Algebra I Lecture Notes

Practice flashcards based on Algebra I lecture notes covering key concepts and terminology.

What is Algebra?

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols, representing unknown values or variables.

Why is Algebra Important?

Algebra is a fundamental building block for higher mathematics and is used in fields like science, engineering, computer science, economics, and everyday life.

What is a Variable?

A symbol (usually a letter like x, y, or a) that represents an unknown or changing value.

What is a Constant?

A fixed value that does not change.

What is a Coefficient?

The numerical factor that multiplies a variable.

What is a Term?

A single number, a single variable, or the product of numbers and variables separated by addition or subtraction.

What is an Expression?

A combination of variables, constants, and operations without an equals sign.

What is an Equation?

A statement that shows two expressions are equal, connected by an equals sign.

What are Like Terms?

Terms that have the same variable(s) raised to the same power(s). Only the coefficients of like terms can be added or subtracted.

What does the Distributive Property state?

Multiplying a sum (or difference) by a number is the same as multiplying each term in the sum (or difference) by that number.

How do you add or subtract algebraic expressions?

Combine like terms, possibly using the distributive property first.

How do you multiply a monomial by a monomial?

Multiply the coefficients and add the exponents of the same variables.

What is a Two-Step Equation?

An equation that requires two inverse operations to isolate the variable.

What is the purpose of an equals sign in an equation?

It signifies that the expression on the left side has the same value as the expression on the right side.

What are Inequalities?

Mathematical statements that compare two expressions using symbols to indicate greater than, less than, or equality.

What is a Function?

A rule that assigns to each input value exactly one output value.

What is the Domain of a Function?

The set of all possible input values for the function.

What happens when you divide by a negative number in an inequality?

You must reverse the direction of the inequality symbol.