Full Practice Exam 8 — Module 2

Questions in this quiz (22)

1. Solve for $$x$$:$$\frac{x-5}{4}+\frac{3x+2}{6}=\frac{11}{6}$$

   • $$\frac{1}{3}$$
   • $$\frac{11}{3}$$
   • $$\frac{1}{2}$$
   • $$\frac{4}{11}$$

2. Two numbers have a sum of $$31$$. When the larger number is tripled and the smaller number is doubled, the difference becomes $$37$$. What is the larger number?

   • $$\frac{5}{37}$$
   • $$\frac{37}{62}$$
   • $$\frac{99}{5}$$
   • $$\frac{7}{6}$$

3. Solve for $$x$$:$$2x^2-5x-12=0$$

   • $$x=-\frac{3}{2}$$, $$x=4$$
   • $$x=-\frac{2}{3}$$, $$x=-4$$
   • $$x=-4$$, $$x=\frac{3}{2}$$
   • $$x=-2$$, $$x=3$$

4. For $$y=(x-4)^2-7$$, what is the minimum value of $$y$$?

   • $$-23$$
   • $$-11$$
   • $$-7$$
   • $$-4$$

5. Let $$f(x)=3x-2$$ and $$g(x)=x^2+4$$.Find $$g(f(-2))$$.

   • $$-8$$
   • $$-2$$
   • $$-64$$
   • $$68$$

6. Which expression is equivalent to $$\frac{x^2-25}{x^2-10x+25}$$for $$x\ne5$$?

   • $$\frac{x-5}{x+5}$$
   • $$\frac{x+5}{x-5}$$
   • $$x+5$$
   • $$x-5$$

7. A bacterial culture doubles every $$6$$ hours. If it begins with $$500$$ cells, how many cells are present after $$24$$ hours?

   • $$4,000$$
   • $$8,000$$
   • $$16,000$$
   • $$32,000$$

8. Solve the inequality $$|x-2|$$ < $$4.$$

   • $$(6,10)$$
   • $$[-2,6)$$
   • $$[-4,2)$$
   • $$(-2,6)$$

9. A chemist mixes $$10$$ liters of a $$20\%$$ solution with $$x$$ liters of a $$50\%$$ solution to make a $$35\%$$ solution. Find $$x$$.

   • $$4$$
   • $$6$$
   • $$8$$
   • $$10$$

10. The mean of $$4$$ numbers is $$13$$. A fifth number is added, and the new mean becomes $$16$$. What is the value of the fifth number?

    • $$22$$
    • $$24$$
    • $$28$$
    • $$32$$

11. A circle has radius $$12$$. A sector has area $$24\pi$$ square units. What is the arc length of the sector, in terms of $$\pi$$?

    • $$4\pi$$
    • $$6\pi$$
    • $$8\pi$$
    • $$10\pi$$

12. In $$\triangle ABC$$, point $$D$$ is on $$\overline{AB}$$ and point $$E$$ is on $$\overline{AC}$$ such that $$\overline{DE}\parallel\overline{BC}$$. If $$AD=4$$, $$AB=16$$, and $$BC=24$$, find $$DE$$.

    • $$4$$
    • $$5$$
    • $$6$$
    • $$7.5$$

13. From a point on the ground, the angle of elevation to the top of a building is $$28^\circ$$. After walking $$20$$ meters closer to the building in a straight line, the angle of elevation becomes $$40^\circ$$. What is the height of the building, to the nearest tenth of a meter?

    • $$32.4$$
    • $$27.6$$
    • $$25.1$$
    • $$29.0$$

14. If $$g(x)=x^2-4x+3$$, find the average rate of change of $$g$$ from $$x=1$$ to $$x=4$$.

    • 1
    • Answer

15. $$p(x)=x^2-3x,$$ $$x\le1$$$$p(x)=4x+2$$,&$$x$$>$$1$$Compute $$p(1)+p(6).$$

    • $$18$$
    • $$20$$
    • $$22$$
    • $$24$$

16. The height (in feet) of a ball is given by $$h(t)=-16t^2+64t+144,$$ where $$t$$ is time in seconds. What is the maximum height of the ball?

    • $$144$$
    • $$192$$
    • $$208$$
    • $$256$$

17. An arithmetic sequence has first term $$7$$ and common difference $$3.5$$. Find the $$15$$th term.

    • $$49$$
    • $$52.5$$
    • $$56$$
    • $$58.5$$

18. A runner jogs $$3$$ miles at a pace of $$7$$ minutes $$20$$ seconds per mile, then runs $$2$$ miles at a pace of $$6$$ minutes $$10$$ seconds per mile. What is the runner’s average speed, in miles per hour, for the entire $$5$$-mile run?

    • $$7.4$$
    • $$8.1$$
    • $$8.4$$
    • $$8.7$$

19. A bag contains $$5$$ red, $$3$$ blue, and $$2$$ green marbles. Two marbles are drawn at random without replacement. What is the probability that both marbles are the same color?

    • $$\frac{7}{45}$$
    • $$\frac{11}{45}$$
    • $$\frac{14}{45}$$
    • $$\frac{17}{45}$$

20. In the $$xy$$-plane, the lines with equations $$3x-y=6$$ and $$y=2x+4$$ each pass through point $$(c,d)$$. What is the value of $$c$$?

    • $$3$$
    • $$4$$
    • $$6$$
    • $$10$$

21. The table above shows the box office revenues, in millions of dollars, for the top seven movies in both $$2020$$ and $$2021$$. Based on the table, what is the difference between the median box office revenue for these movies in $$2021$$ and the median revenue in $$2020$$?

    • $$47.9$$ millions
    • $$93.8$$ millions
    • $$113.6$$ millions
    • $$125.7$$ millions

22. Function $$f$$ is a quadratic function where $$f(4)=0$$ and $$f(16)=0$$. The graph of $$y=f(x)$$ in the $$xy$$-plane has a vertex at $$(h,25)$$. What is the value of $$h$$?

    • $$9$$
    • $$10$$
    • $$11$$
    • $$13$$