Full Practice Exam 10 — Module 2

Questions in this quiz (22)

1. The total value of a rare comic book collection is $120 less than 7 times the number of comics, $$c$$. If the collection is worth 1,980 dollars, which equation represents this situation?

   • $$7c+120=1980$$
   • $$7c-120=1980$$
   • $$120-7c=1980$$
   • $$7(c-120)=1980$$

2. In the $$xy$$-plane, the line defined by $$y=\frac{3}{4}x-6$$ is line $$m$$. Line $$n$$ is perpendicular to line $$m$$. What is the slope of line $$n$$?

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

3. A basket contains $$5$$ green apples, $$4$$ red apples, and $$3$$ yellow apples. If one apple is chosen at random, what is the probability that the apple chosen is yellow?

   • $$\frac{1}{4}$$
   • $$\frac{1}{3}$$
   • $$\frac{1}{5}$$
   • $$\frac{1}{6}$$

4. A scientist begins with $$1200$$ bacteria in a petri dish. The bacteria population doubles every $$3$$ hours. Which equation models the population, $$P$$, after $$t$$ three-hour periods?

   • $$P=1200+t^2$$
   • $$P=1200(2)^t$$
   • $$P=2400t$$
   • $$P=1200\left(\frac{1}{2}\right)^t$$

5. A shipping company determines that the total weight, $$w$$, in pounds, of packages loaded onto a truck must be at least $$250$$ pounds less than $$180$$ times the number of crates, $$c$$. Which inequality represents this relationship?

   • $$w\le180c-250$$
   • $$w\ge180c-250$$
   • $$w\le250-180c$$
   • $$w\ge250-180c$$

6. A random sample of $$800$$ residents in a city found an average monthly electric bill of 92 dollars with a margin of error of 4 dollars. Which conclusion is most reasonable?

   • Every resident pays between 88 dollars and 96 dollars each month.
   • The average monthly electric bill for all residents is exactly 92 dollars.
   • The plausible average monthly electric bill for all residents is between 88 dollars and 96 dollars.
   • No conclusions can be made because only a sample was surveyed.

7. The perimeter of a rectangle is $$54$$ feet. The length is $$3$$ feet longer than twice the width. What is the width of the rectangle?

   • $$6$$
   • $$8$$
   • $$12$$
   • $$15$$

8. Circle $$A$$ has a radius that is $$14$$ times the radius of Circle $$B$$. The area of Circle $$A$$ is $$k$$ times the area of Circle $$B$$. What is the value of $$k$$?

   • $$14$$
   • $$28$$
   • $$196$$
   • $$392$$

9. In the equation $$7x+3sx=42$$, $$s$$ is a constant. If the equation has no solution, what is the value of $$s$$?

   • $$-\frac{7}{3}$$
   • $$\frac{7}{3}$$
   • $$-3$$
   • $$3$$

10. The frequency table below summarizes the scores of $$60$$ students on a mathematics competition.A new student joins the competition and earns a score of $$20$$. The new score is added to the data set. Which statement best compares the mean and median of the new data set to those of the original data set?

    • The mean decreases and the median decreases.
    • The mean decreases and the medians are equal.
    • The mean increases and the median decreases.
    • The mean increases and the medians are equal.

11. A square park has a perimeter of $$480$$ meters. A walking path is built along one diagonal of the square. The length of the diagonal is expressed as $$k\sqrt{2}$$ meters, where $$k$$ is a constant. What is the value of $$k$$?

    • 120

12. In triangle $$ABC$$, the measure of angle $$B$$ is $$90^\circ$$, and $$BP$$ is an altitude to hypotenuse $$AC$$. The length of $$AB$$ is $$12$$, and the length of the hypotenuse $$AC$$ is $$4$$ greater than the length of $$AB$$. What is the value of the ratio $$\frac{BC}{BP}$$?

    • $$\frac{4}{3}$$
    • $$\frac{3}{2}$$
    • $$\frac{8}{3}$$
    • $$\frac{16}{3}$$

13. If $$a$$ and $$b$$ are numbers such that $$(a-4)(b+6)=0$$, then what is the smallest possible value of $$a^2+b^2$$?

    • 16

14. The function $$f$$ is graphed in its entirety above. If the function $$g$$ is defined so that $$g(x)=f(-x)$$, then for what value of $$x$$ does $$g$$ attain its maximum value?

    • $$-3$$
    • $$-2$$
    • $$0$$
    • $$2$$
    • $$3$$

15. The value of $$y$$ increased by $$12$$ is directly proportional to the value of $$x$$ decreased by $$6$$. If $$y=16$$, what is the value of $$x$$ when $$y=8$$.

    • $$8$$
    • $$\frac{52}{7}$$
    • $$16$$
    • $$\frac{10}{7}$$

16. The curve $$y=\frac{x^2}{2}$$ and the line $$y=\frac{x}{2}$$ intersect at the origin and at the point $$(a,b)$$, as shown in the figure above. What is the value of $$b$$?

    • $$\\frac{1}{8}$$
    • $$\\frac{1}{4}$$
    • $$\\frac{1}{2}$$
    • $$1$$

17. In the $$xy$$-plane, a parabola has vertex $$(9,-14)$$ and intersects the $$x$$-axis at two points. If the equation of the parabola is written in the form $$y=ax^2+bx+c$$, where $$a$$, $$b$$, and $$c$$ are constants, which of the following could be the value of $$a+b+c$$?

    • $$-23$$
    • $$-19$$
    • $$-14$$
    • $$-12$$

18. The table below shows student grades in four subjects.If one student grade is selected at random from all $$120$$ grades, which of the following is the probability that the selected grade is at least a $$B$$?

    • $$\frac{19}{30}$$
    • $$\frac{23}{40}$$
    • $$\frac{31}{60}$$
    • $$\frac{7}{20}$$

19. The table below shows the results of a student council election in three schools.Suppose a survey of $$350$$ randomly selected voters from all three schools accurately reflected the election results. Approximately how many of the surveyed voters would most likely have been supporters of Candidate X from North High?

    • $$72$$
    • $$84$$
    • $$96$$
    • $$108$$

20. If $$(x+1)^2=4$$ and $$(x-1)^2=16$$, what is the value of $$x$$?

    • $$-3$$
    • $$-1$$
    • $$1$$
    • $$3$$

21. The function $$q$$ is defined by $$q(x)=a|x-9|-53|x-9|+b$$, where $$a$$ and $$b$$ are constants, and $$a$$ > $$b$$ > $$53$$. If $$q(539)=h$$ and $$q(-521)=k$$, where $$h$$ and $$k$$ are constants, what is the value of $$32(-539)^{h-k}+347(9)^{k-h}$$?

    • 379

22. The point $$(a,b)$$ is an intersection of the system of equations below when graphed in the $$xy$$-plane.$$3x^2-y-26=0$$$$y=-3x+10$$What is a possible value of $$a$$?

    • $$-4$$
    • $$6$$
    • $$20$$
    • $$26$$