| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find derivative of simple polynomial (integer powers) |
| Difficulty | Easy -1.8 This is a straightforward differentiation exercise testing only the power rule on simple functions. Part (i) is direct application; part (ii) requires rewriting the root as a fractional power first. Both are routine recall with minimal steps, making this easier than average even for basic A-level questions. |
| Spec | 1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks | Guidance |
|---|---|---|
| \(-10x^{-6}\) isw | B1 | for \(-10\) or for \(x^{-6}\) ignore \(+c\) and \(y=\); if B0B0 then SC1 for \(-5x^2 \cdot x^{-1}\) or better soi |
| Answer | Marks | Guidance |
|---|---|---|
| \(y = x^{1/3}\) soi; \(kx^{n-1}\); \(\frac{1}{3}x^{-2/3}\) isw | B1, M1, A1 | condone \(y' = x^{1/3}\) if differentiation follows ft their fractional \(n\); ignore \(+c\) and \(y=\); allow 0.333 or better |
### Part (i)
$-10x^{-6}$ isw | B1 | for $-10$ or for $x^{-6}$ ignore $+c$ and $y=$; if B0B0 then SC1 for $-5x^2 \cdot x^{-1}$ or better soi
### Part (ii)
$y = x^{1/3}$ soi; $kx^{n-1}$; $\frac{1}{3}x^{-2/3}$ isw | B1, M1, A1 | condone $y' = x^{1/3}$ if differentiation follows ft their fractional $n$; ignore $+c$ and $y=$; allow 0.333 or betterFind $\frac{dy}{dx}$ when
\begin{enumerate}[label=(\roman*)]
\item $y = 2x^{-5}$. [2]
\item $y = ^4\sqrt{x}$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2013 Q1 [5]}}