Section I Part B — Full Practice Exam 1

Questions in this quiz (12)

1. Given the function $$f(x)=(x^2-4)(x-1)(2x-3)$$, at what value of $$x$$ does the absolute maximum of $$f(x)$$ occur on the interval $$[-2,3]$$?

   • $$-2$$
   • $$-1$$
   • $$1$$
   • $$3$$

2. Approximate $$\log_a 18$$, given that $$\log_a 2\approx 0.4307$$ and $$\log_a 3\approx 0.6826$$.

   • $$1.1133$$
   • $$1.7959$$
   • $$2.0459$$
   • $$0.6826$$

3. Solve for $$x$$: $$2^{x+1}=4^{x-2}$$.

   • $$2$$
   • $$3$$
   • $$4$$
   • $$5$$

4. Which of the following choices is equivalent to the complex number $$2-2\sqrt{3}i$$?

   • $$4\left(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\right)$$
   • $$4\left(\cos\left(-\frac{\pi}{3}\right)+i\sin\left(-\frac{\pi}{3}\right)\right)$$
   • $$2\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right)$$
   • $$2\left(\cos\left(-\frac{\pi}{6}\right)+i\sin\left(-\frac{\pi}{6}\right)\right)$$

5. Find all solutions in the interval $$[0,2\pi]$$ for the trigonometric equation $$4\cos^2 x-4=0$$.

   • $$0,\pi$$
   • $$\frac{\pi}{2},\frac{3\pi}{2}$$
   • $$0,\frac{\pi}{2},\pi,\frac{3\pi}{2}$$
   • $$0,\pi,2\pi$$

6. Give an algebraic expression for $$\sin(\cos^{-1} x)$$.

   • $$\sqrt{1-x^2}$$
   • $$-\sqrt{1-x^2}$$
   • $$1-x^2$$
   • $$\sqrt{1+x^2}$$

7. How long will it take for $$500$$ dollars to double in an investment when interest is compounded continuously at the rate of $$6\%$$ per annum? Round to the nearest year.

   • $$10$$ years
   • $$11$$ years
   • $$12$$ years
   • $$13$$ years

8. An object is launched straight up from ground level with an initial velocity of $$40$$ ft/s. The height is given by $$h(t)=-16t^2+40t$$. At approximately what value of $$t$$ will the object be at a height of $$24$$ feet and moving downward?

   • $$0.8$$ seconds
   • $$1.2$$ seconds
   • $$1.5$$ seconds
   • $$2.2$$ seconds

9. Suppose a ball is dropped from a height of $$10$$ feet. After each bounce, it reaches $$80\%$$ of its previous height. How high will the ball rebound after the third bounce, to the nearest tenth?

   • $$4.1$$ feet
   • $$5.1$$ feet
   • $$6.4$$ feet
   • $$8.0$$ feet

10. Let $$f(x)=-x^5+10x^4$$. For what values of $$x$$ does the graph of $$f$$ have a point of inflection?\n\nI. $$x=0$$\nII. $$x=2$$\nIII. $$x=6$$

    • I only
    • II only
    • III only
    • I, II, and III

11. After performing analyses on a set of data, a student examined the scatterplot of residual values. Which scatterplot indicates the best linear fit?

    • Residuals form a curved pattern
    • Residuals show increasing trend
    • Residuals are randomly scattered around zero
    • Residuals show strong clustering above axis

12. Given the graph of the function $$f(x)=x^2$$, find the average rate of change from the vertex $$(0,0)$$ to the point $$P(4,16)$$.

    • $$2$$
    • $$4$$
    • $$8$$
    • $$16$$