Full Practice Exam 28 — Module 1

Questions in this quiz (22)

1. A company rents bicycles to tourists. The cost to rent a bicycle consists of a one-time fee of $$\$8$$ plus $$\$5$$ for each hour the bicycle is rented. Which equation represents the total cost $$C$$, in dollars, for renting the bicycle for $$h$$ hours?

   • $$C=5h$$
   • $$C=8h+5$$
   • $$C=5h+8$$
   • $$C=13h$$

2. The table shows several values of $$x$$ and $$g(x)$$ for a linear function $$g$$. Which equation defines the function?

   • $$g(x)=2x+3$$
   • $$g(x)=3x+1$$
   • $$g(x)=2x+1$$
   • $$g(x)=x+5$$

3. Which expression is equivalent to $$\sqrt[6]{b}\cdot b^{\frac12}$$?

   • $$b$$
   • $$b^2$$
   • $$b^{\frac12}$$
   • $$b^{\frac23}$$

4. For the equation $$y=kx$$, where $$k$$ is a constant, $$y=24$$ when $$x=6$$. What is the value of $$x$$ when $$y=12$$?

   • $$2$$
   • $$3$$
   • $$6$$
   • $$12$$

5. The equation $$ax^2+bx+c=3x^2+12x+27$$ is true for all values of $$x$$. What is the value of $$a+b+c$$?

   • $$36$$
   • $$39$$
   • $$42$$
   • $$45$$

6. The function $$P(t)=250+15t$$ represents the amount of money, in dollars, in an account after $$t$$ weeks. What does the number $$250$$ represent?

   • The amount added each week
   • The amount in the account after one week
   • The initial amount in the account
   • The total profit earned

7. On a map, $$1$$ inch represents $$4$$ miles. A rectangular park measures $$3$$ inches by $$5$$ inches on the map. What is the actual area of the park, in square miles?

   • $$60$$
   • $$120$$
   • $$240$$
   • $$480$$

8. A driver travels $$360$$ miles. The first $$180$$ miles take $$3$$ hours, and the remaining $$180$$ miles take $$5$$ hours. What is the driver's average speed for the entire trip?

   • $$30$$ miles per hour
   • $$40$$ miles per hour
   • $$45$$ miles per hour
   • $$60$$ miles per hour

9. The graph shows the value of an airplane, in dollars, over several years after purchase. If the airplane continues to decrease in value at a linear rate, at what year after purchase will the plane first closely approximate a value of zero dollars?

   • $$10$$ years after purchase
   • $$15$$ years after purchase
   • $$20$$ years after purchase
   • $$25$$ years after purchase

10. If a quantity $$n$$ is increased by $$300\%$$, which expression represents the new value?

    • $$2n$$
    • $$3n$$
    • $$4n$$
    • $$5n$$

11. How many $$x$$-intercepts does the graph of $$y=c$$ have if $$c$$ is a positive constant?

    • Zero
    • One
    • Two
    • Cannot be determined

12. The table shows the number of correct answers on a quiz for two classes.What is the median score of the combined data set?

    • 2

13. What value of $$x$$ satisfies the equation $$\frac{x^2-9}{x-3}=6?$$

    • $$-3$$
    • $$3$$
    • $$6$$
    • There are no solutions.

14. $$x(x-6)+6(x-4)=(x+a)(x-a)$$ The expression is true for some constant $$a$$. Which of the following could be the value of $$a$$?I. $$2\sqrt6$$II. $$2$$III. $$6$$

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

15. Before $$2025$$, $$18$$ of the $$45$$ people who had served as governors of a certain state had previously served as lieutenant governor. If $$G$$ represents the total number of governors and $$L$$ represents the number who previously served as lieutenant governor, which equation models the relationship?

    • $$L=18G$$
    • $$L=\frac25G$$
    • $$L=\frac52G$$
    • $$L=\frac1{18}G$$

16. $$-\frac12x+\frac14y=8$$$$y=2x+k$$The system of equations above has infinitely many solutions. What is the value of $$k$$?

    • 32

17. The triangles $$ABC$$ and $$DEF$$ are similar to one another, with angle $$B$$ corresponding to angle $$E$$. In triangle $$DEF$$, $$DE=10$$, $$DF=24$$, and $$EF=26$$. What is the tangent of angle $$C$$?

    • $$\frac5{13}$$
    • $$\frac5{12}$$
    • $$\frac{10}{13}$$
    • $$\frac{12}{13}$$

18. Two friends are organizing a concert. Adult tickets cost $$\$25$$ each, and student tickets cost $$\$15$$ each. They want to sell more than $$300$$ tickets while collecting less than $$\$6,000$$ in total revenue. If $$a$$ represents the number of adult tickets and $$s$$ represents the number of student tickets, which system of inequalities represents the situation?

    • $$a+s\le300$$ $$25a+15s\ge6000$$
    • $$a+s$$ > $$300$$ $$25a+15s$$ < $$6000$$
    • $$a+s$$ < $$300$$$$25a+15s$$ > $$6000$$
    • $$a+s\ge300$$$$25a+15s\le6000$$

19. There are $$5,280$$ feet in a mile. Which value is closest to $$45$$ miles per hour expressed in feet per second?

    • $$44$$ feet per second
    • $$66$$ feet per second
    • $$88$$ feet per second
    • $$132$$ feet per second

20. At a café, each smoothie contains $$80$$ milligrams of vitamin C, and each juice contains $$35$$ milligrams of vitamin C. A customer purchases only smoothies and juices. The number of smoothies purchased is twice the number of juices purchased, and the total amount of vitamin C purchased is $$585$$ milligrams. How many smoothies did the customer purchase?

    • $$2$$
    • $$3$$
    • $$4$$
    • $$6$$

21. In the figure, $$ABCD$$ and $$AEFG$$ are similar rectangles. If $$AB$$ is $$4$$ units long, $$BC$$ is $$6$$ units long, and $$FG$$ is $$10$$ units long, what is the perimeter of rectangle $$AEFG$$?

    • $$24$$ units
    • $$48$$ units
    • $$50$$ units
    • $$72$$ units

22. The circle graphed has center $$C$$, a radius of $$7$$ units, and a central angle $$\angle ACB$$ with a measure of $$100^\circ$$. What is the area of the sector of the circle designated by $$\angle ACB$$ to the nearest whole square unit?

    • 122