Full Practice Exam 7 — Module 2

Questions in this quiz (22)

1. If $$x=4$$, what is $$5(x-1)+3x$$?

   • $$21$$
   • $$24$$
   • $$30$$
   • $$27$$

2. $$\left(x-\frac{3}{5}\right)\left(x+\frac{1}{2}\right)=0$$What is the product of the solutions to the equation above?

   • $$-\frac{1}{10}$$
   • $$-\frac{10}{3}$$
   • $$-\frac{3}{10}$$
   • $$\frac{3}{10}$$

3. At a certain university, $$32\%$$ of all students are majoring in engineering or computer science. If there are a total of $$5,500$$ students at the university, how many of the students would have an engineering or computer science major?

   • 1760
   • Answer

4. Lina consistently practices piano for $$3$$ hours per day. Which expression gives the number of hours that Lina would practice in $$w$$ weeks?

   • $$3w$$
   • $$7w$$
   • $$21w$$
   • $$24w$$

5. $$T=4C+6M$$A café charges $$4$$ dollars for each coffee, $$C$$, and $$6$$ dollars for each muffin, $$M$$. The equation above represents the total amount, $$T$$, that Jordan paid for his order. If the total cost was $$54$$ dollars and Jordan purchased $$5$$ muffins, how many coffees did he purchase?

   • $$4$$
   • $$6$$
   • $$5$$
   • $$8$$

6. A circle with an original area of $$25\pi$$ square units increases in area by $$44\%$$. What is the radius of the new circle?

   • 6
   • Answer

7. $$2x+3y=21$$$$x-y=3$$Given that $$(x,y)$$ is a solution to the above system of equations, what is the value of $$x$$?

   • $$5$$
   • $$8$$
   • $$6$$
   • $$4$$

8. If the city of Phoenix has a population density of $$3,200$$ persons per square mile, and there are $$165$$ square miles of land within the city, what would most closely approximate the total population of the city?

   • $$480000$$
   • $$528000$$
   • $$560000$$
   • $$640000$$

9. A cylindrical tank has a base with a diameter of $$12$$ feet and a volume of $$288\pi$$ cubic feet. What is the height of this tank in feet?

   • $$8$$
   • $$6$$
   • $$12$$
   • $$3$$

10. If the function $$g(x)=\frac{x^2-5}{3x}$$ when $$x\ne0$$, what is the value of $$g(3)$$?

    • $$\frac{9}{4}$$
    • $$\frac{4}{3}$$
    • $$\frac{4}{9}$$
    • $$\frac{5}{9}$$

11. After a championship game, viewers could go to a sports website and vote in an online poll for which team they thought played better. Approximately $$4,000$$ viewers chose to fill out responses. Would the results from the online poll provide an accurate representation of the opinions of all sports fans?

    • Yes, because $$4000$$ responses is a large sample size.
    • Yes, because an online poll always gives a random sample.
    • No, because the poll was taken before the game ended.
    • No, because the poll uses a voluntary response sample, which is biased.

12. In the $$xy$$-plane, which of these equations would represent the graph of $$y=x^2+3$$ shifted downward $$4$$ units?

    • $$y=x^2-4$$
    • $$y=x^2-1$$
    • $$y=x^2+1$$
    • $$y=x^2+7$$

13. Which of the following expressions is equivalent to $$-3(2x^2-5x+4)+2(x^2-3x-6)$$?

    • $$-8x^2-x-24$$
    • $$-8x^2+9x-24$$
    • $$-4x^2+9x-18$$
    • $$-4x^2+9x-24$$

14. If $$\frac{2x+3}{x-4}=\frac{5}{2}$$, what is the value of $$x$$?

    • $$\frac{7}{2}$$
    • $$\frac{13}{2}$$
    • $$7$$
    • $$26$$

15. If $$\frac{x^2-16}{5}=9$$, what is the value of $$\frac{x-4}{x+4}$$?

    • $$\frac{1}{2}$$
    • $$\frac{2}{3}$$
    • $$\frac{3}{5}$$
    • $$\frac{5}{9}$$

16. Point $$P$$ is an external point to a circle with center $$O$$. A tangent segment $$PA$$ touches the circle at point $$A$$. A secant segment $$PBC$$ passes through the center $$O$$, with points $$B$$ and $$C$$ on the circle such that $$B$$ is between $$P$$ and $$O$$. If the measure of $$\angle APB$$ is $$30^\circ$$, what is the measure of $$\angle AOC$$?

    • $$60^\circ$$
    • $$90^\circ$$
    • $$120^\circ$$
    • $$150^\circ$$

17. A number $$x$$ satisfies two conditions. First, three times the difference between $$x$$ and $$5$$ is no more than the sum of $$x$$ and $$7$$. Second, $$x$$ must be greater than twice the sum of $$x$$ and $$2$$ minus $$10$$. Which of the following inequalities represents all possible values of $$x$$?

    • $$x$$ < $$6$$
    • $$x\le11$$
    • $$6\le x\le11$$
    • $$x$$ > $$6$$

18. A data set of $$10$$ distinct positive integers has a mean of $$25$$ and a median of $$23$$. If a new integer $$x$$ is added to the data set, what is the smallest possible value for the median of the new data set?

    • $$20$$
    • $$21$$
    • $$22$$
    • $$23$$

19. A school has two clubs: the Science Club and the Art Club. In the Science Club, there are $$40$$ juniors and $$25$$ seniors. In the Art Club, there are $$35$$ juniors and $$20$$ seniors. A student is selected at random from the students in both clubs. What is the probability that the selected student is from the Science Club, given that the student is a junior?

    • $$\frac{7}{15}$$
    • $$\frac{8}{15}$$
    • $$\frac{5}{8}$$
    • $$\frac{8}{11}$$

20. In a certain study, researchers created the scatterplot above to summarize the ages of the participants and the number of hours of sleep they required each night. Which of the following is the closest to the age, in years, of the participant who required the least amount of sleep each night?

    • $$35$$
    • $$40$$
    • $$55$$
    • $$60$$

21. In the $$xy$$-plane, the graph of the function $$f(x)=x^2-3x+c$$ is tangent to the line with equation $$y=2x-7$$. The constant $$c$$ is a real number. What is the value of $$c$$?

    • $$-\frac{3}{4}$$
    • $$\frac{5}{7}$$
    • $$-\frac{7}{5}$$
    • $$\frac{25}{4}$$

22. In right triangle $$PQR$$, $$\angle Q$$ is the right angle. Point $$S$$ is on the hypotenuse $$PR$$ such that $$QS\perp PR$$. If the length of side $$PQ$$ is $$12$$ and $$\cos(\angle QPR)=\frac{3}{5}$$, what is the length of segment $$PS$$?

    • $$\frac{18}{5}$$
    • $$\frac{36}{5}$$
    • $$\frac{48}{5}$$
    • $$\frac{64}{5}$$