Full Practice Exam 21 — Module 1

Questions in this quiz (22)

1. Which of the following equations has infinitely many solutions?

   • $$3(2x-5)=6$$
   • $$3(2x-5)=6x$$
   • $$3(2x-5)=6x-15$$
   • $$3(2x-5)=6x+15$$

2. What is the solution to the equation $$4(x+7)-9=35$$?

   • $$2$$
   • $$4$$
   • $$5$$
   • $$7$$

3. The given expression $$\sqrt{x^9}$$ is equivalent to $$x^{\frac{c}{2}}$$, where $$c$$ is a constant. What is the value of $$c$$?

   • $$7$$
   • $$8$$
   • $$9$$
   • $$10$$

4. The line shown represents the number of gallons of water in a tank as a function of the number of minutes a pump has been running to empty the water from the tank. How many gallons of water were in the tank when the pump started running?

   • $$0$$
   • $$\frac{50}{3}$$
   • $$60$$
   • $$1000$$

5. $$8x+6y=26$$$$4x+2y=10$$The solution to the given system of equations is $$(x,y)$$. What is the value of $$y$$?

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

6. Which of the following is an equation of a line in the $$xy$$-plane that has a slope of $$-2$$ and a y-intercept of $$4$$?

   • $$2x+y=4$$
   • $$2x-y=4$$
   • $$x+2y=4$$
   • $$x-2y=4$$

7. The shaded region shown represents all of the solutions for which of the following inequalities?

   • $$x+y\ge1$$
   • $$x+y\le1$$
   • $$x-y\ge1$$
   • $$x-y\le1$$

8. In March 2015, there were $$150.5$$ million jobs in the United States. The number of jobs increased approximately $$0.3$$ million per month for the next $$48$$ months. Which equation represents this situation, where $$j$$ is the number of jobs, in millions, and $$t$$ is the time, in months, since March 2015?

   • $$j=150.5t+0.3$$
   • $$j=0.3t+150.5$$
   • $$j=48t+150.5$$
   • $$j=150.5t+48$$

9. The equation $$3x^2-12x+5=0$$ has solutions that can be expressed in the form $$\frac{12\pm\sqrt{n}}{6}$$, where $$n$$ is a positive integer. What is the value of $$n$$?

   • $$84$$
   • $$96$$
   • $$108$$
   • $$144$$

10. The graph shows the speed of an object over a period of time. Which is closest to the time, in seconds, it took for the object's speed to change from $$4$$ meters per second to $$8$$ meters per second?

    • $$1$$
    • $$4$$
    • $$6$$
    • $$15$$

11. If $$x=\frac{\pi}{6}$$ radians, what is the value of $$\sin x$$?

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

12. What is the sum of the solutions to the equation $$|3x-4|=20$$?

    • $$-\frac{8}{3}$$
    • $$\frac{8}{3}$$
    • $$\frac{20}{3}$$
    • $$\frac{40}{3}$$

13. The given expression $$(1-x)(1+x+x^2+x^3+x^4)$$ is equivalent to $$1-x^n$$, where $$n$$ is a constant. What is the value of $$n$$?

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

14. In the figure, four lines intersect as shown. Which of the following additional pieces of information is sufficient to prove that angle $$SWR$$ is congruent to angle $$TVR$$?

    • Angle $$VTR$$ is congruent to angle $$TSW$$.
    • Angle $$VTR$$ is congruent to angle $$WSR$$.
    • Angle $$TRV$$ is congruent to angle $$SWR$$.
    • Angle $$TSW$$ is congruent to angle $$WSR$$.

15. A rectangular prism has edge lengths of $$5$$ inches, $$9$$ inches, and $$12$$ inches. What is the surface area, in square inches, of the prism?

    • $$306$$
    • $$318$$
    • $$366$$
    • $$426$$

16. If $$(x+4)^2=25$$, what is one possible value of $$x-1$$?

    • $$-10$$
    • $$-9$$
    • $$1$$
    • $$4$$

17. A pet store sells only dogs, cats, and rabbits. On Saturday, $$25\%$$ of the animals were dogs and $$45\%$$ were cats. If there were $$20$$ dogs at the store, how many rabbits were there?

    • $$16$$
    • $$20$$
    • $$24$$
    • $$24.8$$

18. The graph of $$y=f(x)$$ is shown. What is the value of $$f(0)$$?

    • $$-6$$
    • $$0$$
    • $$3$$
    • $$f(0)$$ is undefined.

19. What is an equation of the graph shown?

    • $$-6x+4y=3$$
    • $$-2x+3y=-18$$
    • $$3x-2y=12$$
    • $$4x-6y=9$$

20. The graph of a quadratic equation is shown. The system consisting of this equation and the equation $$y=k$$, where $$k$$ is a constant, has two real solutions. Which of the following could be the value of $$k$$?

    • $$0$$
    • $$1$$
    • $$2$$
    • $$3$$

21. The graph of a certain parabola in the $$xy$$-plane intersects the $$y$$-axis once and the $$x$$-axis twice. Which of the following forms of the parabola's equation gives the $$x$$-values of the $$x$$-intercepts as constants?

    • $$y=(3x+4)(2x-5)$$
    • $$y=6\left(x+\frac{4}{3}\right)\left(x-\frac{5}{2}\right)$$
    • $$y=6x^2-7x-20$$
    • $$y=6\left(x-\frac{7}{12}\right)^2-\frac{529}{24}$$

22. What is the graph of the equation $$y=24\left(\frac{1}{2}\right)^x$$?

    • A graph has a $$y$$-intercept of $$24$$ and passes through approximately $$(1,12)$$, $$(2,6)$$, $$(3,3)$$, and $$(4,1.5)$$.
    • A graph has a $$y$$-intercept of $$24$$ and passes through approximately $$(1,8)$$, $$(2,\frac{8}{3})$$, $$(3,\frac{8}{9})$$, and $$(4,\frac{8}{27})$$.
    • A graph has a $$y$$-intercept of $$12$$ and passes through approximately $$(1,6)$$, $$(2,3)$$, $$(3,1.5)$$, and $$(4,0.75)$$.
    • A graph has a $$y$$-intercept of $$24$$ and passes through approximately $$(1,18)$$, $$(2,13.5)$$, $$(3,10.125)$$, and $$(4,7.594)$$.