Full Practice Exam 8 — Module 1

Questions in this quiz (22)

1. A theater is selling tickets for a show. One group bought $$3$$ adult tickets and $$2$$ child tickets for a total of $$52$$ dollars. Another group bought $$5$$ adult tickets and $$1$$ child ticket for a total of $$71$$ dollars. What is the price, in dollars, of one adult ticket?

   • $$6.37$$
   • $$12.86$$
   • $$14.57$$
   • $$70.25$$

2. If $$f(x)=x^2-6x+10$$ and $$g(x)=4x-2$$, for which value of $$x$$ will $$f(x)=g(x)$$?

   • $$-\sqrt{13},\sqrt{13}$$
   • $$-5,5$$
   • $$10-\sqrt{13},10+\sqrt{13}$$
   • $$5-\sqrt{13},5+\sqrt{13}$$

3. What is the diameter of the circle in the $$xy$$-plane with the equation $$(x-3)^2+(y+4)^2=49$$?

   • $$7$$
   • $$14$$
   • $$49$$
   • $$98$$

4. The table shows the frequency distribution of the $$14$$ values in data set $$M$$.Data set $$N$$ is created by adding $$12$$ to each value in data set $$M$$. Which of the following correctly compares the means and the standard deviations of data sets $$M$$ and $$N$$?

   • The mean of data set $$N$$ is equal to the mean of data set $$M$$, and the standard deviation of data set $$N$$ is equal to the standard deviation of data set $$M$$.
   • The mean of data set $$N$$ is greater than the mean of data set $$M$$, and the standard deviation of data set $$N$$ is greater than the standard deviation of data set $$M$$.
   • The mean of data set $$N$$ is greater than the mean of data set $$M$$, and the standard deviation of data set $$N$$ is equal to the standard deviation of data set $$M$$.
   • The mean of data set $$N$$ is equal to the mean of data set $$M$$, and the standard deviation of data set $$N$$ is greater than the standard deviation of data set $$M$$.

5. $$x-y=2$$$$x+y=y^2-1$$Which ordered pair is a solution?

   • $$(-5,3)$$
   • $$(1,1)$$
   • $$(1,-1)$$
   • $$(-5,-3)$$

6. Which expression is equivalent to $$256x^2-81$$?

   • $$(16x-9)^2$$
   • $$(16x-81)(16x+81)$$
   • $$(8x-9)(8x+9)$$
   • $$(16x-9)(16x+9)$$

7. The weekly revenue, in thousands of dollars, from selling a product can be modeled by the function $$R(p)=-2p^2+40p-120,$$ where $$p$$ is the price of the product in dollars. Based on the model, which statement best interprets the equation $$R(10)=80$$?

   • When the price of the product is $$10$$, the weekly revenue is $$80$$.
   • When the price of the product is $$10$$, the weekly revenue is $$80,000$$.
   • When the price of the product is $$80$$, the weekly revenue is $$10,000$$.
   • When $$10$$ products are sold, the weekly revenue is $$80,000$$.

8. $$\frac{w}{w^2-9}+\frac{3w}{w+3}=\frac{1}{w-3}$$What value of $$w$$ satisfies the equation above?

   • $$\frac{3-\sqrt{13}}{2},\frac{3+\sqrt{13}}{2}$$
   • $$\frac{-3}{2}$$
   • $$-3$$
   • $$\frac{-1}{2}$$

9. Rectangle $$A$$ has a length of $$w$$ centimeters and a width of $$\frac{w}{2}$$ centimeters. Rectangle $$B$$ has a perimeter that is $$60$$ centimeters greater than the perimeter of rectangle $$A$$. The function $$g$$ gives the area of rectangle $$B$$, in square centimeters. Which of the following defines $$g$$?

   • $$g(w)=(w+20)(\frac{w}{2}+30)$$
   • $$g(w)=w\left(\frac{w}{2}+30\right)$$
   • $$g(w)=(w+20)(w+30)$$
   • $$g(w)=(w-15)(w+15)$$

10. The equation $$(x-4)^2+(y+1)^2=36$$ represents circle $$P$$. Circle $$Q$$ is obtained by shifting circle $$P$$ left $$3$$ units in the $$xy$$-plane. Which of the following equations represents circle $$Q$$?

    • $$(x-1)^2+(y+1)^2=36$$
    • $$(x-7)^2+(y+1)^2=36$$
    • $$(x-4)^2+(y-2)^2=36$$
    • $$(x+1)^2+(y+1)^2=36$$

11. A cube has edge lengths that are $$12$$ times the edge lengths of another cube. The volume of the larger cube is $$k$$ times the volume of the smaller cube. What is the value of $$k$$?

    • $$144$$
    • $$930$$
    • $$1200$$
    • $$1728$$

12. The table shows two values of $$x$$ and their corresponding values of $$y$$.In the $$xy$$-plane, the graph of the linear equation representing this relationship passes through the point $$\left(\frac{1}{3},k\right)$$. What is the value of $$k$$?

    • $$4$$
    • $$\frac{17}{3}$$
    • $$\frac{19}{3}$$
    • $$3$$

13. A researcher conducted an experiment to study whether people tend to choose the last item when given a list of choices. In the experiment, $$500$$ people were shown a set of $$6$$ videos arranged in random order. Each person was asked to choose the most interesting video. Of the first $$250$$ participants, $$62$$ chose the last video in the set. Among the remaining $$250$$ participants, $$p$$ people chose the last video in the set. If more than $$25\%$$ of all participants chose the last video in the set, which of the following inequalities best describes the possible values of $$p$$?

    • $$p$$ > $$0.25(500-62)$$, where $$p\le250$$
    • $$p$$ > $$0.25(500+62)$$, where $$p\le250$$
    • $$p-62$$ > $$0.25(500)$$, where $$p\le250$$
    • $$p+62$$ > $$0.25(500)$$, where $$p\le250$$

14. The graph of $$y=h(x)$$ is shown in the $$xy$$-plane. A new function is defined by $$f(x)=2h(x)-1$$. For what value of $$x$$ > $$0$$ does $$f(x)=5$$?

    • $$2$$
    • $$3$$
    • $$5$$
    • $$6$$

15. $$AB=42$$$$BC=56$$$$CA=70$$Right triangle $$ABC$$ is similar to triangle $$DEF$$, where $$A$$ corresponds to $$D$$ and $$B$$ corresponds to $$E$$. The lengths of the sides of triangle $$ABC$$ are given. What is the value of $$cos(D)$$?

    • $$\frac{1}{5}$$
    • $$\frac{2}{5}$$
    • $$\frac{3}{5}$$
    • $$\frac{4}{5}$$

16. In parallelogram $$PQRS$$, the length of $$PQ$$ is one-fourth the length of $$PS$$. If the perimeter of the parallelogram is $$60$$ inches, what is the length, in inches, of $$RS$$?

    • $$5$$
    • $$6$$
    • $$12$$
    • $$24$$

17. A dealership manager tracked the resale value of a specific car model. The scatterplot shows the value, in thousands of dollars, and the age, in years, for several cars of this model. What was the value, in thousands of dollars, of a car that was $$6$$ years old, according to the scatterplot?

    • $$12$$
    • $$13$$
    • $$15$$
    • $$18$$

18. The function $$f$$ is defined by $$f(x)=3(2)^x-7$$. What is the $$y$$-intercept of the graph of $$y=f(x)$$ in the $$xy$$-plane?

    • $$(0,-4)$$
    • $$(0,-1)$$
    • $$(0,3)$$
    • $$(0,7)$$

19. The positive number $$a$$ is $$160\%$$ of the number $$b$$, and $$a$$ is $$80\%$$ of the number $$c$$. If $$c$$ is $$k\%$$ of $$b$$, which of the following is closest to the value of $$k$$?

    • 200

20. The data set below gives the number of hours a student spent studying each day for $$7$$ consecutive days.$$3,5,2,8,2,6,2$$What is the mean number of hours the student spent studying per day?

    • $$4$$
    • $$5$$
    • $$5.5$$
    • $$6$$

21. A company that manufactures desks has a fixed monthly cost and a cost per desk produced. The graph shows the company's total estimated cost $$C$$, in thousands of dollars, to produce $$n$$ desks in a month. What is the estimated total cost, in thousands of dollars, to produce $$300$$ desks in a month?

    • $$140$$
    • $$150$$
    • $$300$$
    • $$440$$

22. A company manufactures two sizes of cylindrical water tanks, each with a height of $$80$$ centimeters. The radius of tank $$A$$ is $$12$$ centimeters, and the radius of tank $$B$$ is $$25\%$$ larger than the radius of tank $$A$$. What is the volume, in cubic centimeters, of tank $$B$$?

    • $$14,400\pi$$
    • $$18,000\pi$$
    • $$22,500\pi$$
    • $$28,800\pi$$