Full Practice Exam 11 — Module 1

Questions in this quiz (22)

1. Which of the following is equivalent to $$4x^3-12x^2+9x$$?

   • $$x(4x-3)^2$$
   • $$x(2x-3)^2$$
   • $$x(2x+3)^2$$
   • $$x(4x^2-9)$$

2. A shipment contains $$72,000,000$$ batteries, and $$6,480,000$$ of them are defective. What percentage of the batteries are defective?

   • $$7\%$$
   • $$8\%$$
   • $$9\%$$
   • $$12\%$$

3. If $$5(2x-7)-9=4(3x+5)-x$$, what is the value of $$8x$$?

   • -512

4. $$11(k+4)-13=12(k+4)$$In the equation above, what is the value of $$k+4$$?

   • $$-13$$
   • $$11$$
   • $$13$$
   • $$17$$

5. A convention center with a total of $$9600$$ square feet is divided into a $$40$$-square-foot media room area and a $$120$$-square-foot exhibit area. The number of sections of each type can be represented by the equation $$40m+120e=9600$$ In this context, which of the following does $$e$$ represent?

   • The number of media room sections
   • The total square footage of exhibit areas
   • The number of exhibit sections
   • The average size of each exhibit section

6. A rectangle has a length that is $$140%$$ of its width. If the width were increased by $$12$$ inches, how would the length need to change to keep the same proportions?

   • Increase by $$12$$ inches
   • Increase by $$16.8$$ inches
   • Decrease by $$12$$ inches
   • Increase by $$28$$ inches

7. If $$\frac{2a}{5}=18-4b$$ and $$a \ne0$$, which of the following correctly expresses $$b$$ in terms of $$a$$?

   • $$b=\frac{90-2a}{20}$$
   • $$b=18-\frac{2a}{5}$$
   • $$b=\frac{a-90}{20}$$
   • $$b=\frac{90+a}{20}$$

8. For all positive values of $$t$$, the expression $$\frac{4}{t+c}$$ is equivalent to $$\frac{20}{5t+35}$$. What is the value of constant $$c$$?

   • $$5$$
   • $$7$$
   • $$20$$
   • $$35$$

9. In the $$xy$$-plane, the equation $$(x+3)^2+(y-5)^2=100$$ defines circle $$A$$, and the equation $$(x+3)^2+(y-5)^2=k$$ defines circle $$B$$. If the radius of circle $$B$$ is $$4$$ less than the radius of circle $$A$$, what is the value of $$k$$?

   • 36

10. A university has received a grant of 45000 dollars to purchase new tablets. Each tablet costs 279 dollars, no tax is charged, and the manufacturer offers a $$12\%$$ discount on orders of at least $$120$$ tablets. What is the maximum number of tablets the university can purchase with the grant?

    • $$160$$
    • $$170$$
    • $$183$$
    • $$192$$

11. The system of equations below is graphed in the $$xy$$-plane.$$2x^2+y-18=0$$$$y=4x-6$$If the point $$(p,q)$$ is an intersection of the graphs, what is a possible value of $$p$$?

    • $$-5$$
    • $$3$$
    • $$3-\sqrt{3}$$
    • $$12$$
    • $$-1-\sqrt{13}$$

12. How many values of $$x$$ satisfy the equation $$8(3x-5)=24x-40$$?

    • Zero
    • Exactly one
    • Exactly two
    • Infinitely many

13. A parabola represents the graph of the function $$g$$ in the $$xy$$-plane, where $$y=g(x)$$. If the vertex of the parabola is $$(7,-9)$$ and one of the $$x$$-intercepts is $$(2,0)$$, what is the other $$x$$-intercept?

    • $$(-3,0)$$
    • $$(5,0)$$
    • $$(12,0)$$
    • $$(16,0)$$

14. If $$k$$ is a constant in the equation $$6x^2-7x+k=0$$ and the equation has no real solutions, which of the following could be the value of $$k$$?

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

15. In the $$xy$$-plane, the graph of a line with an $$x$$-intercept of $$(m,0)$$ and a $$y$$-intercept of $$(0,n)$$ is represented by the equation $$5x+2y=20$$. What is the value of $$\frac{m}{n}$$?

    • $$\frac{2}{5}$$
    • $$\frac{5}{2}$$
    • $$4$$
    • $$10$$

16. $$-12 + 3a = cb$$$$18b - 36 = 6a - 24$$If $$c$$ is a constant and the system above has infinitely many solutions, what is the value of $$c$$?

    • 9

17. Triangle $$P$$ has angles measuring $$30^\circ$$, $$60^\circ$$, and $$90^\circ$$. What is the perimeter, in centimeters, of this triangle if the shortest side has length $$12$$ centimeters?

    • $$24+12\sqrt{3}$$
    • $$36+12\sqrt{3}$$
    • $$48+24\sqrt{3}$$
    • $$24\sqrt{3}$$

18. The table below shows four values of $$x$$ and their corresponding values of $$h(x)$$ for the linear function $$h$$.The equation $$h(x)=mx+n$$ defines function $$h$$, where $$m$$ and $$n$$ are constants. What is the value of $$m-n$$?

    • $$-2$$
    • $$10$$
    • $$14$$
    • $$-32$$

19. The numbers $$128$$, $$132$$, $$137$$, and $$143$$ are part of a data set consisting of $$6$$ positive integers greater than $$120$$. What is the greatest possible value of the median of the entire data set if the mean of all $$6$$ integers is an integer less than $$140$$?

    • 140

20. A company gives bonuses to employees based on completed projects. Employees earn $$12$$ points for each of the first $$40$$ completed projects and $$7$$ points for each additional completed project beyond $$40$$. When $$p\ge40$$, which function $$B$$ gives the total number of bonus points earned for completing $$p$$ projects?

    • $$B(p)=7p+200$$
    • $$B(p)=7p+480$$
    • $$B(p)=12p+280$$
    • $$B(p)=19p-480$$

21. In triangles $$RST$$ and $$UVW$$, $$RS=30$$, $$UV=15$$, and angles $$R$$ and $$U$$ both measure $$68^\circ$$. Which of the following pieces of information would be sufficient to prove that the triangles are similar?I. Angle $$S$$ measures $$52^\circ$$II. Angle $$V$$ measures $$52^\circ$$III. Angle $$W$$ measures $$44^\circ$$

    • No additional information is necessary.
    • I and II together provide enough information.
    • II and III together provide enough information.
    • I and III together provide enough information.

22. Which equation defines function $$g$$, if the graph of $$y=g(x)-10$$ is shown above?

    • $$y=\frac{3}{5}x-15$$
    • $$y=\frac{3}{5}x-5$$
    • $$y=\frac{3}{5}x+5$$
    • $$y=\frac{3}{5}x+10$$