| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiation from First Principles |
| Type | Chord gradient estimation |
| 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, requiring minimal insight. Both parts are routine calculations with no conceptual challenge beyond basic understanding of gradient approximation. |
| Spec | 1.07b Gradient as rate of change: dy/dx notation |
| Answer | Marks |
|---|---|
| 5 | (ii)) ad of chord = (23.1 − 23)/0.1 |
| Answer | Marks |
|---|---|
| answer in range (5.36, 5.74) | M1 |
| Answer | Marks |
|---|---|
| A1 | or chord with ends x = 3± h, |
| Answer | Marks |
|---|---|
| gradient formula in parts (i) and (ii) | 4 |
Question 5:
5 | (ii)) ad of chord = (23.1 − 23)/0.1
o.e.
= 5.74 c.a.o.
(iiii) rrect use of A and C where
for C, 2.9 < x < 3.1
answer in range (5.36, 5.74) | M1
A1
M1
A1 | or chord with ends x = 3± h,
where 0 < h ≤ 0.1
s.c.1 for consistent use of reciprocal of
gradient formula in parts (i) and (ii) | 4In 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 Q5 [4]}}