Full Practice Exam 2 — Module 1

Questions in this quiz (22)

1. Diego has $$12400$$ pesos that he will convert to US dollars. The exchange rate is $$1$$ peso $$= 0.064$$ US dollars. The service charges a $$3.5\%$$ fee on the converted US dollar amount. After the fee, Diego uses the remaining dollars to buy concert tickets costing $$48$$ dollars each. How many tickets can he buy?

   • $$14$$
   • $$15$$
   • $$16$$
   • $$18$$

2. Consider the following system of equations with variables $$A$$ and $$B$$ and constant integers $$R$$ and $$S$$:$$4A+5B=40$$$$RA+SB=10R$$For the system to have infinitely many solutions, the second equation must be a scalar multiple of the first. By what number must the sum $$R+S$$ be divisible?

   • $$4$$
   • $$5$$
   • $$8$$
   • $$9$$

3. If $$\frac{1}{5}x+\frac{1}{4}x+\frac{1}{10}x=14,$$ what is the value of $$x$$?

   • $$\frac{280}{11}$$
   • $$25$$
   • $$\frac{11}{20}$$
   • $$11$$

4. A person can ride a roller coaster if height $$x$$ is between $$36$$ inches and $$72$$ inches. Which inequality models all possible permitted heights?

   • $$|x-36|$$ < $$72$$
   • $$|x-54|$$ < $$18$$
   • $$|x+38|$$ < $$42$$
   • $$|x+36|$$ < $$72$$

5. A clinic surveyed $$400$$ patients about whether they had diabetes and whether they had hypertension. The table shows the results.A patient is selected at random from the $$400$$ patients. What is the probability in percent that the patient has at least one of the two conditions, diabetes or hypertension?

   • $$50%$$
   • $$52%$$
   • $$57.5%$$
   • $$72.5%$$

6. A school collected data on the number of students who achieved certain test score ranges on a recent standardized exam.School administrators are concerned that too many students are scoring unusually high, causing the average test score to be inflated. They want to ensure that the distribution of scores better reflects typical performance levels. If administrators want to reduce score inflation, which of the following statistics would be most important to bring closer to the national average score of $$70$$?

   • Mean
   • Median
   • Mode
   • Range

7. $$(\frac{n^{2}-n^{3}}{n^{4}})^{-2}$$is equivalent to which of the following?

   • $$\frac{n^{2}}{(1+n)^{4}}$$
   • $$\frac{n^{3}}{(1-n)^{4}}$$
   • $$\frac{n}{(1+n)^{4}}$$
   • $$\frac{n^{4}}{(1-n)^{2}}$$

8. A rectangular garden is to be built with a perimeter of $$80$$ feet. The gardener wants the area of the garden to be $$384$$ square feet. What must the length and width of the garden be if the gardener wants the length to be greater than 21 feet?

   • Length=$$21$$ feet and Width=$$19$$ feet.
   • Length=$$24$$ feet and Width=$$16$$ feet.
   • Length=$$28$$ feet and Width=$$12$$ feet.
   • Length=$$22$$ feet and Width=$$18$$ feet.

9. What is the solution with the least possible $$y$$-value that satisfies both of the following inequalities?$$y\ge3x-4$$$$5-y\le2x$$

   • $$(1,-1)$$
   • $$(0,-4)$$
   • $$(-1,-7)$$
   • $$(2,2)$$

10. A circle has a radius of $$6$$ and a sector with a central angle of $$45°$$. What is the area of the sector?

    • $$3\pi$$
    • $$4\pi$$
    • $$4.5\pi$$
    • $$6\pi$$

11. A line in the $$xy$$-plane has a slope of $$-\frac{4}{7}$$ and passes through the point $$(14,-3)$$. Which of the following points also lies on the line?

    • $$(5,6)$$
    • $$(0,5)$$
    • $$(21,-7)$$
    • $$(7,1)$$

12. If $$\frac{a}{b}=-4$$ what is the value of $$-3\left(\frac{b}{a}\right)^{2}$$?

    • $$\frac{16}{3}$$
    • $$-\frac{3}{16}$$
    • $$-\frac{1}{4}$$
    • $$\frac{1}{16}$$

13. Towns $$X$$ and $$Y$$ are 180 miles apart. Maria leaves Town $$X$$ heading toward Town $$Y$$ at 2:00 P.M. driving $$50$$ miles per hour. Jordan leaves Town $$Y$$ heading toward Town $$X$$ at $$3:00$$ P.M. driving $$35$$ miles per hour. At what time will they meet to the nearest minute?

    • $$4:14$$ P.M
    • $$5:06$$ P.M
    • $$4:32$$ P.M
    • $$5:32$$ P.M

14. A salesperson earns a bonus $$B$$ based on the number of internet packages sold n if $$B$$ is positive. The bonus is modeled by the equation $$B=40n+30(n-80)-1600$$. What is the least number of internet packages the salesperson must sell to earn a bonus?

    • $$58$$
    • $$72$$
    • $$74$$
    • $$80$$

15. The equation $$y=-0.5x^2+6x+72,$$ gives the estimated number of tickets sold $$y$$ for a concert, where $$x$$ is the number of days after ticket sales begin and $$0\le x\le 12$$. Which statement is the best interpretation of the point $$(2,82)$$ in this context?

    • Ticket sales increase by $$82$$ tickets every day after sales begin.
    • Ticket sales increase by $$2$$ tickets every $$82$$ days after sales begin.
    • $$2$$ days after ticket sales begin, the estimated number of tickets sold is $$82$$.
    • $$82$$ days after ticket sales begin, the estimated number of tickets sold is $$2$$.

16. The equation above defines the function $$g(x)=6x^2-24x+19.$$ For what value of $$x$$ does $$g(x)$$ reach its minimum?

    • $$2$$
    • $$6$$
    • $$19$$
    • $$24$$

17. Consider the equation $$y=-3(x-a)^2(x+b)(x-c),$$ where $$a$$, $$b$$, and $$c$$ are distinct positive constants. When the equation is graphed in the $$xy$$-plane, how many distinct $$x$$-intercepts does the graph have?

    • 2
    • 3
    • 4
    • 5

18. The table shows the total amount of money in a savings account.Alex opened a savings account at a bank. The table shows the exponential relationship between the time $$t$$ in years since Alex opened the account and the total amount $$d$$ in dollars in the account. If Alex made no additional deposits or withdrawals, which equation best represents the relationship between $$t$$ and $$d$$?

    • $$d=0.02(1+1200)^t$$
    • $$d=1200(1+0.02)^t$$
    • $$d=(1+0.02)^t$$
    • $$d=(1+1200)^t$$

19. The table shows the distribution, by state and power capacity, of the $$18$$ largest solar projects in the United States in $$2018$$.The total power capacity of the six solar projects located in Arizona was $$3600$$ megawatts, and the total power capacity of all $$18$$ solar projects was $$9900$$ megawatts in $$2018$$. The amount of energy produced in one hour at a rate of one megawatt is one megawatt hour. If each of the six Arizona solar projects operated continuously for $$12$$ hours at their maximum rate of power generation, approximately how many megawatt hours of energy would the six projects have produced?

    • $$4550$$
    • $$43200$$
    • $$95700$$
    • $$120300$$

20. The length of a rectangle's diagonal is $$10\sqrt{17}$$, and the length of the rectangle's shorter side is $$10$$. What is the length of the rectangle's longer side?

    • $$10$$
    • $$20$$
    • $$30$$
    • $$40$$

21. What is the volume, in cubic centimeters, of a right rectangular prism that has a length of $$6$$ centimeters, a width of $$5$$ centimeters, and a height of $$8$$ centimeters?

    • 120
    • 160
    • 180
    • 240

22. In the figure, $$(P)$$ and $$(Q)$$ are parallel. What is the value of y?

    • $$40^\circ$$
    • $$50^\circ$$
    • $$60^\circ$$
    • $$65^\circ$$