Full Practice Exam 5 — Module 2

Questions in this quiz (22)

1. Isabel grows potatoes in her garden. This year, she harvested $$900$$ potatoes. She saved $$12$$ percent of them to plant next year and planned to sell the rest at the farmers market. However, $$8$$ percent of the potatoes she planned to sell spoiled and could not be sold. How many potatoes did Isabel successfully sell?

   • 729
   • Answer

2. A rectangular field is $$0.8$$ kilometers long and $$350$$ meters wide. What is the area of the field in square centimeters?$$(1\text{ kilometer}=1000\text{ meters})$$$$(1\text{ meter}=100\text{ centimeters})$$

   • $$2.8\times10^7$$
   • $$2.8\times10^9$$
   • $$2.8\times10^{11}$$
   • $$2.8\times10^{13}$$

3. A bus is traveling along a straight road at a constant speed. The distance $$d$$, in feet, of the bus from a road marker $$t$$ seconds after passing the marker is given by $$d=40t.$$ A car passes the same marker $$15$$ seconds after the bus passes it and travels in the same direction at a constant speed of $$55$$ feet per second. How many seconds after the bus passes the marker will the car catch up to the bus?

   • $$40$$
   • $$45$$
   • $$55$$
   • $$60$$

4. If $$3(2y+5)=4y+31,$$ what is the value of $$y$$?

   • $$5$$
   • $$6$$
   • $$7$$
   • $$8$$

5. A factory's total monthly operating cost in dollars is modeled by the function$$C(x)=95000+5200x$$where $$x$$ represents the number of workers employed that month. If $$32$$ workers are employed this month what is the total operating cost in dollars for the factory this month?

   • $$161,400$$
   • $$161,600$$
   • $$261,400$$
   • $$261,600$$

6. A fair coin is flipped $$3$$ times. What is the probability that the result shows exactly $$2$$ heads?

   • $$\frac{1}{8}$$
   • $$\frac{3}{8}$$
   • $$\frac{1}{3}$$
   • $$\frac{1}{2}$$

7. The area of Maria's square garden is $$144$$ square feet. The length of each side of David's square garden is $$\frac{1}{3}$$ the length of each side of Maria's garden. Which of the following expressions represents the area of David's garden, in square feet?

   • $$\frac{144}{3}$$
   • $$144 \times 3$$
   • $$144\left(\frac{1}{3}\right)^2$$
   • $$144^2\left(\frac{1}{3}\right)^2$$

8. A city government is organizing a community cleanup program and has at most $$36000$$ dollars to spend in total. The city will spend this money on planting trees and recycling waste. Each tree planted costs $$75$$ dollars, and each container of waste recycled costs $$120$$ dollars. Let $$t$$ represent the number of trees planted and $$c$$ represent the number of waste containers recycled. In addition to the budget limitation, the city also requires that at least twice as many waste containers must be recycled as trees planted. Which system of inequalities best represents this situation?

   • $$75t+120c\le36000$$ $$c\ge2t$$
   • $$75t+120c\ge36000$$ $$c\le2t$$
   • $$75t+120c\le36000$$ $$t\ge2c$$
   • $$75t+120c\ge36000$$ $$t\le2c$$

9. The equation below relates the positive numbers $$a$$, $$b$$, $$x$$, and $$y$$:$$\frac{2}{5b}=\frac{7x}{3y}$$If $$y=4a$$, which of the following correctly expresses $$x$$ in terms of $$a$$ and $$b$$?

   • $$\frac{6a}{35b}$$
   • $$\frac{35a}{24b}$$
   • $$\frac{24a}{35b}$$
   • $$\frac{12a}{7b}$$

10. The system of inequalities is:$$y$$ < $$20$$$$3x+y$$ > $$8$$The point $$(x,17)$$ is a solution to the system in the $$xy$$-plane. Which of the following could be the value of $$x$$?

    • $$-6$$
    • $$-4$$
    • $$-3$$
    • $$1$$

11. Line $$p$$ is defined by $$4x-3y=12$$. Line $$r$$ is perpendicular to line $$p$$ and passes through the point $$(6,-1)$$. What is the equation of line $$r$$?

    • $$y=-\frac{3}{4}x+\frac{7}{2}$$
    • $$y=-\frac{4}{3}x+9$$
    • $$y=\frac{4}{3}x+7$$
    • $$y=-\frac{3}{2}x-\frac{19}{2}$$

12. The graph of $$x^2-4x+y^2+6y=12$$ in the $$xy$$-plane is a circle. What is the length of the circle's radius?

    • $$25$$
    • $$\sqrt{5}$$
    • $$\sqrt{13}$$
    • $$5$$

13. Consider the system of equations:$$5x+3y=19$$$$2x+y=k$$If the system has the solution $$(x,y)$$ where $$y=3$$, what is the value of $$k$$?

    • 7

14. A cube has an edge length of $$x$$ inches. A second cube has an edge length that is $$3$$ inches longer than the first cube. If the difference in their volumes is $$10413$$ cubic inches, what is the value of $$x$$?

    • $$31$$
    • $$34$$
    • $$20$$
    • $$24$$

15. The function $$p(t)=120000(1.08)^t$$ models the population of a city $$t$$ years after a census. A new function $$r(m)$$ models the population $$m$$ months after the census. Starting immediately after the census, the annual growth rate decreases from $$8$$ percent to $$6$$ percent. Which function best models the population $$m$$ months after the census?

    • $$r(m)=120000(1.08)^{12m}$$
    • $$r(m)=120000(1.06)^{\frac{m}{12}}$$
    • $$r(m)=120000\left(\frac{1.06}{12}\right)^m$$
    • $$r(m)=120000(1.08)^{\frac{m}{12}}$$

16. The five numbers $$14,19,12,22,x$$ have a mean equal to the median. Which of the following is NOT a possible value of $$x$$?

    • $$3$$
    • $$\frac{67}{4}$$
    • $$13$$
    • $$28$$

17. An isosceles right triangle has a perimeter of $$60+30\sqrt{2}$$ inches. A second isosceles right triangle is formed by scaling the first triangle so that each side length is multiplied by a constant factor $$k$$. If the perimeter of the second triangle is $$120+60\sqrt{2}$$ inches, what is the length, in inches, of one leg of the second triangle?

    • $$30$$
    • $$30\sqrt{2}$$
    • $$60$$
    • $$60\sqrt{2}$$

18. Data set $$A$$ consists of the test scores of $$40$$ students and has a mean of $$78$$. Data set $$B$$ consists of the test scores of $$60$$ students and has a mean of $$85$$. Data set $$C$$ consists of the test scores of the $$100$$ students from data sets $$A$$ and $$B$$. What is the mean of data set $$C$$?

    • $$80$$
    • $$81.8$$
    • $$82.2$$
    • $$83$$

19. The graph of the function $$f$$ is shown above. A new function is defined as $$g(x)=f(x)-3.$$ Which of the following statements is true about the graph of $$g$$?

    • $$g$$ has no $$x$$-intercept and no $$y$$-intercept.
    • $$g$$ has an $$x$$-intercept but no $$y$$-intercept.
    • $$g$$ has a $$y$$-intercept but no $$x$$-intercept.
    • $$g$$ has both an $$x$$-intercept and a $$y$$-intercept.

20. In the figure above, lines $$p$$ and $$q$$ are parallel, and line $$m$$ is a transversal. What is the value of $$x$$?

    • $$30^\circ$$
    • $$40^\circ$$
    • $$50^\circ$$
    • $$60^\circ$$

21. The graph of a function $$f$$ is shown above. The graph consists of two branches and is undefined at $$x=4$$. Which of the following statements about the function $$f$$ is true?

    • The function has a horizontal asymptote at $$y=2$$.
    • The function has a vertical asymptote at $$x=1$$.
    • The function is increasing for all real values in its domain.
    • The function has a maximum value of $$8$$.

22. In the $$xy$$-plane, a circle has its center at $$(5,2)$$ and is tangent to the line with equation $$3x-4y+10=0$$. What is the area of the circle?

    • $$\frac{289}{25}\pi$$
    • $$\frac{17}{5}\pi$$
    • $$17\pi$$
    • $$25\pi$$