Basic Arithmetic and Algebra Quiz

Variables: Symbols representing numbers (e.g., x, y).
Equations: Mathematical statements that assert the equality of two expressions (e.g., 2x + 3 = 7).
Functions: A relation between a set of inputs and a set of possible outputs (e.g., f(x) = x^2).

Shapes: Basic figures (e.g., triangles, squares, circles).
Area: The space within a shape (e.g., Area of a rectangle = length × width).
Perimeter: The distance around a shape (e.g., Perimeter of a rectangle = 2(length + width)).
Volume: The amount of space an object occupies (e.g., Volume of a cube = side^3).

Sine (sin): Opposite side over hypotenuse in a right triangle.
Cosine (cos): Adjacent side over hypotenuse in a right triangle.
Tangent (tan): Opposite side over adjacent side in a right triangle.
Pythagorean Theorem: In a right triangle, a² + b² = c², where c is the hypotenuse.

Limits: The value that a function approaches as the input approaches some value.
Derivatives: Measure of how a function changes as its input changes; the slope of the tangent line.
Integrals: Represents accumulation of quantities; the area under a curve.

Mean: Average of a data set.
Median: Middle value when data is ordered.
Mode: Most frequently occurring value in a data set.
Standard Deviation: Measure of the amount of variation or dispersion in a set of values.

Event: A set of outcomes of a random experiment.
Probability (P): A measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
Independent Events: The outcome of one event does not affect another.

Prime Numbers: Natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
Composite Numbers: Natural numbers that have more than two distinct positive divisors.
Greatest Common Divisor (GCD): The largest positive integer that divides two or more numbers without leaving a remainder.

Proof: A logical argument demonstrating the truth of a statement.
Induction: A method of proof used to establish the truth for all natural numbers.
Contradiction: A technique where one assumes the opposite of what is to be proven, showing it leads to a contradiction.

Addition (+) is the process of combining two or more quantities to yield a total, e.g., 2 + 3 = 5.
Subtraction (−) determines the difference between numbers, e.g., 7 − 4 = 3.
Multiplication (×) involves adding a number to itself a specified number of times, e.g., 4 × 3 = 12.
Division (÷) is splitting a total into equal parts or groups, e.g., 12 ÷ 4 = 3.

Variables are symbols, commonly letters like x and y, that represent unknown quantities.
Equations express the equality of two expressions, such as 2x + 3 = 7, which can be solved for x.
Functions define a relationship where each input corresponds to exactly one output, exemplified by f(x) = x².

Shapes refer to basic geometric figures, including familiar forms like triangles, squares, and circles.
Area measures the size of a two-dimensional surface within a shape; for instance, the area of a rectangle is calculated by length × width.
Perimeter is the total distance around a shape, calculated for a rectangle as 2(length + width).
Volume indicates the space occupied by a three-dimensional object, such as the volume of a cube, which is found by side³.

Sine (sin) calculates the ratio of the length of the opposite side to the hypotenuse in a right triangle.
Cosine (cos) computes the ratio of the length of the adjacent side to the hypotenuse in a right triangle.
Tangent (tan) represents the ratio of the opposite side to the adjacent side in a right triangle.
Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (c²) is equal to the sum of the squares of the other two sides (a² + b²).

Limits denote the value a function approaches as the input nears a specific point.
Derivatives quantify the rate of change of a function based on changes in its input, often visualized as the slope of a tangent line at any given point.
Integrals measure the accumulation of quantities and correspond to the area beneath a curve on a graph.

Mean refers to the average of a set of numbers, calculated by summing values and dividing by the count.
Median is the middle value in an ordered dataset, dividing it into two equal halves.
Mode identifies the most frequently occurring number in a dataset.
Standard Deviation quantifies the degree of variation or dispersion of values from the mean in a dataset.

Event describes a specific outcome or group of outcomes from a random experiment.
Probability (P) indicates the chance of an event occurring, expressed as a value between 0 (impossible event) and 1 (certain event).
Independent Events refer to cases where the occurrence of one event does not affect the outcome of another.

Prime Numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves, e.g., 2, 3, 5.
Composite Numbers have more than two distinct positive divisors, e.g., 4, 6, 8.
Greatest Common Divisor (GCD) identifies the largest integer that can evenly divide two or more numbers.

Proof is a logical argument that certifies the truth of a mathematical statement.
Induction is a method of proof that validates a statement for all natural numbers by demonstrating it for a base case and an inductive step.
Contradiction involves assuming the opposite of what one aims to prove and showing that such an assumption leads to an untenable conclusion.