Full Practice Exam 23 — Module 1

Questions in this quiz (22)

1. A university offers courses that are either $$2$$ credits or $$5$$ credits per semester. A student registered for a total of $$19$$ credits for the spring semester. Which equation represents the possible number of $$2$$-credit courses, $$x$$, and $$5$$-credit courses, $$y$$, that the student could have registered for?

   • $$2x+5y=19$$
   • $$2x+5y=7$$
   • $$x+y=19$$
   • $$x+y=7$$

2. The function $$f$$ is defined by $$f(x)=x-4.$$ What is the $$y$$-intercept of the graph of $$y=f(x)$$ in the $$xy$$-plane?

   • $$(0,-4)$$
   • $$(0,-1)$$
   • $$(0,1)$$
   • $$(0,4)$$

3. Which polynomial is equivalent to $$(9x^4+7x^2-3)+(5x^4-2x^2+8x+6)?$$

   • $$14x^4+9x^2+8x+3$$
   • $$14x^4+5x^2+8x+3$$
   • $$14x^8+5x^2+8x+3$$
   • $$14x^4+5x^2+11x+3$$

4. If $$4x-8=12,$$ what is the value of $$3x$$?

   • 15

5. The equation $$y=\frac{x+a}{b}$$ relates the positive numbers $$a$$, $$b$$, $$x$$, and $$y$$. Which equation correctly expresses $$x$$ in terms of $$a$$, $$b$$, and $$y$$?

   • $$x=\frac{a}{by}$$
   • $$x=by+a$$
   • $$x=by-a$$
   • $$x=\frac{y}{ab}$$

6. Trapezoid A and trapezoid B shown are similar. The length of each side of trapezoid A is $$8$$ times the length of the corresponding side of trapezoid B. The area of trapezoid A is how many times as large as the area of trapezoid B?

   • $$8$$
   • $$16$$
   • $$32$$
   • $$64$$

7. $$\sqrt{x^2-16}=3$$What is the positive solution to the given equation?

   • 5

8. The linear function $$h(x)=-0.05x+2.4$$ models the annual percentage increase in the population of a city $$x$$ years after $$2000$$. What is the best interpretation of $$h(10)=1.9$$ in this context?

   • $$1.9$$ years after $$2000$$, the population increase was $$10\%$$.
   • $$10$$ years after $$2000$$, the percentage increase in the population was $$1.9\%$$ over the previous year.
   • $$10$$ years after $$2000$$, the population was $$1.9$$ times its population in $$2000$$.
   • $$1.9$$ years after $$2000$$, the population was $$10$$ times its population in $$2000$$.

9. For the quadratic function $$f(x)=a(x-b)(x-c),$$ where $$a$$, $$b$$, and $$c$$ are constants, the graph of $$y=f(x)$$ opens upward and the coordinates of its vertex are both positive. Which of the following could be true?

   • $$a$$ < $$0$$, $$b$$ < $$0$$, $$c$$ < $$0$$
   • $$a$$ < $$0$$, $$b$$ > $$0$$, $$c$$ > $$0$$
   • $$a$$ > $$0$$, $$b$$ > $$0$$, $$c$$ > $$0$$
   • $$a$$ > $$0$$, $$b$$ < $$0$$, $$c$$ < $$0$$

10. $$|3x-9|+2=8$$What is the sum of the solutions to the given equation?

    • $$4$$
    • $$6$$
    • $$8$$
    • $$12$$

11. $$3x+9y=6$$$$3(x+y)=6$$How many solutions does the given system of equations have?

    • Zero
    • Exactly one
    • Exactly two
    • Infinitely many

12. Line $$m$$ is defined by $$3y-6x=12.$$ Line $$n$$ is perpendicular to line $$m$$ in the $$xy$$-plane. What is the slope of line $$n$$?

    • $$-\frac{1}{4}$$
    • $$-\frac{1}{2}$$
    • $$\frac{1}{4}$$
    • $$2$$

13. The graph shown models the monthly revenue, in millions of dollars, for a particular marketing company from June $$2009$$ through October $$2010$$. According to the model, which of the following is closest to this company’s monthly revenue, in millions of dollars, for June $$2009$$?

    • $$8.5$$
    • $$22.5$$
    • $$62$$
    • $$100$$

14. The function $$f$$ is defined by $$f(x)=(-5)(4)^x-3.$$ What is the $$y$$-intercept of the graph of $$y=f(x)$$ in the $$xy$$-plane?

    • $$(0,-8)$$
    • $$(0,-5)$$
    • $$(0,-3)$$
    • $$(0,4)$$

15. If $$\frac{5x}{4}-3=\frac{x}{4}+5,$$ what is the value of $$4x$$?

    • 32

16. The shaded region shown represents the solutions to which inequality?

    • $$3x-y\le-3$$
    • $$3x-y\ge-3$$
    • $$3x+y\le3$$
    • $$3x+y\ge3$$

17. Which of the following expressions is equivalent to $$\left(\sqrt{5a}+\sqrt{5b}\right)^{\frac{2}{3}},$$ where $$a$$ > $$0$$ and $$b$$ > $$0$$?

    • $$(5a+5b)^{\frac{1}{3}}$$
    • $$\sqrt[3]{5a+5b}$$
    • $$\sqrt[3]{5a+2\sqrt{25ab}+5b}$$
    • $$\sqrt[3]{5a+10\sqrt{ab}+5b}$$

18. The graph shown models the height, $$y$$, in feet, of a volleyball $$x$$ seconds after it was hit by a player. Which equation represents the relationship between the height of the volleyball and the time since the volleyball was hit?

    • $$y=-16x^2+5$$
    • $$y=-16(x-5)^2$$
    • $$y=-16(x-0.86)^2$$
    • $$y=-16(x-0.25)^2+6$$

19. Over a period of one year, two points on opposite sides of a tectonic plate boundary moved $$6$$ centimeters farther apart. What is this distance, in meters? $$(1\text{ meter}=100\text{ centimeters})$$

    • 0.06

20. Points $$P$$ and $$Q$$ lie on a circle with radius $$6$$ meters, and minor arc $$PQ$$ has a length of $$\frac{3\pi}{2}$$ meters. What fraction of the circumference of the circle is the length of arc $$PQ$$?

    • $$\frac{1}{8}$$
    • $$\frac{1}{4}$$
    • $$\frac{2}{3}$$
    • $$\frac{3}{2}$$

21. In the figure shown, right triangle $$ABC$$ is similar to right triangle $$EDC$$, where $$\angle ACB$$ is congruent to $$\angle ECD$$ and $$AE=15$$. What is the length of $$\overline{CE}$$?

    • $$4$$
    • $$5$$
    • $$8$$
    • $$10$$

22. If $$9(x+2)=3(x+2),$$ what is the value of $$x+2?$$

    • 0