Section I Part B — Full Practice Exam 2

Questions in this quiz (12)

1. A deposit of $$8000$$ is made in an account that earns $$6\%$$ interest compounded monthly. The balance after $$n$$ months is given by $$a_n=8000\left(1+\frac{0.06}{12}\right)^n$$. Find the balance after $$3$$ years.

   • $$9524.36$$
   • $$9742.11$$
   • $$9825.78$$
   • $$10102.47$$

2. If $$\log_{0.4}(x-2)$$>$$\log_{0.16}(x-2)$$, then $$x$$ lies in which of the following intervals?

   • $$(2,\\infty)$$
   • $$(-\\infty,2)$$
   • $$(2,3)$$
   • $$(-2,0)$$

3. If $$\\theta$$ is an angle in standard position and its terminal side passes through the point $$(-0.6,-0.8)$$ on the unit circle, which of the following is a possible radian value of $$\\theta$$ to the nearest hundredth?

   • $$3.82$$
   • $$4.07$$
   • $$5.36$$
   • $$2.21$$

4. The cost $$C(x)$$, in dollars, of operating a business is modeled by $$C(x)=x^2-12x+500$$, where $$x$$ is the number of items produced daily. Find the minimum cost to the nearest dollar.

   • $$464$$
   • $$428$$
   • $$436$$
   • $$450$$

5. The height $$h(t)$$, in meters, of a ball thrown upward is given by $$h(t)=5+18t-4t^2$$. Find the average rate of change of the height over the first $$3$$ seconds.

   • $$6$$
   • $$9$$
   • $$12$$
   • $$15$$

6. Find the solution set for the rational inequality $$\frac{x-1}{x+3}$$ < $$2.$$

   • $$( -3,5 )$$
   • $$(-\infty,-7)\cup(-3,\infty)$$
   • $$( -3,\infty )$$
   • $$(-\infty,5)$$

7. The table below shows selected values of a continuous polynomial function.Based on the table, within which interval must there exist a zero?

   • $$(-4,-2)$$
   • $$(-2,0)$$
   • $$(0,2)$$
   • $$(2,4)$$

8. Find the domain of the function $$f(x)=\sqrt{x-2}-\frac{1}{\sqrt{10-x}}.$$

   • $$[2,10)$$
   • $$(2,10]$$
   • $$(2,10)$$
   • $$(-\infty,\infty)$$

9. Find the difference between the largest and smallest real solutions of $$3x^4-x^2-2=0$$ rounded to two decimal places.

   • $$1.15$$
   • $$1.41$$
   • $$1.73$$
   • $$2.00$$

10. The population of a town is shown in the table below, in thousands. If the same pattern continues, what will the population be in $$2030$$, to the nearest thousand?

    • $$36{,}000$$
    • $$40{,}000$$
    • $$48{,}000$$
    • $$60{,}000$$

11. A box with an open top is made from a rectangular sheet of cardboard measuring $$10$$ inches by $$20$$ inches by cutting out squares of side length $$x$$ from each corner and folding up the sides. What value of $$x$$ maximizes the volume?

    • $$1.67$$
    • $$2.11$$
    • $$3.33$$
    • $$5.00$$

12. Given the rectangular coordinates $$(-3,3\sqrt{3})$$, find the polar coordinates.

    • $$\left(6,\frac{2\pi}{3}\right)$$
    • $$\left(6,\frac{5\pi}{6}\right)$$
    • $$\left(6,\frac{4\pi}{3}\right)$$
    • $$\left(6,\frac{\pi}{3}\right)$$