Apex Algebra 2 Flashcards Semester 1
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Questions and Answers

What is a mathematical expression?

  • A symbol representing an unknown value
  • A collection of numbers and operations arranged in a meaningful order (correct)
  • A display of data in rows and columns
  • An equation that states two expressions are equal
  • What is an algebraic expression?

    A mathematical expression that contains one or more variables.

    What is the definition of an expression?

    A combination of numbers, variables, and operations that does not contain an equal sign or inequality sign.

    What defines an equation?

    <p>A mathematical statement that says two expressions are equal.</p> Signup and view all the answers

    What is an inequality?

    <p>A mathematical sentence that has two or more expressions separated by inequality signs.</p> Signup and view all the answers

    What is a variable?

    <p>A symbol that represents unknown or changeable values.</p> Signup and view all the answers

    What is a pattern in mathematics?

    <p>A consistent form, style, or method used to connect various objects or ideas.</p> Signup and view all the answers

    What does a table represent in mathematics?

    <p>An organized display of data in rows and columns.</p> Signup and view all the answers

    What are coordinates?

    <p>The x- and y-values that describe the location of a point in an xy-plane.</p> Signup and view all the answers

    What is a factor?

    <p>A number or expression that can be multiplied by another to create a product.</p> Signup and view all the answers

    What is a term in an algebraic expression?

    <p>Part of an algebraic expression separated by + or - signs.</p> Signup and view all the answers

    What is a coefficient?

    <p>A number that multiplies a variable.</p> Signup and view all the answers

    What is a constant?

    <p>A value in an expression that does not change.</p> Signup and view all the answers

    What is a linear equation?

    <p>An equation whose graph is a straight line.</p> Signup and view all the answers

    What is the Distributive Property?

    <p>The rule that states a(b + c) = ab + ac.</p> Signup and view all the answers

    What is standard form?

    <p>A linear equation written in the form Ax + By + C = 0.</p> Signup and view all the answers

    What are inverse operations?

    <p>An operation that reverses the action of another operation.</p> Signup and view all the answers

    What are like terms?

    <p>Terms in an expression that have the same variables raised to the same powers.</p> Signup and view all the answers

    What does it mean to simplify an expression?

    <p>To rewrite an expression as simply as possible.</p> Signup and view all the answers

    What is a no solution expression?

    <p>An expression that is never true, regardless of the value of x.</p> Signup and view all the answers

    What is meant by infinitely many solutions?

    <p>An equation that is always true, no matter what value x takes.</p> Signup and view all the answers

    What is a compound inequality?

    <p>Two or more simple inequalities joined together.</p> Signup and view all the answers

    What is the absolute value?

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

    What are the rules for absolute value equations?

    <p>Can have one, two, or no solutions; equal to a negative number means no solutions.</p> Signup and view all the answers

    How do you solve absolute value equations?

    <p>Make the expression by itself, rewrite as two equations, and solve each.</p> Signup and view all the answers

    What are the rules for absolute value inequalities?

    <p>Greater-than sign leads to 'or' statements; less-than leads to 'and' statements.</p> Signup and view all the answers

    How do you solve absolute value inequalities?

    <p>Get absolute value on one side, work two problems: one original, one flipped.</p> Signup and view all the answers

    What is a union in mathematics?

    <p>The set of all solutions found in an 'or' statement.</p> Signup and view all the answers

    What is an intersection in mathematics?

    <p>The set of numbers appearing in the solution sets of two inequalities.</p> Signup and view all the answers

    What is a literal equation?

    <p>An equation involving two or more variables.</p> Signup and view all the answers

    What is a formula?

    <p>An equation describing an important mathematical relationship.</p> Signup and view all the answers

    How do you solve literal equations?

    <p>Isolate the variable using reverse operations on both sides of the equation.</p> Signup and view all the answers

    What is a relation in mathematics?

    <p>A pairing of one set of information with another.</p> Signup and view all the answers

    What is a function?

    <p>A kind of relation where each input variable is paired with one output variable.</p> Signup and view all the answers

    What is an independent variable?

    <p>The input variable in a function.</p> Signup and view all the answers

    What is a dependent variable?

    <p>The output variable in a function.</p> Signup and view all the answers

    What is functional notation?

    <p>An expression denoted as y = f(x); it suggests y depends on x.</p> Signup and view all the answers

    What is the domain of a function?

    <p>The x values of a function or independent variables.</p> Signup and view all the answers

    What is the range of a function?

    <p>The y values of a function or dependent variables.</p> Signup and view all the answers

    Study Notes

    Mathematical Expressions

    • A mathematical expression is a meaningful arrangement of numbers and operations.
    • Algebraic expressions contain one or more variables and may not include numerals.

    Types of Expressions

    • An expression combines numbers, variables, and operations without equal or inequality signs (e.g., 3x + 4y).
    • An equation states that two expressions are equal (e.g., 2x = 6).
    • An inequality involves expressions separated by inequality signs (e.g., 4x - 5 ≥ 11), with rules for solving including flipping signs when multiplying/dividing by negatives.

    Variables & Patterns

    • Variables represent unknown values, typically denoted by letters like x and y (e.g., 4x - 5y = 9).
    • Patterns demonstrate consistent relationships, such as each number in a sequence being multiplied by a constant (e.g., 2, 6, 18,... multiplies by 3).

    Tables & Coordinates

    • Tables organize data systematically in rows and columns.
    • Coordinates denote the location of points in a Cartesian plane, expressed as ordered pairs (e.g., (4, -3)).

    Algebraic Components

    • Factors are numbers or expressions that combine to yield a product (e.g., 8 and 3 in 8 x 3 = 24).
    • Terms are parts of an algebraic expression, separated by + or - signs, and may contain numbers, variables, or exponents (e.g., 5x² + 2x + 7).

    Coefficients & Constants

    • Coefficients are the numbers multiplying variables in an expression (e.g., 4 and 6 are coefficients in x²y² + 4x + 6y + 10 = 0).
    • Constants are fixed values that do not change (e.g., 10 and 0 in the same expression).

    Linear Equations

    • A linear equation's graph is a straight line and can be expressed in slope-intercept form (y = mx + b), with no exponents on variables (e.g., y = 2x - 3).
    • Solving linear equations involves applying the distributive property, simplifying, and isolating variables through inverse operations.

    Inequalities & Absolute Values

    • Compound inequalities combine simple inequalities (e.g., -3 < x < 15) and can be graphed with arrows indicating direction.
    • Absolute value measures distance from zero, always resulting in a positive number (e.g., |x| = 3 for both 3 and -3).
    • Rules for absolute values include potential for one, two, or no solutions based on equation set to a negative value.

    Functions

    • A function pairs each input (x-value) with a unique output (y-value), denoted in functional notation y = f(x).
    • The domain consists of all possible x-values, while the range includes y-values resulting from the function.

    Literal Equations & Formulas

    • Literal equations feature two or more variables, allowing for expressions like 20x + 5y = 40.
    • Formulas describe crucial mathematical relationships (e.g., perimeter of a rectangle: P = 2l + 2w).

    Solving Techniques

    • Solving literal equations requires isolating the desired variable using reverse operations.
    • Simplifying expressions involves reducing terms and fractions to their simplest forms (e.g., 8/10 simplifies to 4/5).

    Unions & Intersections

    • The union denotes all solutions in an "or" statement, while the intersection represents numbers appearing in both solution sets of inequalities.

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    Test your knowledge with these flashcards for Apex Algebra 2, Semester 1. Explore key concepts like mathematical expressions, algebraic expressions, and more. Enhance your understanding of algebraic terminology and improve your skills in manipulating expressions.

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