Mini Exam 10 — Timed Mini Exams

Questions in this quiz (10)

1. A geometric sequence has $$a_3=18$$ and $$a_5=162$$. Which explicit formula represents the sequence?

   • $$6\cdot3^{n-1}$$
   • $$2\cdot3^{n-1}$$
   • $$6\cdot3^{n-3}$$
   • $$18\cdot3^{n-3}$$

2. A geometric sequence has $$a_3=18$$ and $$a_5=162$$. Which explicit formula represents the sequence?

   • $$6\cdot3^{n-1}$$
   • $$2\cdot3^{n-1}$$
   • $$6\cdot3^{n-3}$$
   • $$18\cdot3^{n-3}$$

3. A bacteria culture triples every $$6$$ hours. Write an equation to model the population $$y$$ after $$t$$ days, given an initial amount $$y_0$$.

   • $$y=y_0\cdot3^{t/6}$$
   • $$y=y_0\cdot3^{4t}$$
   • $$y=y_0\cdot3^{t/4}$$
   • $$y=y_0\cdot3^{4/t}$$

4. A bacteria culture triples every $$6$$ hours. Write an equation to model the population $$y$$ after $$t$$ days, given an initial amount $$y_0$$.

   • $$y=y_0\cdot3^{t/6}$$
   • $$y=y_0\cdot3^{4t}$$
   • $$y=y_0\cdot3^{t/4}$$
   • $$y=y_0\cdot3^{4/t}$$

5. Is the function $$f(x)=2\sin(5x)+3\cos(5x)$$ sinusoidal on its domain?

   • $$\text{No, contains sine and cosine}$$
   • $$\text{No, coefficients differ}$$
   • $$\text{Yes, same angular frequency}$$
   • $$\text{Yes, any sum works}$$

6. Given the point $$(-4,\sqrt{12})$$ on the terminal side of angle $$\theta$$, what is $$\tan\theta$$?

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

7. Given the rectangular coordinate $$(-2,-2\sqrt{3})$$, what is an equivalent polar coordinate with $$0\le\theta$$<$$2\pi$$ and $$r$$<$$0$$?

   • $$(-4,\frac{\pi}{3})$$
   • $$(-4,\frac{4\pi}{3})$$
   • $$(-4,\frac{7\pi}{6})$$
   • $$(-4,\frac{5\pi}{3})$$

8. The range of the function $$f(x)=3\sec(2x-\pi)-2$$ is:

   • $$(-\infty,-5]\cup[1,\infty)$$
   • $$(-\infty,-1]\cup[1,\infty)$$
   • $$(-\infty,-2]\cup[4,\infty)$$
   • $$(-\infty,-3]\cup[3,\infty)$$

9. Is the function $$f(x)=2\sin(5x)+3\cos(5x)$$ sinusoidal on its domain?

   • $$\text{No, contains sine and cosine}$$
   • $$\text{No, coefficients differ}$$
   • $$\text{Yes, same angular frequency}$$
   • $$\text{Yes, any sum works}$$

10. Given the point $$(-4,\sqrt{12})$$ on the terminal side of angle $$\theta$$, what is $$\tan\theta$$?

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