Full Practice Exam 6 — Module 2

Questions in this quiz (22)

1. If $$a+b=8$$, what is the value of $$3^a3^b$$?

   • $$3^8$$
   • $$3^{16}$$
   • $$9^8$$
   • $$9^{16}$$

2. $$4x-15y=7$$$$2x-15y=11$$The solution to the given system of equations is $$(x,y)$$. What is the value of $$x$$?

   • $$-2$$
   • $$-1$$
   • $$4$$
   • $$6$$

3. A sports memorabilia store sells two types of cards:$$r$$: rare cards for $$\$20$$ each.$$c$$ common cards for $$\$2$$ each.A collector purchases 40 cards for a total of $$\$296$$. Which system of equations represents this situation?

   • $$20c+2r=40$$$$r+c=296$$
   • $$20c+2r=296$$$$r+c=40$$
   • $$20r+2c=40$$$$r+c=296$$
   • $$20r+2c=296$$$$r+c=40$$

4. A line is shown in the $$xy$$-plane. What is the $$y$$-intercept of the graph?

   • $$(0,-8)$$
   • $$(0,-4)$$
   • $$(0,4)$$
   • $$(0,8)$$

5. The average cost of a gallon of gas from 2001 to 2007 is displayed in a line graph. According to the graph, how much more did a gallon of gas cost in 2007 than in 2003?

   • $$\$1.00$$
   • $$\$1.25$$
   • $$\$1.75$$
   • $$\$2.00$$

6. A scatterplot shows the prices, in dollars, of a cheese pizza and a veggie pizza for ten different pizzerias. A line of best fit is also shown. According to the line of best fit, which value is closest to the price, in dollars, of a cheese pizza at a pizzeria that charges $$\$15$$ for a veggie pizza?

   • $$5$$
   • $$10$$
   • $$15$$
   • $$25$$

7. Which of the following expressions is equivalent to: $$y^2-8y+2$$?

   • $$(y-4)^2-14$$
   • $$(y-4)^2+14$$
   • $$(y+4)^2-14$$
   • $$(y+4)^2+14$$

8. A construction worker is digging a hole. The equation $$d=1.8t+4.5$$ represents the depth $$d$$, in meters, that the construction worker has reached $$t$$ minutes after beginning to dig. Which of the following is the best interpretation of the number $$1.8$$ in this context?

   • The time it takes the construction worker to dig to a depth of 4.5 meters
   • The depth, in meters, of the hole when the construction worker started to dig
   • The depth, in meters, of the hole 4.5 minutes after the construction worker started to dig
   • The depth, in meters, that the construction worker digs each minute

9. A bakery's specialty flour is a mixture of almond flour and coconut flour. The ratio of almond flour to coconut flour is $$7:38$$ by volume. If the bakery uses 152 cups of coconut flour in one day, what is the volume, in cups, of almond flour used that day?

   • $$4$$
   • $$28$$
   • $$114$$
   • $$152$$

10. The ratio of $$x$$ to $$y$$ is 4 to 3, and the ratio of $$x$$ to $$z$$ is 1 to 2. What is the ratio of $$y$$ to $$z$$?

    • $$3:8$$
    • $$2:3$$
    • $$3:2$$
    • $$8:3$$

11. The value of a certain stock decreased by $$20\%$$ from the beginning of 2020 to the beginning of 2021. The value then increased by $$15\%$$ from the beginning of 2021 to the beginning of 2022. What was the net percentage decrease in the value of the stock from the beginning of 2020 to the beginning of 2022?

    • $$5\%$$
    • $$8\%$$
    • $$23\%$$
    • $$35\%$$

12. The function $$f$$ is defined by: $$f(x)=|7x-4|$$What is the value of $$f(-3)$$?

    • 25
    • $$25$$

13. A scatterplot shows the number of hours, $$h$$, that a child spent on homework in relation to her age, $$x$$, in years. Which equation best models the data, where $$6\le x\le12$$?

    • $$h(x)=-2.5x-0.5$$
    • $$h(x)=-0.5x-2.5$$
    • $$h(x)=0.5x-2.5$$
    • $$h(x)=2.5x-0.5$$

14. A student is reading a book for class. The number of pages the student has left to read can be modeled by the function: $$f(x)=252-47x$$ where $$x$$ is the number of days after the book was assigned. Which of the following is the best interpretation of the number 252 in this context?

    • The student will finish reading the book in 252 days.
    • The book contains 252 pages.
    • The student reads 252 pages per day.
    • The student reads 252 pages every 47 days.

15. The function $$m(x)=300(1.06)^x$$ gives the total money, $$m$$, in dollars, in an interest-generating savings account $$x$$ months after the account was opened. What is the best interpretation of the statement “$$m(0)$$ is equal to 300” in this context?

    • The account had a value of $$\$0$$ when it was opened.
    • The account will have a value of $$\$0$$ when it has been open for 300 months.
    • The account had a value of $$\$300$$ when it was opened.
    • The account will have a value of $$\$300$$ when it has been open for 300 months.

16. In a figure, line $$l$$ intersects parallel lines $$m$$ and $$n$$. What is the value of $$a$$?

    • 42

17. The area of a certain rectangle is given by the equation: $$72=(2w)(w)$$What is the value of $$w$$?

    • 6

18. In triangle $$LMN$$, point $$P$$ lies on segment $$MN$$, and $$LP$$ is perpendicular to $$MN$$. The measure of angle $$LNP$$ is equal to the measure of angle $$MLP$$. If $$MP=8$$ and the length of $$LN$$ is twice the length of $$LM$$, what is the length of $$LP$$?

    • $$4$$
    • $$8$$
    • $$16$$
    • $$32$$

19. If $$b$$ is a fraction such that $$\frac14\le b\le\frac34,$$ which of the following is a true statement?

    • $$b\ge b^2\ge b^{-1}$$
    • $$b\le b^2\ge b^{-8}$$
    • $$b\ge b^2\ge b^{-1}$$
    • $$b\ge b^2\ge b^8$$

20. At Sing&Dance, customers can rent singing and dancing rooms in increments of 1 minute with a minimum total of 30 minutes. The singing room costs $$\$10$$ per minute, and the dancing room costs $$\$20$$ per minute. If the total cost must be at least $$\$500$$, which of the following choices indicates a possible combination of singing and dancing minutes that can be rented?

    • $$(15,15)$$
    • $$(15,16)$$
    • $$(15,17)$$
    • $$(15,18)$$

21. A graph shows a linear function and a quadratic function. How many solutions does the system represented by the graph have?

    • $$0$$
    • $$1$$
    • $$2$$
    • $$3$$

22. If $$g(x)$$ is obtained by shifting the function $$f(x)=\sqrt{3x+5}$$ 4 units to the right, what is $$g(6)$$?

    • $$\sqrt{11}$$
    • $$\sqrt{17}$$
    • $$\sqrt{35}$$
    • $$\sqrt{39}$$