Algebra Fundamentals

Algebra

What is Algebra?

• Branch of mathematics that deals with variables and their relationships
• Studies the properties and behavior of variables and their operations

Key Concepts:

• Variables: Symbols that represent unknown values or quantities
• Constants: Numbers that do not change value
• Expressions: Combinations of variables, constants, and mathematical operations
• Equations: Statements that express the equality of two expressions
• Inequalities: Statements that compare two expressions using greater than, less than, or equal to

Types of Algebra:

• Elementary Algebra: Deals with solving linear equations and inequalities, graphing lines, and quadratic equations
• Intermediate Algebra: Covers systems of equations, functions, and quadratic equations
• College Algebra: Includes advanced topics such as polynomial and rational expressions, and functions

Algebraic Operations:

• Addition and Subtraction: Combine like terms by combining coefficients
• Multiplication and Division: Distribute numbers and variables according to the order of operations (PEMDAS)
• Exponents and Roots: Simplify expressions using exponent rules and properties of roots

Solving Equations and Inequalities:

• Addition and Subtraction Properties: Add or subtract the same value to both sides to isolate a variable
• Multiplication and Division Properties: Multiply or divide both sides by a coefficient to isolate a variable
• Inverse Operations: Use opposite operations to isolate a variable (e.g., addition and subtraction, multiplication and division)

Graphing and Functions:

• Coordinate Plane: Graph points in a two-dimensional plane using x and y axes
• Linear Equations: Graph lines using slope-intercept form (y = mx + b)
• Quadratic Equations: Graph parabolas using vertex form (y = a(x - h)^2 + k)