Algebra and Geometry Concepts

Definition: Branch of mathematics dealing with symbols and rules for manipulating those symbols.
Key Concepts:
- Variables: Symbols representing numbers (e.g., x, y).
- Expressions: Combinations of variables and constants (e.g., 3x + 2).
- Equations: Mathematical statements that two expressions are equal (e.g., 2x + 3 = 7).
- Functions: Relations where each input has a single output (e.g., f(x) = x^2).
- Linear Equations: Equations of the first degree, graph as straight lines.
- Quadratic Equations: Equations of the second degree, in the form ax^2 + bx + c = 0.

Definition: Study of shapes, sizes, and properties of space.
Key Concepts:
- Points, Lines, and Angles: Basic elements of geometry.
- Shapes:
  - 2D: Circles, triangles, rectangles, polygons.
  - 3D: Spheres, cubes, cylinders, pyramids.
- Theorems: Important rules such as Pythagorean theorem (a² + b² = c² in right triangles).
- Congruence and Similarity: Conditions under which shapes are identical or proportional.
- Area and Volume: Calculations for surface area and capacity of shapes.

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 (slope of the tangent line).
- Integrals: Measure of the area under a curve; reverse process of differentiation.
- Fundamental Theorem of Calculus: Connects differentiation and integration.
- Applications: Used in physics, engineering, economics for optimization and modeling.

Definition: Study of data collection, analysis, interpretation, and presentation.
Key Concepts:
- Descriptive Statistics: Summarizing data (mean, median, mode, variance).
- Inferential Statistics: Making predictions or inferences about a population based on a sample.
- Probability: Measure of the likelihood of an event occurring.
- Distributions: Normal distribution, binomial distribution, etc.
- Hypothesis Testing: Procedure for testing if a hypothesis about a data set is true.

Definition: Study of relationships between angles and sides of triangles.
Key Concepts:
- Basic Functions: Sine (sin), cosine (cos), tangent (tan) and their reciprocals (cosecant, secant, cotangent).
- Right Triangle Relationships:
  - SOH-CAH-TOA for finding sides and angles.
- Unit Circle: Circle with a radius of 1, helps define trigonometric functions.
- Identities:
  - Pythagorean identities, angle sum and difference identities.
- Applications: Used in physics, engineering, and computer science for modeling periodic phenomena.

Branch of mathematics focused on symbols and rules for manipulation.
Variables serve as symbols for numbers; common examples are x and y.
Expressions consist of variables and constants, such as 3x + 2.
Equations declare equivalence between two expressions; e.g., 2x + 3 = 7.
Functions represent a relation where one input produces a single output; noted as f(x) = x².
Linear equations, first-degree equations, graph as straight lines.
Quadratic equations are second-degree, typically expressed as ax² + bx + c = 0.

Discipline examining shapes, sizes, and spatial properties.
Basic elements include points, lines, and angles.
Two-dimensional shapes include circles, triangles, rectangles, and polygons.
Three-dimensional shapes comprise spheres, cubes, cylinders, and pyramids.
Important theorems, like the Pythagorean theorem (a² + b² = c²), define relationships in right triangles.
Congruence signifies identical shapes, while similarity pertains to proportional shapes.
Area and volume calculations are essential for determining surface area and capacity of various shapes.

Field studying change and motion, primarily through derivatives and integrals.
Limits define the value functions approach as inputs get closer to specific points.
Derivatives measure the rate of change of a function, represented by the slope of its tangent line.
Integrals compute the area beneath a curve, functioning as the reverse of differentiation.
The Fundamental Theorem of Calculus links differentiation and integration, establishing foundational relationships.
Applications span various fields, including physics, engineering, and economics, particularly for optimization and modeling scenarios.

Branch focused on data collection, analysis, interpretation, and presentation.
Descriptive statistics summarize data characteristics, including mean, median, mode, and variance.
Inferential statistics facilitate predictions or inferences about broader populations based on a smaller sample.
Probability quantifies the likelihood of specific events occurring.
Different distributions, such as normal and binomial distributions, are vital for understanding data behavior.
Hypothesis testing evaluates the validity of assumptions related to datasets.

Field dedicated to the interplay between angles and sides of triangles.
Basic trigonometric functions include sine (sin), cosine (cos), and tangent (tan), along with their reciprocals.
SOH-CAH-TOA serves as a mnemonic for finding relationships in right triangles: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
The unit circle, with a radius of 1, is key for defining trigonometric functions.
Trigonometric identities, such as Pythagorean identities and angle sum/difference identities, are fundamental.
Applications of trigonometry are broad, including fields like physics, engineering, and computer science, particularly in modeling periodic phenomena.