Full Practice Exam 1 — Module 1

Questions in this quiz (22)

1. $$|3x+2|=10$$If $$b$$ is a solution to the equation above and $$b$$ < $$0$$, what is the value of $$b?$$

   • $$\frac{8}{3}$$
   • $$\frac{10}{3}$$
   • $$-4$$
   • $$-\frac{8}{3}$$

2. Line $$t$$ is perpendicular to line $$s$$. Given that the equation for line $$s$$ is $$3y=2x-9,$$ which of the following could be the equation for line $$t$$?

   • $$y=-\frac{2}{3}x+9$$
   • $$y=-\frac{3}{2}x+1$$
   • $$y=\frac{3}{2}x+3$$
   • $$y=\frac{2}{3}x+3$$

3. What is the center of the circle given by the equation: $$x^2+y^2+8x-6y=20?$$

   • $$(4,-3)$$
   • $$(-3,4)$$
   • $$(3,-4)$$
   • $$(-4,3)$$

4. If $$(2^x)^3 \times 8^x$$ is equivalent to $$\left(\frac{2^{ax}}{4^x}\right)^x$$, what is the value of $$a$$?

   • 3
   • 8
   • 6
   • 4

5. Consider the system of inequalities:$$2x-1$$ < $$y$$$$y$$ < $$3x+5$$If (x,y) is a solution to the above system, which of the following could be $$(x,y)$$?

   • $$(0,0)$$
   • $$(2,3)$$
   • $$(2,1)$$
   • $$(2,2)$$

6. If $$f(x)=3(x+4)^2-7$$ is transformed to $$g(x)=3(x+1)^2-2,$$ which of the following describes the transformation?

   • The $$x$$ coordinate moves to the left 3 units and the $$y$$ coordinate moves 5 units up
   • The $$x$$ coordinate moves to the right 3 units and the $$y$$ coordinate moves 5 units up
   • The $$x$$ coordinate moves to the left 3 units and the $$y$$ coordinate moves 5 units down
   • The $$x$$ coordinate moves to the right 3 units and the $$y$$ coordinate moves 5 units down

7. $$4(x-2)-2(3x+1)=px+6$$What is the value of $$p$$ if the equation above has no solutions?

   • $$4$$
   • $$-2$$
   • $$-4$$
   • $$6$$

8. Maria and Lucas live 180 miles apart. They start driving toward each other at the same time along a straight road connecting their homes. Maria drives at a constant rate of 45 miles per hour, while Lucas drives at a constant rate of 35 miles per hour. How many miles are they from Maria's house when they meet?

   • 75
   • 90
   • 99
   • 105

9. A box contains 5 green marbles, 8 blue marbles, and 7 orange marbles. If three marbles are selected at random from the box without replacement, what is the probability that all three marbles are orange?

   • $$\frac{3}{7}$$
   • $$\frac{3}{20}$$
   • $$\frac{7}{228}$$
   • $$\frac{7}{20}$$

10. On a certain standardized test, 85% of students either went too fast and made mistakes or ran out of time and left questions unanswered. Of those students, 60% went too fast and made mistakes, while the remaining 40% ran out of time. If 240,000 students took the test in total, how many students went too fast and made mistakes?

    • $$122400$$
    • $$204000$$
    • $$144000$$
    • $$174000$$

11. Which of the following ordered pairs $$(x,y)$$ satisfies the inequality$$\frac{3}{4}x-\frac{5}{2}y$$ < $$6?$$I. $$(4,-2)$$II. $$(-2,0)$$III. $$(8,1)$$

    • I, II
    • I, III
    • II, III
    • I, II and III

12. Given the equations below, what is the value of x?$$5(x+2y)=45$$$$y+3x=12$$

    • $$3$$
    • $$6$$
    • $$-6$$
    • $$5$$

13. For what values of x is the expression $$2x^2-5x-12$$ equal to 0?

    • $$x=-2, x=\frac{7}{2}$$
    • $$x=-3, x=4$$
    • $$x=-\frac{3}{2}, x=4$$
    • $$x=3, x=-4$$

14. If $$f(x)=3x-4$$ and $$g(x)=2x+5$$, what is the value of $$g(f(g(2)))$$?

    • $$23$$
    • $$25$$
    • $$27$$
    • $$51$$

15. Which of the following could be the equation for a line of best fit for the data shown in the scatterplot above?

    • $$y=3-0.8x$$
    • $$y=0.8-3x$$
    • $$y=0.8+3x$$
    • $$y=3+0.8x$$

16. A rectangular solid measures 3 units by 7 units by 8 units. What is the surface area of the solid?

    • 142 square units
    • 166 square units
    • 202 square units
    • 262 square units

17. In the figure, lines m and n are parallel. If $$x=6k+13$$ and $$y=8k-29$$, what is the value of $$z$$?

    • $$41^\circ$$
    • $$21^\circ$$
    • $$139^\circ$$
    • $$30^\circ$$

18. In right triangle $$XYZ$$, the side lengths are $$XY=15$$, $$YZ=36$$, and $$XZ=39$$. Triangle $$XYZ$$ is similar to triangle $$PQR$$, where $$Y$$ corresponds to $$Q$$ and $$Z$$ corresponds to $$R$$. What is the value of $$\tan R$$?

    • $$\frac{15}{39}$$
    • $$\frac{5}{12}$$
    • $$\frac{1}{3}$$
    • $$\frac{\sqrt{3}}{3}$$

19. A population of bacteria is observed in a laboratory dish. At the initial observation, there are 200000 bacteria. The population triples every 4 hours. How many bacteria will there be after 12 hours?

    • $$2500000$$
    • $$3500000$$
    • $$5400000$$
    • $$6500000$$

20. When $$m=3$$ and $$n=4$$, $$\frac{8m^2}{2n^2}+\frac{5m}{2n}=?$$

    • $$\frac{9}{4}$$
    • $$\frac{33}{8}$$
    • $$\frac{15}{8}$$
    • $$\frac{9}{16}$$

21. $$h(x)=(6-3x)(10+x)$$The function $$h$$ is defined by the given equation. For what value of $$x$$ does $$h(x)$$ reach its maximum?

    • $$-4$$
    • $$-6$$
    • $$-10$$
    • $$2$$

22. Jordan burns 8 kilocalories per minute swimming and 6 kilocalories per minute jogging. Which of the following equations represents the total number of kilocalories, $$K$$, Jordan has burned after swimming for 40 minutes and jogging for $$t$$ minutes?

    • $$K=14t+40$$
    • $$K=40t+8$$
    • $$K=6t+320$$
    • $$K=8t+240$$