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?

<p>a + b = b + a</p> Signup and view all the answers

What does the Commutative Property of Multiplication state?

<p>ab = ba</p> Signup and view all the answers

What does the Associative Property of Multiplication state?

<p>a(bc) = (ab)c</p> Signup and view all the answers

What is the Identity Property of Multiplication?

<p>a * 1 = a</p> Signup and view all the answers

What is the Distributive Property of Multiplication?

<p>a(b+c) = ab + ac</p> Signup and view all the answers

What is the Associative Property of Addition?

<p>a + (b + c) = (a + b) + c</p> Signup and view all the answers

What is the Identity Property of Addition?

<p>a + 0 = a</p> Signup and view all the answers

What is exponential form?

<p>A simplified form of writing repeated multiplication.</p> Signup and view all the answers

What is a prime number?

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

What is a composite number?

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

What is the greatest common factor?

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

What is a formula?

<p>An equation that expresses the relationship between related quantities.</p> Signup and view all the answers

What is the order of operations?

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

What is algebra?

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

What is a monomial?

<p>An algebraic expression with one term.</p> Signup and view all the answers

What is a binomial?

<p>An algebraic expression with two terms.</p> Signup and view all the answers

What is a trinomial?

<p>An algebraic expression with three terms.</p> Signup and view all the answers

What is a polynomial?

<p>An algebraic expression with one or more terms.</p> Signup and view all the answers

What does it mean to isolate the variable?

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

What is an algebraic expression?

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

What is a constant?

<p>A fixed number.</p> Signup and view all the answers

What is a variable?

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

What is the domain?

<p>The set of numbers of the variable.</p> Signup and view all the answers

What is the negative exponent property?

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

What does it mean to evaluate an expression?

<p>To calculate the numerical value of an expression.</p> Signup and view all the answers

What is substitution?

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

What is a numerical coefficient?

<p>The numerical factor accompanying the variables in a term.</p> 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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