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\begin{enumerate}
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\item {\bf D}
\begin{enumerate}
\item Average rate of change of $f$ is $\frac{f(3) - f(1)}{3 - 1} = \frac{5}{2}$. (True)
\item Not enough information given. (False)
\item Average value of $f^\prime$ is the average rate of change of $f$. (True)
\end{enumerate}
\item {\bf A}
\begin{eqnarray}
\frac{1}{(x-1)(x+3)} & = & \frac{A}{x-1} + \frac{B}{x+3} \\
& = & \frac{A}{x-1}\left(\frac{x+3}{x+3}\right) + \frac{B}{x+3}\left(\frac{x-1}{x-1}\right) \\
& = & \frac{A(x+3)}{(x-1)(x+3)} + \frac{B(x-1)}{(x-1)(x+3)} \\
& = & \frac{A(x+3) + B(x-1)}{(x-1)(x+3)} \\
& \Rightarrow & A(x+3) + B(x-1) = 1
\end{eqnarray}
Let $x = 1 \Rightarrow A = \frac{1}{4}$
\end{enumerate}
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