Section I Part A — Full Practice Exam 3
Multiple-choice non-calculator section
Questions in this quiz (25)
What is the fifth term in the expansion of $$(2x-3y)^6$$?
- $$240x^2y^4$$
- $$-720x^2y^4$$
- $$4860x^2y^4$$
- $$720x^3y^3$$
What is the expression $$\tan\theta(\sec\theta-\sin\theta)$$ equivalent to?
- $$\frac{\sin\theta}{\cos^2\theta}-\sin^2\theta$$
- $$\frac{\sin\theta}{\cos^2\theta}-\frac{\sin^2\theta}{\cos\theta}$$
- $$\frac{\sin\theta(1-\cos\theta)}{\cos^2\theta}$$
- $$\frac{1-\cos\theta}{\cos\theta}$$
Evaluate: $$\sec\left(\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)\right)$$.
- $$\frac{2}{\sqrt{3}}$$
- $$\sqrt{3}$$
- $$2$$
- $$\frac{\sqrt{3}}{2}$$
If $$f(x)$$ is an even function, which of the following must also be an even function?
- $$x\cdot f(x)$$
- $$f(x^2)$$
- $$f(x)+x$$
- $$f(x-1)$$
For what value of $$k$$ is $$(x+2)$$ a factor of the function $$f(x)=2x^4-x^3+kx^2+5x-6$$?
- $$-6$$
- $$2$$
- $$-2$$
- $$4$$
Which of the following is equivalent to $$\lim_{x\to\infty}\frac{6x^4-5x+1}{-3x^4+8x^2-7}$$?
- $$-2$$
- $$-\frac{1}{2}$$
- $$2$$
- $$0$$
Find the solution set for the inequality $$\frac{x+1}{x-3}\le2$$.
- $$(-\infty,3)\cup[7,\infty)$$
- $$(-\infty,3)\cup(7,\infty)$$
- $$(3,7]$$
- $$[3,7]$$
Given $$f(x)=4x+5$$, evaluate and simplify $$\frac{f(x+h)-f(x)}{h}$$.
- $$4+\frac{5}{h}$$
- $$4$$
- $$h$$
- $$\frac{4x+5}{h}$$
Find the exact value of the expression $$\sin\left(\frac{5\pi}{12}\right)\cos\left(\frac{\pi}{6}\right)-\cos\left(\frac{5\pi}{12}\right)\sin\left(\frac{\pi}{6}\right)$$.
- $$\frac{\sqrt{2}}{2}$$
- $$\frac{1}{2}$$
- $$\frac{\sqrt{3}}{2}$$
- $$-\frac{\sqrt{2}}{2}$$
The graph of which of the following equations has $$y=3$$ as a horizontal asymptote?
- $$y=\frac{3x-1}{x+2}$$
- $$y=\frac{x+3}{x-1}$$
- $$y=\frac{3x^2+1}{x+4}$$
- $$y=\frac{x-2}{3x+1}$$
If $$f(x)=3x-k$$ and $$g(x)=\frac{2x-1}{3}$$, for what value of $$k$$ is $$f(g(x))=g(f(x))$$?
- $$-1$$
- $$0$$
- $$-2$$
- $$2$$
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 $$y=f(2x-1)$$?
- $$(2,-2)$$
- $$(3,-2)$$
- $$(1,-2)$$
- $$(2,-4)$$
If $$f(x)=\frac{x-2}{4}$$ and $$g(x)=4x+k$$ are inverse functions, what is the value of $$k$$?
- $$-8$$
- $$-2$$
- $$2$$
- $$8$$
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
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?
- $$12+5(n-1)$$
- $$12+\frac{5(n-1)}{2}$$
- $$12-5n^2$$
- $$12+\frac{5(n-1)^2}{2}$$
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?
- $$12+5(n-1)$$
- $$12+\frac{5(n-1)}{2}$$
- $$12-5n^2$$
- $$12+\frac{5(n-1)^2}{2}$$
Which of the following functions could represent $$f(x)$$ if $$\lim_{x\to0^-}f(x)=\infty$$ and $$\lim_{x\to0^+}f(x)=-\infty$$?
- $$f(x)=\frac{1}{x^2}$$
- $$f(x)=\frac{1}{x(x+2)}$$
- $$f(x)=-\frac{1}{x}$$
- $$f(x)=\frac{1}{x-1}$$
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. $$g_n=2\cdot2^n$$
- $$\text{I and II only}$$
- $$\text{I and III only}$$
- $$\text{II and III only}$$
- $$\text{I, II, and III}$$
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?
- $$-14$$
- $$0$$
- $$4$$
- $$6$$
Which of the following equations is equivalent to $$y=\log_a(x^2)$$ where $$x>0$$ and $$a>1$$?
- $$a^y=x^2$$
- $$a^{2y}=x$$
- $$y^a=x^2$$
- $$x^y=a^2$$
What is the logarithmic expression $$\log_2\left(\frac{\sqrt[3]{x^2}\sqrt[4]{y^3}}{z^5}\right)$$ equivalent to?
- $$\frac{2}{3}\log_2 x+\frac{3}{4}\log_2 y-5\log_2 z$$
- $$\frac{1}{3}\log_2 x+\frac{1}{4}\log_2 y-5\log_2 z$$
- $$\frac{2}{3}\log_2 x+\frac{3}{4}\log_2 y-\log_2 z$$
- $$\frac{2}{3}\log_2 x+\frac{3}{4}\log_2 y-2\log_2 z$$
Evaluate $$\log_{m^2}(m^{6n-2})$$
- $$3n-1$$
- $$6n-2$$
- $$3n-2$$
- $$\frac{6n-2}{2}$$
Which of the following is the end behavior asymptote for the function $$f(x)=\frac{2x^2-5x+4}{x+1}$$?
- $$y=2x-7$$
- $$y=2x-3$$
- $$y=x-3$$
- $$y=2x+1$$
Solve for $$x$$ given the equation $$3^{2x-1}=\frac{1}{27}$$
- $$-1$$
- $$0$$
- $$\frac{1}{2}$$
- $$2$$
Which of the following functions are equivalent? I. $$f(x)=9^x$$ II. $$g(x)=(27)^{\frac{2x}{3}}$$ III. $$h(x)=3^{2x}$$
- $$\text{I and II only}$$
- $$\text{II and III only}$$
- $$\text{I and III only}$$
- $$\text{I, II, and III}$$