| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Find derivative of composite quotient/product |
| Difficulty | Moderate -0.3 This question tests standard differentiation techniques (product rule and quotient rule) with straightforward algebraic expressions. Both parts are routine textbook exercises requiring direct application of rules with minimal algebraic manipulation, making it slightly easier than the average A-level question which typically involves more steps or conceptual depth. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07q Product and quotient rules: differentiation |
\begin{enumerate}[label=(\alph*)]
\item Differentiate $x^2(x + 1)^6$ with respect to $x$. [3]
\item Find the gradient of the curve $y = \frac{x^2 + 3}{x^2 - 3}$ at the point where $x = 1$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q3 [6]}}