Section I Part A — Full Practice Exam 1

Questions in this quiz (27)

1. What is the numerical coefficient of the term containing $$x^2y^3$$ in the expansion of $$(x+3y)^5$$?

   • $$90$$
   • $$135$$
   • $$270$$
   • $$405$$

2. If $$f(x)=x^3+Ax^2+Bx+2$$ and $$f(1)=6$$ and $$f(-1)=-2$$, what is the value of $$2A+B$$?

   • $$2$$
   • $$3$$
   • $$4$$
   • $$6$$

3. If $$f(x)=x^3-3x+2$$, then $$f(-1)=$$

   • $$0$$
   • $$2$$
   • $$4$$
   • $$6$$

4. What is the domain of $$f(x)=\frac{x+2}{x^2+16}$$?

   • All real numbers except $$x=-2$$
   • All real numbers
   • All real numbers except $$x=4$$
   • All real numbers except $$x=\pm 4$$

5. What is the domain of $$g(x)=\frac{\sqrt{x-2}}{x^2-4x}$$?

   • All real numbers except $$x=0,4$$
   • $$x\ge 2,\ x\ne 0,4$$
   • $$x\ge 2,\ x\ne 4$$
   • $$x>4$$

6. Which of the following is equivalent to the expression $$\sqrt[3]{\frac{a^3b^2}{c}}$$?

   • $$\frac{ab^{2/3}}{c^{1/3}}$$
   • $$\frac{a^{1/3}b^{2/3}}{c}$$
   • $$\frac{ab^2}{c^{1/3}}$$
   • $$\frac{a^{1/3}b^{2/3}}{c^{1/3}}$$

7. Identify the vertical asymptote(s) for the function $$f(x)=\frac{x^2-9}{x^3-3x^2}$$.

   • $$x=0$$
   • $$x=0,\ x=3$$
   • $$x=3$$
   • $$x=-3,\ x=3$$

8. Given $$f(x)=\begin{cases}x^2+4,&x\le 0\\(x+1)^2,&x>0\end{cases}$$, find $$f(-2)$$.

   • $$0$$
   • $$2$$
   • $$8$$
   • $$12$$

9. Find the slant asymptote of $$f(x)=\frac{x^2+3x+2}{x-1}$$.

   • $$y=x+1$$
   • $$y=x+3$$
   • $$y=x+4$$
   • $$y=2x+1$$

10. In polar coordinates, which of the following choices is not equivalent to $$(3,\frac{2\pi}{3})$$?

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

11. Which of the following represents zeros of $$r=3-3\cos 2\theta$$?

    • $$0,\pi$$
    • $$\frac{\pi}{4},\frac{3\pi}{4}$$
    • $$\frac{\pi}{2},\frac{3\pi}{2}$$
    • $$\frac{\pi}{6},\frac{5\pi}{6}$$

12. Evaluate $$\sin\left[\arctan\left(\frac{4}{3}\right)\right]$$.

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

13. Which of the following is equivalent to $$\sin 4x\cos 2x-\cos 4x\sin 2x$$?

    • $$\sin 6x$$
    • $$\sin 2x$$
    • $$\cos 6x$$
    • $$\cos 2x$$

14. Given $$\cos x=\frac{3}{5}$$ and $$\tan x>0$$, find $$\sin 2x$$.

    • $$\frac{24}{25}$$
    • $$\frac{12}{25}$$
    • $$\frac{6}{25}$$
    • $$\frac{18}{25}$$

15. Determine the period of the function $$y=3\sin\left(\frac{1}{4}x+\pi\right)$$.

    • $$2\pi$$
    • $$4\pi$$
    • $$8\pi$$
    • $$\pi$$

16. Solve the equation $$\log_a 5-\log_a b=c$$ for $$b$$.

    • $$\frac{5}{a^c}$$
    • $$5a^c$$
    • $$\frac{a^c}{5}$$
    • $$a^5c$$

17. Which of the following statements is true about the function $$g(x)=x^5+x^3+\sin x$$?

    • The function is even and symmetric about the y-axis.
    • The function is odd and symmetric about the origin.
    • The function is neither even nor odd.
    • The function is even and symmetric about the origin.

18. Which of these is an equation for the linear function $$f$$ that satisfies $$f(-1)=3$$ and $$f(3)=-5$$?

    • $$y-3=-2(x+1)$$
    • $$y+5=-2(x-3)$$
    • $$y-3=-2(x-3)$$
    • $$y+5=-2(x+1)$$

19. Given the functions $$f(x)=x^2+1$$ and $$g(x)=\sqrt{x-1}$$, determine the composition $$(g\circ f)(x)$$.

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

20. Given the function $$g(x)=-(5x-2)^2(2x+3)^3$$, determine $$\lim_{x\to-\infty} g(x)$$.

    • $$-\infty$$
    • $$0$$
    • $$1$$
    • $$\infty$$

21. Evaluate $$\lim_{x\to\infty} 2^{-x}+5$$.

    • $$0$$
    • $$2$$
    • $$5$$
    • $$\infty$$

22. What is the function whose graph is a reflection over the $$y$$-axis of the graph of $$f(x)=2^x+1$$?

    • $$g(x)=2^{-x}+1$$
    • $$g(x)=2^x-1$$
    • $$g(x)=1-2^x$$
    • $$g(x)=2^{x+1}$$

23. Which of the following functions does not have an inverse function?

    • $$y=\cos x,\ 0\le x\le \pi$$
    • $$y=x^3-1$$
    • $$y=\frac{x^2}{x+1}$$
    • $$y=e^x$$

24. The table shows the predicted growth of a certain plant after several days. Write an explicit formula for the sequence.

    • $$a_n=12n$$
    • $$a_n=n+12$$
    • $$a_n=6n$$
    • $$a_n=12n+12$$

25. Which of the following equations could represent the graph shown below?

    • $$y=3\sin 2x$$
    • $$y=2\sin 3x$$
    • $$y=3\sin x$$
    • $$y=2\sin 4x$$

26. What are the points where the graph of the polynomial $$f(x)=4(x-3)(x+2)^2$$ passes through the $$x$$-axis?

    • $$x=3$$ only
    • $$x=-2$$ only
    • $$x=-2$$ and $$x=3$$
    • Nowhere

27. Evaluate $$\lim_{x\to\infty}\frac{2x^2-5x+1}{4x^2+3x-7}$$.

    • Does not exist
    • $$0$$
    • $$\frac{1}{2}$$
    • $$\frac{2}{4}$$