Full Practice Exam 22 — Module 2

Questions in this quiz (22)

1. The temperature of a storage room, $$T$$, must be kept between $$18^\circ C$$ and $$24^\circ C$$, inclusive. Which of the following equations represents all possible temperatures of the storage room?

   • $$3\ge|21-T|$$
   • $$3\le|21-T|$$
   • $$21\ge|3-T|$$
   • $$21\le|3-T|$$

2. $$42.5\%$$ of $$16$$ is equivalent to $$1.7\%$$ of what number?

   • $$40$$
   • $$400$$
   • $$4,000$$
   • $$40,000$$

3. A restaurant charges a fee of $$2.50$$ dollars plus $$1.20$$ dollars per pound of food for takeout orders. After the subtotal is calculated, a sales tax of $$8\%$$ is added. Which equation gives the total cost, $$C$$, for $$n$$ pounds of food after tax?

   • $$C=0.08(2.50+1.20n)$$
   • $$C=1.08(2.50+1.20n)$$
   • $$C=0.08(2.50+120n)$$
   • $$C=1.08(2.50+120n)$$

4. A company manufactures two types of calculators. The cost, $$C$$, of producing $$n$$ copies of the basic calculator is $$C=15n+2500,$$ while the cost of producing $$n$$ copies of the scientific calculator is $$C=10n+4000.$$ If the company wants the production costs to be equal for the two calculator types, how many copies of each calculator should it produce?

   • $$250$$
   • $$300$$
   • $$350$$
   • $$400$$

5. A model airplane is built using a scale ratio of $$1:40$$. The actual airplane is $$200$$ feet long. A second model is built using a scale ratio of $$1:20$$. How much longer is the second model than the first model?

   • $$5$$ feet
   • $$10$$ feet
   • $$15$$ feet
   • $$20$$ feet

6. A culture contains $$80,000$$ bacteria. Every $$4$$ hours, the population decreases by half. Which function represents the number of bacteria, $$f(t)$$, present in the culture after $$t$$ hours?

   • $$f(t)=80,000\left(\frac{1}{2}\right)^{4t}$$
   • $$f(t)=80,000\left(\frac{1}{2}\right)^{t/4}$$
   • $$f(t)=80,000\left(\frac{1}{4}\right)^t$$
   • $$f(t)=80,000(2)^{t/4}$$

7. If $$-5$$ < $$3k+4\le7,$$ which of the following is not a possible value of $$k$$?

   • $$-2.5$$
   • $$-2$$
   • $$0$$
   • $$2$$

8. The function $$f$$ is defined by $$f(x)=|bx-8|,$$ where $$b$$ is a constant. In the $$xy$$-plane, the graph of $$f$$ intersects the $$x$$-axis at the two points $$(4,0)$$ and $$(c,0)$$. What is a possible value of $$b+c$$?

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

9. Which of the following best describes the range of $$f(x)=2x^2-8x+11?$$

   • $$(3,\infty)$$
   • $$[3,\infty)$$
   • $$(-\infty,3]$$
   • $$(-\infty,\infty)$$

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

    • $$f(x)=\sqrt{(x-1)^2}$$
    • $$f(x)=\sqrt{(x-2)^2}+1$$
    • $$f(x)=-\sqrt{(x-2)^2}+1$$
    • $$f(x)=\sqrt{(x+2)^2}+1$$

11. If $$\sqrt{3x^2+2}=x+4,$$ then $$x=$$?

    • $$1\pm\sqrt{44}$$
    • $$2\pm\sqrt{11}$$
    • $$-4\pm\sqrt{11}$$
    • $$-4\pm2\sqrt{44}$$

12. The function $$f$$ satisfies $$f(x+1)=3x-2.$$ What is the value of $$f(4)$$?

    • $$4$$
    • $$5$$
    • $$7$$
    • $$10$$

13. An online tile company sells ceramic tile by the box. Each box covers $$25$$ square feet of floor area and costs $$89.95$$ dollars. If a family wants to tile a $$15\times18$$ square foot room, how much will they pay?

    • $$899.50$$
    • $$989.45$$
    • $$1,079.40$$
    • $$1,169.35$$

14. The admission price for a museum is $$15$$ dollars for adults and $$9$$ dollars for children. The museum needs to collect more than $$1,500$$ dollars in ticket sales. If $$120$$ people attended, which of the following combinations of adult tickets, $$a$$, and child tickets, $$c$$, could have met the museum’s goal?

    • $$a=30,\ c=90$$
    • $$a=45,\ c=75$$
    • $$a=60,\ c=60$$
    • $$a=75,\ c=45$$

15. $$x^2+y^2=2$$$$x=y$$If $$(x,y)$$ is a solution to the system below, what is a possible value of $$x+y$$?

    • $$-\sqrt{2}$$
    • $$-\frac{1}{2}$$
    • $$\frac{1}{2}$$
    • $$2$$

16. A company uses the formula below to calculate its customer satisfaction rate, $$R$$, based on the number of satisfied customers, $$S$$, and dissatisfied customers, $$F$$.$$R=\frac{S}{S+F}$$Which of the following expresses $$S$$ in terms of the other variables?

    • $$S=\frac{F}{R-1}$$
    • $$S=\frac{F}{1-R}$$
    • $$S=\frac{RF}{R-1}$$
    • $$S=\frac{RF}{1-R}$$

17. A national survey is given to $$1,200$$ randomly selected high-school seniors. The mean GPA is $$3.0$$, and the margin of error is $$0.020$$. Another survey is given to $$600$$ randomly selected high-school seniors, and a mean GPA of $$2.95$$ is obtained. The margin of error of the second survey is most likely

    • Four times as small as that of the first survey
    • Twice as small as that of the first survey
    • Equal to that of the first survey
    • Larger than that of the first survey

18. 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?

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

19. In the figure above, $$MNPQ$$ is a rectangle. Which of the following must be true?

    • $$\cos(\angle MNQ)=\sin(\angle QNP)$$
    • $$\cos(\angle MNQ)=\sin(\angle QPN)$$
    • $$\cos(\angle NMQ)=\sin(\angle QPN)$$
    • $$\cos(\angle NQM)=\sin(\angle QPN)$$

20. In the circle with center $$O$$, $$OD=DB$$ and arc $$DB=2\pi$$. What is the area of the circle?

    • $$36\pi$$
    • $$16\pi$$
    • $$12\pi$$
    • $$4\pi$$

21. The two box plots show the distribution of the number of books read over the summer by students in two different English classes. What is the positive difference between the ranges of number of books read over the summer for the two classes?

    • 4

22. If the area of $$\triangle ABC$$ is $$21$$, and the length of the height minus the length of the base equals $$1$$, which of the following is equal to the base of the triangle?

    • $$2$$
    • $$4$$
    • $$6$$
    • $$7$$