| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Second derivative calculation |
| Difficulty | Moderate -0.8 This is a straightforward differentiation exercise requiring the quotient rule (or simplification first) followed by a second differentiation. While it involves two derivatives and algebraic manipulation to reach the given form, it's a standard C1-level question with no conceptual challenges—students follow routine procedures and verify a given answer. |
| Spec | 1.07e Second derivative: as rate of change of gradient1.07i Differentiate x^n: for rational n and sums |
\begin{enumerate}
\item Given that
\end{enumerate}
$$y = \frac { x ^ { 4 } - 3 } { 2 x ^ { 2 } } ,$$
(i) find $\frac { \mathrm { d } y } { \mathrm {~d} x }$,\\
(ii) show that $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = \frac { x ^ { 4 } - 9 } { x ^ { 4 } }$.\\
\hfill \mbox{\textit{OCR C1 Q4 [6]}}