| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2007 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Find equation of normal |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard product rule application and normal line equation. Part (a) is trivial recall, part (b) is routine product rule with ln x, and part (c) requires finding gradient at a point and using perpendicular gradient formula—all standard textbook exercises with no novel problem-solving required. Slightly easier than average due to the scaffolded structure and straightforward algebra. |
| Spec | 1.07l Derivative of ln(x): and related functions1.07m Tangents and normals: gradient and equations1.07q Product and quotient rules: differentiation |
1
\begin{enumerate}[label=(\alph*)]
\item Differentiate $\ln x$ with respect to $x$.
\item Given that $y = ( x + 1 ) \ln x$, find $\frac { \mathrm { d } y } { \mathrm {~d} x }$.
\item Find an equation of the normal to the curve $y = ( x + 1 ) \ln x$ at the point where $x = 1$.
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2007 Q1 [7]}}