Algebra Basics

Study Notes

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.

Elementary Algebra: deals with the basic concepts of algebra, including linear equations, quadratic equations, and functions.
Intermediate Algebra: builds upon elementary algebra, covering topics such as systems of equations, inequalities, and functions.
College Algebra: covers advanced topics, including polynomial and rational functions, exponential and logarithmic functions, and series and sequences.

Variables and Expressions:
- Variables: letters or symbols that represent unknown values or quantities.
- Expressions: combinations of variables, constants, and mathematical operations.
Equations and Inequalities:
- Equations: statements that two expressions are equal.
- Inequalities: statements that one expression is greater than, less than, or equal to another.
Functions:
- Domain: the set of input values for a function.
- Range: the set of output values for a function.
- Composition of functions: combining two or more functions to create a new function.

Addition and Subtraction:
- Combining like terms: combining terms with the same variable and coefficient.
- Combining unlike terms: combining terms with different variables or coefficients.
Multiplication and Division:
- Distributive property: multiplying a single value to multiple terms.
- Factoring: expressing an expression as a product of simpler expressions.

Graphing:
- Cartesian coordinate system: a system of axes used to graph equations.
- Graphing linear equations: using the slope-intercept form (y = mx + b) to graph lines.
Solving Equations and Inequalities:
- Linear equations: solving for x in equations of the form ax + by = c.
- Quadratic equations: solving for x in equations of the form ax^2 + bx + c = 0.

Algebra is a branch of mathematics dealing with variables and their relationships, expressed through symbols, equations, and functions.

Elementary Algebra covers linear equations, quadratic equations, and functions.
Intermediate Algebra builds upon elementary algebra, covering systems of equations, inequalities, and functions.
College Algebra covers advanced topics like polynomial and rational functions, exponential and logarithmic functions, and series and sequences.

Variables are letters or symbols representing unknown values or quantities.
Expressions are combinations of variables, constants, and mathematical operations.

Equations are statements that two expressions are equal.
Inequalities are statements that one expression is greater than, less than, or equal to another.

Domain is the set of input values for a function.
Range is the set of output values for a function.
Composition of functions combines two or more functions to create a new function.

Cartesian coordinate system is a system of axes used to graph equations.
Graphing linear equations uses the slope-intercept form (y = mx + b) to graph lines.