Full Practice Exam 4 — Module 1

Questions in this quiz (22)

1. $$f(x)=(x-2)(x+1)(x+4)$$The function $$f$$ is given. Which table of values represents $$y=f(x)+2$$?

2. One of the factors of $$3x^3+27x^2+60x$$ is $$x+k$$, where $$k$$ is a strictly positive constant. What is the smallest possible value of $$k$$?

   • $$0$$
   • $$1$$
   • $$4$$
   • $$5$$

3. One gallon of sealant will cover $$180$$ square feet of surface area. A deck has a total surface area of $$d$$ square feet. Which equation represents the total amount of sealant $$S$$, in gallons, needed to seal the deck three times?

   • $$S=\frac{d}{180}$$
   • $$S=\frac{3d}{180}$$
   • $$S=180d$$
   • $$S=540d$$

4. The number $$m$$ is $$80\%$$ greater than the number $$n$$. The number $$n$$ is $$75\%$$ less than 64. What is the value of $$m$$?

   • $$12.5$$
   • $$20.6$$
   • $$28.8$$
   • $$36.7$$

5. $$68,71,72,74,76,79,81,83,88$$What is the median of the data shown?

   • $$72$$
   • $$74$$
   • $$76$$
   • $$79$$

6. $$(a^3b^{-2}c^4)\left(\frac{b^5c^{-3}}{a^{-4}}\right)(a^{-2}bc^{-1})$$Which of the following is equivalent to the expression above, where $$a$$, $$b$$, and $$c$$ are positive?

   • $$a^5b^4$$
   • $$a^3b^{-2}c^{-1}$$
   • $$a^{-3}b^{-1}c^{2}$$
   • $$a^{5}b^{-1}c^{4}$$

7. $$3x=24$$$$5x+y=-7$$The solution to the given system of equations is $$(x,y)$$. What is the value of $$x+y$$?

   • $$-39$$
   • $$-19$$
   • $$11$$
   • $$19$$

8. The function $$h(d)=-0.08d+15.6$$ models the number of gallons of gasoline that remains in a car's gas tank after driving $$d$$ miles. According to the model, about how many gallons of gasoline are used to drive each mile?

   • $$0.08$$
   • $$0.15$$
   • $$1.25$$
   • $$15.6$$

9. $$y$$ > $$10$$$$3x+y$$ < $$25$$The point $$(x,40)$$ is a solution to the system of inequalities in the $$xy$$-plane. Which of the following could be the value of $$x$$?

   • $$3$$
   • $$6$$
   • $$-5$$
   • $$-12$$

10. The function $$g(t)=12000(0.8)^t$$ models the number of subscribers a company has at the end of each year, where $$t$$ represents the number of years since the end of $$2010$$and $$0\le t\le 6$$. If $$y=g(t)$$ is graphed in the $$ty$$-plane, what is the best interpretation of the $$y$$-intercept of the graph in this context?

    • The estimated number of subscribers the company had at the end of 2010 was 12,000.
    • The estimated number of subscribers the company had at the end of 2010 was 9,600.
    • The minimum estimated number of subscribers the company had during the 6 years was 12,000.
    • The minimum estimated number of subscribers the company had during the 6 years was 9,600.

11. Which expression is equivalent to $$\frac{5x(x-4)-2(x-4)}{3x-12}$$ where $$x$$ > $$4$$?

    • $$\frac{x-4}{3}$$
    • $$\frac{5x-2}{3}$$
    • $$\frac{5x^2-2x-8}{3x-12}$$
    • $$\frac{5x^2-2x-40}{3x-12}$$

12. Triangle $$ABC$$ is similar to triangle $$DEF$$ such that $$A,B,C$$ correspond to $$D,E,F$$, respectively. The measure of $$\angle C$$ is $$30^\circ$$, and $$2AB=DE$$. What is the measure of $$\angle F$$?

    • $$15^\circ$$
    • $$30^\circ$$
    • $$45^\circ$$
    • $$60^\circ$$

13. A wildlife reserve has an area of $$7920000$$ square feet. What is the approximate area, in square miles, of this reserve? $$(1\text{ mile}=5280\text{ feet})$$

    • $$2.84$$
    • $$2.25$$
    • $$5.54$$
    • $$0.284$$

14. Which of the following equations represents a circle in the $$xy$$ plane that intersects the $$x$$ axis at exactly one point?

    • $$(x-3)^2+(y-5)^2=9$$
    • $$(x+4)^2+(y-1)^2=16$$
    • $$(x-2)^2+y^2=4$$
    • $$x^2+(y+5)^2=25$$

15. A right triangle has legs with lengths of $$15$$ centimeters and $$36$$ centimeters. If the length of this triangle's hypotenuse, in centimeters, can be written in the form $$5\sqrt{d}$$, what is the value of $$d$$?

    • $$\frac{1296}{35}$$
    • $$61$$
    • $$\frac{1521}{25}$$
    • $$85$$

16. The function $$f(x)=5x^2$$ is defined. In the $$xy$$-plane, the graph of $$y=h(x)$$ is the result of shifting the graph of $$y=f(x)$$ up $$4$$ units. Which equation defines the function $$h$$?

    • $$h(x)=5(x+4)^2$$
    • $$h(x)=5x^2+4$$
    • $$h(x)=5(x-4)^2$$
    • $$h(x)=\frac{5}{4}x^2$$

17. The table shows the distribution of students' choices for a new school lunch option among $$90$$ students.If one student is selected at random, what is the probability that the student chose pizza?

    • $$\frac{2}{9}$$
    • $$\frac{5}{18}$$
    • $$\frac{13}{18}$$
    • $$\frac{1}{3}$$

18. The function $$P(t)=25000(2^{t/6})$$ gives the number of cells in a culture $$t$$ minutes after an initial observation. How many minutes does it take for the number of cells to double?

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

19. $$\sqrt{(x+3)^2}=\sqrt{4x+28}$$What is the smallest solution of the equation above?

    • $$1-2\sqrt{5}$$
    • $$-\sqrt{2}$$
    • $$-2\sqrt{2}$$
    • $$-1-2\sqrt{5}$$

20. The scatterplot above shows the relationship between the number of hours a student studies for a test, $$x$$, and the student’s test score, $$y$$. The line drawn represents the line of best fit for the data. According to the line of best fit, which of the following is the best prediction for the test score of a student who studies for $$4$$ hours?

    • $$9$$
    • $$10$$
    • $$11$$
    • $$12$$

21. A teacher distributed pens to $$10$$ student groups, as shown in the bar graph. The teacher plans to redistribute the pens so that each group has the same number of pens as Group $$6$$ currently has. How many pens must be taken away from Group $$2$$ and Group $$8$$ combined?

    • $$24$$
    • $$30$$
    • $$36$$
    • $$42$$

22. The graph shows the total cost, in dollars, of renting a bicycle for $$x$$ hours. The rental company charges a flat fee plus an hourly rental rate. Which of the following is the best interpretation of the slope of the line in the graph?

    • The flat fee charged to rent the bicycle
    • The total cost of renting the bicycle
    • The number of hours the bicycle is rented
    • The hourly rate charged to rent the bicycle