras to any triangle: the square of one side equals the sum of the squares of the other two minus twice their product times the cosine of the included angle.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs; the converse also holds and can test whether an angle is right.

The study of geometric figures using coordinates, where points are located by ordered pairs and distances, midpoints, and slopes are computed from those coordinates.

The slope of a line, equal to the change in y divided by the change in x between two points; it measures steepness and direction of the line.

An algebraic description of a straight line, commonly y = mx + b where m is the slope and b is the y-intercept, or in general form ax + by + c = 0.

The branch of mathematics that counts arrangements and selections of objects, using tools such as permutations, combinations, and the multiplication principle.

An arrangement of objects in which order matters. The number of permutations of n distinct objects is n factorial, the product of all integers from n down to 1.

A number between 0 and 1 expressing how likely an event is, computed in simple cases as the number of favorable outcomes divided by the total number of equally likely outcomes.

The set of all input values for which a function is defined; for example, a square root requires a nonnegative radicand and a fraction requires a nonzero denominator.

The direction in which a curve bends. A parabola is concave upward when its leading coefficient is positive and concave downward when that coefficient is negative.

Three principles of classical mechanics: a body stays at rest or in uniform motion unless a net force acts; force equals mass times acceleration; and every action has an equal and opposite reaction.

The single force equivalent to all forces acting on a body added as vectors; it determines the body's acceleration according to Newton's second law.

A contact force opposing relative motion or the tendency to move between surfaces; its maximum value depends on the normal force and the roughness of the surfaces.

In a system where only conservative forces do work, the sum of kinetic and potential energy stays constant, so energy shifts between forms but the total does not change.

The energy a body possesses because of its motion, equal to one half the mass multiplied by the square of its speed; it is always nonnegative.

The energy transferred when a force moves a body along a displacement; it equals the product of force, displacement, and the cosine of the angle between them.

The relationship stating that the current through a conductor is proportional to the voltage across it and inversely proportional to its resistance, written U = R·i.

The rate at which electrical energy is transferred in a device, equal to voltage times current; it can also be written as resistance times current squared.

A connection in which components form a single path, so the same current flows through all of them and the total resistance is the sum of individual resistances.

The calculation of quantities of reactants and products in a chemical reaction using the balanced equation and molar relationships between substances.

The amount of substance containing as many elementary entities as there are atoms in twelve grams of carbon-12, approximately 6.02 × 10²³ particles.

The process of adjusting coefficients in a chemical equation so that the number of atoms of each element is the same on both sides, respecting conservation of mass.

A measure of how much solute is present in a given amount of solution, commonly expressed in moles per liter or in grams per liter.

The set of inheritance principles derived from Mendel's experiments, including segregation of alleles and independent assortment of genes located on different chromosomes.

Genotype is the genetic makeup of an organism, the particular alleles it carries; phenotype is the observable trait resulting from that genotype interacting with the environment.

A diagram using squares for males and circles for females, with shading for affected individuals, to trace how a trait is inherited across generations of a family.

A sequence showing how energy and matter pass from producers to herbivores and then to successive predators, with decomposers recycling nutrients back into the ecosystem.

The movement of carbon among the atmosphere, living organisms, soil, and oceans through processes such as photosynthesis, respiration, decomposition, and combustion.

A community of living organisms interacting with one another and with the nonliving environment, exchanging energy and matter as a functional unit.