Algebra and Probability Concepts Quiz

Definition: Branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Key Concepts:
- Variables: Symbols used to represent unknown values.
- Expressions: Combinations of variables and constants (e.g., 3x + 4).
- Equations: Statements that two expressions are equal (e.g., 2x + 3 = 7).
- Functions: Relationships between sets of values, typically expressed as f(x).
- Linear Equations: Equations of the first degree; graph is a straight line.
- Quadratic Equations: Equations of the second degree; standard form: ax² + bx + c = 0.

Definition: Study of randomness and uncertainty; quantifies the likelihood of events.
Key Concepts:
- Experiment: A procedure that produces outcomes.
- Sample Space (S): The set of all possible outcomes.
- Event: A subset of the sample space.
- Probability (P): Measure of the likelihood of an event occurring, ( P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} ).
- Independent Events: Events where the outcome of one does not affect the other.
- Conditional Probability: Probability of an event given that another event has occurred, ( P(A|B) ).

Definition: Study of shapes, sizes, and properties of space.
Key Concepts:
- Points, Lines, and Planes: Basic building blocks of geometry.
- Angles: Formed by two rays with a common endpoint; measured in degrees.
- Triangles: Three-sided polygons; types include equilateral, isosceles, and scalene.
- Circles: Set of points equidistant from a center point; key terms include radius, diameter, and circumference.
- Area and Volume: Measurements for two-dimensional and three-dimensional shapes, respectively.
- The Pythagorean Theorem: In right triangles, ( a² + b² = c² ).

Definition: Branch of mathematics dealing with the properties and relationships of numbers, particularly integers.
Key Concepts:
- 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 positive divisors.
- Divisibility: A number a is divisible by b if ( a = b \cdot k ) for some integer k.
- Greatest Common Divisor (GCD): The largest positive integer that divides two or more integers without a remainder.
- Least Common Multiple (LCM): The smallest positive integer that is divisible by two or more integers.

Definition: Study of change and motion; focuses on rates of change (differentiation) and accumulation of quantities (integration).
Key Concepts:
- Limits: The value that a function approaches as the input approaches a certain point.
- Derivatives: Measure the rate of change of a function; denoted as ( f'(x) ) or ( \frac{dy}{dx} ).
- Integrals: Measure of the accumulation of quantities; represented as ( \int f(x)dx ).
- Fundamental Theorem of Calculus: Links differentiation and integration, providing a way to evaluate definite integrals.
- Applications: Used in physics, engineering, economics, and statistics for modeling and solving real-world problems.

Branch of mathematics focused on symbols and their manipulative rules.
Variables represent unknown values, enabling representation of general relationships.
Expressions are combinations of variables and constants, such as 3x + 4.
Equations assert equality between two expressions, exemplified by 2x + 3 = 7.
Functions define relationships between input and output values, often represented as f(x).
Linear equations are first-degree equations whose graphs produce straight lines.
Quadratic equations, in the form ax² + bx + c = 0, represent second-degree relationships.

Field concerned with randomness and quantifying event likelihood.
An experiment produces various possible outcomes.
Sample space (S) contains all outcomes from an experiment.
An event is a specific subset of the sample space.
Probability (P) quantifies the likelihood of an event as ( P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} ).
Independent events do not influence each other's outcomes.
Conditional probability considers the likelihood of an event given another event's occurrence, expressed as ( P(A|B) ).

Discipline dedicated to examining shapes, sizes, and spatial properties.
Basic components include points, lines, and planes, foundational to geometric concepts.
Angles arise from two rays joining at a common endpoint, measured in degrees.
Triangles are polygons with three sides, categorized into equilateral, isosceles, or scalene types.
Circles consist of all points equidistant from a central point, with key terminologies like radius and circumference.
Area and volume represent two-dimensional and three-dimensional measurements, respectively.
The Pythagorean theorem ( a² + b² = c² ) applies to right triangles.

Area of mathematics focused on integers and their properties.
Prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves.
Composite numbers possess more than two positive divisors.
A number a is divisible by b if ( a = b \cdot k ) for some integer k.
The greatest common divisor (GCD) is the largest integer that divides two or more numbers without a remainder.
The least common multiple (LCM) is the smallest integer divisible by two or more integers.

A mathematical field analyzing change and motion through differentiation and integration.
Limits describe the value a function approaches as variables approach specific points.
Derivatives measure instantaneous rates of change, often denoted as ( f'(x) ) or ( \frac{dy}{dx} ).
Integrals represent the accumulation of quantities, expressed as ( \int f(x)dx ).
The fundamental theorem of calculus establishes a connection between differentiation and integration for evaluating definite integrals.
Widely applied in fields like physics, engineering, economics, and statistics for modeling and resolving practical issues.