Full Practice Exam 7 — Module 2

Questions in this quiz (22)

1. A market analyst models the number of tickets sold $$T$$ for a concert as a linear function of the ticket price $$p$$. When the ticket price is $$25$$, $$18,000$$ tickets are sold. When the ticket price is $$35$$, $$14,000$$ tickets are sold. Based on this model, how many tickets are sold when the ticket price is $$30$$?

   • $$10,000$$
   • $$12,000$$
   • $$16,000$$
   • $$28,000$$

2. An object is suspended from a rubber band. The formula $$L=18+3m.$$ relates the length $$L$$, in centimeters, of the rubber band to the mass $$m$$, in kilograms, of the object. Which of the following best describes the meaning of the $$3$$ in this context?

   • The length, in centimeters, of the rubber band when no mass is attached
   • The mass, in kilograms, of an object that will stretch the rubber band $$18$$ centimeters
   • The increase in the mass, in kilograms, of the object for each one-centimeter increase in the length of the rubber band
   • The increase in the length, in centimeters, of the rubber band for each one-kilogram increase in the mass of the object

3. The line with the equation $$\frac{3}{4}x-\frac{2}{5}y=6,$$ is graphed in the $$xy$$-plane. What is the $$x$$-coordinate of the $$x$$-intercept of the line?

   • $$6$$
   • $$8$$
   • $$10$$
   • $$16$$

4. If $$6x+\frac{3}{4}=9.$$ what is the value of $$12x-3$$?

   • $$-6$$
   • $$0$$
   • $$\frac{27}{2}$$
   • $$\frac{11}{8}$$

5. $$3x+7y=82$$$$5x+3y=58$$If the solution is $$(x,y)$$ what is the value of $$x+y$$?

   • $$9$$
   • $$\frac{19}{3}$$
   • $$3$$
   • $$\frac{46}{3}$$

6. $$3(q-2)+5(q+4)=4q$$What value of $$q$$ is the solution?

   • $$-\frac{7}{2}$$
   • $$-\frac{7}{4}$$
   • $$4$$
   • $$7$$

7. In the $$xy$$-plane, line $$\ell$$ intersects the $$y$$-axis at the point $$(0,4)$$ and passes through the point $$(3,-2)$$. If the point $$(15,w)$$ lies on line $$\ell$$, what is the value of $$w$$?

   • $$-26$$
   • $$-2$$
   • $$4$$
   • $$34$$

8. What is the length of one side of a square that has the same area as a circle with radius $$3$$?

   • $$3\pi$$
   • $$3\sqrt{\pi}$$
   • $$9\pi$$
   • $$9$$

9. In the figure, $$BE=40$$ units, $$DC=20$$ units, and $$CE=12$$ units. What is the area, in square units, of triangle $$ABC$$?

   • $$\frac{5408}{3}$$
   • $$\frac{208}{3}$$
   • $$\frac{260}{3}$$
   • $$\frac{27040}{9}$$

10. In the figure, points $$A$$, $$D$$, $$C$$, and $$F$$ are collinear, and segment $$BC$$ intersects segment $$DE$$ at point $$I$$. The measures of $$\angle EDF$$, $$\angle EFD$$, $$\angle DIB$$, and $$\angle BAC$$ are $$55^\circ$$, $$30^\circ$$, $$70^\circ$$, and $$60^\circ$$, respectively. What is the measure, in degrees, of $$\angle ABC$$?

    • $$15^\circ$$
    • $$20^\circ$$
    • $$45^\circ$$
    • $$105^\circ$$

11. A right circular cone has a height of $$15$$ centimeters and a base with a radius of $$4$$ centimeters. The volume of this cone is $$k\pi$$ cubic centimeters. What is the value of $$k$$?

    • $$40$$
    • $$80$$
    • $$160$$
    • $$240$$

12. The graph above shows, for various temperatures, what percent of the fluid in a car’s radiator should be antifreeze in order to protect the radiator from freezing. At $$-20$$°F, approximately what percent of the fluid should be antifreeze?

    • $$10\%$$
    • $$20\%$$
    • $$30\%$$
    • $$40\%$$

13. If $$k$$ is an integer greater than $$2$$, which of the following correctly orders the three quantities $$\sqrt{k^2-1}$$, $$k-\frac{1}{k}$$, and $$\sqrt{k^2+1}$$ from least to greatest?

    • $$\sqrt{k^2-1}$$ < $$k-\frac{1}{k}$$ < $$\sqrt{k^2+1}$$
    • $$k-\frac{1}{k}$$ < $$\sqrt{k^2-1}$$ < $$\sqrt{k^2+1}$$
    • $$\sqrt{k^2-1}$$ < $$\sqrt{k^2+1}$$ < $$k-\frac{1}{k}$$
    • $$\sqrt{k^2+1}$$ < $$k-\frac{1}{k}$$ < $$\sqrt{k^2-1}$$

14. If $$k$$ is a constant such that $$x-2$$ and $$x+2$$ are factors of the polynomial $$100x^2+k$$, what is the value of $$k$$?

    • $$-400$$
    • $$-150$$
    • $$-125$$
    • $$150$$

15. Each day from March $$1$$ through March $$6$$, the number of daily visitors $$v$$ at a science museum is estimated by $$v=900+3^d$$, where $$d$$ is the day of the month. How many more visitors are estimated to be at the museum on March $$5$$ than on March $$2$$?

    • $$114$$
    • $$234$$
    • $$345$$
    • $$454$$

16. Yesterday, a wildlife center treated $$4$$ birds, $$5$$ rabbits, $$7$$ turtles, and no other animals. What was the ratio of the number of rabbits treated to the total number of animals treated?

    • $$1$$ to $$3$$
    • $$5$$ to $$16$$
    • $$5$$ to $$21$$
    • $$5$$ to $$12$$

17. What is the area of the shaded region in the figure above?

    • $$30$$
    • $$21$$
    • $$18$$
    • $$12$$

18. A high school surveyed $$300$$ students about their participation in three extracurricular activities: Sports, Drama, and Music. Each student participates in at least one of the three activities. The Venn diagram below summarizes the data:If $$25\%$$ of the students who participate in Sports also participate in both Drama and Music, what is the value of $$x$$?

    • $$18$$
    • $$30$$
    • $$50$$
    • $$54$$

19. Today is Wednesday. A project is scheduled to begin $$18$$ days from today. The project will last $$47$$ days. On what day of the week will the project end?

    • Sunday
    • Tuesday
    • Wednesday
    • Friday

20. The test scores of a class are shown in the table below.There are $$12$$ students total. Let $$m$$ be the mean of the scores and $$M$$ be the median of the scores. If $$M-m=\frac{1}{2}$$, what is the value of $$x$$?

    • $$76$$
    • $$88$$
    • $$96$$
    • $$104$$

21. The line graph shows the enrollment (in thousands) for College $$R$$ at $$10$$-year intervals from $$1950$$ to $$2000$$. Between $$1950$$ and $$1960$$. Assume that from $$2000$$ to $$2010$$, enrollment changes by the same percentage as it did from $$1950$$ to $$1960$$. And from $$2010$$ to $$2020$$, enrollment increases by twice that percentage. What is the expected enrollment, in students, in $$2020$$?

    • $$6125$$
    • $$6560$$
    • $$7250$$
    • $$7656$$

22. The box plot represents the distribution of time spent at the gym on a certain day, in hours, of $$20$$ Monster Gym members. Which of the following interpretations of the box plot is true?

    • At least $$5$$ gym members spent more than $$4.1$$ hours at the gym.
    • The mean hours spent at the gym is $$2.15$$.
    • The median hours spent at the gym is $$2.15$$.
    • At least $$15$$ gym members spent more than $$1.15$$ hours at the gym.