| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2008 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find derivative of simple polynomial (integer powers) |
| Difficulty | Moderate -0.8 This is a straightforward numerical differentiation question using chord gradients. Part (i) requires simple substitution into y=2^x and calculating (y₂-y₁)/(x₂-x₁). Part (ii) tests understanding that a smaller interval gives better approximation—students just need to choose points closer to x=3. No calculus, proof, or problem-solving required; purely mechanical application of a basic concept. |
| Spec | 1.07a Derivative as gradient: of tangent to curve |
In Fig. 5, A and B are the points on the curve $y = 2^x$ with $x$-coordinates 3 and 3.1 respectively.
\includegraphics{figure_5}
\begin{enumerate}[label=(\roman*)]
\item Find the gradient of the chord AB. Give your answer correct to 2 decimal places. [2]
\item Stating the points you use, find the gradient of another chord which will give a closer approximation to the gradient of the tangent to $y = 2^x$ at A. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2008 Q5 [4]}}