Keystone Algebra 1 Flashcards
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Questions and Answers

What is a relation?

  • An equation
  • Two quantities paired together (correct)
  • A line on a graph
  • A single quantity

    • What is a function?

    Each x value is only paired with one y value.

    What does the vertical line test determine?

    It determines if a graph represents a function.

    What does a mapping diagram represent?

    <p>It represents multiple ordered pairs.</p> Signup and view all the answers

    What is the rate of change?

    <p>Slope.</p> Signup and view all the answers

    What are the 4 kinds of slope?

    <p>Negative</p> Signup and view all the answers

    What is the y-intercept?

    <p>Where the line crosses the y-axis.</p> Signup and view all the answers

    What does a box and whisker plot do?

    <p>Divides data into four parts (quartiles).</p> Signup and view all the answers

    What is absolute value?

    <p>A number's distance from zero.</p> Signup and view all the answers

    An open circle means a number is part of the solution.

    <p>False</p> Signup and view all the answers

    A closed circle means a number is part of the solution.

    <p>True</p> Signup and view all the answers

    What are the x values also known as?

    <p>Domain</p> Signup and view all the answers

    What are the y values also known as?

    <p>Dependent variable</p> Signup and view all the answers

    What is the mean?

    <p>Average.</p> Signup and view all the answers

    What does the median represent?

    <p>Middle value.</p> Signup and view all the answers

    What is the mode?

    <p>The number that occurs the most.</p> Signup and view all the answers

    What is the range?

    <p>Difference of highest and lowest numbers.</p> Signup and view all the answers

    What is the rule for multiplying like bases?

    <p>Add exponents.</p> Signup and view all the answers

    What is the rule for dividing like bases?

    <p>Subtract exponents.</p> Signup and view all the answers

    What happens when you raise a power to a power?

    <p>Multiply exponents.</p> Signup and view all the answers

    What does it mean to evaluate an expression?

    <p>Solve.</p> Signup and view all the answers

    What does it mean to interpret a function?

    <p>Explain.</p> Signup and view all the answers

    A linear equation creates a straight line.

    <p>True</p> Signup and view all the answers

    A nonlinear equation creates a straight line.

    <p>False</p> Signup and view all the answers

    What does GCF stand for?

    <p>Greatest common factor.</p> Signup and view all the answers

    What does LCM stand for?

    <p>Least common multiple.</p> Signup and view all the answers

    What is probability?

    <p>What you want to happen over the total number of outcomes.</p> Signup and view all the answers

    Independent events mean one event affects the other.

    <p>False</p> Signup and view all the answers

    What are the steps in factoring?

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

    Negative exponents make a number negative.

    <p>False</p> Signup and view all the answers

    What are like terms?

    <p>Same variable and exponent.</p> Signup and view all the answers

    A rational number is one that ends or repeats.

    <p>True</p> Signup and view all the answers

    An irrational number ends or repeats.

    <p>False</p> Signup and view all the answers

    What is a binomial?

    <p>Two terms.</p> Signup and view all the answers

    What is a trinomial?

    <p>Three terms.</p> Signup and view all the answers

    What is a monomial?

    <p>One term.</p> Signup and view all the answers

    What does degree of 0 represent?

    <p>Constant.</p> Signup and view all the answers

    What does degree of 1 represent?

    <p>Linear.</p> Signup and view all the answers

    What does degree of 2 represent?

    <p>Quadratic.</p> Signup and view all the answers

    What does degree of 3 represent?

    <p>Cubic.</p> Signup and view all the answers

    What are the 3 kinds of inequalities?

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

    What signifies an equation?

    <p>Equal sign.</p> Signup and view all the answers

    What signifies an inequality?

    <p>Greater than or less than sign.</p> Signup and view all the answers

    What is a system in algebra?

    <p>Trying to solve two or more equations at the same time.</p> Signup and view all the answers

    What are the 3 methods of solving systems?

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

    What does one solution in a system indicate?

    <p>Intersecting line: x=# y=#.</p> Signup and view all the answers

    What does infinite solutions in a system indicate?

    <p>One line: 3=3.</p> Signup and view all the answers

    What does no solution in a system indicate?

    <p>Parallel lines: 0=3.</p> Signup and view all the answers

    What are the 2 kinds of sequences?

    <p>Arithmetic</p> Signup and view all the answers

    What is a sample space?

    <p>All the possible outcomes.</p> Signup and view all the answers

    What is a favorable outcome?

    <p>What you want to happen.</p> Signup and view all the answers

    Study Notes

    Key Concepts in Algebra 1

    • Relation: Pairing of two quantities, essential in understanding relationships between variables.

    • Function: A specific type of relation where each x-value corresponds to a single y-value, ensuring consistency in outputs.

    • Vertical Line Test: A graphical method to determine if a relation is a function; if a vertical line intersects a graph more than once, it is not a function.

    • Mapping Diagram: Visual representation that shows multiple ordered pairs and how inputs are related to outputs.

    • Rate of Change: Commonly known as slope; indicates how much the y-value changes for a change in the x-value.

    • Types of Slope:

      • Positive: rises from left to right.
      • Negative: falls from left to right.
      • Undefined: vertical line with no slope.
      • Zero: horizontal line with no rise.

    • Y-Intercept: The point where a line intersects the y-axis, indicating the output when x is zero.

    • Box and Whisker Plot: A statistical tool that divides data into quartiles, effectively showing distribution and variability.

    • Absolute Value: Represents the distance of a number from zero on the number line, always non-negative.

    • Open Circle: Indicates that a number is not included in a solution set.

    • Closed Circle: Signifies that a number is included in a solution set.

    • X Values: Refers to the domain, which includes all possible inputs or independent variables.

    • Y Values: Correspond to the range, encompassing all possible outputs or dependent variables.

    • Mean: The average of a data set, calculated by summing all values and dividing by the count.

    • Median: The middle value in an ordered data set, effectively separating the higher half from the lower half.

    • Mode: The value that appears most frequently in a data set.

    • Range: The difference between the highest and lowest values in a data set, providing insight into variability.

    • Operations with Exponents:

      • Multiply like bases: Add the exponents.
      • Divide like bases: Subtract the exponents.
      • Power to a power: Multiply the exponents.

    • Evaluate: The process of solving mathematical expressions for a specific value.

    • Interpret: The act of explaining or making sense of information or data.

    • Linear Function: Represented by straight lines; constant rate of change.

    • Nonlinear Function: Represented by curves; variable rate of change.

    • GCF (Greatest Common Factor): The largest factor that two or more numbers share.

    • LCM (Least Common Multiple): The smallest multiple that is common to two or more numbers.

    • Probability: The likelihood of an event occurring, calculated as favorable outcomes over total possible outcomes.

    • Independent Events: Events that do not influence each other's outcomes.

    • Factoring: The process of breaking down expressions into simpler components. Key questions include GCF extraction and recognition of patterns like difference of squares.

    • Negative Exponents: Do not result in negative values but instead represent reciprocal relationships.

    • Like Terms: Terms that share the same variable and exponent, allowing for combination in simplification.

    • Rational Numbers: Numbers that can be expressed as a fraction terminating or repeating.

    • Irrational Numbers: Numbers that cannot be expressed as a simple fraction; they neither terminate nor repeat.

    • Binomial: An algebraic expression consisting of two terms.

    • Trinomial: An algebraic expression that includes three terms.

    • Monomial: An algebraic expression that consists of a single term.

    • Degrees of Polynomials:

      • Degree of 0: Constant
      • Degree of 1: Linear
      • Degree of 2: Quadratic
      • Degree of 3: Cubic

    • Inequalities:

      • Types include one variable, two variable, and compound inequalities.
      • Notation includes greater than or less than signs.

    • Equation: A mathematical statement that asserts equality between two expressions.

    • System of Equations: A set of equations with the same variables, solved simultaneously.

    • Systems Solutions:

      • One solution: Lines intersect at one point (e.g., x=#, y=#).
      • Infinite solutions: Lines overlap (e.g., one line represented by an equation like 3=3).
      • No solution: Lines are parallel and never intersect (e.g., 0=3).

    • Types of Sequences:

      • Arithmetic: Constant difference between terms.
      • Geometric: Constant ratio between terms.

    • Sample Space: The set of all possible outcomes in a statistical experiment.

    • Favorable Outcome: The specific result you desire from an event or experiment.

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    Test your understanding of key concepts in Algebra 1 with these flashcards. This quiz covers essential definitions such as relations, functions, and the vertical line test, which are crucial for mastering algebraic principles. Perfect for students looking to reinforce their knowledge.

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