Full Practice Exam 15 — Module 2

Questions in this quiz (22)

1. An energy company models the efficiency ratio of a machine with the formula $$E=\frac{M-N}{M+N}$$ where $$M$$ is the machine's output power and $$N$$ is the power lost due to friction. Which of the following expresses $$N$$ in terms of $$M$$ and $$E$$?

   • $$N=\frac{M-EM}{E+1}$$
   • $$N=\frac{EM}{E+1}$$
   • $$N=\frac{M+EM}{E-1}$$
   • $$N=\frac{EM-M}{E+1}$$

2. The data below show the heights, in inches, of five plants grown in two greenhouses.Greenhouse A: $$12,\ 15,\ 17,\ 18,\ 22$$Greenhouse B: $$10,\ 16,\ 17,\ 20,\ 24$$According to the data, which of the following accurately compares the median height of the plants from Greenhouse A with that of the plants from Greenhouse B?

   • The median height of the plants from Greenhouse A is $$2$$ inches less than that of the plants from Greenhouse B.
   • The median height of the plants from Greenhouse A is $$1$$ inch less than that of the plants from Greenhouse B.
   • The median height of the plants from Greenhouse A is the same as that of the plants from Greenhouse B.
   • The median height of the plants from Greenhouse A is $$3$$ inches greater than that of the plants from Greenhouse B.

3. Morgan deposits $$2500$$ dollars into a savings account that earns $$6\%$$ interest compounded annually. If Morgan withdraws $$400$$ after $$4$$ years, which of the following represents the total amount in the account after $$9$$ years?

   • $$2500(1.06)^9-400$$
   • $$2500(1.06)^4+2100(1.06)^5$$
   • $$2500(1.06)^4-400(1.06)^5$$
   • $$2500(1.06)^9-400(1.06)^5$$

4. The function $$g(x)=18-0.4x$$ gives the amount of gasoline remaining in a tank, in gallons, $$x$$ hours after a leak begins. Which of the following is the best interpretation of $$18$$ in this context?

   • The estimated amount of gasoline, in gallons, in the tank before the leak began.
   • The estimated amount of gasoline, in gallons, that leaks out each hour.
   • The estimated number of hours required for the tank to become empty.
   • The estimated amount of gasoline remaining after $$18$$ hours.

5. Consider the system of equations:$$3x+4y=26$$$$5x-2y=14$$What is the value of $$x$$?

   • $$2$$
   • $$\frac{14}{5}$$
   • $$4$$
   • $$\frac{54}{13}$$

6. The expression $$(9x-5)(4x+7)$$ is equivalent to the expression $$ax^2+bx+c$$, where $$a$$, $$b$$, and $$c$$ are constants. What is the value of $$b$$?

   • $$43$$
   • $$52$$
   • $$59$$
   • $$68$$

7. A data set consists of $$17$$ values. The frequency distribution is shown below.What is the median of the data set?

   • $$2$$
   • $$3$$
   • $$3.5$$
   • $$4$$

8. In the $$xy$$-plane, an equation of circle A is $$(x+2)^2+(y-4)^2=25$$. Circle B has the same center as circle A but has a radius that is twice the radius of circle A. Which equation represents circle B?

   • $$(x+2)^2+(y-4)^2=50$$
   • $$(x+2)^2+(y-4)^2=100$$
   • $$(x+2)^2+(y-4)^2=125$$
   • $$(x+2)^2+(y-4)^2=200$$

9. The function $$g(x)=(x+p)(x-2)(2x-8)$$, where $$p$$ is a constant. The graph of $$y=g(x)$$ passes through the point $$(-5,0)$$. What is the value of $$g(0)$$?

   • $$-80$$
   • $$-40$$
   • $$40$$
   • $$80$$

10. A store owner wants to order notebooks that cost $$6$$ dollars each and binders that cost $$10$$ dollars each. The store owner needs to order at least $$40$$ items total and can spend no more than $$320$$. Which system of inequalities represents this situation, where $$n$$ is the number of notebooks and $$b$$ is the number of binders?

    • $$n+b\ge40$$ and $$6n+10b\le320$$
    • $$n+b\le40$$ and $$6n+10b\ge320$$
    • $$n+b\ge40$$ and $$6n+10b\ge320$$
    • $$n+b\le40$$ and $$6n+10b\le320$$

11. A quality control analyst selected $$2$$ random samples of batteries to estimate average lifespan in hours. The first sample gave an estimate of $$920$$ hours with a margin of error of $$30$$ hours. The second sample gave an estimate of $$950$$ hours with a margin of error of $$75$$ hours. Why did the first sample obtain a smaller margin of error?

    • The first sample contained more batteries than the second sample.
    • The first sample contained fewer batteries than the second sample.
    • The first sample had a longer average lifespan than the second sample.
    • The first sample had a shorter average lifespan than the second sample.

12. $$4x-3ky=14$$$$jx+6ky=18$$Consider the system where $$j$$ and $$k$$ are constants. The lines intersect at $$(3,y)$$. What is the value of $$j$$?

    • $$-\frac{2}{3}$$
    • $$0$$
    • $$\frac{2}{3}$$
    • $$\frac{22}{3}$$

13. The equation $$9x^2-54x+c=0$$ has a solution of $$x=3+\sqrt{5}$$. What is the value of $$c$$?

    • $$36$$
    • $$56$$
    • $$72$$
    • $$96$$

14. A figure has an area of $$7200$$ square inches. What is the area, in square feet, of this figure?

    • $$50$$
    • $$60$$
    • $$500$$
    • $$600$$

15. The equation $$\frac{x}{6}+\frac{y}{8}=\frac{7}{6}$$ models a mixture problem. According to this equation, what is the positive difference between the two concentrations represented by the coefficients of $$x$$ and $$y$$?

    • $$\frac{1}{24}$$
    • $$\frac{1}{12}$$
    • $$\frac{1}{8}$$
    • $$\frac{1}{6}$$

16. A right circular cone has a volume of $$972\pi$$ cubic centimeters and the area of its base is $$81\pi$$ square centimeters. What is the slant height, in centimeters, of the cone?

    • $$5\sqrt{2}$$
    • $$15$$
    • $$21$$
    • $$9\sqrt{17}$$

17. The function $$p(x)=ax^3+bx^2+cx+d$$, where $$a,\ b,\ c,$$ and $$d$$ are integers, passes through the points $$(-4,0)$$ and $$(0,24)$$. The point $$(m,0)$$ is also on the graph of $$p(x)$$. Which of the following could be the value of $$m$$?

    • $$8$$
    • $$-8$$
    • $$8$$ and $$-8$$
    • Neither $$8$$ nor $$-8$$

18. A rectangular prism has a square base with side length $$s$$ and a height of $$3s$$. If the total surface area of the prism is $$448$$ square units, what is the volume, in cubic units, of the prism?

    • $$4\sqrt{2}$$
    • $$8\sqrt{2}$$
    • $$16\sqrt{2}$$
    • $$384\sqrt{2}$$

19. A point $$P(0,1)$$ lies on a circle. The point $$O(0,0)$$ is the center of the circle, while point $$Q(-1,0)$$ also lies on the circle. Which of the following could be the measure of $$\angle POQ$$?

    • $$-\frac{35\pi}{2}$$
    • $$-17\pi$$
    • $$-14\pi$$
    • $$-\frac{29\pi}{2}$$

20. Which of the following expressions is a factor of $$x^4+14bx^2+49b^2-81$$?

    • $$x^2+7b-9$$
    • $$x^2-7b+9$$
    • $$x^2-7b-9$$
    • $$x^2-7b+9$$

21. The scatterplot above shows the relationship between revenue and advertising expenses for 16 companies. The line of best fit is also shown. Which of the following is the best interpretation of the meaning of the slope of the line of best fit?

    • The expected increase in revenue for every one dollar increase in advertising expenses
    • The expected increase in revenue for every one thousand dollar increase in advertising expenses
    • The expected increase in advertising expenses for every one thousand dollar increase in revenue
    • The expected revenue of a company that has no advertising expenses

22. In the figure above, square $$DBCE$$ has a side length of $$3$$. If $$OE=4$$, what is the length of $$AD$$?

    • $$3$$
    • $$\frac{15}{4}$$
    • $$5$$
    • $$\frac{23}{4}$$