Full Practice Exam 18 — Module 1

Questions in this quiz (22)

1. A class has $$12$$ students. Eight students participate in a science club, and $$4$$ do not. Three of the students who do not participate in the science club are boys. If one student is selected at random, what is the probability of selecting a boy who does not participate in the science club?

   • $$\frac{1}{4}$$
   • $$\frac{1}{3}$$
   • $$\frac{1}{6}$$
   • $$\frac{1}{2}$$

2. Selected values of a continuous function $$g$$ are shown below.In which interval might a zero of the function not be located?

   • $$0.5$$ < $$x$$ < $$2.0$$
   • $$2.0$$ < $$x$$ < $$3.8$$
   • $$3.8$$ < $$x$$ < $$5.5$$
   • $$5.5$$ < $$x$$ < $$7.2$$

3. If the equation $$3x^2+6x=8+a$$ has no real solution, what is the value of $$a$$?

   • $$-20$$
   • $$-14$$
   • $$12$$
   • Both $$-20$$ and $$-14$$

4. A city experiences a population decline of $$8\%$$ every $$10$$ years. In $$1990$$, the population was $$42,000$$. Assuming exponential decay, which model describes the population $$P(n)$$, where $$n$$ is the number of years after $$1990$$?

   • $$P(n)=42000(0.92)^{n/10}$$
   • $$P(n)=42000(1.08)^{n/10}$$
   • $$P(n)=42000(0.92)^n$$
   • $$P(n)=42000(0.08)^{n/10}$$

5. A school recorded the results of students on Science and History exams.What is the probability that a student passed Science, given that the student passed History?

   • $$\frac{2}{5}$$
   • $$\frac{4}{5}$$
   • $$\frac{3}{5}$$
   • $$\frac{12}{25}$$

6. The ratio of the area of a square to the area of a circle is $$\frac{5}{4}$$. If the area of the square increases by $$21\%$$, by what percent must the radius of the circle increase so that the ratio remains unchanged?

   • $$10\%$$
   • $$15\%$$
   • $$21\%$$
   • $$25\%$$

7. If $$ax^2+bx+c=(15x-2)(4x+3)$$ for all values of $$x$$, what is the value of $$a+b+c$$?

   • $$70$$
   • $$76$$
   • $$84$$
   • $$91$$

8. Rectangular prism A is similar to rectangular prism B. The ratio of the length of a side of prism A to the corresponding side of prism B is $$\frac{4}{3}$$. If the area of a face of prism A is $$112$$ square units, what is the area of the corresponding face of prism B?

   • $$49$$
   • $$63$$
   • $$72$$
   • $$84$$

9. Data Set A: $$6.1,\ 6.0,\ 6.2,\ 5.9,\ 6.1,\ 6.0$$Data Set B: $$2.0,\ 8.5,\ 1.7,\ 9.0,\ 4.2,\ 7.6$$Which statement must be true?

   • Data Set A has the smaller standard deviation and the smaller margin of error.
   • Data Set B has the smaller standard deviation and the smaller margin of error.
   • Data Set A has the larger standard deviation.
   • The standard deviations are equal.

10. The function $$f(x)=(x+2)(x-4)(x-7)$$ is shifted horizontally $$4$$ units to the right. The resulting function is called $$g(x)$$. What is the value of $$g(0)$$?

    • -176

11. The pressure of water at depth $$h$$ meters is modeled by $$P=P_0+\rho gh$$, where $$P_0=101325$$ pascals, $$\rho=1000$$, and $$g=9.8$$. A diver is currently at a depth where the pressure is $$2.5P_0$$. If the maximum safe pressure is $$3P_0$$, how many more meters can the diver descend?

    • $$5.17$$ meters
    • $$6.03$$ meters
    • $$7.76$$ meters
    • $$8.42$$ meters

12. A botanist studied a tree whose trunk weighs $$180$$ kilograms, representing $$60\%$$ of the tree's total mass. Of the remaining mass, $$40\%$$ is branches and the rest is leaves. To the nearest kilogram, what is the mass of the branches?

    • $$48$$ kilograms
    • $$60$$ kilograms
    • $$72$$ kilograms
    • $$84$$ kilograms

13. Consider the polynomial $$P(x)=x^3-4x^2-x+4$$. Which of the following contains factors of the polynomial?

    • $$(x-1)$$ and $$(x+1)$$
    • $$(x-2)$$ and $$(x+2)$$
    • $$(x-4)$$ and $$(x+1)$$
    • $$(x-2)$$ and $$(x-1)$$

14. $$4x+y=5$$$$4x+by=2$$$$ax+2y=8$$$$x-y=1$$The systems have the same solution. What is the value of $$a+b$$?

    • $$-\frac{23}{3}$$
    • $$6$$
    • $$\frac{38}{7}$$
    • $$7$$

15. A rental company charges $$120$$ dollars for the first day, $$80$$ dollars per day for the next $$2$$ days, and $$60$$ dollars for each additional day after that. If $$x$$ is the number of days rented and $$x$$ > $$3$$, which function represents the total rental cost $$C(x)$$?

    • $$C(x)=100+60x$$
    • $$C(x)=160+60x$$
    • $$C(x)=220+60x$$
    • $$C(x)=280+60x$$

16. Given $$a^{3/4}=16,\quad x^{-1/m}=a^{-2/3}$$, where $$m$$ > $$0$$, $$a$$ > $$0,$$ and $$x=64$$, what is the value of $$m$$?

    • $$\frac{32}{9}$$
    • $$\frac{4}{3}$$
    • $$\frac{27}{16}$$
    • $$\frac{16}{3}$$

17. A system of inequalities is defined by:$$y\le x+c$$$$y$$ > $$x+d$$If Quadrant III is not contained in the solution region, which relationship between $$c$$ and $$d$$ must be true?

    • $$c$$ > $$d$$
    • $$d$$ > $$c$$
    • $$c$$ > $$d\ge0$$
    • $$d$$ > $$c\ge0$$

18. The period $$T$$ of a pendulum is given by $$T=2\pi\sqrt{\frac{L}{g}}$$, where $$L$$ is the length of the pendulum and $$g$$ is the gravitational acceleration. Which expression gives $$L$$ in terms of $$T$$ and $$g$$?

    • $$L=\frac{gT}{2\pi}$$
    • $$L=\frac{gT^2}{(2\pi)^2}$$
    • $$L=\frac{(2\pi)^2}{gT^2}$$
    • $$L=\frac{T^2}{2\pi g}$$

19. The figure above shows a sector $$O$$ with radius $$r$$. If the area of the sector is $$3\pi$$, what is the approximate perimeter of the sector?

    • $$10$$
    • $$12.5$$
    • $$13.4$$
    • $$15.6$$

20. The scatterplot above shows the distance traveled in hours for $$10$$ taxi drivers and the line of best fit for the data. Which of the following is closest to the average speed, in miles per hour, for the drivers?

    • $$54$$
    • $$59$$
    • $$65$$
    • $$68$$

21. The equation of the graph of line $$\ell$$ in the $$xy$$-plane above is $$y=mx+6,$$ where $$m$$ is a constant. If the line passes through the point $$(3,2)$$, what is the value of $$m$$?

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

22. Triangle $$XYZ$$ is similar to triangle $$RST$$ such that $$X$$, $$Y$$, and $$Z$$ correspond to $$R$$, $$S$$, and $$T$$, respectively. The measure of $$\angle Z$$ is $$20^\circ$$ and $$2XY=RS$$. What is the measure of $$\angle T$$?

    • $$2^\circ$$
    • $$10^\circ$$
    • $$20^\circ$$
    • $$40^\circ$$