Algebra II Vocabulary Flashcards
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Questions and Answers

What is a complex number?

  • A number greater than zero
  • A number with a real part only
  • A number that consists of both real (a) and imaginary (bi) parts (correct)
  • A negative number
  • What is the absolute value?

    The distance between a number and zero.

    Define an expression in mathematics.

    A representation of a quantity that may contain numbers, variables, or operation symbols.

    What is a variable?

    <p>A quantity that may change within the context of a mathematical problem or experiment.</p> Signup and view all the answers

    What is a term in mathematics?

    <p>Either a single number or variable, or numbers and variables multiplied together.</p> Signup and view all the answers

    Define a polynomial.

    <p>The general term for algebraic expressions such as monomials, binomials, and trinomials.</p> Signup and view all the answers

    What does the degree of a polynomial refer to?

    <p>The largest exponent or the largest sum of exponents of a term within a polynomial.</p> Signup and view all the answers

    What is the leading coefficient?

    <p>The coefficient of the first term of a polynomial written in descending order of exponents.</p> Signup and view all the answers

    What are the factors of a monomial?

    <p>The number(s) and/or variable(s) that are multiplied together to form a monomial.</p> Signup and view all the answers

    What is a prime polynomial?

    <p>A polynomial that cannot be factored into a product of lesser degree polynomial factors.</p> Signup and view all the answers

    If $ab = 0$, then $a = 0$ or $b = 0$.

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

    What are zeros in a function?

    <p>The values of x where the function is equal to zero.</p> Signup and view all the answers

    What are x-intercepts?

    <p>Where the graph crosses the x-axis and where $f(x) = 0$.</p> Signup and view all the answers

    What is a vertical line represented by?

    <p>x = a (where a can be any real number); always has an undefined slope.</p> Signup and view all the answers

    What is a horizontal line represented by?

    <p>y = c (where c can be any real number); always has a zero slope.</p> Signup and view all the answers

    Define an inequality.

    <p>An algebraic sentence comparing two quantities.</p> Signup and view all the answers

    What is the domain of a function?

    <p>The set of all possible values of the independent variable.</p> Signup and view all the answers

    What is the range of a function?

    <p>The set of all possible values of the dependent variable.</p> Signup and view all the answers

    What is function notation?

    <p>f(x) is read as 'the value of f at x' or 'f of x'; other letters can be used to name functions.</p> Signup and view all the answers

    What represents direct variation?

    <p>y = kx where k is the constant of variation.</p> Signup and view all the answers

    Define inverse variation.

    <p>k = xy where k is the constant of variation.</p> Signup and view all the answers

    What does joint variation represent?

    <p>y = kxz where k is the constant of variation; one variable depends on two or more other variables.</p> Signup and view all the answers

    Define an arithmetic sequence.

    <p>A sequence of numbers that has a common difference between every two consecutive terms.</p> Signup and view all the answers

    What is a geometric sequence?

    <p>A sequence of numbers where each term after the first is obtained by multiplying the previous term by a constant ratio.</p> Signup and view all the answers

    Define a permutation.

    <p>An ordered arrangement of a group of objects.</p> Signup and view all the answers

    What is a combination?

    <p>The number of possible ways to select or arrange objects when there is no repetition and order does not matter.</p> Signup and view all the answers

    Define a z-score.

    <p>The number of standard deviations an element is away from the mean.</p> Signup and view all the answers

    What is a literal equation?

    <p>A formula or equation that consists primarily of variables.</p> Signup and view all the answers

    What is the standard form of a quadratic equation?

    <p>ax² + bx + c = 0</p> Signup and view all the answers

    What is the vertex of a quadratic function?

    <p>Given standard form: (-b/2a, f(-b/2a)); Given vertex form: (h, k).</p> Signup and view all the answers

    What does the quadratic formula do?

    <p>Used to find the solutions to any quadratic equation written in standard form.</p> Signup and view all the answers

    What are increasing/decreasing intervals?

    <p>A function can be described as increasing, decreasing, or constant over a specified interval or the entire domain.</p> Signup and view all the answers

    What are extrema in a function?

    <p>The largest (maximum) and smallest (minimum) value of a function within a given interval or on the entire domain.</p> Signup and view all the answers

    Define end behavior in terms of functions.

    <p>The value of a function as x approaches positive or negative infinity.</p> Signup and view all the answers

    What is the linear parent function?

    <p>f(x) = x</p> Signup and view all the answers

    What is the quadratic parent function?

    <p>f(x) = x²</p> Signup and view all the answers

    Define the absolute value parent function.

    <p>f(x) = |x|</p> Signup and view all the answers

    What is the square root parent function?

    <p>f(x) = √x</p> Signup and view all the answers

    What is the cubic parent function?

    <p>f(x) = x³</p> Signup and view all the answers

    Define the cube root function.

    <p>f(x) = ³√x</p> Signup and view all the answers

    What is the rational parent function?

    <p>f(x) = 1/x; the reciprocal of a linear function.</p> Signup and view all the answers

    What does the exponential growth parent function represent?

    <p>f(n) = bⁿ where b &gt; 1.</p> Signup and view all the answers

    What is the logarithmic parent function?

    <p>f(x) = logₙ(x) where n &gt; 1.</p> Signup and view all the answers

    What does translation of a parent function involve?

    <p>f(x - h) + k; any parent function can be shifted horizontally h units or vertically k units.</p> Signup and view all the answers

    What does dilation of a parent function refer to?

    <p>a·f(x) or f(ax); any parent function can be stretched or compressed either vertically or horizontally.</p> Signup and view all the answers

    Define reflection of a parent function.

    <p>-f(x) or f(-x); any parent function can be flipped over either axis.</p> Signup and view all the answers

    What is the inverse of a function?

    <p>Graphically, the reflection of the original graph over the line, y = x.</p> Signup and view all the answers

    Define continuity in functions.

    <p>A function that is continuous at every point in its domain.</p> Signup and view all the answers

    What is an asymptote?

    <p>A line that continually approaches a given curve but does not meet it at any finite distance.</p> Signup and view all the answers

    Define a hole in graphing functions.

    <p>Exists on the graph of a rational function at any input value causing both the numerator and denominator to be equal to zero.</p> Signup and view all the answers

    What is the fundamental counting principle?

    <p>If there are m ways for one event to occur and n ways for a second event to occur, then there are $m imes n$ ways for both events to occur.</p> Signup and view all the answers

    What is the permutation formula?

    <p>nPr(n, r)</p> Signup and view all the answers

    What is the combination formula?

    <p>nCr(n, r)</p> Signup and view all the answers

    What does ∑ (capital sigma) represent?

    <p>A summation symbol.</p> Signup and view all the answers

    Define the empirical rule in statistics.

    <p>68-95-99.7 rule; approximate percentage of element distribution.</p> Signup and view all the answers

    Study Notes

    Complex Numbers and Absolute Value

    • A complex number is represented as a ± bi, combining real (a) and imaginary (bi) parts.
    • Absolute value reflects the distance of a number from zero on the number line.

    Algebraic Concepts

    • An expression constitutes numbers, variables, and operation symbols.
    • Variables, like x or y, represent quantities that can adjust in mathematical scenarios.
    • Terms can be a single number/variable or a product of both, separated by addition or subtraction.

    Polynomials and Their Characteristics

    • Polynomials encompass algebraic expressions such as monomials, binomials, and trinomials.
    • The degree of a polynomial is defined by the largest exponent or sum of exponents in its terms.
    • The leading coefficient is the coefficient of the first term when written in decreasing order of exponents.

    Functions and Graphs

    • Zeros of a function indicate where the function equals zero (f(x) = 0).
    • X-intercepts occur where the graph crosses the x-axis.
    • Vertical lines have an equation x = a with undefined slopes; horizontal lines are y = c with a zero slope.

    Relationships and Variations

    • Inequalities compare two quantities in algebraic sentences.
    • Domain refers to all possible values that an independent variable can take.
    • Range represents all possible values of a dependent variable.

    Variations Defined

    • Direct variation follows the formula y = kx, indicating a constant ratio between x and y.
    • Inverse variation is expressed as k = xy, indicating a constant product relationship.
    • Joint variation presents y = kxz, where one variable depends on two or more others.

    Sequences and Combinatorics

    • An arithmetic sequence has a consistent difference between consecutive terms.
    • A geometric sequence involves multiplying each term by a constant ratio.
    • Permutations are ordered arrangements; combinations involve selection without regard to order.

    Statistical Measures

    • Z-score indicates how many standard deviations an element is from the mean.
    • Literal equations predominantly consist of variables, often used to express relationships.

    Quadratic Functions

    • Standard form for quadratic equations is ax² + bx + c = 0.
    • Vertex of a quadratic function can be found using special formulas based on its standard and vertex forms.
    • The quadratic formula x = -b ± √(b² - 4ac)/2a solves quadratic equations.

    Function Behavior

    • Increasing/decreasing intervals characterize the behavior of functions over specified ranges.
    • Extrema denote the maximum and minimum values of functions, either locally or globally.
    • End behavior describes the function's value as x approaches positive or negative infinity.

    Parent Functions

    • Parent functions represent the simplest forms:
      • Linear: f(x) = x
      • Quadratic: f(x) = x²
      • Absolute Value: f(x) = |x|
      • Square Root: f(x) = √x
      • Cubic: f(x) = x³
      • Cube Root: f(x) = ³√x
      • Rational: f(x) = 1/x
      • Exponential Growth: f(n) = bⁿ (b > 1)
      • Logarithmic: f(x) = logₙ(x) (n > 1)

    Transformations and Inverses

    • Translations of parent functions shift graphs horizontally/vertically.
    • Dilations stretch or compress graphs either vertically or horizontally.
    • Reflections flip graphs over axes, altering their orientations.

    Continuity and Discontinuities

    • Continuity indicates a function is unbroken at all points in its domain.
    • Asymptotes are lines that approach a curve but do not intersect it, indicating discontinuity.
    • Holes in functions occur where both the numerator and denominator are zero, causing discontinuity.

    Counting Principles

    • Fundamental counting principle: If there are m ways for one event and n ways for another, there are m ∙ n ways for both.
    • Permutations and combinations have specific formulas: nPr for permutations and nCr for combinations.

    Statistical Distribution

    • The empirical rule (68-95-99.7 rule) describes the distribution of elements in a normal distribution curve.

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    Test your understanding of key terms in Algebra II with these flashcards. Each card includes a word and its definition to enhance your vocabulary. Ideal for students preparing for the Virginia SOL exams.

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