Questions and Answers
What is the absolute value?
What are opposite numbers?
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?
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What does the Commutative Property of Multiplication state?
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What does the Associative Property of Multiplication state?
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What is the Identity Property of Multiplication?
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What is the Distributive Property of Multiplication?
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What is the Associative Property of Addition?
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What is the Identity Property of Addition?
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What is exponential form?
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What is a prime number?
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What is a composite number?
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What is the greatest common factor?
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What is a formula?
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What is the order of operations?
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What is algebra?
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What is a monomial?
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What is a binomial?
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What is a trinomial?
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What is a polynomial?
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What does it mean to isolate the variable?
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What is an algebraic expression?
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What is a constant?
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What is a variable?
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What is the domain?
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What is the negative exponent property?
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What does it mean to evaluate an expression?
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What is substitution?
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What is a numerical coefficient?
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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.
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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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Test your knowledge of key algebra concepts with these flashcards. This quiz covers essential terminology such as absolute value, opposite numbers, and mathematical properties. Perfect for quick reviews and reinforcing your understanding of Algebra 2 topics.