Algebra Basics

Study Notes

Algebra

Definition

Algebra is a branch of mathematics that deals with the study of variables and their relationships, often expressed through the use of symbols, equations, and functions.

Key Concepts

Variables: Letters or symbols that represent unknown values or quantities.
Constants: Numbers that do not change value.
Algebraic Expressions: Combinations of variables, constants, and mathematical operations.
Equations: Statements that express the equality of two algebraic expressions.
Functions: Relations between variables, often represented as f(x) =...

Operations

Addition and Subtraction: Combining like terms and applying the distributive property.
Multiplication and Division: Applying the rules of exponents and the order of operations (PEMDAS).
Exponents: Rules for multiplying and dividing expressions with exponents.

Equations and Inequalities

Linear Equations: Equations in which the highest power of the variable(s) is 1.
- Example: 2x + 3 = 5
Quadratic Equations: Equations in which the highest power of the variable(s) is 2.
- Example: x^2 + 4x + 4 = 0
Systems of Equations: Sets of two or more equations with multiple variables.
Inequalities: Statements that express a relationship between expressions using <, >, ≤, or ≥.

Graphing

Cartesian Coordinates: A system of graphing points on a plane using x and y axes.
Graphs of Functions: Visual representations of functions, including linear, quadratic, and polynomial functions.

Solving Equations and Inequalities

Substitution Method: Replacing variables with values to solve for a specific variable.
Elimination Method: Adding or subtracting equations to eliminate a variable.
Graphing Method: Using the intersection of graphs to solve systems of equations.
Quadratic Formula: A formula for solving quadratic equations: x = (-b ± √(b^2 - 4ac)) / 2a.

Description

This quiz covers the fundamental concepts of algebra, including variables, constants, algebraic expressions, equations, and functions. It also explores operations, equations, and inequalities, as well as graphing and solving equations and inequalities.