Algebra 1 - Module 1 Lesson 1 Vocabulary

Questions and Answers

What is an algebraic expression?

A numerical symbol or variable symbol

The result of placing expressions into operators

Both A and B (correct)

None of the above

What is the constant term of a polynomial in standard form?

The value obtained by substituting 0 into all variable symbols of the polynomial.

How is the degree of a monomial determined?

It is the sum of the exponents of the variable symbols in the monomial.

What defines the degree of a polynomial in standard form?

The highest degree of the terms in the polynomial. Signup and view all the answers

What does it mean for two algebraic expressions to be equivalent?

One expression can be converted into the other through various properties. Signup and view all the answers

How can two numerical expressions be considered equivalent?

They evaluate to the same number. Signup and view all the answers

What is the graph of an equation in two variables?

The set of all points in the coordinate plane that are solutions to the equation. Signup and view all the answers

What is the leading term of a polynomial in standard form?

The number in front of the polynomial. Signup and view all the answers

What is considered a monomial?

A polynomial expression that uses only the multiplication operator. Signup and view all the answers

Define a numerical expression.

An algebraic expression containing only numerical symbols that evaluates to a single number. Signup and view all the answers

What is a numerical symbol?

A symbol that represents a specific number. Signup and view all the answers

What is a piecewise linear function?

A function defined by linear functions on non-overlapping intervals. Signup and view all the answers

What constitutes a polynomial expression?

A numerical expression or variable symbol, or the result of combining two polynomial expressions. Signup and view all the answers

What is a solution in the context of an equation with one variable?

A number that makes the equation true when substituted. Signup and view all the answers

What is a solution set?

The set of all solutions to an equation. Signup and view all the answers

What is a variable symbol?

A symbol that represents a placeholder for a number. Signup and view all the answers

What does the Zero Product Property state?

If $ab=0$, then either $a=0$, $b=0$, or both. Signup and view all the answers

Study Notes

Algebraic Concepts

Algebraic Expression: Can be a numerical symbol, variable symbol, or the result of placing algebraic expressions into operators (addition, subtraction, multiplication, division) or exponentiation with rational exponents.
Constant Term of a Polynomial: Achieved by substituting 0 for variable symbols in a polynomial, yielding 'a sub zero'.
Degree of a Monomial: Calculated by summing the exponents of variable symbols in a nonzero monomial.
Degree of a Polynomial: Determined by identifying the highest degree among the terms within the polynomial.

Expressions and Equivalence

Equivalent Algebraic Expressions: Two expressions are equivalent if one can be transformed into the other using commutative, associative, distributive properties, and rational exponent properties.
Equivalent Numerical Expressions: Two numerical expressions are equivalent if they produce the same numerical result.

Graphs and Functions

Graph of an Equation in Two Variables: Represents all points in the coordinate plane that satisfy the equation.
Piecewise Linear Function: Defined over finite non-overlapping intervals with different linear functions applying to each interval.

Polynomial Characteristics

Leading Term and Leading Coefficient: The leading term is the first term of a polynomial in standard form, and the leading coefficient is the numerical factor in front of this term.
Monomial: A type of polynomial expression formed exclusively through multiplication. Consists of products of numerical or variable symbols.
Polynomial Expression: Can consist of a numerical expression, variable symbol, or the result of adding/multiplying two polynomial expressions.

Solutions and Properties

Solution: A number that makes an equation true when substituted for the variable.
Solution Set: The collection of all solutions to an equation.
Variable Symbol: Represents a placeholder for a number; its constraints may vary by context (e.g., integers or positive real numbers).
Zero Product Property: States that if the product of two numbers equals zero, at least one of those numbers must also be zero.

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Description

Test your knowledge of key vocabulary from Algebra 1 Module 1 Lesson 1. This quiz introduces essential terms, including algebraic expressions and constant terms, helping you build a solid foundation in algebra. Perfect for beginners or as a refresher!