Advanced Quizzes — Quiz 9

Questions in this quiz (10)

1. The function $$f$$ is defined by the equation $$f(x)=|8-5x|$$ For what value of $$k$$ does $$f(k)=6k+3$$?

   • $$-11$$
   • $$\frac{5}{11}$$
   • $$-63$$
   • $$\frac{63}{11}$$

2. Let $$m$$ be an even integer. How many possible values of $$m$$ satisfy $$\sqrt{m+7}$$ < $$3$$?

   • One
   • Two
   • Three
   • Four

3. In the $$xy$$-plane, a unit circle with center at the origin contains point $$A$$ with coordinates $$(1,0)$$ and point $$B$$ with coordinates $$\left(\frac{5}{\sqrt{34}},-\frac{3}{\sqrt{34}}\right)$$. If the measure of angle $$AOB$$ is $$p$$ radians, what is the value of $$\frac{\cos p}{\sin p}$$?

   • $$-\frac{5}{3}$$
   • $$\frac{3}{2}$$
   • $$\frac{3}{2}$$
   • $$\frac{3}{34}$$

4. $$\sin(a^\circ)=\cos(b^\circ)$$ where $$a$$ and $$b$$ are positive constants. The number $$a$$ is $$50\%$$ greater than the number $$b$$. What is the value of $$a$$?

   • 54

5. Let $$a$$ and $$b$$ be numbers such that $$a^3=b^2$$. Which of the following is equivalent to $$b\sqrt{a}$$?

   • $$b^{\frac{2}{3}}$$
   • $$b^{\frac{4}{3}}$$
   • $$b^2$$
   • $$b^3$$

6. An object's speed, in meters per hour, is increasing at a rate of $$1530$$ meters per hour per second. Which of the following is closest to this rate in feet per second squared? Use $$1$$ meter $$=3.28$$ feet.

   • $$0.13$$
   • $$1.39$$
   • $$7.77$$
   • $$83.6$$

7. Let $$m$$ and $$n$$ be positive integers such that one-third of $$m$$ is $$n$$ less than one-half of $$m$$. Which of the following is a possible value of $$m$$?

   • $$15$$
   • $$21$$
   • $$24$$
   • $$26$$

8. For groups of $$28$$ or more people, an arcade charges 9 dollars per person for the first $$28$$ people and 15 dollars for each additional person. How many total people were in attendance if the group paid 447 dollars to go to the arcade?

   • 41

9. The density of a certain type of wood is $$353$$ kilograms per cubic meter. A sample of this type of wood is in the shape of a cube and has a mass of $$345$$ kilograms. To the nearest hundredth of a meter, what is the length of one edge of this sample?

   • $$0.98$$
   • $$0.99$$
   • $$1.01$$
   • $$1.02$$

10. In the figure above, $$3$$ < $$a$$ < $$5$$ and $$6$$ < $$b$$ < $$8$$. Which of the following represents all possible values of $$c$$?

    • $$0$$ < $$c$$ < $$3$$
    • $$0$$ < $$c$$ < $$13$$
    • $$1$$ < $$c$$ < $$13$$
    • $$1$$ < $$c$$ < $$3$$