Full Practice Exam 16 — Module 1

Questions in this quiz (22)

1. The function $$g(t)=250+40t$$ gives the amount of money, in dollars, in Leo’s savings account after $$t$$ monthly deposits. What is the best interpretation of $$40$$ in this context?

   • With each monthly deposit, the amount in Leo’s savings account increased by $$40$$ dollars.
   • Before Leo made any monthly deposits, the amount in his savings account was $$40$$ dollars.
   • After $$1$$ monthly deposit, the amount in Leo’s savings account was $$40$$ dollars.
   • Leo made a total of $$40$$ monthly deposits.

2. For the linear function $$f$$, the table shows three values of $$x$$ and their corresponding values of $$f(x)$$.Which equation defines $$f(x)$$?

   • $$f(x)=4x+18$$
   • $$f(x)=18x+4$$
   • $$f(x)=26x+18$$
   • $$f(x)=22x+4$$

3. A customer spent $$48$$ dollars to purchase apples at $$4$$ dollars per pound. How many pounds of apples did the customer purchase?

   • $$10$$
   • $$12$$
   • $$16$$
   • $$20$$

4. Maya bought $$8$$ notebooks that were each the same price. She used a coupon for $$56$$ dollars off the entire purchase. The cost of the entire purchase after using the coupon was $$40$$. What was the original price, in dollars, of $$1$$ notebook?

   • $$10$$
   • $$11$$
   • $$12$$
   • $$13$$

5. The equation $$4b+6r=120$$ describes the relationship between the number of birds, $$b$$, and the number of reptiles, $$r$$, that can be cared for at an animal shelter on a given day. If the shelter cares for $$12$$ reptiles on a given day, how many birds can it care for on that day?

   • $$0$$
   • $$12$$
   • $$24$$
   • $$48$$

6. Line $$m$$ in the $$xy$$-plane has a slope of $$\frac{2}{5}$$ and passes through the point $$(5,4)$$. Which equation defines line $$m$$?

   • $$y=\frac{2}{5}x+4$$
   • $$y=\frac{2}{5}x+2$$
   • $$y=\frac{2}{5}x-2$$
   • $$y=5x+4$$

7. For a certain rectangular region, the ratio of its length to its width is $$24$$ to $$8$$. If the width of the rectangular region increases by $$5$$ units, how must the length change to maintain this ratio?

   • It must decrease by $$15$$ units.
   • It must increase by $$15$$ units.
   • It must decrease by $$5$$ units.
   • It must increase by $$5$$ units.

8. Square A has a side length of $$x$$ inches. Square B has a perimeter that is $$120$$ inches greater than the perimeter of Square A. The function $$g$$ gives the area of Square B, in square inches. Which function defines $$g$$?

   • $$g(x)=(x+30)^2$$
   • $$g(x)=(x+120)^2$$
   • $$g(x)=(30x+30)^2$$
   • $$g(x)=(120x+120)^2$$

9. The function $$h(x)=500(1.02)^x$$ models the value, in dollars, of a bank account by the end of each year from $$2010$$ through $$2025$$, where $$x$$ is the number of years after $$2010$$. Which of the following is the best interpretation of “$$h(4)$$ is approximately equal to $$541$$”?

   • The value of the account is approximately $$541$$ in $$2014$$.
   • The value of the account increased by $$541$$ from $$2010$$ to $$2014$$.
   • The value of the account is $$4$$ times greater in $$2014$$ than in $$2010$$.
   • The account increases by $$541$$ dollars every $$4$$ years.

10. The equation $$\frac{10x}{3y}=5\sqrt{w+11}$$ relates the distinct positive real numbers $$w$$, $$x$$, and $$y$$. Which equation correctly expresses $$w$$ in terms of $$x$$ and $$y$$?

    • $$w=\left(\frac{2x}{3y}\right)^2-11$$
    • $$w=\sqrt{\frac{2x}{3y}}-11$$
    • $$w=\left(\frac{10x}{3y}\right)^2-11$$
    • $$w=\frac{2x}{3y}-11$$

11. A right triangle has side lengths $$3\sqrt{2}$$, $$4\sqrt{2}$$, and $$10$$ units. What is the area of the triangle, in square units?

    • $$12$$
    • $$24$$
    • $$36$$
    • $$48$$

12. Point $$O$$ is the center of a circle. The measure of arc $$AB$$ on this circle is $$140^\circ$$. What is the measure, in degrees, of its associated central angle $$AOB$$?

    • $$70$$
    • $$120$$
    • $$140$$
    • $$280$$

13. The expression $$9x^2+bx-28$$, where $$b$$ is a constant, can be rewritten as $$(3x+m)(3x+n)$$, where $$m$$ and $$n$$ are integers. Which of the following must be an integer?

    • $$\frac{b}{3}$$
    • $$\frac{b}{m}$$
    • $$\frac{28}{m}$$
    • $$\frac{28}{b}$$

14. The expression $$4\sqrt[3]{x^5}\cdot\sqrt[3]{x^4}$$ is equivalent to $$ax^b$$, where $$a$$ and $$b$$ are positive constants and $$x$$ > $$1$$. What is the value of $$a+b$$?

    • $$\frac{19}{3}$$
    • $$7$$
    • $$\frac{22}{3}$$
    • $$8$$

15. Consider the system $$y=x^2-10x+16$$ $$y=2x+a$$ where $$a$$ is a constant. The graphs of the equations intersect at exactly one point $$(x,y)$$. What is the value of $$x$$?

    • $$4$$
    • $$5$$
    • $$6$$
    • $$8$$

16. In the $$xy$$-plane, a parabola has vertex $$(4,-9)$$ and intersects the $$x$$-axis at two points. If the equation of the parabola is written in the form $$y=ax^2+bx+c$$, where $$a,\ b,$$ and $$c$$ are constants, which of the following could be the value of $$a+b+c$$?

    • $$-15$$
    • $$-10$$
    • $$-9$$
    • $$-5$$

17. An isosceles right triangle has a hypotenuse of length $$20$$ inches. What is the perimeter, in inches, of this triangle?

    • $$20\sqrt{2}$$
    • $$20+20\sqrt{2}$$
    • $$40+20\sqrt{2}$$
    • $$40\sqrt{2}$$

18. Function $$f(x)=-a^x+b$$, where $$a$$ and $$b$$ are constants. In the $$xy$$-plane, the graph of $$y=f(x)-8$$ has a $$y$$-intercept at $$(0,\frac{41}{5})$$. The product of $$a$$ and $$b$$ is $$\frac{54}{5}$$. What is the value of $$a$$?

    • $$\frac{27}{43}$$
    • $$3$$
    • $$\frac{54}{43}$$
    • $$5$$

19. The line graph above shows the monthly precipitation in Kathmandu last year. According to the graph, the total precipitation in September was what percentage of the total precipitation in June?

    • $$40\%$$
    • $$50\%$$
    • $$60\%$$
    • $$75\%$$

20. The table above shows the results of a test that is designed to give a positive indicator when patients are infected with a certain virus and a negative indicator when they are not infected. According to the results, what is the probability that the test gives the incorrect indicator?

    • $$5\%$$
    • $$8\%$$
    • $$10\%$$
    • $$12\%$$

21. The dot plot above summarizes the number of flights taken in a year by $$19$$ college students. If the student who took $$6$$ flights in a year is removed from the data, which of the following correctly describes the changes to the statistical measures of the data?I. The mean decreases.II. The median decreases.III. The range decreases.

    • III only
    • I and II only
    • I and III only
    • I, II, and III

22. In the figure above, $$AB=12$$, $$AC=13$$, and $$DE=3$$. What is the length of $$AE$$?

    • $$\frac{169}{20}$$
    • $$\frac{5}{12}$$
    • $$\frac{36}{5}$$
    • $$\frac{12}{13}$$