Comprehensive Review Lecture Notes: Mathematics, Science, and Language

Flashcards summarizing key definitions from Mathematics, Biology, Chemistry, Physics, and Language studies based on lecture materials.

Set

A collection of well-defined elements or objects described by listing them or through a mathematical relationship.

Union

A set operation representing the collection of objects that belong to set $A$ OR to set $B$, denoted as $A \bigcup B$.

Intersection

A set operation representing the collection of objects that belong to set $A$ AND set $B$, denoted as $A \bigcap B$.

Cardinality

The number of elements of a finite set, denoted by $n(A)$.

Equal Sets

Sets that contain the exact same elements such that every element of $A$ belongs to $B$ and vice versa.

Equivalent Sets

Sets that have a one-to-one correspondence between their elements, indicating they are the same size.

Integers

Numbers without fractional components consisting of zero ($0$), positive whole numbers, and their inverses, denoted by a boldface $\mathbf{Z}$.

Function

A representation of dependence between a control variable $x$ ($domain$) and an outcome $y$ ($range$) with a one-to-one or many-to-one correspondence.

Synthetic Division

A shorthand method of division applied when the divisor is specifically in the form $x - a$.

Limit

The value $L$ that $f(x)$ approaches as Variable $x$ assumes values closer to a constant $a$ without reaching it.

Differentiation

The process of determining the derivative of a function, which represents the instantaneous rate-of-change of a curve at a given point.

Antidifferentiation

The process of finding the integral or antiderivative of a function, often expressed as $F(x) + C$.

Slope

The measure of the steepness of a line calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Polygon

A flat, closed figure consisting of straight line segments called sides that meet at vertices.

Qualitative Data

Types of research data that yield categorical responses based on characteristics.

Quantitative Data

Types of research data that yield numerical responses, categorized further into discrete or continuous values.

Median

The middle observation of data arranged from lowest to highest, or the average of the two middle values if the dataset size is even.

Permutation

An arrangement of all or part of a set of objects where the order of selection matters, denoted by $n!$ for full linear arrangements.

Combination

A selection of $r$ objects from $n$ distinct objects where the order of the selected items does not matter.

Hypothesis

A tentative answer or prediction formulated to address a specific scientific question.

Metabolism

The sum total of all chemical reactions occurring within the cells of an organism.

Mitosis

A process of nuclear division in eukaryotic cells that conserves chromosome numbers by allocating replicated chromosomes equally to daughter nuclei.

Genotype

The internal genetic makeup of an organism represented by its specific combination of alleles.

Phenotype

The observable physical traits of an organism resulting from its genetic makeup and environmental factors.

Molarity

A unit of solution concentration defined as the number of moles of solute per liter volume of solution, expressed as $M = \frac{n}{V}$.

Displacement

A vector quantity describing the shortest straight-line distance between the initial and final positions of an object with direction toward the final position.

Inertia

The property of a body to resist changes in its state of motion unless acted upon by an external force.

Work

The transfer of energy produced by motion, measured by multiplying force and displacement in the line of action.

Antecedent

The specific noun or noun referent to which a pronoun refers.

Parallelism

The grammatical placement of equal ideas in similar words, phrases, or clauses to maintain balance in a sentence.

Pandiwa

Bahagi ng pananalita sa Filipino na nagsasaad ng kilos o galaw.

Tayutay

Matalinghagang pahayag na ginagamit upang maging masining ang paglalarawan or Figures of Speech.