Full Practice Exam 14 — Module 1

Questions in this quiz (22)

1. The volume of a water tank is modeled by the equation $$V=t^2-4t+5$$. What is the volume of the tank after $$4$$ hours?

   • $$5$$
   • $$9$$
   • $$13$$
   • $$17$$

2. If $$(x+1)^2+(y-2)^2+(z-5)^2=0$$, what is the value of $$x+y+z$$?

   • $$2$$
   • $$4$$
   • $$6$$
   • $$8$$

3. If $$2^{x-1}=16$$, what is the value of $$x$$?

   • $$3$$
   • $$4$$
   • $$5$$
   • $$8$$

4. A faulty cash register records only $$6$$ dollars for every $$9$$ dollars deposited. If the register shows a total balance of $$54$$, what is the actual balance?

   • $$72$$
   • $$81$$
   • $$90$$
   • $$96$$

5. In the $$xy$$-plane, the line $$y=mx+4$$ is parallel to the line $$3x-2y=8$$. What is the value of $$m$$?

   • $$\frac{3}{2}$$
   • $$-\frac{3}{2}$$
   • $$\frac{2}{3}$$
   • $$-\frac{2}{3}$$

6. The graph of a parabola in the $$xy$$-plane has $$x$$-intercepts at $$\frac{2}{3}$$ and $$-4$$. Which of the following could be the equation of the parabola?

   • $$y=(3x-2)(x+4)$$
   • $$y=(3x+2)(x-4)$$
   • $$y=(3x-2)(x-4)$$
   • $$y=(3x+2)(x+4)$$

7. For a smoothie stand, the total cost $$c$$, in dollars, of selling $$n$$ smoothies is given by $$c=150+2.5n$$. What is the best interpretation of the number $$150$$ in this equation?

   • The cost of each smoothie
   • The number of smoothies sold
   • The fixed startup cost
   • The maximum total cost

8. During a bike ride, Maria had traveled $$24$$ miles by $$2:00$$ PM and $$36$$ miles by $$3:00$$ PM. She traveled at a constant rate. At what time had she traveled a total of $$60$$ miles?

   • $$4:30$$ PM
   • $$5:00$$ PM
   • $$5:30$$ PM
   • $$6:00$$ PM

9. The equation $$\frac{kx^2+10x-12}{2x+1}=4x+3-\frac{9}{2x+1}$$ is true for all values of $$x\ne-\frac{1}{2}$$, where $$k$$ is a constant. What is the value of $$k$$?

   • $$6$$
   • $$8$$
   • $$10$$
   • $$12$$

10. The expression $$\frac{2x^2+7}{x-2}$$ is equivalent to which of the following?

    • $$2x+4+\frac{15}{x-2}$$
    • $$2x-4+\frac{15}{x-2}$$
    • $$2x+4+\frac{7}{x-2}$$
    • $$2x-4+\frac{7}{x-2}$$

11. If $$|x+2|$$ > $$5$$ and $$x$$ is positive, what is one possible value of $$x$$?

    • $$1$$
    • $$2$$
    • $$3$$
    • $$4$$

12. Which of the following is equivalent to $$\left(\frac{1}{m}\right)^2+2\left(\frac{1}{m}\right)\left(\frac{1}{n}\right)+\left(\frac{1}{n}\right)^2$$?

    • $$\left(\frac{1}{m}+\frac{1}{n}\right)^2$$
    • $$\left(\frac{1}{m}-\frac{1}{n}\right)^2$$
    • $$\frac{1}{(m+n)^2}$$
    • $$\frac{2}{m^2+n^2}$$

13. In the table above, if $$y=x^2-2x-2$$, what is the value of $$k$$?

    • $$-3$$
    • $$4$$
    • $$-4$$
    • $$3$$

14. If $$k^2+6k=27$$ and $$k$$ > $$0$$, what is the value of $$k+3$$?

    • $$6$$
    • $$7$$
    • $$8$$
    • $$9$$

15. For what real value of $$x$$ is the equation $$x^3-6x^2+12x-8=0$$ true?

    • $$1$$
    • $$2$$
    • $$3$$
    • $$4$$

16. If the area of the shaded region in the figure above is $$24\pi$$ and the radius of circle $$O$$ is $$6$$, what is the value of $$x$$?

    • $$15$$
    • $$30$$
    • $$45$$
    • $$60$$

17. The graph above gives the inside temperature of a refrigerator as it is being adjusted over time. On which of the following intervals does the temperature change (in absolute value) by $$5$$ degrees Fahrenheit?

    • $$0$$ to $$5$$ minutes
    • $$5$$ to $$10$$ minutes
    • $$10$$ to $$15$$ minutes
    • $$20$$ to $$25$$ minutes

18. John is training for the $$100$$-meter dash. The graph shows his average speed at different points during the race. According to the graph, what percentage of the race had John completed before he reached his maximum average speed?

    • $$10\%$$
    • $$20\%$$
    • $$40\%$$
    • $$50\%$$

19. In the figure above, $$\overline{DE}$$ is parallel to $$\overline{AB}$$. If $$AD=6$$, $$DC=3$$, and $$AB=18$$, what is the length of $$DE$$?

    • $$3$$
    • $$6$$
    • $$9$$
    • $$12$$

20. The average speed of serve and number of years of training were recorded for $$20$$ tennis players and plotted in the grid above. Which of the following statements is supported by the plotted data?

    • The player with the least number of years of training had the slowest serve.
    • The player with the highest number of years of training had the fastest serve.
    • More than half of the players had a serve exceeding $$110$$ miles per hour.
    • More than half of the players had more than $$5$$ years of training.

21. The function $$f$$ is graphed in the $$xy$$-plane above. If $$f(c)=f(3)$$, which of the following could be the value of $$c$$?

    • $$-3$$
    • $$-2$$
    • $$-1$$
    • $$2$$

22. The mean tire pressure of the cars at Dealer A is equal to the mean tire pressure of the cars at Dealer B. However, while the standard deviation of the tire pressures of the cars at Dealer A is $$2.5$$ psi, the standard deviation of the tire pressures of the cars at Dealer B is $$1.2$$ psi. Which of the following statements must be true?

    • The mean tire pressure of the cars at Dealer A is $$1.3$$ psi less than the mean tire pressure of the cars at Dealer B.
    • The median tire pressure of the cars at Dealer A is $$1.3$$ psi less than the median tire pressure of the cars at Dealer B.
    • The median tire pressure of the cars at Dealer A is $$1.3$$ psi greater than the median tire pressure of the cars at Dealer B.
    • The tire pressures of the cars at Dealer A are more variable than the tire pressures of the cars at Dealer B.