Algebra End of Year Review
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Questions and Answers

What is the Arithmetic Sequence Formula?

  • an=a1(r)^n-1
  • an=a1+(n-1)d (correct)
  • y=x^2
  • y = mx + b

    • What is the Geometric Sequence Formula?

  • y=x^2
  • y = mx + b
  • an=a1(r)^n-1 (correct)
  • an=a1+(n-1)d

    • What is the Exponential Function?

    y = 3^x

    What is the Quadratic Function?

    <p>y = x^2</p> Signup and view all the answers

    What is the Linear Function?

    <p>y = mx + b</p> Signup and view all the answers

    What is a Prime number?

    <p>A number that has no factor but itself and 1</p> Signup and view all the answers

    What is a Perfect Square?

    <p>A number times itself</p> Signup and view all the answers

    What does < represent?

    <p>Less than</p> Signup and view all the answers

    What does > represent?

    <p>Greater than</p> Signup and view all the answers

    What is the Sum?

    <p>The answer to an addition problem</p> Signup and view all the answers

    What is the Product?

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

    What is the Difference?

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

    What is the Quotient?

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

    What is the Mean?

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

    What is the Mode?

    <p>Most frequently occurring number</p> Signup and view all the answers

    What is the Median?

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

    What is a Quadrant?

    <p>One of four sections into which the coordinate plane is divided</p> Signup and view all the answers

    What is the Commutative Property?

    <p>a + b = b + a</p> Signup and view all the answers

    What is the Associative Property?

    <p>(a + b) + c = a + (b + c)</p> Signup and view all the answers

    What is the Distributive Property?

    <p>a(b + c) = ab + ac</p> Signup and view all the answers

    What is the Property of Equality?

    <p>What you do to one side of the equation, you MUST do to the other.</p> Signup and view all the answers

    What is the Lead Coefficient?

    <p>The number in front of the variable with the highest exponent</p> Signup and view all the answers

    What does STAT refer to in statistics?

    <p>Key used to determine mean and median</p> Signup and view all the answers

    What are Integers?

    <p>Positive and negative whole numbers and zero</p> Signup and view all the answers

    What is Slope?

    <p>The 'm' in y = mx + b</p> Signup and view all the answers

    What is the Additive Identity Property?

    <p>a + 0 = a</p> Signup and view all the answers

    What is a Binomial?

    <p>Having two terms</p> Signup and view all the answers

    What is a Linear Function?

    <p>A function in which the graph of the solutions forms a line</p> Signup and view all the answers

    What is the Origin in coordinates?

    <p>(0, 0)</p> Signup and view all the answers

    What is a Variable?

    <p>The letter used in an expression or equation</p> Signup and view all the answers

    What is a Coefficient?

    <p>The # in front of the variable</p> Signup and view all the answers

    What is the Degree of a polynomial?

    <p>Largest exponent in an expression</p> Signup and view all the answers

    What are the KEYS: ALPHA, Y=?

    <p>Creates fraction boxes</p> Signup and view all the answers

    What is the key combination to clear the calculator?

    <p>The keys: 2nd, +, 7, 1, 2</p> Signup and view all the answers

    What do the KEYS: STAT, EDIT allow you to do?

    <p>Allows me to create a table</p> Signup and view all the answers

    What creates the absolute value symbol?

    <p>The KEYS: 2nd, 0, abs</p> Signup and view all the answers

    What is the square root of 36?

    <p>6 or -6</p> Signup and view all the answers

    What is the square root of 25?

    <p>5 or -5</p> Signup and view all the answers

    What is the square root of 4?

    <p>2 or -2</p> Signup and view all the answers

    In y = ax + b, what does 'a' represent?

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

    In y = mx + b, what does 'b' represent?

    <p>Y-intercept</p> Signup and view all the answers

    What is a System of Equations?

    <p>Two or more equations</p> Signup and view all the answers

    What is the Degree of a polynomial?

    <p>Largest exponent of an expression</p> Signup and view all the answers

    What is a Variable?

    <p>A letter used to represent a number</p> Signup and view all the answers

    What is the expansion of (x + 2)(x + 7)?

    <p>x^2 + 9x + 14</p> Signup and view all the answers

    What is the expansion of (x - 6)(x - 6)?

    <p>x^2 - 12x + 36</p> Signup and view all the answers

    What is the expansion of (x + 8)(x + 8)?

    <p>x^2 + 16x + 64</p> Signup and view all the answers

    What is the expansion of (x + 5)(x + 6)?

    <p>x^2 + 11x + 30</p> Signup and view all the answers

    What is the expansion of (x + 3)(x + 4)?

    <p>x^2 + 7x + 12</p> Signup and view all the answers

    What is the expansion of (x - 4)(x - 4)?

    <p>x^2 - 8x + 16</p> Signup and view all the answers

    If f(x) = 3x + 2, find f(4).

    <p>14</p> Signup and view all the answers

    If f(x) = 5x, what is f(3)?

    <p>15</p> Signup and view all the answers

    If g(x) = x - 7, what is g(0)?

    <p>-7</p> Signup and view all the answers

    If m(x) = x^2 - 1, what is m(7)?

    <p>48</p> Signup and view all the answers

    If f(x) = 10x + 1, then f(5) is

    <p>51</p> Signup and view all the answers

    If f(x) = 2x + 7, then f(10) =

    <p>27</p> Signup and view all the answers

    What is the Vertical Line Test used for?

    <p>To determine if a graph is a function</p> Signup and view all the answers

    What ordered pair would make this set NOT a function? {(2,3), (3,4),(4,5)}

    <p>(2, 6)</p> Signup and view all the answers

    Study Notes

    Algebra Concepts

    • Arithmetic Sequence Formula: an = a1 + (n-1)d, used to find the nth term in an arithmetic sequence.
    • Geometric Sequence Formula: an = a1(r)^(n-1), used for determining terms in a geometric sequence.
    • Exponential Function: Represented as y = 3^x, a function where the variable is an exponent.
    • Quadratic Function: Expressed as y = x^2, a polynomial function of degree 2, forming a parabola.
    • Linear Function: Defined by y = mx + b, where m is the slope and b the y-intercept.

    Key Mathematical Terms

    • Prime: A whole number greater than 1 that has no positive divisors other than 1 and itself.
    • Perfect Square: A number that can be expressed as the square of an integer.
    • Inequalities Symbols: "<" indicates "less than" with a dashed line and shading downward; ">" indicates "greater than" with a dashed line and shading upward.
    • Sum, Product, Difference, Quotient: Terms describing the results of addition, multiplication, subtraction, and division, respectively.

    Statistics and Properties

    • Mean: The average of a set of numbers.
    • Mode: The number that occurs most frequently in a data set.
    • Median: The middle value in a set of numbers.
    • Quadrant: One of four sections in the coordinate plane, defined by the x and y axes.

    Algebraic Properties

    • Commutative Property: a + b = b + a, demonstrating that addition is independent of order.
    • Associative Property: (a + b) + c = a + (b + c), showing grouping does not affect the result in addition.
    • Distributive Property: a(b + c) = ab + ac, illustrating how multiplication distributes over addition.
    • Property of Equality: A principle stating that actions performed on one side of an equation must be performed on the other side.

    Functions and Equations

    • Lead Coefficient: The coefficient in front of the variable with the highest exponent in a polynomial.
    • System of Equations: A set of two or more equations with the same variables.
    • Derivative Concepts: In the context of y = ax + b, "a" signifies the slope while "b" signifies the y-intercept.
    • Function Identification: The Vertical Line Test is used to determine if a graph represents a function.

    Calculator Functions

    • STAT Key: Utilized to compute mean and median values.
    • Creating Tables: The keys STAT and EDIT enable the user to generate data tables.
    • Fraction Box Creation: Keys ALPHA and Y= facilitate the creation of fraction boxes in calculations.

    Expressions and Evaluations

    • Quadratic Expansions: Examples provided include:
      • (x + 2)(x + 7) = x^2 + 9x + 14
      • (x - 6)(x - 6) = x^2 - 12x + 36
    • Function Evaluations: Examples of evaluating functions at given points:
      • f(x) = 3x + 2; find f(4) = 14
      • g(x) = x - 7; find g(0) = -7

    Graphs and Functions

    • Ordered Pairs: Understanding conditions under which a set of points constitutes a function and identifying pairs that disrupt this criterion, like (2, 6) when (2, 3), (3, 4), and (4, 5) exist.

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    Description

    This quiz covers essential algebraic concepts and formulas, including arithmetic sequences, geometric sequences, and various types of functions such as linear and quadratic. Test your knowledge and understanding of these foundational ideas to prepare for your end-of-year assessments.

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