| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Second derivative and nature determination |
| Difficulty | Easy -1.2 This is a straightforward differentiation exercise requiring only basic power rule application (rewriting 1/x² as x^(-2)) and computing the second derivative. No chain rule is actually needed despite the topic label, and it's purely mechanical recall with no problem-solving element—easier than average for A-level. |
| Spec | 1.07d Second derivatives: d^2y/dx^2 notation1.07i Differentiate x^n: for rational n and sums |
1 Given that $y = x ^ { 5 } + \frac { 1 } { x ^ { 2 } }$, find\\
(i) $\frac { \mathrm { d } y } { \mathrm {~d} x }$,\\
(ii) $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$.
\hfill \mbox{\textit{OCR C1 2009 Q1 [5]}}