Full Practice Exam 5 — Module 1

Questions in this quiz (22)

1. What is the value of $$x$$ in the equation:$$\frac{5}{2}x-3=\frac{7}{4}x+1?$$

   • $$\frac{4}{7}$$
   • $$\frac{16}{3}$$
   • $$\frac{4}{3}$$
   • $$\frac{3}{4}$$

2. A train travels the first part of its journey at $$48$$ miles per hour and the remaining part at $$64$$ miles per hour. The total travel time is $$3.5$$ hours, and the time traveled at $$48$$ miles per hour is $$1.25$$ hours longer than the time traveled at $$64$$ miles per hour. How many total miles did the train travel?

   • $$64$$
   • $$72$$
   • $$114$$
   • $$186$$

3. A writer has already completed $$4800$$ words of a research paper. For the first t minutes of work, she types at a rate of $$60$$ words per minute. After taking a short break, she becomes fatigued and types at a slower rate of $$45$$ words per minute for the next $$2t$$ minutes. Let $$W(t)$$ represent the total number of words she has written after all typing is finished. Which expression gives $$W(t)$$ in terms of $$t$$?

   • $$W(t)=150t$$
   • $$W(t)=4800+45t$$
   • $$W(t)=4800+150t$$
   • $$W(t)=4800t$$

4. Which of the following is a solution to the equation below?$$(x-5)^{2}-4(x-5)-77=0$$?

   • $$-16$$
   • $$-7$$
   • $$-2$$
   • $$5$$

5. A water slide requires riders to be at least $$42$$ inches tall. Given that there are approximately $$2.54$$ centimeters in an inch, how tall must a rider be, to the nearest whole centimeter, to use the water slide?

   • $$102$$
   • $$107$$
   • $$113$$
   • $$119$$

6. Which of the following expressions is equivalent to $$12a^{2}b-18ab^{2}+6abc-9b^{2}c?$$

   • $$6ab(2a−3b+c)$$
   • $$3b(4a^2−6ab+2ac−3bc)$$
   • $$3ab(4a−6b-c)$$
   • $$3ab(4a-6b+2c-3c)$$

7. The expression $$\left(\frac{7}{3}x-\frac{4}{5}\right)\left(\frac{2}{7}x+\frac{3}{4}\right)$$ is?

   • A linear expression
   • A constant
   • A rational expression
   • A quadratic expression

8. If $$\frac{3x-5}{4}=\frac{7}{2}$$ then $$\frac{6(x-4)}{-18}$$ is equal to which of the following?

   • $$\frac{19}{3}$$
   • $$-\frac{1}{9}$$
   • $$-\frac{7}{9}$$
   • $$\frac{1}{3}$$

9. In the isosceles trapezoid $$ABCD$$, $$AB$$ is parallel to $$CD$$ and the legs $$AD$$ and $$BC$$ are congruent. The top base angle at $$A$$ measures $$112^\circ$$. What is the measure of the smallest interior angle of the trapezoid?

   • $$25^\circ$$
   • $$27^\circ$$
   • $$34^\circ$$
   • $$68^\circ$$

10. When $$x$$ > $$0$$, which of the following expressions is equivalent to $$\frac{5}{6x}-\frac{3}{4x}+\frac{1}{9x}$$?

    • $$\frac{4}{36x}$$
    • $$\frac{7}{36x}$$
    • $$\frac{5}{6x}$$
    • $$\frac{3}{4x}$$

11. On a college campus, the ratio of graduate students to undergraduate students is $$5$$ to $$7$$. Of the undergraduates, $$60$$ percent are women and $$40$$ percent are men. Of the graduate students, 45 percent are women and $$55$$ percent are men. If the total number of students on campus is $$4000$$, how many more women than men are on the campus?

    • $$300$$
    • $$240$$
    • $$180$$
    • $$120$$

12. The expression $$\left(\frac{5}{4}x+2\right)\left(\frac{3}{2}x-1\right)-\frac{1}{8}x^{2}$$ can be written in the form $$ax^{2}+bx+c$$, where $$a$$, $$b$$, and $$c$$ are constants. What is the value of $$a+b+c$$?

    • $$\frac{3}{2}$$
    • $$\frac{7}{4}$$
    • $$\frac{7}{2}$$
    • $$-2$$

13. The depreciation rate of a car is given by $$\frac{V_{start}-V_{end}}{V_{start}}\times100.$$ For which value of $$V_{end}$$ would the depreciation rate be zero?

    • $$\frac{V_{start}}{2}$$
    • $$\frac{V_{start}}{4}$$
    • $$V_{start}$$
    • $$2V_{start}$$

14. A line has the equation $$3y+6x=12.$$ What is the slope of a line that is perpendicular to this line?

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

15. An equilateral triangle has a side length of $$10$$ centimeters. What is the area of the equilateral triangle?

    • $$25$$
    • $$25\sqrt{3}$$
    • $$25\sqrt{2}$$
    • $$10\sqrt{2}$$

16. A garden's width is three-fourths of its length. Fertilizer is sold for $$15$$ dollars per bag, and one bag covers $$48$$ square feet. What expression gives the cost, in dollars, of the fertilizer needed to cover the entire garden if the garden is $$L$$ feet long? Assume partial bags can be purchased.

    • $$\frac{L^{2}}{4}$$
    • $$\frac{5L^{2}}{16}$$
    • $$\frac{15L^{2}}{65}$$
    • $$\frac{45L^{2}}{65}$$

17. A wildlife rescue center cares only for owls and hawks. Each hawk requires $$3$$ pounds of meat and $$4$$ vitamins per day, while each owl requires $$2$$ pounds of meat and $$1$$ vitamin per day. The center has a total of $$600$$ pounds of meat and $$700$$ vitamins available per day. If the center houses $$h$$ owls and $$k$$ hawks, which system of inequalities represents all possible numbers of owls and hawks the center could care for?

    • $$2h+3k\le600$$ and $$4h+k\le700$$
    • $$3h+2k\le600$$ and $$4h+k\le700$$
    • $$2h+3k\le600$$ and $$h+4k\le700$$
    • $$3h+2k\le600$$ and $$h+4k\le700$$

18. A linear function $$g$$ gives a store’s revenue, in dollars, for selling $$x$$ items. The store’s revenue is $$150$$ when it sells $$5$$ items, and $$270$$ when it sells $$9$$ items. Which equation defines $$g$$?

    • $$g(x)=150x+270$$
    • $$g(x)=9x+270$$
    • $$g(x)=30x$$
    • $$g(x)=5x+150$$

19. The box plots summarize the test scores of Group $$A$$ and Group $$B$$ on a standardized exam. Based on the box plots, which of the following statements must be true?

    • The mean score of Group A is greater than the mean score of Group B.
    • The mean score of Group A is less than the mean score of Group B.
    • The median score of Group A is greater than the median score of Group B.
    • The median score of Group A is less than the median score of Group B.

20. The table shows the number of tickets sold.The manager estimated that the percent increase from $$2018$$ to $$2019$$ would be double the percent increase from $$2019$$ to $$2020$$. How many tickets did the manager expect would be sold in $$2020$$?

    • $$420$$
    • $$231$$
    • $$4620$$
    • $$4851$$

21. The frequency distribution summarizes a set of data, where $$b$$ is a positive integer.How much greater is the mean of the data set than the median?

    • $$0$$
    • $$6$$
    • $$9$$
    • $$54$$

22. A coffee shop recorded data on beverage orders during a given month. Each patron bought exactly one beverage. The four beverages sold are cappuccino, espresso, latte, and americano.What is the probability that the beverage was a latte purchased by a woman age $$18$$ or older?

    • $$\frac{18}{3142}$$
    • $$\frac{1573}{3142}$$
    • $$\frac{1530}{3142}$$
    • $$\frac{265}{1571}$$