| Exam Board | OCR MEI |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2021 |
| Session | November |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiation from First Principles |
| Type | Chord gradient estimation |
| Difficulty | Moderate -0.8 This is a straightforward application of chord gradient calculation using two given points, followed by basic understanding that a closer point gives a better approximation. Part (a) requires simple substitution into (x/4)^(-x) and calculating (y₂-y₁)/(x₂-x₁). Part (b) only requires stating that any x-value closer to 1 (e.g., 1.05 or 1.01) would work. No calculus, proof, or problem-solving insight needed—purely computational with standard first principles concepts. |
| Spec | 1.07a Derivative as gradient: of tangent to curve |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{4.13746\ldots - 4}{1.1 - 1}\) | M1 (1.1a) | Attempt to find gradient; Condone 4.13 or 4.14 for M1 |
| \(1.37\) | A1 (1.1) | Do not penalise more accurate answer \(1.37(46\ldots)\) |
| Answer | Marks | Guidance |
|---|---|---|
| Suitable value | B1 (1.1) | Anything between 1 and 1.1 |
## Question 4:
**Part (a):**
$\frac{4.13746\ldots - 4}{1.1 - 1}$ | M1 (1.1a) | Attempt to find gradient; Condone 4.13 or 4.14 for M1
$1.37$ | A1 (1.1) | Do not penalise more accurate answer $1.37(46\ldots)$
[2 marks]
**Part (b):**
Suitable value | B1 (1.1) | Anything between 1 and 1.1
[1 mark]
---4 The diagram shows points $A$ and $B$ on the curve $y = \left( \frac { x } { 4 } \right) ^ { - x }$.\\
The $x$-coordinate of A is 1 and the $x$-coordinate of B is 1.1 .\\
\includegraphics[max width=\textwidth, alt={}, center]{a0d9573f-8273-4562-a2d3-07f15d9da1af-4_522_707_1758_278}
\begin{enumerate}[label=(\alph*)]
\item Find the gradient of chord AB . Give your answer correct to 2 decimal places.
\item Give the $x$-coordinate of a point C on the curve such that the gradient of chord AC is a better approximation to the gradient of the tangent to the curve at A .
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 3 2021 Q4 [3]}}