Section I Part A — Full Practice Exam 3

Questions in this quiz (25)

1. What is the fifth term in the expansion of $$(2x-3y)^6$$?

   • $$240x^2y^4$$
   • $$-720x^2y^4$$
   • $$4860x^2y^4$$
   • $$720x^3y^3$$

2. What is the expression $$\tan\theta(\sec\theta-\sin\theta)$$ equivalent to?

   • $$\frac{\sin\theta}{\cos^2\theta}-\sin^2\theta$$
   • $$\frac{\sin\theta}{\cos^2\theta}-\frac{\sin^2\theta}{\cos\theta}$$
   • $$\frac{\sin\theta(1-\cos\theta)}{\cos^2\theta}$$
   • $$\frac{1-\cos\theta}{\cos\theta}$$

3. Evaluate: $$\sec\left(\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)\right)$$.

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

4. If $$f(x)$$ is an even function, which of the following must also be an even function?

   • $$x\cdot f(x)$$
   • $$f(x^2)$$
   • $$f(x)+x$$
   • $$f(x-1)$$

5. For what value of $$k$$ is $$(x+2)$$ a factor of the function $$f(x)=2x^4-x^3+kx^2+5x-6$$?

   • $$-6$$
   • $$2$$
   • $$-2$$
   • $$4$$

6. Which of the following is equivalent to $$\lim_{x\to\infty}\frac{6x^4-5x+1}{-3x^4+8x^2-7}$$?

   • $$-2$$
   • $$-\frac{1}{2}$$
   • $$2$$
   • $$0$$

7. Find the solution set for the inequality $$\frac{x+1}{x-3}\le2$$.

   • $$(-\infty,3)\cup[7,\infty)$$
   • $$(-\infty,3)\cup(7,\infty)$$
   • $$(3,7]$$
   • $$[3,7]$$

8. Given $$f(x)=4x+5$$, evaluate and simplify $$\frac{f(x+h)-f(x)}{h}$$.

   • $$4+\frac{5}{h}$$
   • $$4$$
   • $$h$$
   • $$\frac{4x+5}{h}$$

9. Find the exact value of the expression $$\sin\left(\frac{5\pi}{12}\right)\cos\left(\frac{\pi}{6}\right)-\cos\left(\frac{5\pi}{12}\right)\sin\left(\frac{\pi}{6}\right)$$.

   • $$\frac{\sqrt{2}}{2}$$
   • $$\frac{1}{2}$$
   • $$\frac{\sqrt{3}}{2}$$
   • $$-\frac{\sqrt{2}}{2}$$

10. The graph of which of the following equations has $$y=3$$ as a horizontal asymptote?

    • $$y=\frac{3x-1}{x+2}$$
    • $$y=\frac{x+3}{x-1}$$
    • $$y=\frac{3x^2+1}{x+4}$$
    • $$y=\frac{x-2}{3x+1}$$

11. If $$f(x)=3x-k$$ and $$g(x)=\frac{2x-1}{3}$$, for what value of $$k$$ is $$f(g(x))=g(f(x))$$?

    • $$-1$$
    • $$0$$
    • $$-2$$
    • $$2$$

12. The point $$(3,-2)$$ is on the graph of $$y=f(x)$$. What are the coordinates of the image of this point on the graph $$y=f(2x-1)$$?

    • $$(2,-2)$$
    • $$(3,-2)$$
    • $$(1,-2)$$
    • $$(2,-4)$$

13. If $$f(x)=\frac{x-2}{4}$$ and $$g(x)=4x+k$$ are inverse functions, what is the value of $$k$$?

    • $$-8$$
    • $$-2$$
    • $$2$$
    • $$8$$

14. Which of the following functions are equivalent?I. $$f(x)=\log_3 x$$II. $$g(x)=\frac{\ln x}{\ln 3}$$III. $$h(x)=\log_9 x$$

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

15. A sequence has first term $$a_1=12$$ and each term increases by $$5$$ more than the previous increase. Which expression represents the $$n$$th term?

    • $$12+5(n-1)$$
    • $$12+\frac{5(n-1)}{2}$$
    • $$12-5n^2$$
    • $$12+\frac{5(n-1)^2}{2}$$

16. A sequence has first term $$a_1=12$$ and each term increases by $$5$$ more than the previous increase. Which expression represents the $$n$$th term?

    • $$12+5(n-1)$$
    • $$12+\frac{5(n-1)}{2}$$
    • $$12-5n^2$$
    • $$12+\frac{5(n-1)^2}{2}$$

17. Which of the following functions could represent $$f(x)$$ if $$\lim_{x\to0^-}f(x)=\infty$$ and $$\lim_{x\to0^+}f(x)=-\infty$$?

    • $$f(x)=\frac{1}{x^2}$$
    • $$f(x)=\frac{1}{x(x+2)}$$
    • $$f(x)=-\frac{1}{x}$$
    • $$f(x)=\frac{1}{x-1}$$

18. Which of the following equations would produce sequences with the same terms? I. $$g_n=4\cdot2^n$$ II. $$g_n=2^{n+2}$$ III. $$g_n=2\cdot2^n$$

    • $$\text{I and II only}$$
    • $$\text{I and III only}$$
    • $$\text{II and III only}$$
    • $$\text{I, II, and III}$$

19. Given the two arithmetic sequences $$a_n=k+3(n-1)$$ and $$a_n=10-2(n+1),$$ what is the value of $$k$$ for the two sequences to have the same fifth term?

    • $$-14$$
    • $$0$$
    • $$4$$
    • $$6$$

20. Which of the following equations is equivalent to $$y=\log_a(x^2)$$ where $$x>0$$ and $$a>1$$?

    • $$a^y=x^2$$
    • $$a^{2y}=x$$
    • $$y^a=x^2$$
    • $$x^y=a^2$$

21. What is the logarithmic expression $$\log_2\left(\frac{\sqrt[3]{x^2}\sqrt[4]{y^3}}{z^5}\right)$$ equivalent to?

    • $$\frac{2}{3}\log_2 x+\frac{3}{4}\log_2 y-5\log_2 z$$
    • $$\frac{1}{3}\log_2 x+\frac{1}{4}\log_2 y-5\log_2 z$$
    • $$\frac{2}{3}\log_2 x+\frac{3}{4}\log_2 y-\log_2 z$$
    • $$\frac{2}{3}\log_2 x+\frac{3}{4}\log_2 y-2\log_2 z$$

22. Evaluate $$\log_{m^2}(m^{6n-2})$$

    • $$3n-1$$
    • $$6n-2$$
    • $$3n-2$$
    • $$\frac{6n-2}{2}$$

23. Which of the following is the end behavior asymptote for the function $$f(x)=\frac{2x^2-5x+4}{x+1}$$?

    • $$y=2x-7$$
    • $$y=2x-3$$
    • $$y=x-3$$
    • $$y=2x+1$$

24. Solve for $$x$$ given the equation $$3^{2x-1}=\frac{1}{27}$$

    • $$-1$$
    • $$0$$
    • $$\frac{1}{2}$$
    • $$2$$

25. Which of the following functions are equivalent? I. $$f(x)=9^x$$ II. $$g(x)=(27)^{\frac{2x}{3}}$$ III. $$h(x)=3^{2x}$$

    • $$\text{I and II only}$$
    • $$\text{II and III only}$$
    • $$\text{I and III only}$$
    • $$\text{I, II, and III}$$