| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2013 |
| Session | November |
| Topic | Differentiating Transcendental Functions |
| Type | Differentiate logarithmic functions |
| Difficulty | Moderate -0.3 Part (a) is a straightforward application of the chain rule to differentiate a logarithmic function, giving 6x/(x²+1). Part (b) requires recognizing that the numerator is (up to a constant) the derivative of the denominator, making it a standard substitution integral. Both parts are routine A-level techniques with no problem-solving insight required, making this slightly easier than average. |
| Spec | 1.07l Derivative of ln(x): and related functions1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates1.08h Integration by substitution |
7
\begin{enumerate}[label=(\alph*)]
\item Differentiate $3 \ln \left( x ^ { 2 } + 1 \right)$.
\item Find $\int \frac { x ^ { 2 } } { 3 - 4 x ^ { 3 } } \mathrm {~d} x$.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2013 Q7}}