Full Practice Exam 22 — Module 1

Questions in this quiz (22)

1. A meteorite with a mass of $$18.0$$ grams is composed of copper and zinc and has a volume of $$3.0$$ cubic centimeters $$(\text{cm}^3)$$. Copper has a density of $$8.0\text{ g/cm}^3$$, and zinc has a density of $$7.0\text{ g/cm}^3$$. Which system of equations represents this situation, where $$c$$ is the volume of copper and $$z$$ is the volume of zinc in the meteorite?

   • $$8.0c+7.0z=18.0$$$$c+z=3.0$$
   • $$8.0c+7.0z=3.0$$$$c+z=18.0$$
   • $$8.0c+7.0z=18.0$$$$c+z=18.0$$
   • $$8.0c+7.0z=3.0$$$$c+z=3.0$$

2. Which expression is equivalent to $$\frac{12x}{3}$$?

   • $$2x$$
   • $$3x$$
   • $$4x$$
   • $$6x$$

3. The function $$f$$ is defined as $$f(x)=x^3+7$$. What is the value of $$f(2)$$?

   • $$11$$
   • $$13$$
   • $$15$$
   • $$17$$

4. The equation $$3x+40y=5,000$$ models the total number of flowers in a park consisting of a $$3$$-hectare garden and a $$40$$-hectare meadow. The total number of flowers is $$5,000$$. Which is the best interpretation of $$x$$ in this context?

   • The total number of flowers in the garden
   • The number of flowers per hectare in the garden
   • The total number of flowers in the meadow
   • The number of flowers per hectare in the meadow

5. $$8x-4y=24$$$$-2x+y=-6$$Which of the following is the solution of the given system of equations?

   • $$(8,-2)$$
   • $$(-2,8)$$
   • $$(-6,4)$$
   • Infinitely many solutions

6. $$x(x-4)(2x+1)=0$$What is the sum of the three values of $$x$$ that satisfy the equation below? Round to the nearest thousandth if necessary.

   • $$2$$
   • $$2.5$$
   • $$3.5$$
   • $$4$$

7. In triangle $$PQR$$ shown, what is the length of $$\overline{PQ}$$?

   • $$4\cos20^\circ$$
   • $$\frac{\cos20^\circ}{4}$$
   • $$4\tan20^\circ$$
   • $$\frac{4}{\tan20^\circ}$$

8. The function $$g$$ is defined as:$$g(x)=5\left(\frac{1}{3}\right)^x$$If the given function $$g$$ is graphed in the $$xy$$-plane, where $$y=g(x)$$, what is the $$y$$-intercept of the graph?

   • $$(0,1)$$
   • $$(0,3)$$
   • $$(0,5)$$
   • $$(0,15)$$

9. Line $$k$$ in the $$xy$$-plane contains the points $$(2,1)$$ and $$(12,6)$$. An equation of line $$k$$ is $$y=mx+b$$, where $$m$$ and $$b$$ are constants. What is the value of $$m$$?

   • $$\frac{1}{2}$$
   • $$\frac{3}{5}$$
   • $$\frac{5}{4}$$
   • $$\frac{5}{3}$$

10. $$|x+7|=12$$What are all the solutions to the given equation?

    • $$5$$ only
    • $$-19$$ only
    • $$5$$ and $$-19$$
    • $$-5$$ and $$19$$

11. The graph of $$y=f(x)-3$$ is shown. Which equation defines the linear function $$f$$?

    • $$f(x)=-3x-4$$
    • $$f(x)=-3x-3$$
    • $$f(x)=-3x+2$$
    • $$f(x)=-3x+8$$

12. $$(y+4)(3x+y)=1$$The given equation relates the positive numbers $$x$$ and $$y$$. Which equation correctly expresses $$y$$ in terms of $$x$$?

    • $$y=\frac{1}{3x+y}-4$$
    • $$y=\frac{1-4(3x+y)}{3x+y}$$
    • $$y=-\frac{1}{3x+y}-4$$
    • $$y=\frac{1}{3x-y}-4$$

13. $$(9,250+90y^2)-10(12y^2+75)$$The given expression can be written in the form $$ay^2+b$$, where $$a$$ and $$b$$ are constants. What is the value of $$a+b$$?

    • 8,470

14. The graph of the linear function $$f$$ is shown. The function can be written as $$f(x)=mx+b$$, where $$m$$ and $$b$$ are constants. What is the value of $$m$$?

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

15. A construction company purchased a bulldozer for $$250,000$$ dollars. The value of the bulldozer is expected to decrease by $$15\%$$ each year. Which equation models the value $$V(t)$$, in dollars, where $$t$$ represents the number of years since purchase?

    • $$V(t)=250,000(0.15)^t$$
    • $$V(t)=250,000(0.85)^t$$
    • $$V(t)=250,000(1.15)^t$$
    • $$V(t)=250,000(1.85)^t$$

16. If $$4x+3+2x=39,$$ what is the value of $$6x$$?

    • 36

17. Which equation has no solution?

    • $$2(x+4)=2x$$
    • $$2(x+4)=4x$$
    • $$2x+8=2x+8$$
    • $$2x+8=4x+8$$

18. Triangle $$ABC$$ is an isosceles triangle with base angles measuring $$35^\circ$$. Triangle $$A'B'C'$$ is similar to triangle $$ABC$$. The length of each side of triangle $$A'B'C'$$ is $$2$$ times the length of the corresponding side of triangle $$ABC$$. What is the measure of each base angle of triangle $$A'B'C'$$?

    • $$35^\circ$$
    • $$45^\circ$$
    • $$70^\circ$$
    • $$110^\circ$$

19. $$f(x)=(x-a)(x-b)$$The function $$f$$ is defined above, where $$a$$ and $$b$$ are integers. If $$f(2)$$ > $$0$$, $$f(5)$$ < $$0$$, and $$f(9)$$ > $$0,$$ what is one possible value of $$a+b$$?

    • 9

20. $$x^2+y^2-6x+4y=12$$The equation of a circle in the $$xy$$-plane is shown above. What is the radius of the circle?

    • 5

21. The entire senior class at a high school voted on the theme for their prom. The results are shown in the table.If a senior is selected at random, what is the probability of selecting a senior who voted for Hollywood?

    • $$\frac{2}{7}$$
    • $$\frac{11}{35}$$
    • $$\frac{3}{7}$$
    • $$\frac{5}{7}$$

22. A data set of $$27$$ different numbers has a mean of $$33$$ and a median of $$33$$. A new data set is created by adding $$7$$ to each number in the original data set that is greater than the median and subtracting $$7$$ from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and new data sets?

    • Median
    • Mean
    • Sum of the numbers
    • Standard deviation