Full Practice Exam 7 — Module 1

Questions in this quiz (22)

1. The graph shows two lines intersecting on the coordinate plane.What system of linear equations represents the lines shown?

   • $$y=-\frac{3}{4}x+6$$$$y=-\frac{3}{8}x+3$$
   • $$y=-\frac{3}{2}x+6$$$$y=-\frac{3}{4}x+3$$
   • $$y=-\frac{4}{3}x+6$$$$y=-\frac{8}{3}x+3$$
   • $$y=-\frac{3}{4}x+6$$$$y=-\frac{3}{4}x+3$$

2. A number $$x$$ is at least $$5$$ less than twice the value of $$y$$. If the value of $$y$$ is $$6$$, what is the greatest possible value of $$x$$?

   • 2
   • 5
   • 6
   • 7

3. Consider the equation $$5x-14px=20$$. In the given equation, $$p$$ is a constant. The equation has no solution. What is the value of $$p$$?

   • $$0$$
   • $$\frac{5}{14}$$
   • $$\frac{7}{5}$$
   • $$2$$

4. The table below shows the coordinates of three points on a line in the $$xy$$-plane, where $$m$$ and $$p$$ are constants.If the slope of the line is $$2$$, what is the value of $$m+p$$?

   • 6
   • 21
   • 27
   • 30

5. One gallon of sealant can cover $$180$$ square feet of surface. A patio has a total floor area of $$a$$ square feet. Which equation represents the total amount of sealant, $$S$$, in gallons, needed to coat the patio three times?

   • $$\frac{a}{180}$$
   • $$\frac{a}{540}$$
   • $$\frac{a}{3}$$
   • $$\frac{3a}{180}$$

6. A delivery company limits the size of packages it will ship using a certain service. For rectangular prism shaped boxes, the restriction states that the sum of the perimeter of the base and the height of the box cannot exceed $$150$$ inches. The perimeter of the base is calculated using the width and length of the box. If a box has a height of $$50$$ inches and its length is $$3$$ times the width, which inequality represents the allowable width $$x$$, in inches, of the box?

   • $$0$$ < $$x\le10\frac{1}{4}$$
   • $$0$$ < $$x\le12\frac{1}{2}$$
   • $$0$$ < $$x\le16$$
   • $$0$$ < $$x\le20$$

7. A right circular cylinder with radius $$r$$ and height $$h$$. A second right circular cylinder has a volume that is $$256$$ times the volume of the cylinder shown. Which of the following could represent the radius $$R$$, in terms of $$r$$, and the height $$H$$, in terms of $$h$$, of the second cylinder?

   • $$R=4r$$ and $$H=16h$$
   • $$R=8r$$ and $$H=4h$$
   • $$R=16r$$ and $$H=h$$
   • All the above

8. A rectangular garden has an area of $$500$$ square feet. A scaled design of the garden is created in which both the length and the width of the original garden are increased by $$10$$ percent. What is the area of the scaled design, in square feet?

   • $$121$$
   • $$600$$
   • $$605$$
   • $$1210$$

9. An isosceles right triangle has a perimeter of $$72+72\sqrt{2}$$ inches. What is the length, in inches, of one leg of this triangle?

   • $$36$$
   • $$36\sqrt{2}$$
   • $$72$$
   • $$72\sqrt{2}$$

10. In the figure, segments $$AC$$ and $$DB$$ intersect at point $$I$$. It is given that $$IA=IB$$ and $$IC=ID$$. What is the measure, in degrees, of $$\angle ABD$$?

    • $$37.5^\circ$$
    • $$65^\circ$$
    • $$75^\circ$$
    • $$105^\circ$$

11. At a currency exchange store, the following rates apply:$$1$$ U.S. Dollar $$=110$$ Japanese Yen$$1$$ U.S. Dollar $$=1.25$$ Canadian Dollars$$1$$ U.S. Dollar $$=1.50$$ Australian DollarsA customer has $$300$$ Australian Dollars and wants to exchange it into Japanese Yen. The store charges a $$3\%$$ fee on the amount of money after it is converted into U.S. dollars. Approximately how many Japanese Yen will the customer receive after the fee?

    • $$21,340$$
    • $$23,650$$
    • $$24,200$$
    • $$26,400$$

12. A company has four stores at different locations in a city. The company gathered data on the price of a particular item before and after a sale, along with the quantities sold.The company wants to estimate the overall average price per item sold, counting all items sold before and after the sale at Stores $$A$$ and $$B$$ only. What is the weighted average price per item sold at Stores $$A$$ and $$B$$ combined, rounded to the nearest cent?

    • $$11.13$$
    • $$11.26$$
    • $$11.39$$
    • $$11.56$$

13. An amusement park researcher wants to know whether the average height of ten-year-old children in a town meets the minimum height requirement for a new ride. The researcher randomly selects $$144$$ ten-year-old children and finds a sample mean height of $$46$$ inches. A $$95\%$$ confidence interval for the population mean height is reported as $$(44.8,47.2)$$ inches. The park will approve the ride only if it is reasonable to conclude that the population mean height is greater than $$45$$ inches. Which conclusion is most reasonable based on the confidence interval?

    • Since $$45$$ is inside the interval, the population mean must equal $$45$$ inches.
    • Since the entire interval is above $$45$$, it is reasonable to conclude the population mean is greater than $$45$$ inches.
    • Since $$95\%$$ of individual ten-year-old children have heights between $$44.8$$ and $$47.2$$ inches, the requirement is met.
    • The population mean can be both greater or smaller than $$45$$ inches.

14. A speed-reading course teaches students how to read $$900$$ words per minute. A graduate reads a book that has $$240$$ pages, with an average of $$275$$ words per page. However, she takes a $$2$$-minute break after every $$15$$ pages she reads. How many total minutes does it take her to finish the entire book, including breaks?

    • $$80.45$$
    • $$92.56$$
    • $$96.35$$
    • $$103.33$$

15. If the graph of $$f(x)$$ passes through the points $$(-1,6)$$ and $$(4,-2)$$, and $$g(x)=f(x+2)-3$$, which two points must be on the graph of $$g(x)$$?

    • $$(1,3)$$ and $$(6,-5)$$
    • $$(-3,3)$$ and $$(2,-5)$$
    • $$(-3,9)$$ and $$(2,1)$$
    • $$(1,9)$$ and $$(6,-1)$$

16. A town’s population was $$12000$$ in $$2020$$ and increases by $$3\%$$ each year. In $$2025$$, an unexpected event causes the population to decrease by $$5\%$$ immediately after the $$2025$$ increase occurs. What is the town’s population at the end of $$2025$$, to the nearest whole number?

    • $$13,201$$
    • $$13,216$$
    • $$13,860$$
    • $$14,400$$

17. If $$f(x)=x^2-3x+2$$ and $$g(x)=f(x-2)$$, what is the value of $$g(-2)$$?

    • $$6$$
    • $$12$$
    • $$20$$
    • $$30$$

18. The parabola $$y=2(x-4)^2-7$$ is graphed in the $$xy$$-plane. Which of the following is the vertex of the parabola?

    • $$(4,-7)$$
    • $$(-4,-7)$$
    • $$(4,7)$$
    • $$(-4,7)$$

19. A ball is launched upward, and its height in meters after $$t$$ seconds is modeled by:$$h(t)=-3t^2+18t+7$$The ball is caught when its height is $$16$$ meters. Which of the following represent the number of seconds between the launch and the catch?

    • $$-3+\sqrt{3}$$
    • $$6+\sqrt{2}$$
    • $$3+\sqrt{6}$$
    • $$-3+3\sqrt{2}$$

20. Which of the following is equivalent to:$$(3x-5)(2x+7)-(x-4)(x+9)?$$

    • $$5x^2+20x-71$$
    • $$5x^2-20x-7$$
    • $$6x^2+10x-7$$
    • $$5x^2+6x+1$$

21. A bag contains $$4$$ red marbles, $$5$$ blue marbles, and $$6$$ green marbles. Two marbles are selected at random without replacement. What is the probability that at least one of the marbles selected is blue?

    • $$\frac{5}{7}$$
    • $$\frac{2}{3}$$
    • $$\frac{4}{7}$$
    • $$\frac{3}{4}$$

22. A movie theater tracks monthly sales over its first $$7$$ months of operation. The lower graph shows the number of soft drinks sold each month. The upper graph shows the combined total of soft drinks and popcorn containers sold each month. Let $$P_m$$ be the number of popcorn containers sold in month $$m$$. Which of the following statements must be true based on the graph?

    • The month with the greatest increase in $$P_m$$ is the same month with the greatest increase in total sales.
    • The value of $$P_m$$ decreased in exactly two months compared to the previous month.
    • The percentage increase in popcorn container sales from Month $$2$$ to Month $$3$$ is greater than the percentage increase from Month $$6$$ to Month $$7$$.
    • The number of popcorn containers sold in Month $$5$$ is less than the number sold in Month $$4$$.