Algebra and Geometry Overview

Definition: A branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Key Concepts:
- Variables: Symbols representing numbers (e.g., x, y).
- Expressions: Combinations of variables and constants (e.g., 2x + 3).
- Equations: Mathematical statements asserting equality (e.g., 2x + 3 = 7).
- Functions: A relation where each input has one output (e.g., f(x) = x^2).
Operations:
- Addition, subtraction, multiplication, division of algebraic expressions.
- Factoring: Breaking down expressions into products (e.g., x^2 - 9 = (x - 3)(x + 3)).
- Solving equations: Finding variable values that satisfy the equation.

Definition: The study of shapes, sizes, relative positions, and properties of space.
Key Concepts:
- Points, Lines, and Planes: Basic building blocks of geometry.
- Angles: Formed by two rays; types include acute, right, obtuse, and straight.
- Shapes:
  - 2D: Circles, triangles, squares, rectangles, polygons.
  - 3D: Cubes, spheres, cylinders, cones, prisms.
- Theorems:
  - Pythagorean theorem: a² + b² = c² for right triangles.
  - Properties of parallel lines and transversals.
Formulas:
- Area (e.g., A = length × width for rectangles).
- Perimeter (e.g., P = 2(length + width)).
- Volume (e.g., V = length × width × height for rectangular prisms).

Definition: The study of data collection, analysis, interpretation, presentation, and organization.
Key Concepts:
- Data Types:
  - Qualitative (categorical) vs. Quantitative (numerical).
- Descriptive Statistics: Summarizing data using measures like mean, median, mode, range, and standard deviation.
- Inferential Statistics: Making predictions or generalizations about a population based on a sample.
Distributions:
- Normal distribution: Bell-shaped curve, key in probability and inferential statistics.
- Other distributions: Binomial, Poisson, uniform.
Key Tools:
- Graphical representations: Histograms, pie charts, box plots.
- Hypothesis testing: Procedures to test assumptions about a population.

A mathematical discipline focused on symbols and the manipulation of these symbols.
Variables represent unknown values, commonly denoted as letters like x and y.
Expressions consist of variables and constants combined through operations (e.g., 2x + 3).
Equations are statements indicating the equality of two expressions (e.g., 2x + 3 = 7).
Functions define a relationship where each input corresponds to exactly one output (e.g., f(x) = x^2).
Operations include addition, subtraction, multiplication, and division applied to algebraic expressions.
Factoring involves breaking down expressions into products, exemplified by x² - 9 = (x - 3)(x + 3).
Solving equations entails determining the values of variables that satisfy the equality.

A field examining shapes, sizes, positions, and spatial properties.
Fundamental elements in geometry include points, lines, and planes.
Angles are formed by two rays and categorized as acute, right, obtuse, or straight.
2D shapes include circles, triangles, squares, rectangles, and various polygons.
3D shapes cover cubes, spheres, cylinders, cones, and prisms.
The Pythagorean theorem expresses a relationship in right triangles: a² + b² = c².
Properties of parallel lines and transversals explore angles and relationships formed by intersecting lines.
Formulas for area, perimeter, and volume include:
- Area of rectangles: A = length × width.
- Perimeter of rectangles: P = 2(length + width).
- Volume of rectangular prisms: V = length × width × height.

Focuses on data gathering, analysis, interpretation, presentation, and organization.
Data can be categorized as qualitative (categorical) or quantitative (numerical).
Descriptive statistics summarizes data through measures such as mean, median, mode, range, and standard deviation.
Inferential statistics involves using a sample to make predictions or generalizations about a larger population.
Distributions include:
- Normal distribution, characterized by a bell-shaped curve and significant in probability.
- Other distributions such as binomial, Poisson, and uniform.
Key statistical tools consist of:
- Graphical elements including histograms, pie charts, and box plots.
- Hypothesis testing helps to evaluate assumptions about a population based on sample data.