Full Practice Exam 5 — Module 2

Questions in this quiz (22)

1. A hiker's distance in miles from the start of a trail can be modeled by the function $$d(t)=3.5t,$$ where $$t$$ is the time in hours. What does the number $$3.5$$ represent in this function?

   • Her constant acceleration
   • Her constant speed
   • Her varying speed
   • Her varying acceleration

2. $$4y\left(\frac{{1}{2} y-7\right)$$ is equivalent to which expression?

   • $$8y^2-7y$$
   • $$4y^2-7y$$
   • $$2y^2-28y$$
   • $$\frac{1}{2}y^2-11y$$

3. If a line has a slope of $$-4$$ and passes through the point $$(3,-2)$$, what is the $$y$$-intercept of the line?

   • $$-12$$
   • $$-2$$
   • $$4$$
   • $$10$$

4. The table shows the numbers of beverages ordered at Tina's Cafe on a Saturday.What is the best estimate of the probability that a randomly selected beverage from the drive-through was a smoothie?

   • $$0.20$$
   • $$0.26$$
   • $$0.32$$
   • $$0.41$$

5. Find the value of $$n$$ in the equation:$$\frac{3n-4}{5}-\frac{2n+1}{3}=2$$

   • $$-47$$
   • $$-15$$
   • $$-5$$
   • $$15$$

6. A school schedules $$5$$ class periods, each lasting $$48$$ minutes, with a $$6$$ minute passing period between consecutive classes. There is also a $$30$$ minutes lunch break after the third class and a $$12$$ minutes homeroom session before the first class begins. How many total minutes are students required to be on campus during a full school day?

   • $$240$$
   • $$264$$
   • $$282$$
   • $$306$$

7. $$\frac{5-2x}{3} \le \frac{x+7}{6}$$Which of the following represents the solution set for $$x$$?

   • $$x \ge \frac{3}{5}$$
   • $$x \ge -\frac{1}{2}$$
   • $$x \ge \frac{17}{4}$$
   • $$x \le \frac{17}{4}$$

8. Which expression is equivalent to: $$49x^{4}-121y^{4}?$$

   • $$(7x^{2}-11y)(7x^{2}+11y)$$
   • $$(7x^{2}-11y^{2}+14xy)(7x^{2}+11y^{2}-14xy)$$
   • $$(7x-11y)^2(7x+11y)^2$$
   • $$(7x^{2}-11y^{2})(7x^{2}+11y^{2})$$

9. For how many points in the xy-plane will the functions $$y=-3x+4$$ and $$6y=-18x-12$$ intersect?

   • $$1$$
   • $$2$$
   • Infinitely many
   • None

10. A circle has a radius of $$6$$ inches. One sector of the circle has a central angle measure of $$45$$ degrees. What is the area of this sector of the circle in square inches?

    • $$\frac{8\pi}{36}$$
    • $$\frac{45\pi}{360}$$
    • $$\frac{9\pi}{2}$$
    • $$\frac{28\pi}{36}$$

11. If a square has a diagonal that measures $$5\sqrt{2}$$ units, what is the square's perimeter in units?

    • $$20\sqrt{2}$$
    • $$20$$
    • $$5\sqrt{2}$$
    • $$5$$

12. If $$4X$$ equal $$5Y$$ and $$2Y$$ equal $$3Z$$, how many $$Z$$ are equivalent to one $$X$$?

    • $$\frac{15Z}{8}$$
    • $$\frac{5Z}{4}$$
    • $$\frac{3Z}{2}$$
    • $$\frac{2Z}{3}$$

13. At an animal shelter, there are four rabbits that weigh an average of $$6$$ pounds each, and two guinea pigs. If one guinea pig weighs $$3$$ pounds, what must the weight of the second guinea pig be if the average weight of all six animals is $$5$$ pounds?

    • $$3$$
    • $$18$$
    • $$24$$
    • $$30$$

14. A shopper orders groceries for delivery. The cost of the groceries, including tax, is $$g.$$ The total price $$T$$ the shopper pays is: $$T=1.15g+5$$This includes the cost of the groceries, a $$15\%$$ tip, and a $$5$$ delivery fee. The delivery company later triples its delivery fee, and the shopper reduces the percent tip by one-third. Which expression represents the new total price for groceries costing $$g$$?

    • $$15g+\frac{5}{3}$$
    • $$3.45g+\frac{5}{3}$$
    • $$2.30g+0.15$$
    • $$1.10g+15$$

15. The costs of bags of premium dog food $$P$$ and standard dog food $$S$$ are directly proportional. The relationship is modeled by:$$P=3S$$Which statement must be true?

    • The premium dog food is one-third as expensive as the standard dog food.
    • The premium dog food is three times as expensive as the standard dog food.
    • The prices of the premium and standard dog food are always equal.
    • Customers buy three times as many bags of standard dog food as premium dog food.

16. If $$\frac{4}{3}x-\frac{5}{2}=\frac{1}{6}$$ then $$-\left(\frac{9}{4x-2}\right)$$ is equivalent to which of the following?

    • $$\frac{5}{2}$$
    • $$\frac{1}{6}$$
    • $$-\frac{3}{2}$$
    • $$\frac{8}{3}$$

17. The vertex form of parabola $$h$$ is $$h(x)=(x-2)^{2}+5.$$ A new function $$k(x)=-h(x)-3.$$ If the vertex of $$h(x)$$ is $$(a,b),$$ what is the vertex of $$k(x)$$ in terms of $$a$$ and $$b$$?

    • $$(-a,b+3)$$
    • $$(a,-b-3)$$
    • $$(-a,b-3)$$
    • $$(a,b+3)$$

18. A fitness app launches in January with $$250$$ users. Each month, the number of users grows by $$8$$ percent, with the increase compounding on the previous month's total. Which description best represents the relationship between time in months and the number of users?

    • A linear relationship with a constant rate of change
    • An exponentially decreasing relationship
    • An exponentially increasing relationship
    • A linear relationship with a rate of change that increases over time

19. Consider a rectangular prism with height $$H$$, length $$L$$, and width $$W$$. How many cones with the same base area (same $$L$$ and $$W$$ dimensions) but one-third the height of the prism could fit into the prism by volume?

    • $$3$$
    • $$6$$
    • $$9$$
    • $$12$$

20. A bookstore records how many books it sells in each of the following price ranges during a single afternoon:Which of the following statements is justifiable based on the table?

    • The range of prices is exactly $$40$$.
    • The mean price is between $$10$$ and $$20$$.
    • The median price is between $$10$$ and $$20$$
    • None of the above

21. The scatterplot shows the amount of electric energy generated, in millions of megawatt-hours, by nuclear sources over a $$10$$-year period. Based on the scatterplot, which statement is best supported by the data?

    • The electric energy generated increased at a constant rate throughout the 10-year period.
    • The electric energy generated reached a maximum during the middle of the 10-year period.
    • The electric energy generated decreased during the first half of the 10-year period and increased during the second half.
    • The electric energy generated fluctuated randomly with no clear trend over time.

22. A warehouse begins the day with a large shipment of boxes that must be loaded onto trucks. The workers load boxes at a constant rate throughout the afternoon. Which type of model best represents the number of boxes remaining to be loaded at any given time during the afternoon?

    • A linear model with a positive slope
    • A linear model with a negative slope
    • An exponential growth model
    • An exponential decay model