Section I Part A — Full Practice Exam 2

Questions in this quiz (25)

1. What is the fourth term in the expansion of $$(2x+y)^5$$?

   • $$80x^2y^3$$
   • $$40x^2y^3$$
   • $$20x^3y^2$$
   • $$10xy^4$$

2. Simplify: $$\ln\left(\sqrt[3]{e^3x^2}\right)$$

   • $$1+\frac{2}{3}\ln x$$
   • $$\frac{1}{3}+\ln x^2$$
   • $$1+\ln x$$
   • $$\frac{2}{3}+\frac{1}{3}\ln x$$

3. If $$\csc x\ne1$$, which of the following is equivalent to $$\frac{\cot^2 x}{1-\csc x}$$?

   • $$\csc x+1$$
   • $$\csc x-1$$
   • $$1-\csc x$$
   • $$-\csc x-1$$

4. If $$\cos\theta=k$$, what is $$\sin\theta\cdot\tan\theta\cdot\cos\theta$$?

   • $$k$$
   • $$1$$
   • $$\sin^2\theta$$
   • $$\cos^2\theta$$

5. Which of the following expressions is equivalent to $$\csc\left(\frac{\pi}{2}\right)$$?

   • $$\cos 0$$
   • $$\tan 0$$
   • $$\sin\left(\frac{\pi}{2}\right)$$
   • $$1$$

6. In which quadrant is the terminal side of angle $$\theta$$ located if both $$\sin\theta$$ and $$\cos\theta$$ are negative?

   • I
   • II
   • III
   • IV

7. Evaluate: $$\sec\left(\tan^{-1}\left(\frac{3}{4}\right)\right)$$

   • $$\frac{5}{4}$$
   • $$\frac{4}{5}$$
   • $$\frac{3}{5}$$
   • $$\frac{5}{3}$$

8. If $$f(\theta)=a\sin\theta+b$$, what is the minimum value of $$f(\theta)$$?

   • $$b-a$$
   • $$b+a$$
   • $$\frac{b-a}{2}$$
   • $$-a$$

9. For the expression $$k-\frac{1}{\csc^2 x}=\cos^2 x$$ to be an identity, what must $$k$$ equal?

   • $$1$$
   • $$0$$
   • $$\sin^2 x$$
   • $$\sec^2 x$$

10. What is the expression $$\frac{\sin 2\theta}{2\sin\theta}$$ equivalent to?

    • $$\cos\theta$$
    • $$\sin\theta$$
    • $$\cot\theta$$
    • $$\sec\theta$$

11. In the interval $$0\le x$$ < $$2\pi$$, what are the solutions to $$\cos^2 x=\cos x$$?

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

12. What is the expression $$\frac{\cos\left(x+\frac{\pi}{2}\right)}{\sin x}$$ equivalent to?

    • $$-1$$
    • $$1$$
    • $$-\cot x$$
    • $$\cot x$$

13. Which of the following points represents the same location as $$\left(5,\frac{7\pi}{6}\right)$$ in polar coordinates? (A) $$\left(5,\frac{19\pi}{6}\right)$$ (B) $$\left(-5,\frac{\pi}{3}\right)$$ (C) $$\left(-5,\frac{13\pi}{6}\right)$$ (D) $$\left(5,\frac{13\pi}{6}\right)$$

    • $$\left(5,\frac{19\pi}{6}\right)$$
    • $$\left(-5,\frac{\pi}{3}\right)$$
    • $$\left(-5,\frac{13\pi}{6}\right)$$
    • $$\left(5,\frac{13\pi}{6}\right)$$

14. Given the polar coordinates $$\left(4,\frac{5\pi}{6}\right)$$, find the rectangular coordinates.

    • $$(-2\sqrt{3},2)$$
    • $$(2\sqrt{3},-2)$$
    • $$(-2\sqrt{3},-2)$$
    • $$(2\sqrt{3},2)$$

15. If $$\log_b(2^4)=\frac{4}{3}$$, what is $$b$$?

    • $$2^3$$
    • $$4$$
    • $$8$$
    • $$16$$

16. If $$f^{-1}(x)$$ is the inverse of $$f(x)=3e^{2x}$$, what is $$f^{-1}(x)$$?

    • $$\frac{1}{2}\ln\left(\frac{x}{3}\right)$$
    • $$\ln\left(\frac{x}{3}\right)$$
    • $$\frac{1}{3}\ln x$$
    • $$\ln(3x)$$

17. Find $$f(x+h)$$ when $$f(x)=x^2-3x+2$$.

    • $$x^2+2xh+h^2-3x-3h+2$$
    • $$x^2+h^2-3x+2$$
    • $$x^2+2xh-3h+2$$
    • $$x^2+2xh+h^2-3x+2$$

18. Using the given values $$g(2)=3$$ and $$f(3)=12$$, evaluate $$(f\circ g)(2)$$.

    • $$3$$
    • $$12$$
    • $$6$$
    • $$9$$

19. Find the horizontal asymptote, if any, for the rational function $$g(x)=\frac{5x^2+2x-1}{2x^2-3x+4}$$.

    • $$y=0$$
    • $$y=\frac{5}{2}$$
    • $$y=\frac{2}{5}$$
    • No horizontal asymptote

20. A farmer has $$800$$ meters of fencing to enclose a rectangular field. Express the area $$A$$ as a function of width $$x$$. What is the correct function and domain?

    • $$A(x)=-x^2+400x,\quad 0<x<400$$
    • $$A(x)=x^2+400x,\quad 0<x<800$$
    • $$A(x)=-x^2+800x,\quad 0<x<800$$
    • $$A(x)=x^2-400x,\quad 0

21. If $$x=-1$$ is a real zero of $$f(x)=x^3+3x^2-x-3$$, write $$f(x)$$ as a product of linear factors.

    • $$(x+1)(x+1)(x-3)$$
    • $$(x+1)(x-1)(x+3)$$
    • $$(x+1)(x^2+2x-3)$$
    • $$(x-1)(x^2+2x+3)$$

22. For $$f(x)=5x-2$$, $$x$$<$$2$$ $$f(x)=3x+1$$, $$2\le x\le 5$$$$f(x)=7-x$$b, $$x$$>$$5$$Evaluate $$f(5)$$.

    • $$12$$
    • $$16$$
    • $$6$$
    • $$2$$

23. If $$f(x)=2x^3-x+4$$ and $$g(x)=3$$, then what does $$g(f(x))$$ equal?

    • $$6x^3-3x+12$$
    • $$3$$
    • $$2x^3-x+4$$
    • $$3x$$

24. Which of the following functions is not odd?

    • $$f(x)=x^3$$
    • $$g(x)=\sin(3x)$$
    • $$h(x)=x^4$$
    • $$j(x)=\frac{x}{x^2+1}$$

25. At what value of $$x$$ do the graphs of $$y=x-1$$ and $$y^2=9x$$ intersect?

    • $$x=1$$
    • $$x=4$$
    • $$x=1\text{ and }x=9$$
    • $$x=\frac{11-3\sqrt{13}}{2}\text{ and }x=\frac{11+3\sqrt{13}}{2}$$