Algebra 2 Unit 1 Review Flashcards
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Questions and Answers

What are natural numbers?

  • Counting numbers from one to infinity (correct)
  • All positive integers
  • Whole numbers starting from zero
  • All integers including negatives
  • Whole numbers include which of the following?

  • Only positive integers
  • All natural numbers (correct)
  • Negative numbers
  • Zero (correct)
  • Integers are defined as:

  • Only positive numbers
  • Natural numbers and their opposites
  • All positive and negative numbers including zero (correct)
  • Only whole numbers
  • Sets are composed of what?

    <p>members or elements</p> Signup and view all the answers

    What does the symbol ∈ signify?

    <p>is a member of</p> Signup and view all the answers

    What characterizes a finite set?

    <p>has a certain number of members</p> Signup and view all the answers

    What is an infinite set?

    <p>has a limitless number of members</p> Signup and view all the answers

    Sets can be designated in one of two ways, which are:

    <p>Both A and B</p> Signup and view all the answers

    What are subsets?

    <p>sets contained in another set</p> Signup and view all the answers

    What is the union of two sets?

    <p>A and B is a set whose elements appear in either Set A or Set B without repetition</p> Signup and view all the answers

    How is the intersection of two sets defined?

    <p>A and B is a set whose elements are common to A and B</p> Signup and view all the answers

    What does D C imply in terms of set operations?

    <p>C ∩ D = D</p> Signup and view all the answers

    What are theorems in mathematics?

    <p>statements about mathematics requiring proof</p> Signup and view all the answers

    Which of the following are examples of general properties?

    <p>All of the above</p> Signup and view all the answers

    Which properties of addition are correctly matched?

    <p>All of the above</p> Signup and view all the answers

    Identify the properties of multiplication.

    <p>All of the above</p> Signup and view all the answers

    What does PEMDAS stand for?

    <p>Parentheses, Exponents, Multiplication or Division, Addition or Subtraction</p> Signup and view all the answers

    What is the domain in a relation or function?

    <p>the first element (x-value) of a relation or function</p> Signup and view all the answers

    Define a function.

    <p>a relation such that for each first element (x-value, input) there exists one unique second element</p> Signup and view all the answers

    What is the input in a relation or function?

    <p>the x-value of a relation or function</p> Signup and view all the answers

    What does output represent in a function?

    <p>the y-value of the relation or function</p> Signup and view all the answers

    What is the range in terms of relations or functions?

    <p>the second element (y-value) of a relation or function</p> Signup and view all the answers

    What defines a relation?

    <p>a set of numbers that can be graphed on a coordinate (x, y) plane</p> Signup and view all the answers

    How can the domain and range be listed?

    <p>in the order given or rearranged numerically, lowest to highest</p> Signup and view all the answers

    What does a graph of an ordered-pair number represent?

    <p>a point on the rectangular coordinate axes</p> Signup and view all the answers

    What is an exponent?

    <p>a small-sized number written above and to the right of a term indicating the number of times a base is used as a factor</p> Signup and view all the answers

    Which of the following is the correct exponent theorem?

    <p>Both A and B</p> Signup and view all the answers

    Study Notes

    Number Types and Sets

    • Natural Numbers: Counting numbers starting from one and extending to infinity.
    • Whole Numbers: Includes all natural numbers plus zero, ranging from zero to infinity.
    • Integers: Comprise all positive and negative whole numbers including zero, spanning from negative infinity to positive infinity.
    • Sets: Collections of distinct objects called members or elements.

    Set Notation and Types

    • Symbol ∈: Indicates membership, read as "is a member of."
    • Finite Set: Contains a specific number of members.
    • Infinite Set: Has an unlimited number of members.
    • Methods of Designating Sets: Utilizes either the list method, which explicitly lists elements, or the rule method using set-builder notation.
    • Subsets: Sets that are contained within other sets.

    Set Operations

    • Union of Two Sets (A ∪ B): A set that contains elements from either Set A or Set B without duplication.
    • Intersection of Two Sets (A ∩ B): A set comprising elements that are common to both Set A and Set B.
    • If D ⊆ C (D is a subset of C): The intersection of C and D equals D (C ∩ D = D).

    Mathematical Theorems and Properties

    • Theorems: Statements within mathematics that require proof, originating from axioms to logical conclusions.
    • General Properties:
      • Reflexive Property: ( a = a ).
      • Symmetric Property: If ( a = b ), then ( b = a ).
      • Transitive Property: If ( a = b ) and ( b = c ), then ( a = c ).

    Arithmetic Properties

    • Properties of Addition:
      • Commutative: ( a + b = b + a ).
      • Associative: ( a + (b + c) = (a + b) + c ).
      • Identity: ( a + 0 = a ).
      • Additive Inverse: ( a + (-a) = 0 ).
    • Properties of Multiplication:
      • Commutative: ( a \cdot b = b \cdot a ).
      • Associative: ( a(b \cdot c) = (a \cdot b)c ).
      • Identity: ( a \cdot 1 = a ).
      • Multiplicative Inverse: ( a \cdot \frac{1}{a} = 1 ) for ( a \neq 0 ).
      • Distributive: ( a(b + c) = (a \cdot b) + (a \cdot c) ).
      • Zero Property: ( a \cdot 0 = 0 ).

    Function Basics

    • Order of Operations: Follow the PEMDAS hierarchy: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
    • Domain: Refers to the first element (x-value) in a relation or function, also known as the input.
    • Function: A relation where each x-value corresponds to one unique y-value; no x-value is repeated.
    • Input: The x-value of a relation or function.
    • Output: The y-value corresponding to the input in a relation or function.
    • Range: The set of all second elements (y-values) of a relation or function, also known as the output.

    Relations

    • Relation: A collection of numbers that can be graphed on a coordinate plane; can be a function but is not required to be.
    • Domain and Range Representation: Can be listed based on the given order or rearranged numerically; no need to list duplicates.
    • Graphing Ordered Pairs: Each ordered pair represents a point on the coordinate axes, with the first element indicating the x-axis and the second the y-axis.

    Exponents

    • Exponent: A small number positioned above and to the right of a base, indicating how many times the base is a factor.
    • Exponent Theorems:
      • When multiplying: ( a^m \cdot a^n = a^{m+n} ).
      • When dividing: ( \frac{a^m}{a^n} = a^{m-n} ).

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    Test your understanding of the foundational elements of Algebra 2 through these flashcards. Explore key concepts including natural numbers, whole numbers, and integers. Perfect for reviewing essential definitions and preparing for exams.

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