Full Practice Exam 19 — Module 1

Questions in this quiz (22)

1. The Ideal Gas Law can be expressed as $$PV=nRT$$, where $$P$$ is the pressure, $$V$$ is the volume, $$n$$ is the number of moles, $$R$$ is the gas constant, and $$T$$ is the temperature. Which of the following correctly expresses $$V$$ in terms of $$P,\ n,\ R,$$ and $$T$$?

   • $$V=\frac{nRT}{P}$$
   • $$V=\frac{Pr}{nR}$$
   • $$V=\frac{PR}{nT}$$
   • $$V=\frac{nP}{RT}$$

2. Functions $$f$$ and $$g$$ are defined by $$f(x)=3(x+2)$$ and $$g(x)=x^2+4$$, respectively. If $$f(g(x))=24$$, what is the value of $$x$$?

   • $$\sqrt{\frac{8}{3}}$$
   • $$2$$
   • $$\sqrt{2}$$
   • $$-2$$

3. Sophia invests $$8000$$ dollars, with $$x$$ dollars in an account earning $$3\%$$ interest and $$y$$ dollars in an account earning $$6\%$$ interest. At the end of one year, she earns $$360$$ dollars in total interest. Which system represents this situation?

   • $$x+y=8000$$$$0.03x+0.06y=360$$
   • $$x+y=360$$$$0.03x+0.06y=8000$$
   • $$x+y=8000$$ $$0.06x+0.03y=360$$
   • $$x+y=360$$$$0.06x+0.03y=8000$$

4. David is saving money to buy a bicycle that costs $$950$$ dollars. He currently has $$230$$ dollars saved. Each week, he saves an additional $$60$$ dollars. How many weeks will it take David to have enough money to buy the bicycle?

   • $$11$$
   • $$12$$
   • $$13$$
   • $$14$$

5. Which of the following expressions is equivalent to $$\sqrt[4]{a^3}\cdot\sqrt[4]{a^5}\cdot a^{-1}$$?

   • $$\sqrt[4]{a}$$
   • $$a$$
   • $$a^2$$
   • $$a^2\sqrt[4]{a}$$

6. A circle in the $$xy$$-plane is centered at $$(-4,3)$$ and has a radius of $$6$$. Which of the following is the equation of the circle?

   • $$(x+4)^2+(y-3)^2=36$$
   • $$(x-4)^2+(y+3)^2=36$$
   • $$(x+3)^2+(y-4)^2=36$$
   • $$(x-3)^2+(y+4)^2=36$$

7. One of the linear equations in a system is $$6x+9y=12$$. If the system has no solution, which of the following could be the other equation?

   • $$2x+3y=4$$
   • $$4x+6y=9$$
   • $$x-y=2$$
   • $$3x+2y=8$$

8. If $$x=\frac{5+\sqrt{21}}{2}$$ is one solution to a quadratic equation, which of the following could be the equation?

   • $$x^2-5x+1=0$$
   • $$x^2+5x-1=0$$
   • $$2x^2-5x-2=0$$
   • $$x^2-2x-5=0$$

9. A gardener wants to build a rectangular flower bed against a wall. He has $$120$$ feet of fencing for the other three sides. The area is modeled by $$A(x)=x(120-2x)$$. Which of the following best describes the factor $$120-2x$$?

   • The width of the flower bed.
   • The length of the flower bed.
   • The perimeter of the flower bed.
   • The diagonal of the flower bed.

10. A right circular cylinder has radius $$r$$ and height $$10$$ units. If the volume increases by $$21\%$$ while the height remains constant, what is the percent increase in the radius? Do not include the percent sign.

    • 10

11. What are all possible solutions to the equation $$|2x-8|=12$$?

    • $$-2,\ 10$$
    • $$2,\ 10$$
    • $$-10,\ 2$$
    • $$-2,\ 8$$

12. Function $$f$$ is defined by $$f(x)=\left(\frac{3}{5}\right)^x+a,$$ where $$-1$$ < $$a$$ < $$0.$$ Which of the following could be the $$x$$-coordinate of the $$x$$-intercept of the graph of $$f$$?

    • $$-8$$ < $$x$$ < $$-5$$
    • $$-2$$ < $$x$$ < $$0$$
    • $$0$$ < $$x$$ < $$2$$
    • $$3$$ < $$x$$ < $$6$$

13. What is the minimum value of the function $$f(x)=(2x-3)(2x+5)$$?

    • -16

14. What is the value of $$n$$ such that the equation $$\frac{x+a}{6}=n\frac{x+a}{3}+4$$ has no solution?

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

15. If the expression $$\frac{4\sqrt[3]{x^{13}}}{16\sqrt[3]{x^3}}$$ is equivalent to $$\frac{1}{4}x^b$$, what is the value of $$b$$?

    • $$2$$
    • $$\frac{9}{5}$$
    • $$\frac{8}{5}$$
    • $$\frac{10}{3}$$

16. Let $$f(x)=3(x-4)(x+1)^2$$. If the graph of the function is shifted horizontally $$2$$ units to the right, which of the following must be a zero of the resulting function?

    • $$2$$
    • $$6$$
    • $$-1$$
    • $$-3$$

17. Consider the system:$$\frac{2}{x}+\frac{3}{y}=1$$$$\frac{4}{x}-\frac{1}{y}=1$$If $$(a,b)$$ is the point of intersection of the graphs of the equations, what is the value of $$a+b$$?

    • $$\frac{2}{7}$$
    • $$\frac{21}{2}$$
    • $$\frac{7}{3}$$
    • $$\frac{4}{3}$$

18. In the equation $$ax^2+by=6$$, $$a$$ and $$b$$ are nonzero constants. If $$a+b=0$$, which of the following must be true?

    • The graph opens upward and $$y(0)$$ < $$0$$ if $$a$$ < $$0$$.
    • The graph opens upward and $$y(0)$$ > $$0$$ if $$a$$ < $$0$$.
    • The graph opens downward and $$y(0)$$ > $$0$$ if $$a$$ < $$0$$.
    • The graph opens downward and $$y(0)$$ < $$0$$ if $$a$$ > $$0$$.

19. Emma plans to visit her cousin, who lives $$20$$ miles away. She first walks one-fifth of the distance. Then she rides a scooter the rest of the way. If the scooter travels at $$30$$ mph and Emma's walking speed is $$0.2$$ times the scooter speed, how long does the trip take?

    • $$\frac{2}{3}$$ hour
    • $$\frac{5}{6}$$ hour
    • $$1$$ hour
    • $$\frac{6}{5}$$ hour

20. If $$f(x+2)=3x^2+6x+4$$, which of the following is the expression for $$f(x)$$?

    • $$3x^2-6x+4$$
    • $$3x^2-6x+8$$
    • $$3x^2+6x+4$$
    • $$3x^2+2x+4$$

21. A map uses a scale of $$1:40{,}000$$. What area of the actual land, in square miles, is represented by $$16$$ square centimeters on the map? Use $$1$$ mile $$=160{,}934.4$$ centimeters.

    • $$0.89$$
    • $$0.99$$
    • $$1.02$$
    • $$1.07$$

22. The table above shows the results of a survey asking 250 residents about their primary pet ownership and their living situation. If a resident selected at random from the survey owns either a dog or a cat, what is the probability that the resident lives in an apartment?

    • $$\frac{7}{20}$$
    • $$\frac{9}{25}$$
    • $$\frac{7}{9}$$
    • $$\frac{7}{25}$$