Algebra-1B Key Terms Quiz
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Questions and Answers

What are perfect squares?

  • Numbers whose square roots are integers (correct)
  • Numbers that cannot be divided
  • Any negative number
  • Any whole number
  • What are rational numbers?

    A real number that can be expressed as a ratio of two integers and has a terminating or repeating decimal.

    Define natural numbers.

    The counting numbers, all positive, not including 0.

    What are whole numbers?

    <p>The non-negative integers, including 0.</p> Signup and view all the answers

    Describe integers.

    <p>Whole numbers that include negative numbers.</p> Signup and view all the answers

    What is an irrational number?

    <p>A number that cannot be expressed as a ratio of two integers.</p> Signup and view all the answers

    What are real numbers?

    <p>Numbers that can be either rational or irrational.</p> Signup and view all the answers

    Define inequality.

    <p>A mathematical sentence comparing the values of two expressions using an inequality symbol.</p> Signup and view all the answers

    What is the distributive property?

    <p>Remove parentheses and simplify expressions involving multiplication.</p> Signup and view all the answers

    Define a constant in mathematics.

    <p>A term that has no variable factor.</p> Signup and view all the answers

    What is a coefficient?

    <p>The numerical factor in a term that contains a variable.</p> Signup and view all the answers

    Define a term in algebra.

    <p>A number, a variable, or a combination of a number and a variable.</p> Signup and view all the answers

    What are like terms?

    <p>Terms with the same variable and exponent, which can be combined.</p> Signup and view all the answers

    What are unlike terms?

    <p>Terms with different variables and/or exponents, which cannot be combined.</p> Signup and view all the answers

    What is a solution to an equation with one variable?

    <p>Any value that makes the equation true.</p> Signup and view all the answers

    Define a solution of an equation with two variables.

    <p>An ordered pair (x, y) that makes the equation true.</p> Signup and view all the answers

    What is the radical in mathematics?

    <p>Another name for a square root.</p> Signup and view all the answers

    Describe prime numbers.

    <p>Whole numbers greater than 1 that have exactly two positive factors: itself and 1.</p> Signup and view all the answers

    What is a factor tree?

    <p>A diagram showing the prime factorization of a number.</p> Signup and view all the answers

    What is the order of operations?

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

    Define an exponent.

    <p>A mathematical notation indicating how many times a number is multiplied by itself.</p> Signup and view all the answers

    What is scientific notation?

    <p>A method of writing numbers using powers of ten.</p> Signup and view all the answers

    What are parallel lines?

    <p>Lines that run side by side and never intersect.</p> Signup and view all the answers

    Define perpendicular lines.

    <p>Lines that intersect to form a 90-degree angle.</p> Signup and view all the answers

    What is slope?

    <p>The rate of change of a line, calculated as $(y2 - y1)/(x2 - x1)$.</p> Signup and view all the answers

    What is Point Slope Form of a linear equation?

    <p>The form $y - y1 = m(x - x1)$ where m is the slope.</p> Signup and view all the answers

    Describe Slope Intercept Form of a linear equation.

    <p>The form $y = mx + b$ where m is the slope and b is the y-intercept.</p> Signup and view all the answers

    What is the Standard Form of a linear equation?

    <p>The form $Ax + By = C$.</p> Signup and view all the answers

    What is a system of linear equations?

    <p>Two or more linear equations to be solved simultaneously.</p> Signup and view all the answers

    List three common methods for solving a system of linear equations.

    <p>Graphing, substitution, elimination.</p> Signup and view all the answers

    What is the process of using substitution to solve a system of linear equations?

    <p>Combine information from both equations to find the variable values.</p> Signup and view all the answers

    Describe the process of using elimination to solve a system of linear equations.

    <p>Adjust the equations to eliminate one variable by adding or subtracting.</p> Signup and view all the answers

    What are linear inequalities?

    <p>An inequality such as $y &gt; -3x + 4$, defining a region of the coordinate plane.</p> Signup and view all the answers

    What happens when multiplying factors with the same base in exponents?

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

    What happens when dividing factors with the same base in exponents?

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

    What occurs when raising a power to a power in exponents?

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

    What is the value of any number raised to the power of zero?

    <ol> <li></li> </ol> Signup and view all the answers

    How do you add or subtract two terms with variables containing exponents?

    <p>The variable and the exponent must be the same to combine them.</p> Signup and view all the answers

    What is a negative exponent?

    <p>It indicates to change to positive exponent by changing the position in a fraction.</p> Signup and view all the answers

    What is a negative fractional exponent?

    <p>It indicates to change to positive exponent by changing the position in a fraction.</p> Signup and view all the answers

    What is the difference between $(-2)^4$ and $-2^4$?

    <p>The first has a negative base, and the second has a positive base.</p> Signup and view all the answers

    What is the rule when exponents appear on terms within parentheses?

    <p>You must distribute the exponent to every term inside the parentheses.</p> Signup and view all the answers

    What is a quotient?

    <p>The answer to a division problem.</p> Signup and view all the answers

    Define a composite number.

    <p>A number that is not prime.</p> Signup and view all the answers

    What is a difference?

    <p>The answer to a subtraction problem.</p> Signup and view all the answers

    What is the greatest common factor (GCF)?

    <p>The largest common factor of two or more given numbers.</p> Signup and view all the answers

    What is exponential growth?

    <p>When a graph is growing with a constant rate.</p> Signup and view all the answers

    What is exponential decay?

    <p>When a graph is reduced with a constant rate.</p> Signup and view all the answers

    Define polynomial.

    <p>An algebraic expression consisting of one or more terms.</p> Signup and view all the answers

    What is the degree of a polynomial?

    <p>The highest combined sum of exponents in the polynomial.</p> Signup and view all the answers

    What does it mean to factor a polynomial?

    <p>To reverse the multiplication process and express it as a product of factors.</p> Signup and view all the answers

    What is a perfect square trinomial?

    <p>An expression of the form $a^2 ± 2ab + b^2$ that factors to $(a ± b)^2$.</p> Signup and view all the answers

    What is the difference of two squares?

    <p>$a^2 - b^2 = (a + b)(a - b)$.</p> Signup and view all the answers

    How do you factor a four-term polynomial by grouping?

    <p>Group the first two and last two terms, and factor out the GCF.</p> Signup and view all the answers

    What is a quadratic function?

    <p>An equation of the form $y = ax^2 + bx + c$.</p> Signup and view all the answers

    Define the standard form of a quadratic function.

    <p>A quadratic function ordered by the exponents of the variables, greatest to least.</p> Signup and view all the answers

    What is a parabola?

    <p>The U-shaped graph of a quadratic equation.</p> Signup and view all the answers

    What is the vertex of a parabola?

    <p>The lowest or highest point on the parabola.</p> Signup and view all the answers

    How many answers can there be when solving a quadratic equation?

    <p>2 if there are two x-intercepts, 1 if there is one, and none if there are no x-intercepts.</p> Signup and view all the answers

    What are the methods to solve a quadratic equation?

    <p>Graphing, factoring, extracting square roots, completing the square, and the quadratic formula.</p> Signup and view all the answers

    How do you factor a quadratic equation?

    <p>Rewrite to standard form and set each factor equal to zero.</p> Signup and view all the answers

    Describe the process of extracting square roots when solving a polynomial.

    <p>Isolate $x^2$ and take the square root of both sides.</p> Signup and view all the answers

    What does completing the square involve when solving a polynomial?

    <p>Add or subtract a constant to form a perfect square trinomial.</p> Signup and view all the answers

    What is the quadratic formula?

    <p>A formula for finding the solutions of a quadratic equation using $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.</p> Signup and view all the answers

    Study Notes

    Number Types

    • Perfect squares: Numbers with integer square roots.
    • Rational numbers: Can be expressed as a fraction of two integers; in decimal form, they are either terminating or repeating.
    • Natural numbers: The set of counting numbers, excluding zero.
    • Whole numbers: Non-negative integers, including zero.
    • Integers: Whole numbers that include negative values.
    • Irrational numbers: Cannot be expressed as a ratio of integers; their decimal representation is nonterminating and nonrepeating.
    • Real numbers: Comprised of both rational and irrational numbers.

    Algebraic Concepts

    • Inequality: Compares two expressions with inequality symbols; graphically represented by open or closed circles.
    • Distributive property: Describes how to remove parentheses in expressions: a(b + c) = ab + ac.
    • Constant: A term without a variable factor.
    • Coefficient: The numerical factor in a term with a variable.
    • Term: May be a number, variable, or a combination of both.
    • Like terms: Terms with the same variable and exponent, which can be combined.
    • Unlike terms: Terms with different variables or exponents that cannot be combined.

    Solutions in Equations

    • Solution of an equation (one variable): Values that satisfy the equation.
    • Solution of an equation (two variables): Ordered pairs that make the equation true.
    • Radical: Another term for square root.

    Geometry

    • Parallel lines: Lines that never intersect and remain equidistant.
    • Perpendicular lines: Lines that intersect at a 90-degree angle.
    • Slope: The rate of change of a line; calculated as (y2 - y1) / (x2 - x1).

    Equation Forms

    • Point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point.
    • Slope-intercept form: y = mx + b, with m as the slope and b as the y-intercept.
    • Standard form: Ax + By = C; useful for finding intercepts.

    Systems of Equations

    • System of linear equations: Two or more equations combined, with potential solutions as intersections of their graphs.
    • Common methods to solve:
      • Graphing: Plot the equations to find can intersect points.
      • Substitution: Solve one equation for a variable and substitute into the other.
      • Elimination: Manipulate equations to eliminate one variable.

    Exponents

    • Exponent basics: Notation indicating repeated multiplication; rules for multiplying, dividing, and raising powers summarized:
      • Multiplying: Add exponents.
      • Dividing: Subtract exponents.
      • Raising a power to a power: Multiply exponents.
    • An exponent of zero equals one, regardless of the base.

    Factoring and Polynomials

    • Polynomial: An expression with one or more terms.
    • Factoring techniques:
      • Greatest common factor (GCF): Identifying and factoring out shared factors.
      • Difference of squares: a² - b² = (a + b)(a - b).
      • Factoring quadratics: Rewrite quadratic as (x - r)(x - s), finding roots.

    Quadratic Functions

    • Quadratic equation: y = ax² + bx + c; graphed as a parabola.
    • Vertex: The highest or lowest point on the parabola, calculated as -(b/2a).
    • Roots: Number of solutions varies: two roots for two intercepts, one for a single intercept, none for no intercepts.

    Solving Quadratic Equations

    • Methods:
      • Graphing: Find x-intercepts where the graph crosses the x-axis.
      • Factoring: Create two binomials and set each equal to zero.
      • Completing the square: Transform the equation into a perfect square trinomial.
      • Quadratic formula: Always applicable for finding solutions.

    Additional Points

    • Accounts for the behavior of exponents with positive/negative bases and the impact of zero and negative exponents.
    • Proper notation involves using the "±" sign for roots when applicable.

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    Description

    Test your understanding of key algebraic terms such as perfect squares, rational numbers, natural numbers, and whole numbers. This quiz will help solidify your knowledge essential for mastering Algebra 1 concepts. Perfect for students looking to enhance their math skills!

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