Full Practice Exam 24 — Module 1

Questions in this quiz (22)

1. A state election featured two candidates, Maria and David, who received a total of $$620$$ electoral votes. Maria received $$48$$ fewer electoral votes than David. Which system of equations represents this situation, where $$m$$ is the number of votes Maria received and $$d$$ is the number of votes David received?

   • $$m+d=620$$ $$m-d=-48$$
   • $$m+d=668$$$$m-d=-48$$
   • $$m+d=620$$$$m=d+48$$
   • $$m+d=668$$$$m=d+48$$

2. $$5p-8=3p+16$$What value of $$p$$ satisfies the given equation?

   • $$10$$
   • $$12$$
   • $$14$$
   • $$16$$

3. The equation $$y=\sqrt{\frac{ab}{x^2}}$$ relates the positive numbers $$a$$, $$b$$, $$x$$, and $$y$$. Which equation correctly expresses $$b$$ in terms of $$a$$, $$x$$, and $$y$$?

   • $$b=\frac{x^2y^2}{a}$$
   • $$b=\frac{ay^2}{x^2}$$
   • $$b=\frac{axy^2}{x^2}$$
   • $$b=\frac{x^2}{ay^2}$$

4. $$|2x-5|=13$$If $$x$$ is a solution to the given equation, what is a possible value of $$2x-5$$?

   • $$-11$$
   • $$11$$
   • $$13$$
   • $$15$$

5. A research institute conducted phone and mail surveys. The total cost of conducting these surveys was $$5,000$$ dollars. The line shown models the possible combinations of phone and mail surveys that the institute could have conducted. According to the model, what was the cost for each phone survey conducted?

   • $$200$$
   • $$125$$
   • $$40$$
   • $$25$$

6. The function $$g$$ is defined by $$g(x)=\frac{x+5}{x-1}.$$ What is the value of $$g(7)$$?

   • 2

7. Line $$k$$ is defined by $$y=\frac{3}{4}x-8.$$ What is the slope of a line that is perpendicular to line $$k$$ in the $$xy$$-plane?

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

8. Which expression is equivalent to $$(7x^4-3x^2+5)-(2x^4+4x^2-9)?$$

   • $$5x^4-7x^2+14$$
   • $$9x^4+x^2-4$$
   • $$5x^4+x^2+14$$
   • $$9x^4-7x^2+14$$

9. The graph of the linear function $$f$$ is shown. Which equation defines $$f$$?

   • $$f(x)=\frac{1}{3}x-8$$
   • $$f(x)=\frac{3}{2}x+5$$
   • $$f(x)=\frac{3}{2}x-8$$
   • $$f(x)=\frac{1}{3}x+5$$

10. Which expression is equivalent to $$y^{\frac{1}{4}}\left(y^{\frac{3}{2}}\right)^2,$$ where $$y$$ > $$0$$?

    • $$\sqrt[4]{y^{13}}$$
    • $$\sqrt[7]{y^{12}}$$
    • $$\sqrt[8]{y^{13}}$$
    • $$\sqrt[4]{y^{11}}$$

11. What is the value of $$\cos\left(\frac{5\pi}{6}\right)?$$

    • $$-\frac{\sqrt{3}}{2}$$
    • $$-\frac{1}{2}$$
    • $$\frac{1}{2}$$
    • $$\frac{\sqrt{3}}{2}$$

12. $$2x+5y=23$$$$4x-3y=5$$The solution to the given system of equations is the ordered pair $$(x,y)$$. What is the value of $$y$$?

    • $$\frac{13}{10}$$
    • $$\frac{23}{5}$$
    • $$\frac{5}{23}$$
    • $$\frac{41}{13}$$

13. The complete graph of the function $$f$$ is shown in the $$xy$$-plane. What is the $$y$$-intercept of the graph of $$y=f(x+2)$$?

    • $$(0,3)$$
    • $$(0,2)$$
    • $$(0,1)$$
    • $$(0,0)$$

14. In $$2010$$, a population of bacteria was $$250$$. The population increased by $$180\%$$ each year. Which equation best models the estimated number of bacteria, $$P$$, $$t$$ years after $$2010$$?

    • $$P=250(1.8)^t$$
    • $$P=250(2.8)^t$$
    • $$P=430(2.8)^t$$
    • $$P=250(0.8)^t$$

15. One of the two equations in a linear system is $$4x-6y=12.$$ The system has no solution. Which equation could be the other equation in the system?

    • $$2x-3y=6$$
    • $$8x-12y=25$$
    • $$4x+6y=12$$
    • $$8x-12y=24$$

16. Rectangular prism $$A$$ is similar to rectangular prism $$B$$. The table gives the volumes of the two prisms. The longest side of rectangular prism $$A$$ is $$21$$ meters. What is the length, in meters, of the longest side of rectangular prism $$B$$?

    • 9

17. A grove has $$6$$ rows of birch trees and $$5$$ rows of maple trees. Each row of birch trees has $$8$$ trees $$20$$ feet or taller and $$6$$ trees shorter than $$20$$ feet. Each row of maple trees has $$9$$ trees $$20$$ feet or taller and $$7$$ trees shorter than $$20$$ feet. A tree from one of these rows will be selected at random. What is the probability of selecting a maple tree, given that the tree is $$20$$ feet or taller?

    • $$\frac{9}{164}$$
    • $$\frac{3}{10}$$
    • $$\frac{15}{31}$$
    • $$\frac{9}{17}$$

18. If $$4\sqrt{x-5}+6=26,$$ what is the value of $$x-5$$?

    • 25

19. $$x^2-12x+20=0$$One solution to the given equation can be written as $$x=6+\sqrt{n},$$ where $$n$$ is a constant. What is the value of $$n$$?

    • 16

20. The table gives the average speed $$s$$, in miles per hour, of each lap around a racetrack for one driver.For how many laps was the average speed greater than or equal to $$150$$ mph?

    • 141

21. Data set A consists of the heights of $$75$$ buildings and has a mean of $$32$$ meters. Data set B consists of the heights of $$50$$ buildings and has a mean of $$62$$ meters. Data set C consists of the heights of the $$125$$ buildings from data sets A and B. What is the mean, in meters, of data set C?

    • 44

22. The scatterplot above shows the price, in dollars, for both a cheese pizza and a veggie pizza for ten different pizzerias. The line of best fit is also shown. According to the line of best fit, which of the following is closest to the predicted increase in the price of a veggie pizza, in dollars, for every $$1$$ dollar increase in the price of a cheese pizza?

    • $$1.5$$
    • $$2.0$$
    • $$2.5$$
    • $$3.0$$