Full Practice Exam 13 — Module 2

Questions in this quiz (22)

1. The graphs of the equations $$x=8$$ and $$y=x^2-20$$ intersect at the point $$(x,y)$$ in the $$xy$$-plane. What is the value of $$y$$?

   • $$28$$
   • $$36$$
   • $$44$$
   • $$64$$

2. In triangle $$\triangle DEF$$, the length of side $$\overline{DE}$$ is equal to the length of side $$\overline{DF}$$. The measure of angle $$\angle E$$ is $$(3x-20)^\circ$$ and the measure of angle $$\angle F$$ is $$(x+40)^\circ$$. What is the measure of angle $$\angle D$$, in degrees?

   • $$20^\circ$$
   • $$40^\circ$$
   • $$60^\circ$$
   • $$80^\circ$$

3. In a circle with center $$O$$, the radius is $$12$$ units. Points $$A$$ and $$B$$ are on the circle such that the measure of central angle $$\angle AOB$$ is $$150^\circ$$. What is the length of chord $$\overline{AB}$$?

   • $$12$$
   • $$12\sqrt{2}$$
   • $$12\sqrt{3}$$
   • $$6(\sqrt{6}+\sqrt{2})$$

4. Points $$A$$, $$B$$, $$C$$, and $$D$$ are distinct points on a circle. The measure of arc $$AB$$ is $$70^\circ$$, the measure of arc $$BC$$ is $$110^\circ$$, and the measure of arc $$CD$$ is $$80^\circ$$. What is the measure, in degrees, of inscribed angle $$\angle BAD$$?

   • $$40$$
   • $$70$$
   • $$95$$
   • $$110$$

5. $$y=x^2-8x+12$$$$y=3x-4$$How many distinct $$(x,y)$$ solutions does the given system of equations have?

   • Exactly one
   • Exactly two
   • Zero
   • Infinitely many

6. In right triangle $$\triangle XYZ$$ with the right angle at $$Y$$, the value of $$\cos(X)$$ is $$\frac{5}{13}$$. What is the value of $$\tan(Z)$$?

   • $$\frac{5}{12}$$
   • $$\frac{12}{5}$$
   • $$\frac{5}{13}$$
   • $$\frac{12}{13}$$

7. Which of the following expressions is equivalent to $$(4x-3y)^2-(2x+5y)(2x-5y)$$?

   • $$12x^2-24xy+34y^2$$
   • $$12x^2-24xy-16y^2$$
   • $$20x^2-24xy+34y^2$$
   • $$20x^2-24xy-34y^2$$

8. A polling organization surveyed $$1,200$$ randomly selected voters in a state to determine support for a new law. The survey found that $$54\%$$ of the voters support the law, with a margin of error of $$2.5\%$$. Based on the survey results, which of the following is the most appropriate conclusion about the proportion of all voters in the state who support the law?

   • Exactly $$54\%$$ of all voters in the state support the law.
   • It is plausible that between $$51.5\%$$ and $$56.5\%$$ of all voters in the state support the law.
   • More than $$56.5\%$$ of all voters in the state support the law.
   • Less than $$51.5\%$$ of all voters in the state support the law.

9. The table shows the results of a survey asking $$300$$ drivers about their age group and preferred vehicle type.If a randomly selected driver from the survey is $$40$$ years old or over, what is the probability that this person prefers an SUV?

   • $$\frac{80}{300}$$
   • $$\frac{80}{150}$$
   • $$\frac{130}{300}$$
   • $$\frac{150}{300}$$

10. A linear function $$h$$ models the total cost, in dollars, of renting a kayak, where $$x$$ is the number of hours rented. A $$3$$-hour rental costs $$27$$ dollars, and a $$7$$-hour rental costs $$51$$ dollars. Which equation defines $$h(x)$$?

    • $$h(x)=6x+9$$
    • $$h(x)=9x$$
    • $$h(x)=5x+12$$
    • $$h(x)=6x+6$$

11. A solid sphere with a radius of $$9$$ centimeters is melted down and recast into several identical solid cylinders. Each cylinder has a height equal to three times its base radius. If the volume of the metal is conserved during the process, and $$18$$ such cylinders are formed, what is the radius, in centimeters, of the base of each cylinder?

    • $$2$$
    • $$3$$
    • $$4$$
    • $$\sqrt[3]{18}$$

12. The value of an investment increased by $$P\%$$ in its first year. In its second year, the value decreased by $$2P\%$$. If the initial value of the investment was $$10,000$$ dollars and its value after two years was $$8,800$$ dollars, what is the value of $$P$$?

    • $$8$$
    • $$9$$
    • $$10$$
    • $$12$$

13. The graph shows the profit of Company X and Company Y in each quarter of last year. In which quarter was Company X's profit twice Company Y's?

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

14. In $$\triangle ABC$$, $$\overline{AB}\cong\overline{AC}$$. Point $$D$$ is on $$\overline{AC}$$ such that $$\overline{BD}\cong\overline{BC}$$. The measure of $$\angle ABD$$ is $$40^\circ$$. What is the measure of $$\angle BAC$$?

    • $$30^\circ$$
    • $$\frac{100}{3}^\circ$$
    • $$48^\circ$$
    • $$\frac{125}{2}^\circ$$

15. The population of trees in a forest has been decreasing by $$6\%$$ every $$4$$ years. The population at the beginning of $$2015$$ was estimated to be $$14,000$$. If $$P$$ represents the population of trees after $$t$$ years from $$2015$$, which equation gives the population of trees over time?

    • $$P=14000(0.06)^{t/4}$$
    • $$P=14000+0.94(4t)$$
    • $$P=14000(0.94)^{4t}$$
    • $$P=14000(0.94)^{t/4}$$

16. The graph of the function $$f$$ and line segment $$\overline{AB}$$ are shown in the $$xy$$-plane. For how many values of $$x$$ between $$-3$$ and $$3$$ does $$f(x)=c$$?

    • 3

17. A community center wants to build a rectangular playground with an area of at least $$480$$ square meters and a perimeter of at least $$100$$ meters. If the length of the playground is $$x$$ meters and the width is $$y$$ meters, which of the following systems of inequalities represents the requirements?

    • $$xy\ge100,\ x+y\ge480$$
    • $$xy\ge240,\ x+y\ge100$$
    • $$xy\ge480,\ x+y\ge50$$
    • $$xy\ge480,\ x+y\ge100$$

18. In the $$xy$$-plane, the line $$y=3x+c$$ intersects the parabola $$y=x^2+cx+7$$ at the point $$(4,k)$$. If $$c$$ is a constant, what is the value of $$k$$?

    • $$12$$
    • $$16$$
    • $$20$$
    • $$\frac{25}{3}$$

19. In the figure, $$\overline{AB}$$ is parallel to $$\overline{GH}$$ and $$\overline{DF}$$ is parallel to $$\overline{BC}$$. If $$DE=1$$, $$EH=3$$, $$EG=2$$, and $$HC=10$$, what is the length of $$AD$$?

    • $$\frac{5}{2}$$
    • $$\frac{3}{2}$$
    • $$\frac{10}{3}$$
    • $$\frac{11}{2}$$

20. The function $$f$$ is defined by $$f(x)=3x+2$$, and the function $$g$$ is defined by $$g(x)=f(2x)-1$$. What is the value of $$g(10)$$?

    • 61

21. A factory produces cables that must measure between $$95$$ meters and $$105$$ meters in length. If $$x$$ is the length, in meters, of a cable that meets this requirement, which inequality expresses the possible values of $$x$$?

    • $$|x-100|$$ < $$5$$
    • $$|x-105|$$ < $$5$$
    • $$|x+100|$$ < $$5$$
    • $$|x-100|\le5$$

22. The dot plot summarizes the number of flights taken in a year by $$19$$ college students. If the student who took $$6$$ flights in a year is removed from the data, which of the following correctly describes the changes to the statistical measures of the data?I. The mean decreases.II. The median decreases.III. The range decreases.

    • III only
    • I and II only
    • I and III only
    • I, II, and III