Algebra Basics Quiz

Definition: Branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Key Concepts:
- Variables: Symbols that represent numbers.
- Expressions: Combinations of variables and constants (e.g., 2x + 3).
- Equations: Statements that two expressions are equal (e.g., 2x + 3 = 7).
- Functions: Relationships between inputs and outputs (e.g., f(x) = x^2).
- Factoring: Breaking down expressions into products (e.g., x^2 - 9 = (x - 3)(x + 3)).
- Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a).

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; measured in degrees (acute, obtuse, right).
- Triangles: Sum of angles is always 180°. Types include scalene, isosceles, and equilateral.
- Circles: Defined by a center and radius; key formulas include circumference (C = 2πr) and area (A = πr²).
- Area and Volume: Area for 2D shapes (e.g., A = lw for rectangles) and volume for 3D objects (e.g., V = lwh for rectangular prisms).

Definition: Study of change and motion, involving derivatives and integrals.
Key Concepts:
- Limits: The value that a function approaches as the input approaches a point.
- Derivatives: Measure of how a function changes as its input changes; represents slope of the tangent line.
- Integrals: Represents the accumulation of quantities, often interpreted as area under a curve.
- Fundamental Theorem of Calculus: Links differentiation and integration.
- Applications: Used in physics, engineering, economics for optimization and modeling.

Definition: Study of data collection, analysis, interpretation, presentation, and organization.
Key Concepts:
- Descriptive Statistics: Summarizes data (mean, median, mode, range).
- Inferential Statistics: Makes predictions or inferences about a population based on sample data.
- Probability: Measures the likelihood of an event occurring; ranges from 0 to 1.
- Distributions: Normal distribution, binomial distribution, and others.
- Hypothesis Testing: Procedure to determine if a hypothesis about a population parameter is supported by sample data.

Definition: Study of the relationships between the angles and sides of triangles.
Key Concepts:
- Sine, Cosine, Tangent: Fundamental ratios in right triangles (SOH-CAH-TOA).
- Unit Circle: Circle with a radius of 1; helps define trigonometric functions for all angles.
- Pythagorean Theorem: a² + b² = c² for right triangles.
- Trigonometric Identities: Equations involving trigonometric functions (e.g., sin²x + cos²x = 1).
- Applications: Used in physics, engineering, and computer graphics for modeling cyclic phenomena.

Branch of mathematics focused on symbols and manipulation rules.
Variables: Symbols (e.g., x, y) that represent unknown numbers.
Expressions: Combinations of variables and constants, such as 2x + 3.
Equations: Mathematical statements asserting two expressions are equal, e.g., 2x + 3 = 7.
Functions: Relationships mapping inputs to outputs, exemplified by f(x) = x².
Factoring: Process of breaking expressions into products, e.g., x² - 9 = (x - 3)(x + 3).
Quadratic Formula: Solution formula for quadratic equations, x = (-b ± √(b² - 4ac)) / (2a).

Study of shapes, sizes, and properties in space.
Points, Lines, and Planes: Fundamental elements forming geometry's framework.
Angles: Formed by two intersecting rays; classified based on measure: acute, obtuse, or right.
Triangles: Polygons with three sides, with a total angle sum of 180°. Types include scalene, isosceles, and equilateral.
Circles: Defined by a center and radius; key formulas include circumference (C = 2πr) and area (A = πr²).
Area and Volume: Calculated for 2D shapes (e.g., A = lw for rectangles) and 3D objects (e.g., V = lwh for rectangular prisms).

Study of change, focusing on rates of change and areas.
Limits: The value a function approaches as inputs near a certain point.
Derivatives: Measure of an instantaneous rate of change, representing the slope of the tangent line at any point on a curve.
Integrals: Represent accumulated quantities and are commonly interpreted as areas under curves.
Fundamental Theorem of Calculus: Establishes the relationship between differentiation and integration processes.
Real-World Applications: Employed in fields like physics, engineering, and economics for optimization and modeling scenarios.

Examination of data through collection, interpretation, and presentation.
Descriptive Statistics: Summarizes data characteristics using measures such as mean, median, mode, and range.
Inferential Statistics: Tools to infer population characteristics based on sample data.
Probability: Quantifies the likelihood of events, with values ranging from 0 (impossible) to 1 (certain).
Distributions: Various types, such as normal and binomial distributions, describe how data is spread.
Hypothesis Testing: Procedure for determining support for a hypothesis regarding a population parameter based on sample analysis.

Focus on angle and side relationships within triangles.
Sine, Cosine, Tangent: Primary ratios in right-angle triangles represented by the mnemonic SOH-CAH-TOA.
Unit Circle: A circle with radius 1, aiding in the definition of trigonometric functions for all angles.
Pythagorean Theorem: Formula a² + b² = c² relates side lengths of right triangles.
Trigonometric Identities: Equations that hold true for trigonometric functions, such as sin²x + cos²x = 1.
Applications: Widely utilized in physics, engineering, and computer graphics for modeling oscillatory phenomena.