Full Practice Exam 4 — Module 1

Questions in this quiz (22)

1. If $$a^2$$ < $$b^2$$, which statement must be correct?

   • $$a$$ < $$b$$
   • $$a$$ > $$b$$
   • $$a \ne b$$
   • $$a \ge b$$

2. What is the product of $$x$$ and $$y$$ given the system of equations below?$$3+y=20x$$$$y=5x-1$$

   • $$\frac{2}{15}$$
   • $$-\frac{2}{45}$$
   • $$-\frac{1}{3}$$
   • $$-\frac{2}{3}$$

3. Maria's trainer recommends that she get an average of $$8$$ hours of sleep each night for good athletic performance. In one week ($$7$$ days), Maria spent a total of $$140$$ hours awake. How many additional hours of sleep should Maria have gotten that week in order to meet her trainer's recommendation?

   • $$28$$
   • $$46$$
   • $$56$$
   • $$68$$

4. What is the difference between $$9x^2+4xy-7y$$ and $$3x^2-2xy+5y$$?

   • $$12x^2+6xy−2y$$
   • $$6x^2+6xy-12y$$
   • $$6x^2+2xy−12y$$
   • $$6x^2+2xy+2y$$

5. $$4a^2-20a-96=0$$What are the values of $$a$$ in this equation?

   • $$8,-3$$
   • $$4,-2$$
   • $$-4,2$$
   • $$-4,-3$$

6. If a circle has a radius of $$7$$ centimeters, what is its circumference rounded to the nearest whole centimeter?

   • $$152$$
   • $$149$$
   • $$49$$
   • $$44$$

7. If $$4(3x-2)+5=3(2x+7)-11,$$ what is the value of $$12x+18$$?

   • $$28$$
   • $$44$$
   • $$56$$
   • $$64$$

8. Jordan is buying a new electric scooter that has a sticker price of $$1480$$ dollars. He is trading in an older scooter, and the dealer offers him a trade in credit equal to $$15\%$$ of the sticker price of the new scooter. The amount Jordan pays is the sticker price minus the trade in credit. He must then pay $$8.25\%$$ sales tax on that reduced price, plus a flat registration fee of $$65$$ dollars. What is the total amount Jordan must pay?

   • $$1426.79$$
   • $$1462.57$$
   • $$1258.27$$
   • $$1458.45$$

9. Which of the following operations could we perform on both sides of the inequality $$-5x+9$$ < $$12$$ in order to make it necessary to reverse the inequality sign, while still keeping $$x$$ on the left-hand side of the inequality?

   • Add $$6$$
   • Subtract $$15$$
   • Multiply by $$3$$
   • Divide by $$-5$$

10. A cylinder has a radius of $$3$$ inches and a height of $$6$$ inches. What is the cylinder's volume, in cubic inches? (Use the formula $$V=\pi r^2 h$$)

    • $$18\pi$$
    • $$36\pi$$
    • $$54\pi$$
    • $$108\pi$$

11. Jordan currently has $$6500$$ dollars in a college savings account. The account earns a steady annual interest rate of $$4$$ percent, compounded once per year. Jordan plans to leave the money untouched for several years. Which function $$g(t)$$ models the amount of money in the account after $$t$$ years?

    • $$g(t)=6500·0.96^t$$
    • $$g(t)=6500·1.04^t$$
    • $$g(t)=6500^t$$
    • $$g(t)=6500·1.4^t$$

12. A cafe keeps a tip jar on the counter that contains only $$0.25$$ dollar quarters and $$0.10$$ dollar dimes. The manager requires that whenever there is $$20.00$$ dollars ($$2000$$ cents) or more in the jar, some money must be removed. Which expression represents the allowable combinations of $$Q$$ quarters and $$D$$ dimes that can be in the jar without needing to remove any money?

    • $$25Q+10D$$ < $$2000$$
    • $$Q+D$$ < $$2000$$
    • $$0.25Q+0.1D$$ < $$2000$$
    • $$0.25Q-0.1D$$ < $$2000$$

13. A parallelogram has one interior angle that measures $$70$$ degrees. What is the measure of the largest interior angle of the parallelogram?

    • $$70$$
    • $$90$$
    • $$110$$
    • $$120$$

14. The variables $$m$$ and $$n$$ are directly proportional, so $$m=kn$$ for some constant $$k$$. When $$m=15$$, $$n=\frac{3}{2}$$. The pair of variables, $$n$$ and $$p$$, are also directly proportional, so $$n=rp$$ for some constant $$r$$. When $$n=12$$, $$p=8$$. If $$m=57,$$ what is the value of $$p$$?

    • $$3$$
    • $$\frac{19}{5}$$
    • $$10$$
    • $$\frac{57}{10}$$

15. A moving company uses the formula $$C=4B+12F+15$$ to determine the total cost $$C$$, in dollars, to move $$B$$ boxes and $$F$$ furniture items. What does the constant $$15$$ most likely represent in this situation?

    • The cost to move one piece of furniture
    • The cost to move one box
    • A fixed service fee charged for every move
    • The minimum cost to move only boxes or only furniture

16. How many more kilograms (to the nearest hundredth) will a $$3$$-cubic-meter balloon filled with air weigh than an identical balloon filled with argon, given that argon has a density of $$1.78$$ kg/m^3 and air has a density of $$1.20$$ $$kg/m^3$$?

    • $$0.58$$
    • $$1.14$$
    • $$1.74$$
    • $$2.98$$

17. A lemonade vendor has fixed costs of $$300$$ dollars for supplies and equipment. Each cup of lemonade costs $$1.50$$ dollars to make after the stand is set up. The total cost $$C(x)$$ for producing $$x$$ cups of lemonade is therefore:$$C(x)=1.5x+300$$Which graph correctly represents the cost function $$C(x)$$?

    • A line with positive slope, crossing the $$y$$-axis near –$$50$$, and rising through $$x=0.05$$ to about $$y=20$$
    • A line with a negative slope, crossing the $$y$$-axis above $$500$$, and decreasing sharply as $$x$$ increases
    • The line that begins at $$(0,300)$$ and rises with slope $$1.5$$
    • A line with positive slope, crossing the $$y$$-axis at $$500$$, rising to about $$1500$$ when $$x$$ is around $$400$$

18. The function $$g(x)=(x-4)(x+1)^{2}(x-2)^{3}$$ will cross the $$x$$-axis how many times?

    • 1
    • 2
    • 3
    • 6

19. On June $$1$$, $$2018$$, there were $$120$$ million mobile phone subscribers in Country $$X$$. By December $$1$$, $$2018$$, the number of mobile phone subscribers had increased to $$138$$ million. The major mobile service providers were $$AlphaTel$$, $$BetaMobile$$, $$GammaCom$$, and $$DeltaNet$$. If a mobile phone subscriber in Country $$X$$ on December $$1$$, $$2018$$, is selected at random, the probability that the person selected was a $$BetaMobile$$ subscriber is $$0.37$$. There were $$q$$ million $$BetaMobile$$ subscribers in Country $$X$$ on December $$1$$, $$2018$$. To the nearest integer, what is the value of $$q$$?

    • $$31$$
    • $$37$$
    • $$47$$
    • $$51$$

20. One of a planet’s moons orbits the planet every $$184$$ days. A second moon orbits the planet every $$219$$ days. How many more days does it take the second moon to orbit the planet $$15$$ times than it takes the first moon to orbit the planet $$15$$ times?

    • $$276$$
    • $$328$$
    • $$525$$
    • $$3285$$

21. The variables $$x$$ and $$y$$ have a linear relationship. The table below contains several corresponding $$x$$ and $$y$$ values for the line:What is the equation of the line represented by the $$x$$–$$y$$ values?

    • $$y=3x-1$$
    • $$y=3x+9$$
    • $$y=3x+8$$
    • $$y=3x-9$$

22. A dot plot represents the $$17$$ values in data set $$C$$. Data set $$D$$ is created by subtracting $$18$$ from each value in data set $$C$$. Which of the following correctly compares the medians and the ranges of data sets $$C$$ and $$D$$?

    • The median of data set D is equal to the median of data set C, and the range of data set D is equal to the range of data set C.
    • The median of data set D is less than the median of data set C, and the range of data set D is greater than the range of data set C.
    • The median of data set D is less than the median of data set C, and the range of data set D is equal to the range of data set C.
    • The median of data set D is equal to the median of data set C, and the range of data set D is less than the range of data set C.