Full Practice Exam 16 — Module 2

Questions in this quiz (22)

1. What is one possible solution to the equation $$|x+4|=9$$?

   • $$-13$$
   • $$-5$$
   • $$4$$
   • $$13$$

2. The function $$f$$ is defined by $$f(x)=180(0.2)^x$$. What is the value of $$f(0)$$?

   • $$0$$
   • $$1$$
   • $$36$$
   • $$180$$

3. The function $$g(x)=5x+8$$ gives the total number of students attending a workshop with $$x$$ teachers. What is the total number of people attending the workshop with $$6$$ teachers?

   • $$30$$
   • $$34$$
   • $$38$$
   • $$42$$

4. To estimate the proportion of voters who support a proposal, a random sample was selected. Based on the sample, the estimated proportion is $$0.62$$ with a margin of error of $$0.03$$. Which of the following is the most appropriate conclusion?

   • It is plausible that the proportion is between $$0.59$$ and $$0.65$$.
   • The proportion is exactly $$0.62$$.
   • It is plausible that the proportion is less than $$0.59$$.
   • It is plausible that the proportion is greater than $$0.65$$.

5. What is the positive solution to the equation $$-3x^2-8x=-20$$?

   • $$\frac{4}{3}$$
   • $$2$$
   • $$\frac{10}{3}$$
   • $$\frac{-4+2\sqrt{19}}{3}$$

6. The table summarizes the distribution of color and size for $$120$$ marbles.If one marble is selected at random, what is the probability that the marble is red?

   • $$\frac{11}{24}$$
   • $$\frac{1}{2}$$
   • $$\frac{55}{65}$$
   • $$\frac{25}{120}$$

7. A delivery van can carry a total weight of no more than $$3800$$ pounds. The van itself weighs $$500$$ pounds, and each package weighs $$110$$ pounds. What is the maximum number of packages the van can carry?

   • $$29$$
   • $$30$$
   • $$31$$
   • $$32$$

8. For the given function $$f(x)=-4x+7$$, the graph of $$y=f(x)$$ in the $$xy$$-plane is parallel to line $$m$$. What is the slope of line $$m$$?

   • $$-7$$
   • $$-4$$
   • $$4$$
   • $$7$$

9. The function $$f(x)=\frac{1}{4}(x-6)^2+2$$ gives a toy car's distance above the floor, $$f(x)$$, in inches, $$x$$ seconds after it begins moving. Which of the following is the best interpretation of the vertex?

   • The toy car's minimum height was $$2$$ inches above the floor.
   • The toy car's maximum height was $$2$$ inches above the floor.
   • The toy car was $$6$$ inches above the floor when it started moving.
   • The toy car reached a height of $$6$$ inches after $$2$$ seconds.

10. In the equation $$-x^2+bx-225=0$$, $$b$$ is a positive integer. The equation has no real solution. What is the greatest possible value of $$b$$?

    • $$29$$
    • $$30$$
    • $$31$$
    • $$32$$

11. In triangle $$ABC$$, $$\cos(A)=\frac{5}{13}$$, and angle $$B$$ is a right angle. What is the value of $$\cos(C)$$?

    • $$\frac{5}{13}$$
    • $$\frac{12}{13}$$
    • $$\frac{13}{5}$$
    • $$\frac{12}{5}$$

12. The equation $$x^2+(y+4)^2=36$$ represents circle A. Circle B is obtained by shifting circle A up $$3$$ units in the $$xy$$-plane. Which equation represents circle B?

    • $$x^2+(y+1)^2=36$$
    • $$x^2+(y+7)^2=36$$
    • $$x^2+(y-1)^2=36$$
    • $$x^2+(y-3)^2=36$$

13. Two identical rectangular prisms each have a height of $$60$$ cm. The base of each prism is a square, and the surface area of each prism is $$K$$ square centimeters. If the prisms are glued together along a square base, the resulting prism has a surface area of $$\frac{44}{23}K$$ square centimeters. What is the side length, in centimeters, of each square base?

    • $$5$$
    • $$\frac{59}{7}$$
    • $$10$$
    • $$\frac{80}{7}$$

14. Last Sunday, Alex went for a run from his house to the park. He rested at the park for a while and then ran back home. Which of the following graphs could represent Alex’s run?

15. Cyclists often change their speed depending on the terrain. The scatterplot below shows the relationship between the speed of a cyclist and the slope of the road they are riding on for 9 different stretches. The line of best fit is also shown. What is the cyclist's speed represented by the data point that is farthest from the line of best fit?

    • 25

16. What is the length of $$DB$$ in the figure above?

    • $$\frac{2\sqrt{3}}{3}$$
    • $$\frac{2\sqrt{6}}{3}$$
    • $$\frac{4\sqrt{6}}{3}$$
    • $$\sqrt{3}$$

17. In $$\triangle ABC$$ above, $$\overline{DE}$$ is parallel to $$\overline{AC}$$, $$AD=2$$, $$DB=3$$, and $$DE=6$$. What is the length of $$AC$$?

    • 10

18. Two parallel lines are shown in the $$xy$$-plane above. If $$AB=15$$ and point $$B$$ has coordinates $$(m,n)$$, what is the value of $$n$$?

    • $$-6$$
    • $$-8$$
    • $$-9$$
    • $$-12$$

19. Researchers created the graph above to compare their population estimates with the actual populations of certain cities in 2010. For which of the cities did the researchers underestimate the population?I. San DiegoII. ChicagoIII. Los Angeles

    • I only
    • I and II only
    • II and III only
    • I, II, and III

20. The manager of a large assembly line uses the table below to keep track of the number of vehicles that are produced during different shifts in a day. If a vehicle is selected at random at the end of the day, which of the following is closest to the probability that the vehicle will be either a car produced during the first shift or a truck produced during the third shift?

    • $$0.193$$
    • $$0.314$$
    • $$0.352$$
    • $$0.421$$

21. The table above gives the distribution of low temperatures for a city over $$28$$ days. What is the median low temperature, in degrees Fahrenheit ($$^\circ\text{F}$$), of the city for these $$28$$ days?

    • 67

22. If $$-\frac{20}{3}$$ < $$-2x+4$$ < $$-\frac{9}{2},$$ what is a possible integer value of $$x-2$$?

    • 3