Timed Mini Exam 24 — Timed Mini Exams

Questions in this quiz (10)

1. What is the period of the function $$f(x)=\csc(4x)$$?

   • $$\frac{\pi}{4}$$
   • $$2\pi$$
   • $$\frac{\pi}{2}$$
   • $$\pi$$

2. Given a positive integer $$n$$ such that $$i^n=1$$, which of the following statements about $$n$$ must be true?Note: $$i^2=-1$$

   • When $$n$$ is divided by 2, the remainder is 2.
   • When $$n$$ is divided by 4, the remainder is 0.
   • When $$n$$ is divided by 4, the remainder is 3.
   • When $$n$$ is divided by 2, the remainder is 1.

3. For $$-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}$$, $$| \sin \theta | \geq 1$$ is true for all and only the values of $$\theta$$ in which of the following sets?

   • $${ -\frac{\pi}{2}, \frac{\pi}{2}}$$
   • $$(-\frac{\pi}{2}, \frac{\pi}{2})$$
   • $$[-\frac{\pi}{2}, \frac{\pi}{2}]$$
   • $$(-\infty, \infty)$$

4. 45 students are in a class.32 are wearing blue and 32 are wearing red. How many are wearing both blue and red?

   • 15
   • 25
   • 35
   • 19

5. On a multiple-choice quiz consisting of six questions, each question offers five answer options, and a student guesses randomly on every question. What is the probability that the student will get all six questions wrong?

   • $$25.50\%$$
   • $$26.21\%$$
   • $$15.50\%$$
   • $$19.36\%$$

6. 64 percent of $$\frac{625}{4}$$ is what proportion of 333?

   • $$\frac{100}{333}$$
   • $$0.03$$
   • $$30%$$
   • $$\frac{3}{10}$$

7. You roll 1000 times a 6-sided dice. What should they add up to?

   • 2100
   • 6000
   • 4100
   • 3500

8. Determine which of the following corresponds to $$x \cdot y$$, if $$(\sqrt{7})^{8x}=2401^{3y}$$

   • $$3$$
   • $$\sqrt{3}$$
   • $$3y^2$$
   • $$x\sqrt{3}$$

9. Two sides of a triangle have lengths of 90 and 50 feet, respectively. The angle formed by these two sides measures 68 degrees. Which of the following is closest to the length of the third side of the triangle?

   • 112
   • 93
   • 103
   • 85

10. One of the following graphs in the standard $$(x,y)$$ coordinate plane is the graph of $$y = \sin^2x + \cos^2x$$ over the domain $$-\frac{\pi}{2} \le x \le \frac{\pi}{2}$$. Which one?