| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiation from First Principles |
| Type | Chord gradient estimation |
| Difficulty | Easy -1.2 This is a straightforward application of chord gradient formula with clear instructions. Part (i) appears to have a typo (both x-values are 4), making it trivial or impossible. Part (ii) is routine: choose a closer point and apply the same formula. No conceptual difficulty beyond basic substitution and arithmetic—well below average A-level challenge. |
| Spec | 1.07a Derivative as gradient: of tangent to curve |
| Answer | Marks | Guidance |
|---|---|---|
| ruled line touching curve at \(x = 2\) | M1 | intent to touch, but must not clearly cut curve |
| their \(\frac{y_2 - y_1}{x_2 - x_1}\) from their *tangent* | M1 | may be on graph or in working; must use correct points from their line; their tangent may be at another point; M0 for reciprocal |
| answer in range 2.5 to 3.0 inclusive | A1 | both M1s must be awarded; (value is approx 2.773) |
| Answer | Marks | Guidance |
|---|---|---|
| 3.482202253... and 4.59479342... rot to 3 or more sf | B1 | |
| 2.78 to 2.7815 or 2.8 | B1 | mark the final answer; 2.781477917... |
## Question 5(i):
ruled line touching curve at $x = 2$ | M1 | intent to touch, but must not clearly cut curve
their $\frac{y_2 - y_1}{x_2 - x_1}$ from their *tangent* | M1 | may be on graph or in working; must use correct points from their line; their tangent may be at another point; **M0** for reciprocal
answer in range 2.5 to 3.0 inclusive | A1 | both **M1**s must be awarded; (value is approx 2.773)
## Question 5(ii):
3.482202253... and 4.59479342... rot to 3 or more sf | B1 |
2.78 to 2.7815 or 2.8 | B1 | mark the final answer; 2.781477917...
---5 The equation of a curve is $y = \sqrt { 1 + 2 x }$.\\
(i) Calculate the gradient of the chord joining the points on the curve where $x = 4$ and $x = 4$. Give your answer correct to 4 decimal places.\\
(ii) Showing the points you use, calculate the gradient of another chord of the curve which is a closer approximation to the gradient of the curve when $x = 4$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{f540b962-ee6b-409a-a2a1-cd7ad4945514-2_1031_1113_273_499}
\captionsetup{labelformat=empty}
\caption{Fig. 5}
\end{center}
\end{figure}
Fig. 5 shows the graph of $y = 2 ^ { x }$.\\
\hfill \mbox{\textit{OCR MEI C2 Q5 [5]}}