| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find second derivative |
| Difficulty | Moderate -0.8 This is a straightforward differentiation exercise requiring only basic power rule application (rewriting 6/x² as 6x⁻² and differentiating twice). It's purely procedural with no problem-solving element, making it easier than average, though not trivial since it requires two derivatives and careful handling of negative powers. |
| Spec | 1.07d Second derivatives: d^2y/dx^2 notation1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Marks: M1 | A1 | B1 [3] |
| Guidance: \(kx^{-3}\) obtained by differentiation | \(-12x^{-3}\) | \(2x\) correctly differentiated to \(2\) |
| Answer | Marks |
|---|---|
| Marks: M1 | A1 [2] |
| Guidance: Attempt to differentiate their (i) i.e. at least one term "correct" | Fully correct cao; No follow through for A mark |
## (i)
**Answer:** $f(x) = 6x^{-2} + 2x$; $f'(x) = -12x^{-3} + 2$
**Marks:** M1 | A1 | B1 [3]
**Guidance:** $kx^{-3}$ obtained by differentiation | $-12x^{-3}$ | $2x$ correctly differentiated to $2$
**Additional notes:** ISW incorrect simplification after correct expression
## (ii)
**Answer:** $f''(x) = 36x^{-4}$
**Marks:** M1 | A1 [2]
**Guidance:** Attempt to differentiate their (i) i.e. at least one term "correct" | Fully correct cao; No follow through for A mark
**Additional notes:** Allow constant differentiated to zero; ISW incorrect simplification after correct expression
---It is given that $f(x) = \frac{6}{x^2} + 2x$.
\begin{enumerate}[label=(\roman*)]
\item Find $f'(x)$. [3]
\item Find $f''(x)$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2013 Q3 [5]}}