Full Practice Exam 27 — Module 2

Questions in this quiz (22)

1. $$6+7r=lm$$$$7r-5m=5m+11$$In the given system of equations, $$l$$ is a constant. If the system has no solution, what is the value of $$l$$?

   • 10

2. $$39x^2+(39s+r)x+rs=0$$In the given equation, $$r$$ and $$s$$ are positive constants. The product of the solutions to the given equation is $$krs$$, where $$k$$ is a constant. What is the value of $$k$$?

   • $$\frac{1}{3}$$
   • $$\frac{1}{9}$$
   • $$\frac{1}{39}$$
   • $$\frac{1}{12}$$

3. A line in the $$xy$$-plane passes through the points $$(6,2)$$, $$(0,5)$$, and $$(c,0)$$. What is the value of $$c$$?

   • $$10$$

4. The table below shows three values of $$x$$ and their corresponding values of $$y$$. The linear relationship between $$x$$ and $$y$$ can be represented by an equation of the form $$Ax+By=C,$$ where $$A,B,$$ and $$C$$ are constants.What is the value of $$\frac{A}{B}$$?

   • 3

5. For groups of $$25$$ or more people, a museum charges $$\$21$$ per person for the first $$25$$ people and $$\$14$$ for each additional person. Which function $$f$$ gives the total charge, in dollars, for a tour group with $$n$$ people, where $$n\ge25$$?

   • $$f(n)=14n+175$$
   • $$f(n)=14n+525$$
   • $$f(n)=35n-350$$
   • $$f(n)=14n+21$$

6. The function $$G(x)=\frac95(x-273)+32$$ converts a temperature of $$x$$ kelvins into degrees Fahrenheit. If a temperature increases by $$3.50$$ kelvins, by how many degrees Fahrenheit does the temperature increase?

   • $$3..2$$
   • $$5.9$$
   • $$6.3$$
   • $$7.2$$

7. $$\frac{21}{17}x-10=\frac{3}{17}(ax+12)$$What is the value of $$a$$ for the equation to have no solution?

   • 7

8. $$y$$ < $$-5x-18$$$$y$$ > $$-2x-6$$Which of the following tables contains only values of $$x$$ and their corresponding $$y$$ values that satisfy both inequalities?

9. $$(x-p)^2=(p-5q)(x-p).$$In the given equation, $$p$$ and $$q$$ are constants, where $$p$$ > $$5q$$. The sum of the solutions to this equation is $$3p+40$$. What is the value of $$q$$?

   • $$-8$$
   • $$-5$$
   • $$3$$
   • $$40$$

10. If $$y=(x-m)(x+n)(x-n),$$ with $$m$$ and $$n$$ positive and $$m$$ > $$n$$, how many distinct $$x$$-intercepts does the graph have?

    • $$1$$
    • $$2$$
    • $$3$$
    • $$4$$

11. A function $$h$$ is defined by $$h(x)=c(4^x)$$. If $$h(3)=192$$, what is the value of $$h(5)$$?

    • $$256$$
    • $$768$$
    • $$3072$$
    • $$4096$$

12. The function $$P(t)=290(1.04)^{\left(\frac46\right)t}$$ models the population, in thousands, of a certain city $$t$$ years after $$2005$$. According to the model, the population is predicted to increase by $$n\%$$ every $$18$$ months. What is the value of $$n$$?

    • $$2$$
    • $$5$$
    • $$3$$
    • $$4$$

13. If $$f(x)=|4x-5|$$ and $$2f(1)=f(x)$$, what is the sum of the solutions for $$x$$?

    • $$2$$
    • $$2.25$$
    • $$2.5$$
    • $$3$$

14. A circle in the $$xy$$-plane has center $$(4,-8)$$ and radius $$10$$. An equation of this circle can be written in the form $$x^2+y^2+Ax+By+C=0,$$ where $$A,B,$$ and $$C$$ are constants. What is the value of $$C$$?

    • $$-20$$
    • $$-80$$
    • $$-120$$
    • $$80$$

15. $$\frac{63}{p}=\frac{63}{q}-\frac{63}{r}-\frac{63}{s}$$The given equation relates the positive variables $$p,q,r,$$ and $$s$$. Which of the following is equivalent to $$q$$ in terms of $$p,r,$$ and $$s$$?

    • $$q=p+r+s$$
    • $$q=\frac{prs}{pr+ps+rs}$$
    • $$q=prs$$
    • $$q=\frac{63}{p+r+s}$$

16. For $$x$$ > $$0$$, the function $$f$$ is defined as follows: $$f(x)$$ equals $$175\%$$ of $$x$$. Which of the following could describe this function?

    • Decreasing exponential
    • Decreasing linear
    • Increasing exponential
    • Increasing linear

17. For a particular machine that produces beads, $$13$$ out of every $$50$$ beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?

    • $$\frac{1}{650}$$
    • $$\frac{13}{50}$$
    • $$\frac{50}{13}$$
    • $$\frac{13}{100}$$

18. Data set A: $$6,9,12,18,22,28$$Data set B: $$7,11,14,19,23,k$$Data sets A and B each consist of $$6$$ values as shown, where $$k$$ is a constant. If the standard deviation of data set A is greater than the standard deviation of data set B, which of the following could be the value of $$k$$?I. $$26$$II. $$30$$III. $$35$$

    • I only
    • II only
    • III only
    • II or III

19. A sample consisting of $$850$$ adults who own televisions was selected at random for a study. Based on the sample, it is estimated that $$36\%$$ of all adults who own televisions use their televisions to watch news programs, with an associated margin of error of $$4.2\%$$. Which of the following is the most plausible conclusion about all adults who own televisions?

    • More than $$40.2\%$$ of all adults who own televisions use their televisions to watch news programs.
    • Between $$31.8\%$$ and $$40.2\%$$ of all adults who own televisions use their televisions to watch news programs.
    • Since the sample included adults who own televisions and not just those who use their televisions to watch news programs, no conclusion can be made.
    • Since the sample did not include all the people who watch news programs, no conclusion can be made.

20. In the figure, $$RT=TU$$. The measure of $$\angle VST$$ is $$35^\circ$$, and the measure of $$\angle RTU$$ is $$98^\circ$$. What is the value of $$x$$?

    • $$104$$

21. The area of a triangle is $$120$$ square centimeters. The length of the base of the triangle is $$8$$ centimeters greater than the height of the triangle. What is the height, in centimeters, of the triangle?

    • $$10$$
    • $$12$$
    • $$15$$
    • $$20$$

22. In $$\triangle PQR$$, $$\overline{PQ}=30$$ and $$\overline{PR}$$ is $$10$$ less than $$\overline{PQ}$$. Point $$S$$ lies on $$\overline{PQ}$$ such that $$\overline{RS}$$ is perpendicular to $$\overline{PQ}$$. What is the value of $$\frac{RQ}{RS}$$?

    • $$\frac12$$
    • $$\frac32$$
    • $$\frac53$$
    • $$\frac13$$