Full Practice Exam 3 — Module 2

Questions in this quiz (22)

1. If $$x\sqrt{3}+\sqrt{7}=\sqrt{9}$$, then $$x$$ is approximately equal to which of the following?

   • $$0.20$$
   • $$0.42$$
   • $$1.42$$
   • $$1.68$$

2. Joe purchases a phone plan that costs 30 dollars a month as a fixed charge plus 33 cents per text message. How much will Joe’s monthly bill be if he sends 334 text messages in one month?

   • $$64.00$$
   • $$140.22$$
   • $$160.30$$
   • $$420.32$$

3. $$a+3c=4$$ $$3b+a=7$$ $$3c+3b=9$$Which ordered triplet $$(a,b,c)$$ satisfies all three equations?

   • $$(2,1,1)$$
   • $$(1,2,1)$$
   • $$(1,1,2)$$
   • $$(2,1,2)$$

4. Pablo has 20 feet of fencing to enclose a rectangular garden. Which inequality represents the possible area $$A$$ of the rectangular garden, assuming the side lengths are positive integers?

   • $$9$$ < $$A$$ <$$20$$
   • $$10\le A\le25$$
   • $$25\le A\le9$$
   • $$9\le A\le25$$

5. A manufacturing company pays interns according to the table above. Interns who work at most 20 hours earn $$\$15$$ per hour, and interns who work more than 20 hours but at most 40 hours earn $$\$20$$ per hour. Sara earns $$\$15$$ per hour and works $$s$$ hours. Tara earns $$\$20$$ per hour and works $$t$$ hours. The total weekly budget is at most $$\$1600$$. Which system of inequalities models the situation?

   • $$15s+20t$$ < $$1600$$$$s$$ > $$0$$$$s$$ < $$20$$$$t$$ > $$20$$$$t$$ < $$40$$
   • $$15s+20t\le1600$$$$0\le s$$$$s\le20$$$$20$$ < $$t$$$$t\le40$$
   • $$15s+20t\le1600$$$$s$$ > $$0$$$$s\le20$$$$t$$ > $$20$$$$t$$ < $$41$$
   • $$15s+20t\le1600$$$$s$$ > $$0$$$$s$$ < $$20$$$$t$$ > $$20$$$$t$$ < $$41$$

6. The graph shows the relationship between gallons $$g$$ and quarts $$q$$. Which equation represents the relationship?

   • $$g=4q$$
   • $$g=2q$$
   • $$q=4g$$
   • $$q=2g$$

7. Alex has 6 red toys and 8 green toys in a box. He picks one toy at random, records its color, and replaces it. He then picks another toy at random. What is the probability that the second toy is green?

   • $$\frac{3}{4}$$
   • $$\frac{4}{7}$$
   • $$\frac{3}{7}$$
   • $$\frac{7}{8}$$

8. A soda company surveyed students about two soda brands. Based on the survey, what percentage of students ages 11–18 like Soda-1 or Soda-2?

   • $$40.32$$
   • $$58.99$$
   • $$92.31$$
   • $$99.32$$

9. Jana drives 6 hours at a speed of 60 miles per hour and 9 hours at a speed of 62 miles per hour. What is her average speed during the 15 hours of driving?

   • $$51.20$$
   • $$58.46$$
   • $$61.20$$
   • $$64.30$$

10. Bacterial culture 1 is modeled by $$y=2^x$$ million, and bacterial culture 2 is modeled by $$y=1.8^x$$ million. What is the difference in the bacterial counts after 7 hours of growth?

    • $$6.12$$ thousand
    • $$61.22$$ thousand
    • $$66.78$$ million
    • $$76.84$$ million

11. The population of Pearl City is reported in the graph above. The percentage decrease from 1925 to 1950 is greater than the percentage decrease from 1900 to 2000 by how many percentage points?

    • $$10$$
    • $$15$$
    • $$25$$
    • $$40$$

12. A square is inscribed in a circle with radius $$8\sqrt{2}$$. What is the area of the square?

    • 256

13. The table shows the population of Morgantown. How many more people are in the 25–50 age group than in the other age groups combined?

    • $$2000$$
    • $$3000$$
    • $$6000$$
    • $$7000$$

14. A botanist surveyed how much time people spend every week in their gardens. Which statement is true?

    • The total number of people spending 3 and 4 hours in the garden is the same as the number spending 0 hours.
    • More than half of the respondents spend less than 3 hours in the garden.
    • 5 respondents spend more than five hours in the garden.
    • Everyone surveyed spends at least one hour in the garden.

15. A 20-watt bulb burning for 50 hours consumes $$20(50)=1000$$ watt-hours, or 1 kilowatt-hour. If the Simpson household consumes 200 kilowatt-hours in January, this consumption is equivalent to how many 20-watt bulbs burning for 8 hours?

    • $$650$$
    • $$1050$$
    • $$1250$$
    • $$2500$$

16. A sculpture worth $$\$5000$$ loses $$5\%$$ of its value each year for 2 years and then loses $$6\%$$ of its value each year for 2 more years. Another sculpture loses $$7\%$$ of its value each year for 2 years and then loses $$9\%$$ of its value each year for 2 more years. If the two sculptures have the same value after the four years of losses, what was the original value of the second sculpture?

    • $$5567.04$$
    • $$4657.05$$
    • $$6765.07$$
    • $$3757.07$$

17. The number of pencils Pam has is inversely proportional to the number of erasers she has. When she has 120 pencils, she has 2 erasers. How many erasers will she have when she has 80 pencils?

    • 3

18. Tim had $$\$100$$ in his bank account at the beginning of the month. During the month, he withdrew $$w$$ dollars and deposited $$d$$ dollars. If the deposit was twice as much as the withdrawal and he had a balance of $$\$150$$ at the end of the month, how much did he deposit?

    • 100

19. In a game, Mark scored 3 more than twice what Nancy scored. Nancy scored 2 less than 4 times what Olivia scored. If Olivia scored 2 points, what did Mark score?

    • $$10$$
    • $$12$$
    • $$15$$
    • $$18$$

20. The sixth graders at Otto Middle School are going to a museum. The boys must be placed in groups of 11, and the girls must be placed in groups of 22. If the same number of boys and girls went to the museum, what is the least possible number of boys who went?

    • 22

21. A ladder 13 feet long leans against a vertical wall. The bottom of the ladder is initially 5 feet from the wall. The bottom is then moved 7 additional feet away from the wall while the top remains against the wall. How many feet does the top of the ladder slide downward?

    • $$4$$
    • $$5$$
    • $$6$$
    • $$7$$

22. The circumference of a circle is $$24\pi$$. A sector with a central angle of $$45^\circ$$ is removed. What is the area of the remaining portion of the circle?

    • $$60\pi$$
    • $$63\pi$$
    • $$72\pi$$
    • $$126\pi$$