Absolute Value Exercises
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Questions and Answers

What is the value of a when |a| = 5?

  • 10
  • Both 5 and -5 (correct)
  • -5
  • 5

    • What is the value of b when b = |­7|?

  • -1
  • 0
  • -7
  • 7 (correct)

    • What is the value of |­5|?

  • -5
  • 0
  • 5 (correct)
  • 10

    • What is the value of |3| + |­3|?

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

    What is the value of |7| ­ |­7|?

    <p>0</p> Signup and view all the answers

    What is the value of |­1.5|?

    <p>1.5</p> Signup and view all the answers

    What is the value of the smallest non­negative integer?

    <p>0</p> Signup and view all the answers

    What is the value of |­3.7|?

    <p>3.7</p> Signup and view all the answers

    What is the term for the small number that tells how many times to multiply the base?

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

    What is the value of 2 to the power 4?

    <p>16</p> Signup and view all the answers

    What is the value of 7 to the power 2?

    <p>72</p> Signup and view all the answers

    What is the correct order of operations to evaluate the expression 13 + 6 ÷ 2?

    <p>Divide then add</p> Signup and view all the answers

    What is the value of 3 to the power 5?

    <p>243</p> Signup and view all the answers

    What is the value of 4 to the power 3?

    <p>64</p> Signup and view all the answers

    What is the value of 2 to the power 3?

    <p>8</p> Signup and view all the answers

    What is the value of 5 to the power 3?

    <p>125</p> Signup and view all the answers

    What is the value of x in the equation 4x = 16?

    <p>4</p> Signup and view all the answers

    What is the value of y in the equation y + 4 = 12?

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

    What is the value of x in the equation x + 3 = 12?

    <p>9</p> Signup and view all the answers

    What is the value of x in the equation 2x = 8?

    <p>4</p> Signup and view all the answers

    What is the value of z in the equation z + 5 = 11?

    <p>4</p> Signup and view all the answers

    What is the value of x in the equation 3x = 12?

    <p>4</p> Signup and view all the answers

    What is a characteristic of a histogram?

    <p>Bars represent data.</p> Signup and view all the answers

    What is the purpose of the horizontal axis in a histogram?

    <p>To group the data into intervals.</p> Signup and view all the answers

    How do you find the median of a set of values when the number of values is odd?

    <p>The median is the middle value exactly.</p> Signup and view all the answers

    What is the range of a set of values?

    <p>The maximum value minus the minimum value.</p> Signup and view all the answers

    What is the purpose of labels in a histogram?

    <p>To identify the axes.</p> Signup and view all the answers

    What is represented on the vertical axis of a histogram?

    <p>The scale of the data.</p> Signup and view all the answers

    How do you find the median of a set of values when the number of values is even?

    <p>The median is the average of the two middle values.</p> Signup and view all the answers

    What is the purpose of a histogram?

    <p>To show numerical data.</p> Signup and view all the answers

    What is the median of the set of values 31, 24, 64, 19, 57?

    <p>31</p> Signup and view all the answers

    What is the lower quartile (Q1) of the set of values 13, 8, 7, 4, 8, 12, 7, 6, 1, 3, 2?

    <p>3</p> Signup and view all the answers

    What is the balance point of the data set 13, 14, 14, 9, 10, 12, 12?

    <p>12</p> Signup and view all the answers

    What is the mean of the set of values 3, 4, 4, 9, using the balanced point method?

    <p>4</p> Signup and view all the answers

    What is the formula to find the missing value in a set of data?

    <p>The missing value = The number of values X The mean - The sum of given values</p> Signup and view all the answers

    What is the mean of the set of values 18, 6, 18, using the fair share method?

    <p>12</p> Signup and view all the answers

    What is the rule to find the mean of a set of numbers?

    <p>Mean = The sum of given values / The number of values</p> Signup and view all the answers

    What is the median of the set of values 32, 24, 64, 19?

    <p>28</p> Signup and view all the answers

    What is the upper quartile (Q2) of the set of values 13, 8, 7, 4, 8, 12, 7, 6, 1, 3, 2?

    <p>8</p> Signup and view all the answers

    What is the mean of the set of values 10, 2, 0, 20, using the rule?

    <p>8</p> Signup and view all the answers

    Study Notes

    Absolute Value

    • The absolute value of a number is its distance from 0 on the number line.
    • |a| = 5 means a can be either 5 or -5.
    • |­7| = 7 because the distance from 0 to -7 is 7.
    • |3| + |­3| = 6 because the distance from 0 to 3 is 3 and the distance from 0 to -3 is 3.

    Order of Operations

    • Follow the order of operations to evaluate expressions: parentheses, exponents, multiplication and division, and addition and subtraction.
    • Examples:
      • 13 + 6 ÷ 2 = 15
      • 2 × 6 – 4 ÷ 2 = 10
      • (3 ­1) + 4 ÷ 2 = 7

    Exponents

    • An exponent is a small number that tells how many times to multiply a number by itself.
    • Examples:
      • 3 × 3 × 3 × 3 × 3 = 3^5
      • 5 × 5 × 5 = 5^3
      • 6 × 6 = 6^2

    Solving Algebraic Equations

    • To solve an algebraic equation, isolate the variable on one side of the equation.
    • Examples:
      • X = 1+1+1 => X = 3
      • X + 3 = 12 => X = 12 – 3 => X = 9
      • 4 X = 16 => X = 16 ÷ 4 => X = 4

    Histograms

    • A histogram is a graph that shows the distribution of a set of data.
    • Characteristics of a histogram:
      • Title
      • Two axes (horizontal and vertical)
      • Labels for each axis
      • Shows numerical data
      • Bars represent data
      • No gaps between bars

    Median and Quartiles

    • The median is the middle value of a set of values when they are arranged in order.
    • The median is the average of the two middle values if the number of values is even.
    • The lower quartile (Q1) is the middle value of the lower half of the set of values.
    • The upper quartile (Q2) is the middle value of the upper half of the set of values.

    Balance of Data Sets

    • The balance point of a data set is a way to find the average of the data.
    • Examples:
      • Find the balance point of the data set 13, 14, 14, 9, 10, 12, 12
      • The balance point is 12 because the sum of the values above 12 equals the sum of the values below 12.

    Interpreting Arithmetic Mean

    • The mean is one measure of central tendency.
    • The mean can be calculated as the balance point or as the fair share.
    • Examples:
      • Calculate the mean of the data set 3, 4, 4, 9 using the balance point method.
      • Calculate the mean of the data set 7, 7, 10, 9, 12 using the fair share method.

    Missing Value in a Data Set

    • The missing value in a data set can be found using the formula: Missing value = [The number of values X The mean] – [The sum of given values].
    • Examples:
      • Find the value of x in the data set 11, 20, x, 7 with a mean of 14.
      • Find the value of x in the data set 8, 6, x, 5 with a mean of 5.

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    Description

    Practice exercises to help you master the concept of absolute values in mathematics. Solve for the absolute value of different numbers and expressions.

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