Mathematics Problem Solving Quiz
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Questions and Answers

What is the total estimated cost in dollars for purchasing one of each type of sport ball, rounded to the nearest dollar?

  • $31.00
  • $32.00 (correct)
  • $36.00
  • $34.00
  • What is the expression that correctly shows how to find the number of boxes of darts, x, Marty can buy?

  • 80 = 56 - 6x
  • 80 = 56 + 6x (correct)
  • 80 = 6x
  • 80 = 56(6x)
  • What is the measure of angle x in a triangle given that two angles are 70° and 30°?

  • 30°
  • 60°
  • 80° (correct)
  • 150°
  • If lines a and b are parallel and line c is a transversal, which of the following statements about the angles is true?

    <p>Alternate interior angles are equal.</p> Signup and view all the answers

    When estimating the cost of five sport balls, which of the following values is NOT rounded correctly?

    <p>Volleyball $6.43 to $6</p> Signup and view all the answers

    If Marty has $80 and spends $56, how much money does he have left for the darts?

    <p>$24</p> Signup and view all the answers

    In the triangle where angle x must be found, which calculation is used to determine x?

    <p>x = 180° - (70° + 30°)</p> Signup and view all the answers

    Which of the following statements correctly describes the relationship between angles m⬔1 and m⬔4?

    <p>They are opposite angles.</p> Signup and view all the answers

    What expression accurately represents 4 less than twice a number, n?

    <p>2n - 4</p> Signup and view all the answers

    What is the mean of Katelyn's bowling scores for the first four weeks?

    <p>136</p> Signup and view all the answers

    What will be the change in Katelyn's mean bowling score after her fifth week score of 126?

    <p>Decrease by 2</p> Signup and view all the answers

    If angles m⬔1 and m⬔6 are supplementary, what can be concluded about their measures?

    <p>Their sum is 180 degrees.</p> Signup and view all the answers

    Using the Pythagorean Theorem, what is the value of c in the figure provided?

    <p>$\sqrt{20}$ units</p> Signup and view all the answers

    Which set of points forms the vertices of a square on the coordinate grid?

    <p>Points A, B, G, F</p> Signup and view all the answers

    Which measure of central tendency is least affected by dropping the outlier value of 40 from the heart rate data?

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

    What is the effect of the outlier heart rate of 40 on the mean heart rate of the data set?

    <p>It decreases the mean slightly.</p> Signup and view all the answers

    What is the correct interpretation of the expression $x \leq -5$?

    <p>x can be any value less than or equal to -5</p> Signup and view all the answers

    What type of shape is defined by points that are equidistant from each other in a coordinate plane?

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

    Which heart rate data is an outlier in the given table?

    <p>40 beats per minute</p> Signup and view all the answers

    In the context of the coordinate grid, which statement is true about the vertices of shape A, B, C, and D?

    <p>They form a rectangle.</p> Signup and view all the answers

    Which of the following statements represents a misinterpretation of the involvement in activities data?

    <p>Students are involved in 180 percent of the activities.</p> Signup and view all the answers

    Calculate the value of $12 + 2(12 - 9)^2$. What is the result?

    <p>30</p> Signup and view all the answers

    What is the value of $\frac{1}{3} + (– \frac{1}{6})$?

    <p>–\frac{1}{2}</p> Signup and view all the answers

    Which expression evaluates to –2?

    <p>–4 + 2</p> Signup and view all the answers

    If Becky rolls a six-sided number cube, what is the probability of rolling a 6 two consecutive times?

    <p>$\frac{1}{36}$</p> Signup and view all the answers

    Which inequality correctly represents the value of x in $6 - 4x \leq 26$?

    <p>x \leq –8</p> Signup and view all the answers

    If the number of students involved in music is the highest, what percentage of students participate in music?

    <p>75%</p> Signup and view all the answers

    Based on the data, which activity has the least number of students involved?

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

    Study Notes

    Sport Balls Cost Estimation

    • Cost of soccer ball: $4.99, baseball: $1.46, basketball: $12.54, football: $8.89, volleyball: $6.43
    • Estimate total cost for one of each ball by rounding:
      • Soccer: $5, Baseball: $1, Basketball: $13, Football: $9, Volleyball: $6
      • Total estimated cost: $34 (Option C).

    Equations for Darts Purchase

    • Marty has $80, spends $56 on a shirt.
    • Cost per box of darts is $6.
    • Correct equation to find number of boxes (x) he can buy: (80 = 56 + 6x) (Option A).

    Triangle Angle Measure

    • Given angles: 70° and 30°.
    • To find angle (x): (180° - (70° + 30°) = 80°) (Option C).

    Angles with Parallel Lines

    • Lines (a) and (b) are parallel, (c) is a transversal.
    • Key angle relation: (m∠1 = m∠4) because they are vertical angles (Option D).

    Expression of Mathematical Relationships

    • "4 less than twice a number (n)" expressed as: (2n - 4) (Option D).

    Katelyn’s Bowling Scores

    • Scores: Week 1: 136, Week 2: 145, Week 3: 123, Week 4: 140.
    • Mean score over four weeks: 136.
    • Fifth week score: 126, new mean will decrease (Option B), calculated decrease is by 2.

    Student Activities Involvement

    • Percent involvement: clubs 45%, sports 60%, music 75%.
    • Misrepresentation example from circle graph: total involvement percent exceeds 100% (Option D).

    Mathematical Expression Evaluation

    • Evaluate (12 + 2(12 - 9)^2):
      • Calculate (12 - 9 = 3); square is (9); then (2 \cdot 9 = 18); finally (12 + 18 = 30) (Option B).

    Fraction Value Calculation

    • Calculate ( \frac{2}{3} + (-\frac{1}{6})):
      • Convert ( \frac{2}{3} ) to sixths: ( \frac{4}{6} + (-\frac{1}{6}) = \frac{3}{6} = \frac{1}{2} ) (Option A).

    Expression Resulting in -2

    • The expression that equals -2: (-4 + 2) (Option D).

    Probability of Rolling a Die

    • Probability of rolling a 6 twice in succession:
      • ( \left( \frac{1}{6} \right) \times \left( \frac{1}{6} \right) = \frac{1}{36} ) (Option A).

    Inequality Expression for x

    • Solve for x in (6 - 4x \leq 26):
      • Rearranging gives (x \geq -5) (Option D).

    Pythagorean Theorem Application

    • Using theorem to find (c) in right triangle with sides 2 and 4:
      • (c = \sqrt{2^2 + 4^2} = \sqrt{20} ) (Option B).

    Identifying Square Vertices

    • Vertices of a square must be equally spaced and form right angles.
    • Correct points include: points A, C, E, D (Option A).

    Heart Rate Data Analysis

    • Heart rates: 78, 71, 79, 80, 40, 71; identified outlier: 40.
    • The measure of central tendency least affected by removing an outlier: median (Option B).

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    Description

    Test your skills in various mathematical concepts including cost estimation, algebraic equations, geometry, and expressions. This quiz covers a range of topics suitable for middle school students and helps reinforce understanding through practical application of math. Get ready to solve problems and enhance your math knowledge!

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