Full Practice Exam 6 — Module 1

Questions in this quiz (22)

1. Consider the system of equations with variables $$x$$ and $$y$$, andconstants $$p$$ and $$q$$:$$x-4y=8$$$$px-4qy=8p$$For the system to have infinitely many solutions, the second equation must be a multiple of the first. For what value must $$p+q$$ be divisible?

   • $$2$$
   • $$4$$
   • $$6$$
   • $$8$$

2. The table shows the exchange rate of Currency $$A$$ to Currency $$B$$ over several years.Which statement best represents the data?

   • As time goes by, Currency $$A$$ is becoming relatively more valuable than Currency $$B$$
   • As time goes by, Currency $$B$$ is becoming relatively more valuable than Currency $$A$$
   • As time goes by, Currency $$A$$ is approaching the same value as Currency $$B$$
   • No clear relationship can be determined between Currency $$A$$ and Currency $$B$$.

3. A line $$L1$$ has equation $$y=6x+3.$$ Line $$L2$$ is perpendicular to $$L1$$ and intersects the $$y$$ axis at a point that is $$4$$ units greater than the $$y$$ intercept of $$L1$$. Line $$L3$$ is parallel to $$L2$$ and passes through the point $$(6,-2).$$ What is the equation of line $$L3$$?

   • $$y=\frac{1}{2}x+1$$
   • $$y=-\frac{1}{6}x-1$$
   • $$y=-\frac{1}{3}x+2$$
   • $$y=-\frac{1}{2}x-3$$

4. For line $$m$$, the table shows three values of $$x$$ and their corresponding values of $$y$$.Line $$n$$ is the result of translating line $$m$$ down $$10$$ units in the $$xy$$-plane. What is the $$x$$-intercept of line $$n$$?

   • $$5$$
   • $$\frac{2}{5}$$
   • $$10$$
   • $$\frac{5}{4}$$

5. The table shows the population of Riverview, Ohio for the years $$2010$$ and $$2020$$.If the relationship between population and year is linear, which of the following functions $$P(t)$$ models the population of Riverview $$t$$ years after $$2010$$?

   • $$P(t)=1240-6t$$
   • $$P(t)=1240-60t$$
   • $$P(t)=1240+6(t-2010)$$
   • $$P(t)=1240-6(t-2010)$$

6. A workshop produces $$12$$-inch, $$8$$-inch, and $$5$$-inch metal rods. On a certain day, the number of $$12$$-inch rods produced is $$4$$ times the number $$m$$ of $$8$$-inch rods, and the number of $$5$$-inch rods produced is $$18$$. During this day, the workshop produces $$94$$ metal rods total. Which equation represents this situation?

   • $$12(4m)+8m+5(18)=94$$
   • $$4m+12=94$$
   • $$4m+18=94$$
   • $$5m+18=94$$

7. $$c(2x-5)+d=4x-7$$In the equation above, $$c$$ and $$d$$ are constants. If the equation has infinitely many solutions, what are the values of $$c$$ and $$d$$?

   • $$c=1,\ d=2$$
   • $$c=2,\ d=3$$
   • $$c=2,\ d=1$$
   • $$c=3,\ d=2$$

8. A model estimates that a hiker walks between $$4.5$$ and $$5.2$$ miles per day on a long trail. Based on this model, which inequality represents the estimated total number of miles, $$m$$, the hiker could walk in $$12$$ days?

   • $$45\le m\le52$$
   • $$45\le m\le62.4$$
   • $$54\le m\le62.4$$
   • $$54\le m\le65$$

9. $$y$$ < $$9x+4$$For which of the following tables are all the values of $$x$$ and their corresponding values of $$y$$ solutions to the given inequality?

10. In the figure, segments $$AE$$ and $$BD$$ intersect at point $$C$$. The lengths are given as $$CD=31$$, $$AC=35$$, $$AB=30$$, and $$BC=60$$. What is the length of $$DE$$?

    • $$30$$
    • $$35$$
    • $$60$$
    • $$\frac{186}{7}$$

11. In the $$xy$$-plane shown, square $$ABCD$$ has its diagonals on the $$x$$- and $$y$$-axes, with vertices $$A(0,-6)$$, $$B(-6,0)$$, $$C(0,6)$$, and $$D(6,0)$$. What is the area, in square units, of square $$ABCD$$?

    • $$36$$
    • $$49$$
    • $$72$$
    • $$96$$

12. In the figure, $$BC=BE$$. The measure of $$\angle DAC$$ is $$30^\circ$$, and the measure of $$\angle EDA$$ is $$40^\circ$$. What is the value of x?

    • $$20^\circ$$
    • $$10^\circ$$
    • $$160^\circ$$
    • $$30^\circ$$

13. $$ABC$$ is a right triangle with a right angle at $$C$$. The lengths of the sides are $$AC=15$$, $$BC=8$$, and $$AB=17$$. What is the value of $$\tan(A)$$?

    • $$\frac{15}{17}$$
    • $$\frac{8}{17}$$
    • $$\frac{8}{15}$$
    • $$\frac{17}{15}$$

14. A company's revenue increased from $$60000$$ in $$2021$$ to $$78000$$ in $$2022$$. In $$2023$$, the company's revenue increased by the same percent from $$2022$$ to $$2023$$ as it did from $$2021$$ to $$2022$$. What was the company's revenue in $$2023$$?

    • $$92,400$$
    • $$97,500$$
    • $$101,400$$
    • $$109,200$$

15. A table shows the number of students who participate in activities:If one student is chosen at random, what is the probability the student is a girl who participates in drama?

    • $$\frac{1}{8}$$
    • $$\frac{3}{8}$$
    • $$\frac{5}{8}$$
    • $$\frac{7}{8}$$

16. A scatterplot shows hours studied versus test score, along with a trend line. Which conclusion is most reasonable?

    • Students who study more do not always get the highest scores.
    • There is a negative relationship between hours studied and test scores.
    • There is a positive correlation between hours studied and test scores.
    • Studying guarantees a perfect score.

17. A data set consists of $$5$$ numbers. The mean of the data set is $$12$$. Four of the numbers are $$6$$, $$10$$, $$14$$, and $$18$$. What is the median of the data set?

    • 10
    • 12
    • 14
    • 18

18. Solve:$$2x^2-7x-15=0$$

    • $$-\frac{3}{2},5$$
    • $$-3,\frac{5}{2}$$
    • $$-\frac{5}{2},3$$
    • $$-2,5$$

19. A population grows by doubling every $$6$$ years. The population is currently $$1250$$. Which of the following is closest to the population after $$15$$ years?

    • $$3500$$
    • $$4550$$
    • $$5080$$
    • $$7070$$

20. The graph of $$y=-2(x+3)^2+7$$ is a parabola. What are the coordinates of its vertex?

    • $$(-3,7)$$
    • $$(3,-7)$$
    • $$(-3,-7)$$
    • $$(3,7)$$

21. If $$f(x)=x^2-4x+7$$, what is the value of $$f(2)+f(-2)$$?

    • $$6$$
    • $$14$$
    • $$22$$
    • $$30$$

22. Which of the following expressions is equivalent to $$\frac{x^2-9}{x-3}-\frac{6}{x+3}$$ for $$x\ne3$$ and $$x\ne-3$$?

    • $$x-\frac{6}{x+3}$$
    • $$x+\frac{3}{x+3}$$
    • $$x+3-\frac{6}{x+3}$$
    • $$x+\frac{6}{x+3}$$