Full Practice Exam 13 — Module 1

Questions in this quiz (22)

1. $$\frac{5(n-3)+7}{3}=\frac{17-(6+5n)}{6}$$What is the value of $$n$$?

   • $$\frac{7}{3}$$
   • $$\frac{7}{2}$$
   • There is no value of $$n$$ that satisfies the equation.
   • $$\frac{9}{5}$$

2. Which of the following is equivalent to $$\frac{24x^3+12x^2-48x}{12x^2}$$?

   • $$2x-\frac{4}{x}+1$$
   • $$24x^3-48x$$
   • $$2x+1-\frac{4}{x}$$
   • $$24x^3-48x+1$$

3. At what value(s) of $$x$$ do the graphs of $$y=-3x+2$$ and $$y=x^2+4x+5$$ intersect?

   • $$-6$$ and $$-1$$
   • $$-5$$ and $$1$$
   • $$-1$$ and $$5$$
   • $$\frac{-7-\sqrt{37}}{2}$$ and $$\frac{-7+\sqrt{37}}{2}$$

4. If $$m=\frac{1}{n^5}$$, where both $$m$$ > $$0$$ and $$n$$ > $$0$$, which of the following gives $$n$$ in terms of $$m$$?

   • $$n=m^5$$
   • $$n=\frac{1}{m^5}$$
   • $$n=\frac{1}{\sqrt[5]{m}}$$
   • $$n=m^{1/5}$$

5. $$y=4x-3$$$$y=\frac{7x+5}{2}$$If $$(x,y)$$ represents the solution to the system below, what is the value of $$y$$?

   • $$9$$
   • $$11$$
   • $$13$$
   • $$41$$

6. If $$1$$ < $$\frac{d}{3}+2$$ < $$5$$, which of the following is NOT a possible value of $$d$$?

   • $$-2$$
   • $$0$$
   • $$3$$
   • $$10$$

7. Which of the following are roots of the equation $$2x^2-4x-7=0$$?

   • $$1\pm\sqrt{15}$$
   • $$\frac{2\pm\sqrt{15}}{2}$$
   • $$\frac{4\pm\sqrt{72}}{4}$$
   • $$\frac{4\pm\sqrt{15}}{2}$$

8. The value of $$\sin35^\circ$$ is the same as which of the following?

   • $$\cos55^\circ$$
   • $$\sin(-35^\circ)$$
   • $$\cos(-55^\circ)$$
   • $$\sin145^\circ$$

9. A company's break-even point occurs when revenue equals expenses. A store pays $$6.25$$ dollars per item and has fixed monthly expenses of $$9,450$$. The store sells each item for $$12.50$$. How many items must the store sell per month to reach the break-even point?

   • $$1260$$
   • $$1512$$
   • $$1800$$
   • $$2100$$

10. If $$\frac{2}{3}-\frac{4}{7}x=-20$$, what is the value of $$8x-6$$?

    • $$210$$
    • $$228$$
    • $$234$$
    • $$\frac{850}{3}$$

11. If $$f(g(3))=2$$ and $$f(x)=x-4$$, then which of the following could define $$g(x)$$?

    • $$g(x)=x+1$$
    • $$g(x)=x+3$$
    • $$g(x)=x+6$$
    • $$g(x)=x+9$$

12. $$k(10x-5)=2(3+x)-7$$If the equation above has infinitely many solutions and $$k$$ is a constant, what is the value of $$k$$?

    • $$\frac{3}{7}$$
    • $$\frac{5}{2}$$
    • $$\frac{1}{5}$$
    • $$\frac{2}{3}$$

13. A right triangle has leg lengths of $$10m$$ and $$24m$$ and a hypotenuse of $$26m$$. What is the value of $$m$$?

    • $$-1$$
    • $$-\frac{5}{2}$$
    • $$-\frac{3}{2}$$
    • All positive values

14. If $$\frac{\sqrt{x}\cdot x^{3/2}\cdot x^4}{\sqrt[3]{x^5}}$$ is combined into a single power of $$x$$ with a positive exponent, what is that exponent?

    • $$\frac{13}{3}$$
    • $$\frac{5}{3}$$
    • $$\frac{8}{3}$$
    • $$\frac{2}{3}$$

15. The figure shows the graph of $$f(x)$$. For which value(s) of $$x$$ does $$f(x)=0$$?

    • $$-3$$ and $$3$$
    • $$-1$$ and $$1$$
    • $$-1$$, $$1$$, and $$2$$
    • $$2$$ only

16. The graph represents new business start-up rates in the United States from $$1977$$ to $$2013$$. If $$t$$ represents the year, which statement correctly describes the function?

    • The function is increasing overall.
    • The function is decreasing overall.
    • The function is increasing for all $$t$$ such that $$1977
    • The function is decreasing for all $$t$$ such that $$1977

17. The line represented by the equation $$y=2x-5$$ is reflected over the x-axis and then shifted up $$4$$ units. What is the new y-intercept of the transformed line?

    • $$(0,-9)$$
    • $$(0,1)$$
    • $$(0,5)$$
    • $$(0,9)$$

18. If the equation of the parabola shown in the graph is written in standard quadratic form, $$y=ax^2+bx+c$$, and $$a=-1$$, what is the value of $$b$$?

    • 6

19. The function $$f$$ is defined by $$f(x)=\frac{kx+1}{x-2}-\frac{x-3}{x+4}$$ where $$k$$ is a constant. The graph of $$y=f(x)$$ in the $$xy$$-plane has a horizontal asymptote at $$y=5$$. What is the value of $$k$$?

    • 6

20. The scatterplot shows the relationship between temperature in degrees Celsius and the number of cricket chirps per minute recorded for a certain species. A line of best fit for the data is given by the equation $$y=4.5x+10$$ where $$x$$ is the temperature in degrees Celsius and $$y$$ is the number of chirps per minute. If the temperature were measured in degrees Fahrenheit instead of degrees Celsius, and the relationship between Celsius $$C$$ and Fahrenheit $$F$$ is given by $$F=1.8C+32$$ which of the following best describes the slope of the new line of best fit relating temperature in degrees Fahrenheit to the number of chirps per minute?

    • For every increase of $$1$$ degree Fahrenheit, the number of chirps per minute is predicted to increase by $$2.5$$.
    • For every increase of $$1$$ degree Fahrenheit, the number of chirps per minute is predicted to increase by $$4.5$$.
    • For every increase of $$1$$ degree Celsius, the number of chirps per minute is predicted to increase by $$2.5$$.
    • For every increase of $$1$$ degree Celsius, the number of chirps per minute is predicted to increase by $$4.5$$.

21. A certain genetic condition affects $$2\%$$ of a population. A screening test is designed to detect the condition. If a person has the condition, the test returns a positive result $$95\%$$ of the time. If a person does not have the condition, the test returns a positive result $$4\%$$ of the time. If a randomly selected person tests positive, what is the probability that the person actually has the condition?

    • $$\frac{95}{100}$$
    • $$\frac{2}{100}$$
    • $$\frac{190}{582}$$
    • $$\frac{4}{100}$$

22. A hiker stands at point $$A$$ on level ground and measures the angle of elevation to the top of a cliff to be $$40^\circ$$. The hiker then walks $$60$$ feet directly toward the base of the cliff to point $$B$$. From point $$B$$, the angle of elevation to the top of the cliff is $$60^\circ$$. What is the height of the cliff, in feet?

    • $$30(\sqrt{3}-1)$$
    • $$30(\sqrt{3}+1)$$
    • $$60(\sqrt{3}-1)$$
    • $$60(\sqrt{3}+1)$$
    • $$97.7$$