Full Practice Exam 26 — Module 1

Questions in this quiz (22)

1. $$(x-5)-4(y+3)=122$$$$(x-5)+4(y+3)=434$$The solution to the given system of equations is $$(x,y)$$. What is the value of $$8(x-5)$$?

   • 2224

2. Consider the linear equation $$\frac35x+\frac47y=12.$$ Which of the following tables lists three ordered pairs $$(x,y)$$ that all satisfy this equation?

3. The cost of renting a backhoe for up to $$10$$ days is $$\$270$$ for the first day and $$\$135$$ for each additional day. Which of the following equations gives the cost $$y$$, in dollars, of renting the backhoe for $$x$$ days, where $$x$$ is a positive integer and $$x\le10$$?

   • $$y=270x-135$$
   • $$y=270x+135$$
   • $$y=135x+270$$
   • $$y=135x+135$$

4. A club sold tickets to a carnival to raise funds. Each child ticket sold for $$\$8$$, and each adult ticket sold for $$\$12$$. The club earned a total of $$\$576$$ from selling these tickets. The equation $$8x+12y=576$$ represents this situation. Which of the following is the best interpretation of $$y$$ in this context?

   • The number of adult tickets sold
   • The number of child tickets sold
   • The price, in dollars, of each adult ticket
   • The price, in dollars, of each child ticket

5. $$y$$ > $$20$$$$3x+y$$ < $$30$$If the point $$(x,25)$$ is a solution to the given the system of inequalities, what could be the value of $$x$$?

   • $$1$$
   • $$3$$
   • $$5$$
   • $$8$$

6. For the parabola $$px^2+qx+r$$, the $$x$$-intercepts are $$(10,0)$$ and $$(m,0)$$. If $$f(25)=f(3)$$, what is the value of $$m$$?

   • $$16$$
   • $$18$$
   • $$20$$
   • $$22$$

7. A function $$G$$ is defined by $$G(x)=8^x+m.$$ The graph of $$G$$ passes through $$(0,-5)$$. What is the value of $$m$$?

   • $$-13$$
   • $$-8$$
   • $$-7$$
   • $$-6$$

8. A certain population $$P(t)$$, measured in thousands, satisfies $$P(t)=400(1.04)^t,$$ where $$t$$ is the number of years after $$2010$$. According to this model, which statement is true?

   • The population increases by $$4\%$$ each year, starting at $$400$$ thousand in $$2010$$.
   • The population decreases by $$96\%$$ each year, starting at $$400$$ in $$2010$$.
   • The population increases by $$1.04$$ persons each year, starting at $$400$$ in $$2010$$.
   • The population is $$400$$ thousand every $$4$$ years.

9. Which of the following absolute-value equations has no real solutions?

   • $$|2x+7|=3$$
   • $$|x-1|=-4$$
   • $$|-3x+2|=2$$
   • $$3|x|=0$$

10. Which of the following points lies on the circle $$(x+1)^2+(y-4)^2=9$$?

    • $$(2,4)$$
    • $$(3,5)$$
    • $$(-1,4)$$
    • $$(2,5)$$

11. In electronics, the equivalent capacitance $$C$$ of two capacitors in parallel is $$C=d+e,$$ but a certain arrangement modifies this to $$\frac1C=\frac1d+\frac1e+\frac1f.$$ Which of the following expresses $$C$$ in terms of $$d$$, $$e$$, and $$f$$?

    • $$C=d+e+f$$
    • $$C=\frac{def}{d+e+f}$$
    • $$C=\frac1{def}\left(\frac1d+\frac1e+\frac1f\right)^{-1}$$
    • $$C=\frac{def}{de+df+ef}$$

12. The value of a collectible comic book increased by $$130\%$$ from the end of $$2015$$ to the end of $$2016$$ and then decreased by $$15\%$$ from the end of $$2016$$ to the end of $$2017$$. What was the percentage increase in the value of the comic book from the end of $$2015$$ to the end of $$2017$$?

    • $$85.0\%$$
    • $$95.5\%$$
    • $$110.5\%$$
    • $$130.0\%$$

13. A local organization has $$130$$ members, categorized by age, less than $$40$$ versus at least $$40$$, and whether they live east or west of a river. The table below shows the distribution:If one member of this organization is selected at random, what is the probability that the selected member is at least $$40$$ years old?

    • $$\frac{26}{130}$$
    • $$\frac{35}{130}$$
    • $$\frac{95}{130}$$
    • $$\frac{104}{130}$$

14. A sample of oak has a density of $$850$$ kilograms per cubic meter. The sample is in the shape of a cube, where each edge has a length of $$0.75$$ meters. To the nearest whole number, what is the mass, in kilograms, of this sample?

    • $$215$$
    • $$359$$
    • $$687$$
    • $$892$$

15. The area of a rectangular region is increasing at a rate of $$350$$ square feet per hour. Which of the following is closest to this rate in square meters per minute? Use $$1$$ meter $$=3.28$$ feet.

    • $$0.54$$
    • $$1.28$$
    • $$15.31$$
    • $$26.03$$

16. Data set A: $$3,3,4,6,7,9,10,12,13,15,15$$Data set B: $$4,5,6,8,8,9,10,11,12,14,14$$Data set A and data set B each have $$11$$ values. Which of the following statements best compares the median of data set A and the median of data set B?

    • The median of data set A is greater than the median of data set B.
    • The median of data set A is less than the median of data set B.
    • The medians of data sets A and B are equal.
    • There is not enough information to compare the medians.

17. The scatterplot shows the relationship between two variables, $$x$$ and $$y$$. Which of the following equations is the most appropriate model for the data shown?

    • $$y=-400+1.4x$$
    • $$y=400-1.4x$$
    • $$y=-400(1.5)^x$$
    • $$y=400(1.5)^x$$

18. In a study of cell phone use, $$850$$ randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table below. Based on the data from the study, an estimate of the percent of US teens who are heavy texters is $$28\%$$, and the associated margin of error is $$2\%$$. Which of the following is a correct statement based on the given margin of error?

    • Approximately $$2\%$$ of the teens in the study who are classified as heavy texters are not really heavy texters.
    • It is not possible that the percent of all US teens who are heavy texters is less than $$26\%$$.
    • The percent of all US teens who are heavy texters is $$30\%$$.
    • It is doubtful that the percent of all US teens who are heavy texters is $$33\%$$.

19. In the figure shown, point $$B$$ lies on segment $$AE$$, and segment $$BC$$ is parallel to segment $$DE$$. The measure of angle $$D$$ is $$32^\circ$$, and the measure of angle $$ABC$$ is $$68^\circ$$. What is the value of $$q-r$$?

    • 80

20. In the $$xy$$-plane, the line segment with endpoints $$(-4,5)$$ and $$(10,-7)$$ represents one of the legs of a right triangle. The area of this triangle is $$54\sqrt{85}$$ square units. What is the length, in units, of the other leg of this triangle?

    • $$54$$
    • $$54\sqrt{85}$$
    • $$27\sqrt{85}$$
    • $$27$$

21. In the figure shown, $$AB=\sqrt{185}$$ units, $$AC=4$$ units, and $$CE=10$$ units. What is the area, in square units, of triangle $$ADE$$?

    • $$637$$
    • $$\frac{91}{2}$$
    • $$\frac{637}{2}$$
    • $$20$$

22. In triangle $$KLM$$, angle $$L$$ is a right angle, the measure of angle $$K$$ is $$33^\circ$$, and the length of $$LM$$ is $$19$$ centimeters. If the area, in square centimeters, of triangle $$KLM$$ can be represented by the expression $$n\cdot\tan(57^\circ)$$, where $$n$$ is a constant, what is the value of $$n$$?

    • $$\frac{361}{2}$$
    • $$\frac{57}{33}$$
    • $$\frac{637}{2}$$
    • $$\frac{185}{16}$$