Full Practice Exam 2 — Module 1

Questions in this quiz (22)

1. $$5,5,5,7,7,9,9,9,9$$Which frequency table correctly represents the data listed?

2. Which expression is equivalent to $$x^2+7x-30$$?

   • $$(x-3)(x+10)$$
   • $$(x-6)(x+5)$$
   • $$(x-10)(x+3)$$
   • $$(x-5)(x+6)$$

3. Sofia hikes at a speed of $$3$$ miles per hour and cycles at a speed of $$9$$ miles per hour. She hikes for $$h$$ hours and cycles for $$c$$ hours for a combined total of $$24$$ miles. Which equation represents this situation?

   • $$9h+3c=24$$
   • $$3h+9c=27$$
   • $$\frac13h+\frac19c=24$$
   • $$3h+9c=24$$

4. In triangle DEF, the measure of angle D is $$61^\circ$$ and the measure of angle E is $$24^\circ$$. What is the measure of $$\angle F$$?

   • $$47^\circ$$
   • $$95^\circ$$
   • $$61^\circ$$
   • $$85^\circ$$

5. The table summarizes the distribution of size and color for $$100$$ marbles in a jar.If one of these marbles is selected at random, what is the probability of selecting a blue marble? (Express your answer as a decimal, not as a percent.)

   • 0.4

6. From a population of $$60000$$ residents, $$1500$$ were randomly surveyed about a new recycling program. Based on the survey, it is estimated that $$48\%$$ of residents support the program, with an associated margin of error of $$2\%$$. Based on these results, which of the following is a plausible value for the total number of residents in the population who support the program?

   • $$20000$$
   • $$25800$$
   • $$31500$$
   • $$28800$$

7. What is the positive solution to the equation $$\frac{36}{x+5}=x$$?

   • $$8$$
   • $$2$$
   • $$4$$
   • $$6$$

8. A train descends from an elevation of $$3200$$ feet to $$1600$$ feet at a constant rate of $$120$$ feet per minute. What type of function best models the relationship between the train’s elevation and time?

   • Decreasing exponential
   • Increasing linear
   • Increasing exponential
   • Decreasing linear

9. $$h(x)=7\left(\frac15\right)^x$$If the given function $$h$$ is graphed in the $$xy$$ plane, where $$y=h(x)$$, what is the $$y$$ intercept of the graph?

   • $$(0,5)$$
   • $$(0,1)$$
   • $$(0,35)$$
   • $$(0,7)$$

10. A rectangle has a length of $$x$$ units and a width of $$(x-12)$$ units. If the rectangle has an area of $$64$$ square units, what is the value of $$x$$?

    • $$4$$
    • $$8$$
    • $$12$$
    • $$16$$

11. Maria opened a savings account at a bank. The table shows the exponential relationship between the time $$t$$, in years, since Maria opened the account and the total amount $$A$$, in dollars, in the account. If Maria made no additional deposits or withdrawals, which of the following equations best represents the relationship between $$t$$ and $$A$$?

    • $$A=(1+0.005)^t$$
    • $$A=1.005(500)^t$$
    • $$A=500(1.005)^t$$
    • $$A=0.005(1+500)^t$$

12. At how many points do the graphs of the equations $$y=3x-7$$ and $$y=-2x+5$$ intersect in the $$xy$$ plane?

    • $$0$$
    • $$1$$
    • $$2$$
    • $$5$$

13. At a school carnival, students can win colored tickets that are worth different numbers of points depending on the color. One student won $$B$$ blue tickets and $$Y$$ yellow tickets worth a total of $$300$$ points. The given equation represents this situation:$$6B+36Y=300$$How many more points is a yellow ticket worth than a blue ticket?

    • $$50$$
    • $$60$$
    • $$30$$
    • $$20$$

14. The number of bacteria in a liquid culture triples every day. There are $$15000$$ bacteria in the culture at the start of an observation. Which represents the number of bacteria, $$y$$, in the culture $$t$$ days after the start of the observation?

    • $$y=\frac13(15000)^t$$
    • $$y=3(15000)^t$$
    • $$y=15000\left(\frac13\right)^t$$
    • $$y=15000(3)^t$$

15. A cylinder has a radius of $$6$$ inches and a height of $$8$$ inches. What is the volume, in cubic inches, of the cylinder?

    • $$72\pi$$
    • $$288\pi$$
    • $$384\pi$$
    • $$576\pi$$

16. $$4x+3y=27$$$$2x+3y=21$$The solution to the given system of equations is $$(x,y)$$. What is the value of $$y$$?

    • $$2$$
    • $$3$$
    • $$5$$
    • $$7$$

17. In triangle $$MNP$$, $$\cos(M)=\frac{9}{41}$$ and angle $$N$$ is a right angle. What is the value of $$\cos(P)$$?

    • $$\frac{1}{41}$$
    • $$\frac{9}{41}$$
    • $$\frac{40}{41}$$
    • $$\frac{16}{41}$$

18. $$g(x)=3x^2-24x+5$$The given equation defines the function $$g$$. For what value of $$x$$ does $$g(x)$$ reach its minimum?

    • $$8$$
    • $$2$$
    • $$7$$
    • $$4$$

19. In the $$xy$$ plane, line $$m$$ passes through the point $$(0,0)$$ and is parallel to the line represented by the equation $$y=-5x+4$$. If line $$m$$ also passes through the point $$(2,k)$$, what is the value of $$k$$?

    • $$-5$$
    • $$-10$$
    • $$-2$$
    • $$0$$

20. In the $$xy$$ plane, a line with equation $$3y=d$$ for some constant $$d$$ intersects a parabola at exactly one point. If the parabola has equation $$y=-x^2+8x$$, what is the value of $$d$$?

    • $$4$$
    • $$19$$
    • $$48$$
    • $$52$$

21. Population density is defined as the number of individuals of a species per unit of area. Two wildlife preserves, Preserve X and Preserve Y, are both in the shape of a square. The side length of the larger preserve, Preserve X, is $$2.5$$ times the side length of the smaller preserve, Preserve Y$$. Each preserve is home to a population of $$500$$ deer. The population density of deer in Preserve X is $$2$$ deer per square mile. What is the population density of deer in Preserve Y, in deer per square mile?

    • 12.5

22. A team of health researchers conducted a study to explore the relationship between regular physical activity and reported energy levels. They recruited $$500$$ adults from various community centers and administered a comprehensive questionnaire. The questionnaire included questions about their weekly physical activity (categorized as "low", "moderate", or "high") and their self-reported average daily energy level on a scale of $$1$$ to $$10$$.The researchers found that participants who reported "high" levels of physical activity also reported significantly higher average daily energy levels compared to those who reported "low" or "moderate" levels of physical activity. Based solely on the design and findings of this study, which of the following conclusions is most appropriate?

    • Engaging in high levels of physical activity causes an increase in daily energy levels.
    • Individuals with naturally higher energy levels are more likely to engage in high levels of physical activity.
    • There is an observed association between higher levels of physical activity and higher self-reported energy levels among the study participants.
    • To increase energy levels, adults should be encouraged to engage in high levels of physical activity.