BOB JONES ALGEBRA 2 Flashcards

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Questions and Answers

What is the absolute value?

The number of units between an integer and 0 on a number line (correct)
The distance between two integers
The additive inverse of a number
The square of a number

What are opposite numbers?

Numbers that are equal
Numbers that are the same distance from 0 but on opposite sides (correct)
Numbers that add up to zero
All of the above

What is a mathematical property?

An equation or statement that is true for any value of the variable.

What does the Commutative Property of Addition state?

a + b = b + a Signup and view all the answers

What does the Commutative Property of Multiplication state?

ab = ba Signup and view all the answers

What does the Associative Property of Multiplication state?

a(bc) = (ab)c Signup and view all the answers

What is the Identity Property of Multiplication?

a * 1 = a Signup and view all the answers

What is the Distributive Property of Multiplication?

a(b+c) = ab + ac Signup and view all the answers

What is the Associative Property of Addition?

a + (b + c) = (a + b) + c Signup and view all the answers

What is the Identity Property of Addition?

a + 0 = a Signup and view all the answers

What is exponential form?

A simplified form of writing repeated multiplication. Signup and view all the answers

What is a prime number?

An integer greater than 1 whose only positive factors are 1 and itself. Signup and view all the answers

What is a composite number?

A non-prime positive integer greater than 1. Signup and view all the answers

What is the greatest common factor?

The largest positive integer that divides evenly into two numbers. Signup and view all the answers

What is a formula?

An equation that expresses the relationship between related quantities. Signup and view all the answers

What is the order of operations?

Perform calculations in parentheses, exponents, multiplication and division from left to right, and finally addition and subtraction from left to right. Signup and view all the answers

What is algebra?

The first branch of mathematics that requires the use of variables which represent unknown values. Signup and view all the answers

What is a monomial?

An algebraic expression with one term. Signup and view all the answers

What is a binomial?

An algebraic expression with two terms. Signup and view all the answers

What is a trinomial?

An algebraic expression with three terms. Signup and view all the answers

What is a polynomial?

An algebraic expression with one or more terms. Signup and view all the answers

What does it mean to isolate the variable?

To place the variable on one side of the equation and the constant on the other side. Signup and view all the answers

What is an algebraic expression?

The result of performing mathematical operations on any collection of variables and constants. Signup and view all the answers

What is a constant?

A fixed number. Signup and view all the answers

What is a variable?

A symbol used to represent any element of a given set of numbers. Signup and view all the answers

What is the domain?

The set of numbers of the variable. Signup and view all the answers

What is the negative exponent property?

x = 1/x, if a is any real number and x is not zero. Signup and view all the answers

What does it mean to evaluate an expression?

To calculate the numerical value of an expression. Signup and view all the answers

What is substitution?

The process of replacing a variable with a value or an algebraic expression. Signup and view all the answers

What is a numerical coefficient?

The numerical factor accompanying the variables in a term. Signup and view all the answers

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Study Notes

Absolute Values and Opposites

Absolute Value: Represents the distance between a number and zero on a number line, always a non-negative value.
Opposite Numbers: Identical distances from zero but located on opposite sides, termed as additive inverses.

Key Mathematical Properties

Mathematical Property: True statements or equations for any variable values, also known as identities.
Commutative Property of Addition: Order does not affect the sum, expressed as (a + b = b + a).
Commutative Property of Multiplication: Order does not affect the product, shown as (ab = ba).
Associative Property of Multiplication: Grouping does not affect the product, exemplified as (2(5 \cdot 3) = (2 \cdot 5)3).
Identity Property of Multiplication: Multiplying by one keeps the number unchanged, expressed as (a \cdot 1 = a).
Distributive Property: Expands multiplication over addition, represented as (a(b + c) = ab + ac).
Associative Property of Addition: Grouping does not affect the sum, represented as (a + (b + c) = (a + b) + c).
Identity Property of Addition: Adding zero does not change the value, expressed as (a + 0 = a).

Algebra Basics

Exponential Form: A shorthand for repeated multiplication, simplifying calculations.
Prime Number: An integer greater than 1 with no positive factors other than 1 and itself.
Composite Number: A non-prime integer greater than 1, having factors beyond 1 and itself.
Greatest Common Factor (GCF): The largest integer that divides two numbers without leaving a remainder.

Equations and Operations

Formula: An equation demonstrating the relationship between two or more quantities.
Order of Operations: A specified sequence to perform calculations:
- Parentheses first
- Exponents
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)
Algebra: A mathematical branch utilizing variables to represent unknown values.

Expressions and Terms

Monomial: An algebraic expression comprising a single term.
Binomial: An algebraic expression consisting of two terms.
Trinomial: An algebraic expression of three terms.
Polynomial: An expression with one or more terms.

Variable Isolation and Value Calculation

Isolate the Variable: The process of moving the variable to one side of the equation while transferring constants to the opposite side for solving.
Algebraic Expression: A combination of variables and constants through mathematical operations.
Constant: A fixed, unchanging numerical value.
Variable: A symbol representing an element from a specified set of numbers.
Domain: The collection of possible values for a variable.

Advanced Concepts

Negative Exponent Property: Expressed as (x^{-n} = \frac{1}{x^n}), where (x \neq 0).
Evaluate: To determine the numerical value of an expression.
Substitution: Replacing a variable with a specific value or algebraic expression.
Numerical Coefficient: The constant factor accompanying a variable within a term.

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