Full Practice Exam 23 — Module 2

Questions in this quiz (22)

1. How many seconds are in $$120$$ minutes?

   • $$6,000$$
   • $$7,200$$
   • $$8,400$$
   • $$12,000$$

2. A cave formation grows at a rate of $$\frac{1}{10}$$ millimeter per year. At this rate, how many years will it take the formation to grow a total of $$5$$ millimeters?

   • 50

3. The function $$g$$ is defined by $$g(x)=5x-3.$$ What is the value of $$g(-2)$$?

   • $$-13$$
   • $$-10$$
   • $$-7$$
   • $$7$$

4. For line segment $$\overline{AC}$$ shown, the length of line segment $$\overline{BC}$$ is $$2$$ times the length of line segment $$\overline{AB}$$. Which equation represents this situation?

   • $$x+2=20$$
   • $$x+2=2$$
   • $$x-2=20$$
   • $$x+2=12$$

5. Two workers paint walls. The table gives their painting rates, in square meters per hour.If each person paints for $$4$$ hours, how much greater an area, in square meters, does Carlos paint than Maya?

   • $$18$$
   • $$28$$
   • $$36$$
   • $$72$$

6. Which expression is equivalent to $$x^3(2x^2-5x+4)?$$

   • $$2x^5-5x^4+4x^3$$
   • $$2x^6-5x^5+4x^4$$
   • $$2x^5+5x^4+4x^3$$
   • $$2x^3-5x^2+4x$$

7. A company manufactures picture frames. The figure shows a frame with a shaded border of width $$x$$ inches and inside dimensions of $$10$$ in by $$18$$ in. The area of the shaded border is $$128$$ square in. What is the value of $$x$$?

   • 2

8. $$x+y=14$$$$x-y=2$$The solution to the given system of equations is $$(x,y)$$. What is the value of $$3y$$?

   • 18

9. The function $$f$$ is defined by $$f(x)=3x+5.$$ What is the $$y$$-intercept of the graph of $$y=f(x)$$ in the $$xy$$-plane?

   • $$(0,5)$$
   • $$(0,3)$$
   • $$(5,0)$$
   • $$(3,0)$$

10. The area, in square centimeters, of a certain right triangle is given by the equation $$A=\frac{1}{2}(3b)b,$$ where $$b$$ is the length, in centimeters, of the shorter leg of the triangle. Which expression represents the length, in centimeters, of the longer leg?

    • $$b$$
    • $$2b$$
    • $$3b$$
    • $$3b^2$$

11. The segmented bar graph above shows the distribution of students at a university by school in $$2010$$ and $$2011$$. There were $$10,000$$ students enrolled at the university in $$2010$$. If there were $$3,000$$ more students enrolled at the School of Engineering in $$2011$$ than in $$2010$$, which of the following best approximates the increase in the total number of students enrolled at the university from $$2010$$ to $$2011$$?

    • $$2,000$$
    • $$3,000$$
    • $$4,000$$
    • $$5,000$$

12. Samantha is training for a cycling event. She rides $$8$$ miles on the first Sunday of her training. Each Sunday after the first, she rides $$3$$ more miles than she rode on the previous Sunday. Which equation represents the number of miles $$m$$ Samantha will ride on the $$n$$th Sunday of her training?

    • $$m=3n+8$$
    • $$m=3n+5$$
    • $$m=3n-5$$
    • $$m=3^n+8$$

13. Which quadratic equation has no real solutions?

    • $$x^2+6x+9=0$$
    • $$x^2+6x+5=0$$
    • $$2x^2+6x+1=0$$
    • $$x^2+6x+10=0$$

14. The graph shown models Earth’s approximate internal temperature $$T$$, in degrees Celsius $$(^\circ C)$$, in terms of the depth $$d$$, in kilometers $$(\text{km})$$, below Earth’s surface. The coordinates of five points on the graph are also shown. Which statement is the best interpretation of point $$B$$ in this context?

    • The approximate internal temperature $$2800$$ km below Earth’s surface is $$2200^\circ C$$.
    • The approximate internal temperature $$2200$$ km below Earth’s surface is $$2800^\circ C$$.
    • From Earth’s surface to $$2800$$ km below Earth’s surface, the approximate internal temperature increases by $$2200^\circ C$$ per kilometer of depth.
    • From Earth’s surface to $$2200$$ km below Earth’s surface, the approximate internal temperature increases by $$2800^\circ C$$ per kilometer of depth.

15. A model for the growth of a social media account estimates that every $$4$$ hours the number of followers increases by $$50\%$$. If the account begins with $$80$$ followers, which equation represents the number of followers, $$y$$, after $$x$$ hours?

    • $$y=80(1.5)^{4x}$$
    • $$y=80(1.5)^{x/4}$$
    • $$y=50(1.8)^{x/4}$$
    • $$y=80(0.5)^{x/4}$$

16. The variables $$x$$ and $$y$$ are related such that each time $$x$$ increases by $$5$$, $$y$$ decreases by $$2$$. If $$y=12$$ when $$x=0$$, which of the following equations expresses the relationship between $$x$$ and $$y$$?

    • $$2x+5y=60$$
    • $$2x+5y=12$$
    • $$5x-2y=24$$
    • $$2x-5y=-60$$

17. $$5x-2y=7$$$$10x-4y=14$$How many solutions does the given system of equations have?

    • Zero
    • Exactly one
    • Exactly two
    • Infinitely many

18. Of the following, which best models the data in the scatterplot shown?

    • $$y=1.6(0.5)^x$$
    • $$y=1.6(1.5)^x$$
    • $$y=0.5(0.6)^x$$
    • $$y=0.5(1.6)^x$$

19. The graph of $$x^2-8x+y^2+10y+5=0$$ in the $$xy$$-plane is a circle. What point $$(x,y)$$ is the center of this circle?

    • $$(4,-5)$$
    • $$(8,-10)$$
    • $$(16,25)$$
    • $$(4,5)$$

20. The surface area of a cube is $$96$$ square centimeters. What is the volume, in cubic centimeters, of the cube?

    • $$64$$
    • $$128$$
    • $$216$$
    • $$512$$

21. A school club is purchasing T-shirts and hoodies for an event. Each T-shirt costs $$10$$ dollars, each hoodie costs $$25$$ dollars, and the club plans to spend a total of $$500$$ dollars. The purchase can be modeled by the equation $$10x+25y=500,$$ where $$x$$ is the number of T-shirts and $$y$$ is the number of hoodies. Which graph represents this situation?

    • A line with $$y$$-intercept $$20$$ and $$x$$-intercept $$50$$
    • A line with $$y$$-intercept $$50$$ and $$x$$-intercept $$20$$
    • A line with $$y$$-intercept $$25$$ and $$x$$-intercept $$25$$
    • A line with $$y$$-intercept $$10$$ and $$x$$-intercept $$50$$

22. In the figure above, $$\triangle ABC$$ and $$\triangle BCD$$ are right triangles. What is the length of $$\overline{DC}$$?

    • $$4$$
    • $$4.5$$
    • $$6$$
    • $$8$$