Full Practice Exam 15 — Module 1

Questions in this quiz (22)

1. What is the sum of the solutions to the equation $$3x^2-12x+7=0$$?

   • $$2$$
   • $$4$$
   • $$6$$
   • $$12$$

2. Let the function $$f$$ be defined by $$f(x)=3x^3+2$$, and let the function $$g$$ be defined by $$g(x)=x^2+4$$. What is the value of $$f(g(2))$$?

   • $$650$$
   • $$730$$
   • $$786$$
   • $$1538$$

3. $$bx+5y=20$$$$4x+10y=7$$In the system of equations, $$b$$ is a constant and $$x$$ and $$y$$ are variables. If the system has no solution, what is the value of $$b$$?

   • $$2$$
   • $$4$$
   • $$8$$
   • $$10$$

4. On Saturday, Maria read $$p$$ pages every $$20$$ minutes for $$3$$ hours, and Lucas read $$q$$ pages every $$30$$ minutes for $$4$$ hours. Which of the following represents the total number of pages read by Maria and Lucas on Saturday?

   • $$9p+8q$$
   • $$12p+8q$$
   • $$8p+12q$$
   • $$180p+120q$$

5. In the equation $$x^2+kx+16=(x+a)^2$$ $$k$$ and $$a$$ are positive constants. If the equation is true for all values of $$x$$, what is the value of $$k$$?

   • $$4$$
   • $$6$$
   • $$8$$
   • $$10$$

6. If $$81^{25}=3^x$$, what is the value of $$x$$?

   • $$50$$
   • $$75$$
   • $$100$$
   • $$125$$

7. The lengths of the three sides of a triangle are different prime numbers. If two of the sides have lengths $$5$$ and $$13$$, which of the following could be the length of the third side?I. $$7$$II. $$11$$III. $$19$$

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

8. If $$\frac{2}{3}x-\frac{1}{4}x=2+\frac{1}{3}$$, what is the value of $$x$$?

   • $$\frac{17}{5}$$
   • $$\frac{23}{4}$$
   • $$\frac{28}{5}$$
   • $$8$$

9. The graph of line $$l$$ is shown in the $$xy$$-plane. The equation of line $$n$$ is $$y=mx+b$$, where $$m$$ and $$b$$ are constants. If line $$l$$ is perpendicular to line $$n$$, which of the following must be true?

   • $$m$$ < $$0$$
   • $$m$$ > $$0$$
   • $$b$$ > $$0$$
   • $$b$$ < $$0$$

10. Four values for the functions $$f$$ and $$g$$ are shown in the table. If $$g(m)=8$$, what is the value of $$f(m)$$?

    • $$3$$
    • $$4$$
    • $$6$$
    • $$7$$

11. The formula $$R=\frac{A-B}{A+B}$$ represents the net gain of a business as a proportion of its total transactions, where $$A$$ is the amount of money earned and $$B$$ is the amount of money spent. Which of the following expresses $$B$$ in terms of $$A$$ and $$R$$?

    • $$B=\frac{AR}{R+1}$$
    • $$B=\frac{A-AR}{R+1}$$
    • $$B=\frac{A+AR}{R-1}$$
    • $$B=\frac{A-AR}{R-1}$$

12. The data below show the weights, in pounds, of fish caught in two lakes.Lake A: $$8,\ 9,\ 10,\ 11,\ 13$$Lake B: $$7,\ 9,\ 10,\ 12,\ 14$$According to the data, which of the following accurately compares the median weight of the fish from Lake A with that of the fish from Lake B?

    • The median weight of the fish from Lake A is $$1$$ pound less than that of the fish from Lake B.
    • The median weight of the fish from Lake A is $$1$$ pound more than that of the fish from Lake B.
    • The median weight of the fish from Lake A is the same as that of the fish from Lake B.
    • The median weight of the fish from Lake A is $$2$$ pounds more than that of the fish from Lake B.

13. Jordan has a savings account earning $$4$$ percent interest compounded annually. If the initial deposit was $$2000$$ dollars and Jordan withdraws $$500$$ after $$2$$ years, which of the following represents the total amount in the account after $$6$$ years?

    • $$2000(1.04)^6-500$$
    • $$2000(1.04)^2+1500(1.04)^4$$
    • $$2000(1.04)^2-500(1.04)^4$$
    • $$2000(1.04)^6-500(1.04)^4$$

14. In the $$xy$$-plane, a point with coordinates $$(h,k)$$ lies in the solution set of the system of inequalities below.$$y\le\frac{1}{2}x-5$$$$y\ge3x-20$$What is the maximum possible value of $$h$$?

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

15. In the figure above, what is the value of $$x$$?

    • 35

16. In rectangle $$ABCD$$ above, $$E$$ is on $$\overline{DC}$$, $$F$$ is on $$\overline{BC}$$, $$DE=6$$, and $$FC=1$$. If angle $$A$$ is trisected by $$\overline{AE}$$ and $$\overline{AF}$$, what is the length of $$BF$$?

    • $$5$$
    • $$5\sqrt{2}-1$$
    • $$5\sqrt{3}-1$$
    • $$6\sqrt{3}-1$$

17. According to the statistical data from the Energy Information Administration, the average price of regular gasoline per gallon from 2014 to 2021 is shown in the line graph above. Which of the following statements must NOT be true?

    • The average rate of change of the price of gasoline from 2014 to 2021 is approximately $0.047 per year.
    • The greatest increase in the price of gasoline occurred from 2016 to 2017.
    • The greatest decrease in the price of gasoline occurred from 2020 to 2021.
    • The average rate of change of the price of gasoline from 2015 to 2019 is greater than the average rate of change from 2019 to 2021.

18. As shown in the figure above, $$\overline{AC}$$ is a diameter of circle $$O$$. $$\overline{BC}$$ is a secant of the circle. Point $$P$$ is outside the circle such that $$\overline{PB}$$ and $$\overline{PA}$$ are tangent to circle $$O$$ at points $$B$$ and $$A$$, respectively. If $$\overline{OP}\parallel\overline{BC}$$, $$OP=8$$, and the radius of the circle is $$2\sqrt{2}$$, what is the length of $$BC$$?

    • $$3$$
    • $$8$$
    • $$2$$
    • $$15$$

19. The bar chart above shows the number of books read in class over the past year for $$19$$ classes in School X and $$15$$ classes in School Y. Which of the following correctly compares the mean and median number of books read in each class for the two schools?

    • The mean and median number of books read in each class are both greater in School X.
    • The mean and median number of books read in each class are both greater in School Y.
    • The mean number of books read in each class is greater in School X, but the median is the same in both schools.
    • The mean and median number of books read in each class are the same in both schools.

20. Which of the following inequalities is represented by the graph in the $$xy$$-plane above?

    • $$|x| \le 3$$
    • $$|x| \ge 3$$
    • $$|y| \le 3$$
    • $$|y| \ge 3$$

21. There are $$50$$ tennis balls in a container, $$20$$ of which are blue. After $$x$$ blue tennis balls are removed, $$25\%$$ of the tennis balls in the container are blue. What is the value of $$x$$?

    • 10

22. The table above summarizes the distribution of living situations for residences in a neighborhood. If a duplex in the neighborhood is to be inspected at random, what is the probability that the residence is occupied by no more than $$2$$ family members?

    • $$\frac{2}{23}$$
    • $$\frac{6}{23}$$
    • $$\frac{17}{69}$$
    • $$\frac{17}{23}$$