Full Practice Exam 14 — Module 2

Questions in this quiz (22)

1. Before a science competition, Olivia completed $$20$$ percent more experiments than Noah. Noah completed $$25$$ percent more experiments than Emma. If Emma completed $$e$$ experiments, how many experiments did Olivia complete in terms of $$e$$?

   • $$(1.20)(1.25)e$$
   • $$\frac{e}{(1.20)(1.25)}$$
   • $$1.45e$$
   • $$\frac{e}{(0.8)(0.75)}$$

2. The table below shows the distribution of age and gym membership status for $$900$$ adults.If an adult who is a gym member is selected at random, what is the probability that the adult is $$40$$ or older?

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

3. The function $$g$$ is defined by $$g(x)=x^2+bx+c$$, where $$b$$ and $$c$$ are constants. If the graph of $$g$$ has $$x$$-intercepts at $$-4$$ and $$5$$, which of the following correctly gives the values of $$b$$ and $$c$$?

   • $$b=-1,\ c=-20$$
   • $$b=1,\ c=-20$$
   • $$b=-1,\ c=20$$
   • $$b=1,\ c=20$$

4. The table shows the amount of fuel burned by several drones.Based on the table, how many drones traveled more than $$20$$ kilometers?

   • Two
   • Three
   • Four
   • Five

5. A grocery store has two recycling bins. The first bin collected $$300$$ plastic bottles and $$200$$ aluminum cans. The second bin collected $$20$$ percent more plastic bottles but $$15$$ percent fewer aluminum cans. By what percent did the total number of recycled items increase from the first bin to the second bin?

   • $$4\%$$
   • $$6\%$$
   • $$8\%$$
   • $$10\%$$

6. Sarah estimates that there are $$s$$ beads in a container. The actual number of beads is $$b$$. Sarah's estimate is within $$12$$ beads inclusive of the actual number. Which inequality represents the relationship between $$s$$ and $$b$$?

   • $$-12\le s-b\le12$$
   • $$s\le b+12$$
   • $$s\ge b-12$$
   • $$s+b\le12$$

7. A circle in the $$xy$$-plane is centered at $$(-2,3)$$ and contains the point $$(-5,7)$$. Which of the following could be the equation of the circle?

   • $$(x+2)^2+(y-3)^2=25$$
   • $$(x-2)^2+(y+3)^2=25$$
   • $$(x+2)^2+(y-3)^2=16$$
   • $$(x-2)^2+(y+3)^2=16$$

8. The value of an investment increases by $$150\%$$ every year. Which of the following best describes the relationship between time and the value of the investment?

   • Increasing linear
   • Decreasing linear
   • Exponential growth
   • Exponential decay

9. If $$\sqrt{x}+\sqrt{y}=5\sqrt{y}$$, where $$x$$ > $$0$$ and $$y$$ > $$0$$, what is $$x$$ in terms of $$y$$?

   • $$9y$$
   • $$16y$$
   • $$25y$$
   • $$36y$$

10. Which of the following scenarios would result in exponential decay of the amount of water in a tank?

    • The tank loses one-fourth of the remaining water each hour.
    • The tank loses $$20$$ gallons each hour.
    • The tank loses $$10\%$$ of its original amount each hour.
    • The tank is emptied in $$8$$ hours by removing equal amounts each hour.

11. During a basketball game, Emma made $$24$$ baskets for a total of $$58$$ points. If she made $$x$$ two-pointers and $$y$$ three-pointers, which system of equations represents the situation?

    • $$x+y=24$$$$2x+3y=58$$
    • $$x+y=58$$$$2x+3y=24$$
    • $$x+y=24$$$$3x+2y=58$$
    • $$x+y=58$$$$3x+2y=24$$

12. The potential energy of an object is given by $$PE=mgh$$, where $$m$$ is mass, $$g$$ is the gravitational constant, and $$h$$ is height. If the potential energy of an object is tripled while its mass remains constant, by what factor must its height increase?

    • $$\sqrt{3}$$
    • $$2$$
    • $$3$$
    • $$9$$

13. $$y+2$$ < $$3x$$$$y$$ > $$x+1$$A system of inequalities and a graph are shown above. Which section of the graph could represent all of the solutions to the system?

    • Section A
    • Section B
    • Section C
    • Section D

14. In a circle with center $$O$$, central angle $$AOB$$ has a measure of $$\frac{7\pi}{8}$$ radians. The area of the sector formed by central angle $$AOB$$ is what fraction of the area of the circle?

    • $$\frac{7}{8}$$
    • $$\frac{7}{16}$$
    • $$\frac{7}{4}$$
    • $$\frac{7}{2}$$

15. The function $$f$$ is defined by $$f(x)=|ax-3|-2,$$ where $$a$$ is a constant. In the $$xy$$-plane, the graph of $$f$$ intersects the $$x$$-axis at the points $$(2.5,0)$$ and $$(b,0)$$. What is a possible value of $$a+b$$?

    • $$0.4$$
    • $$2.4$$
    • $$2.5$$
    • $$4.5$$

16. The graph above shows the frequency distribution of the speed limits of all of the roads in a certain county. What is the median of the list of numbers?

    • $$40$$
    • $$44$$
    • $$45$$
    • $$50$$

17. The table below shows values of a function $$f$$.Which function best models the data above?

    • $$f(x)=\sqrt{(x+2)^2}$$
    • $$f(x)=\sqrt{(x-2)^2}$$
    • $$f(x)=-\sqrt{(2-x)^2}$$
    • $$f(x)=\sqrt{(-x-2)^2}$$

18. Point $$O$$ is the center of the circle above. What is the area of the shaded region?

    • $$\frac{16\pi}{3}$$
    • $$\frac{64\pi}{3}$$
    • $$\frac{64\pi}{3}-16\sqrt{3}$$

19. If $$\left(5^y-\frac{3}{5^y}\right)^2=24,$$ what is the value of $$25^y+\frac{9}{25^y}?$$

    • 30

20. The table below classifies the $$36$$ species of animals at a local wildlife preserve as reptile, amphibian, or mammal.The wildlife preserve is partitioned into $$3$$ distinct sections. What fraction of all of the reptiles and amphibians at the wildlife preserve are in Section B?

    • $$\frac{1}{5}$$
    • $$\frac{2}{5}$$
    • $$\frac{3}{5}$$
    • $$\frac{4}{5}$$

21. The median of a set of $$22$$ consecutive even integers is $$25$$. What is the largest number in the set?

    • 46

22. Equilateral triangle $$DEF$$ is inscribed in equilateral triangle $$ABC$$ such that $$ED\perp AC$$. What is the ratio of the area of $$\triangle DEF$$ to the area of $$\triangle ABC$$?

    • $$1:3$$
    • $$1:4$$
    • $$1:5$$
    • $$5:8$$