Full Practice Exam 21 — Module 2

Questions in this quiz (22)

1. A factory produces 48 million batteries every 24 hours. At what rate are the batteries produced, in millions of batteries per hour?

   • 1.5
   • 2.0
   • 2.5
   • 3.0

2. In the $$xy$$-plane, the graph of the equation $$y=\frac{3x+8}{x+2}$$ intersects the $$y$$-axis at $$(0,c)$$. What is the value of $$c$$?

   • 2
   • 3
   • 4
   • 8

3. A student recorded the results of an experiment.Which of the following types of functions best models the crystal mass, in grams, as a function of the salt concentration?

   • Increasing linear
   • Decreasing linear
   • Increasing exponential
   • Decreasing exponential

4. The table shows the score range and the number of students in each score range for $$437$$ students.If the scores are only integer values, what is one possible median score for the $$437$$ students?

   • 63

5. The initial mass of carbon-14 in a sample is 20 grams. The mass of carbon-14 in the sample decreases by half every 10 years. Which of the following equations represents the mass $$y$$, in grams, of carbon-14 in the sample after $$x$$ years?

   • $$y=\left(\frac{1}{2}\right)^{\frac{x}{10}}$$
   • $$y=20\left(\frac{1}{2}\right)^{\frac{x}{10}}$$
   • $$y=10\left(\frac{1}{2}\right)^{\frac{x}{20}}$$
   • $$y=20(2)^{\frac{x}{10}}$$

6. A hiking trail is approximately 1,800 miles long. A hiker starts at one end and walks at a constant speed of 12 miles per day. The equation $$12x=1,800$$ represents this situation. What does the solution to the equation represent?

   • The number of days the hiker takes to complete the trail
   • The number of miles the hiker walks in 12 days
   • The distance, in miles, the hiker walks in 1 day
   • The distance, in miles, the hiker walks in 12 days

7. For a linear function $$f$$, the graph of $$y=f(x)$$ in the $$xy$$-plane passes through the points $$(2,11)$$ and $$(6,31)$$. Which equation defines $$f$$?

   • $$f(x)=5x+1$$
   • $$f(x)=5x+11$$
   • $$f(x)=-5x+21$$
   • $$f(x)=-5x-1$$

8. If $$5(k+2)=25-5(k+2),$$ what is the value of $$k+2?$$

   • $$2$$
   • $$\frac{5}{2}$$
   • $$3$$
   • $$\frac{7}{2}$$

9. The table summarizes the number of colleges in a state by type and enrollment.If a university or college with enrollment greater than $$8,000$$ is selected at random, what is the probability that it is a public university or college? Express your answer as a fraction or decimal.

   • $$\frac{2}{7}$$
   • $$\frac{4}{7}$$
   • $$\frac{5}{7}$$
   • $$\frac{6}{7}$$

10. The points on the scatterplot show the Index of Consumer Sentiment values for US consumers each year from $$2008$$ to $$2016$$. A line of best fit for the data is also shown. For $$2015$$, which of the following is closest to the difference between the actual Index of Consumer Sentiment value and the value predicted by the line of best fit?

    • $$4.6$$
    • $$2.1$$
    • $$1.0$$
    • $$0.2$$

11. $$6y-9x=27$$ $$2y-3x=9$$How many solutions does the given system of equations have?

    • Zero
    • Exactly one
    • Exactly two
    • Infinitely many

12. A psychologist surveyed employees from three departments. The results are summarized in the table.If a surveyed employee who prefers a hybrid schedule is chosen at random, what is the probability that the employee is from department X or department Z?

    • $$0.20$$
    • $$0.25$$
    • $$0.52$$
    • $$0.75$$

13. If $$\frac{p}{q}=\frac{6p}{xq},$$ what is the value of $$x$$?

    • $$1$$
    • $$3$$
    • $$6$$
    • $$12$$

14. In the figure shown, $$\overline{BD}$$ is parallel to $$\overline{AE}$$. What is the length of $$\overline{AE}$$?

    • $$6$$
    • $$13$$
    • $$16$$
    • $$27$$

15. The diameter of circle A is 8 times the diameter of circle B. The circumference of circle A is how many times the circumference of circle B?

    • $$4$$
    • $$8$$
    • $$16$$
    • $$64$$

16. The dot plots below represent data set A and data set B. Which statement best compares the means of the two data sets?

    • The mean of data set A is greater than the mean of data set B.
    • The mean of data set A is equal to the mean of data set B.
    • The mean of data set A is less than the mean of data set B.
    • There is not enough information to compare the means.

17. For positive values of $$x$$ and $$n$$, $$x$$ is $$n\%$$ of $$40$$. Which expression represents $$n$$ in terms of $$x$$?

    • $$100\left(\frac{40}{x}\right)$$
    • $$100\left(\frac{x}{40}\right)$$
    • $$100\left(\frac{20}{x}\right)$$
    • $$100\left(\frac{x}{20}\right)$$

18. The graph of $$y=w(x)$$ is shown in the $$xy$$-plane. If $$a$$, $$b$$, and $$c$$ are positive constants, which of the following could define the function $$w$$?

    • $$w(x)=-a(x+b)^2-c$$
    • $$w(x)=-a(x-b)^2-c$$
    • $$w(x)=a(x+b)^2-c$$
    • $$w(x)=a(x-b)^2-c$$

19. Line $$L$$ is tangent to a circle at point $$P$$. A chord $$\overline{PQ}$$ is drawn from point $$P$$ to point $$Q$$ on the circle. If the measure of the angle formed by line $$L$$ and chord $$\overline{PQ}$$ is $$65^\circ$$, what is the measure of arc $$PQ$$?

    • $$32.5^\circ$$
    • $$65^\circ$$
    • $$130^\circ$$
    • $$230^\circ$$

20. Juliet is painting figurines of superheroes as part of an art project. She paints $$3$$ figurines per day for the first $$5$$ days of the project. Realizing that she needs to finish sooner, Juliet increases her workload to paint $$5$$ figurines per day for the remaining duration of the project. She plans to sell $$80\%$$ of the figurines. What is the least number of days Juliet needs to paint figurines for the rest of the project in order to sell at least $$112$$ figurines?

    • 25

21. Data set $$X$$: $$2,3,4,10,16,17,18$$Data set $$Y$$: $$8,9,10,10,10,11,12$$The means of data sets $$X$$ and $$Y$$ are both $$10$$. Which of the following is true about the comparison of the standard deviations of the two data sets?

    • The standard deviation of data set $$X$$ is less than the standard deviation of data set $$Y$$.
    • The standard deviation of data set $$X$$ is greater than the standard deviation of data set $$Y$$.
    • The standard deviations of the two data sets are equal.
    • There is not enough information to compare the standard deviations.

22. The amount of heat $$Q(t)$$, in calories, required to raise the temperature of 25 grams of water by $$t$$ degrees Celsius is defined by a linear function $$Q$$. If $$Q(0)=0$$ and $$Q(4)=40,$$ how many calories of heat are required to raise the temperature of the water from $$5^\circ C$$ to $$11^\circ C$$?

    • $$30$$
    • $$40$$
    • $$60$$
    • $$80$$