Full Practice Exam 19 — Module 2

Questions in this quiz (22)

1. A fair spinner has $$8$$ equal sections numbered from $$1$$ to $$8$$. If the spinner is spun twice, what is the probability that the sum of the two results is greater than $$10$$?

   • $$\frac{15}{64}$$
   • $$\frac{21}{64}$$
   • $$\frac{9}{32}$$
   • $$\frac{25}{64}$$

2. A truck has a fuel efficiency of $$24$$ miles per gallon. During a $$6$$-hour trip, the truck uses $$18$$ gallons of fuel. Based on the truck's fuel efficiency, what is the average speed of the truck during the trip?

   • $$60$$ miles per hour
   • $$72$$ miles per hour
   • $$84$$ miles per hour
   • $$96$$ miles per hour

3. Given the system of inequalities:$$2x+y$$ > $$5$$$$x$$ > $$-2$$Which of the following points lies in the solution region?

   • $$(0,3)$$
   • $$(1,1)$$
   • $$(-3,10)$$
   • $$(1,4)$$

4. The average cost of a movie ticket increases by approximately $$4\%$$ each year. If the average ticket price was $$12$$ dollars at the beginning of $$2020$$, which equation best models the price $$P$$, in dollars, after $$x$$ years?

   • $$P=(1.04)^x$$
   • $$P=12(1.04)^x$$
   • $$P=12(1.4)^x$$
   • $$P=12+0.04x$$

5. Consider the system:$$4x+3y=k+2$$$$2x+y=5$$$$x-y=1$$What is the value of $$k$$ such that all three equations pass through the same point?

   • $$9$$
   • $$16$$
   • $$17$$
   • $$18$$

6. A survey shows that $$54.8\%$$ of residents support a proposed measure. If a town has a population of $$400,000$$, approximately how many residents support the measure?

   • $$199,200$$
   • $$219,200$$
   • $$239,200$$
   • $$259,200$$

7. The relationship between Celsius temperature $$C$$ and Fahrenheit temperature $$F$$ is given by $$C=\frac{5}{9}(F-32)$$. If the temperature increases by $$15^\circ$$ Celsius, what is the corresponding increase in Fahrenheit?

   • $$18$$
   • $$23$$
   • $$27$$
   • $$35$$

8. If $$a-3b=2$$, what is the value of $$\frac{9^a}{27^{2b}}$$?

   • 81

9. The table below shows the relationship between time $$t$$ and distance $$d$$.If the relationship is quadratic, which of the following could represent it?

   • $$d(t)=2t^2+5t+8$$
   • $$d(t)=3t^2+4t+8$$
   • $$d(t)=2t^2+7t+8$$
   • $$d(t)=t^2+6t+8$$

10. The function $$f(x)=a(x-h)^2+k$$ has $$a$$ < $$0$$ and $$k$$ > $$0$$. Which of the following cannot be true?

    • $$f(2)$$ < $$k$$
    • $$f(h)=k$$
    • $$f(-1)$$ > $$k$$
    • $$f(0)=4$$

11. A fruit punch mixture sells for $$3$$ dollars per liter. If $$40$$ liters of juice costing $$4$$ dollars per liter are mixed with another juice costing $$2$$ dollars per liter, how many liters of the second juice are needed?

    • 40

12. A circle has center $$(-1,2)$$ and passes through the point $$(3,5)$$. What is the area of the circle?

    • $$4\pi$$
    • $$8\pi$$
    • $$16\pi$$
    • $$25\pi$$

13. If $$5a+2b$$ is equal to $$4$$ times $$2a$$, what is the value of $$\frac{a-b}{a+b}$$?

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

14. A population of algae triples every $$80$$ hours. If there are initially $$200$$ algae, which formula models the population after $$t$$ hours?

    • $$P(t)=200\cdot3^t$$
    • $$P(t)=200\cdot3^{t/80}$$
    • $$P(t)=200\cdot e^{t/80}$$
    • $$P(t)=200\cdot80^t$$

15. Consider the system:$$x=3y-4$$$$y=(x-1)(x+4)$$How many ordered pairs satisfy both equations?

    • 2

16. A data set consists of $$8$$ numbers:$$10,\ 14,\ 17,\ 19,\ 21,\ 24,\ 28,\ 32.$$If the number $$32$$ in the data set is replaced with $$20$$, which of the following statements is true?

    • The mean decreases, and the median remains the same.
    • The mean increases, and the median remains the same.
    • The mean remains the same, and the median decreases.
    • Both the mean and the median decrease.

17. In a right triangle, $$\theta$$ is an acute angle such that $$\cos(\theta)=\frac{8}{17}.$$ What is the value of $$\tan(\theta)$$?

    • $$\frac{15}{8}$$
    • $$\frac{8}{15}$$
    • $$\frac{15}{17}$$
    • $$\frac{17}{8}$$

18. In $$\triangle XYZ$$, the measure of $$\angle YXZ$$ is $$60^\circ$$. Point $$W$$ lies on $$\overline{YZ}$$ such that $$\overline{XW}$$ bisects $$\angle YXZ$$. If the measure of $$\angle XYZ$$ is $$50^\circ$$, what is the measure, in degrees, of $$\angle XWY$$?

    • $$30^\circ$$
    • $$50^\circ$$
    • $$80^\circ$$
    • $$100^\circ$$

19. The scatterplot above shows the relationship between age, in years, and shoe size for $$24$$ males between $$10$$ and $$20$$ years old. The line of best fit is shown. Based on the data, how many $$19$$-year-old males had a shoe size greater than the one predicted by the line of best fit?

    • $$1$$
    • $$2$$
    • $$3$$
    • $$4$$

20. The graph above gives the aquarium's energy usage, in joules per hour, at different outside temperatures, in degrees Celsius. The function $$E(x)=a(x-20)^2+300$$ is used to model the aquarium's energy usage, where $$x$$ is the outside temperature in $$^\circ\text{C}$$. Which of the following values of $$a$$ best approximates the values given by the graph?

    • $$8$$
    • $$11$$
    • $$14$$
    • $$25$$

21. An employment agency surveyed a random sample of $$200$$ engineers working in Chicago and found the mean annual salary of the engineers in the sample was $$100,000$$ dollars with an associated margin of error of $$10,000$$ dollars. Which of the following conclusions is the most reasonable based on this data?

    • Most of the engineers working in Chicago earn exactly $$100,000$$ in annual salary.
    • All engineers working in Chicago earn between $$90,000$$ and $$110,000$$ in annual salary.
    • It is unlikely that an engineer working in Chicago has an annual salary below $$100,000.$$
    • The mean annual salary for all engineers working in Chicago is between $$90,000$$ and $$110,000.$$

22. Two samples of water of equal mass are heated to $$60^\circ\text{C}$$. One sample is poured into an insulated container, and the other is poured into a non-insulated container. The samples are then left for $$70$$ minutes to cool in a room with a temperature of $$25^\circ\text{C}$$. The graph above shows the temperature of each sample at $$10$$-minute intervals. Which of the following statements correctly compares the average rates at which the temperatures of the two samples change?

    • In every $$10$$-minute interval, the magnitude of the rate of change of temperature of the insulated sample is greater than that of the non-insulated sample.
    • In every $$10$$-minute interval, the magnitude of the rate of change of temperature of the non-insulated sample is greater than that of the insulated sample.
    • In the intervals from $$0$$ to $$10$$ minutes and from $$10$$ to $$20$$ minutes, the rates of change of temperature of the insulated sample are of greater magnitude, whereas in the intervals from $$40$$ to $$50$$ minutes and from $$50$$ to $$60$$ minutes, the rates of change of temperature of the non-insulated sample are of greater magnitude.
    • In the intervals from $$0$$ to $$10$$ minutes and from $$10$$ to $$20$$ minutes, the rates of change of temperature of the non-insulated sample are of greater magnitude, whereas in the intervals from $$40$$ to $$50$$ minutes and from $$50$$ to $$60$$ minutes, the rates of change of temperature of the insulated sample are of greater magnitude.