| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| 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 introduction to differentiation through chord gradients. Part (i) requires basic coordinate calculation, part (ii) tests understanding that closer points give better approximations (simple conceptual check), and part (iii) is routine differentiation of a power function. All steps are standard textbook exercises with no problem-solving required, making it easier than average but not trivial due to the multi-part structure. |
| Spec | 1.07a Derivative as gradient: of tangent to curve1.07b Gradient as rate of change: dy/dx notation1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks |
|---|---|
| 9 | (i) −0.93, -0.930, -0.9297… |
| Answer | Marks |
|---|---|
| (iii) y′ = −8/x3 , gradient = −1 | 2 |
| Answer | Marks |
|---|---|
| M1A1 | M1 for grad = (1 – their y )/(2 − 2.1) |
| Answer | Marks |
|---|---|
| don’t allow 1.9 recurring | 5 |
Question 9:
9 | (i) −0.93, -0.930, -0.9297…
(iiii)) answer strictly between 1.91
2 or 2 and 2.1
(iii) y′ = −8/x3 , gradient = −1 | 2
B1
M1A1 | M1 for grad = (1 – their y )/(2 − 2.1)
B
if M0, SC1 for 0.93
don’t allow 1.9 recurring | 5A is the point $(2, 1)$ on the curve $y = \frac{4}{x^2}$.
B is the point on the same curve with $x$-coordinate $2.1$.
\begin{enumerate}[label=(\roman*)]
\item Calculate the gradient of the chord AB of the curve. Give your answer correct to 2 decimal places. [2]
\item Give the $x$-coordinate of a point C on the curve for which the gradient of chord AC is a better approximation to the gradient of the curve at A. [1]
\item Use calculus to find the gradient of the curve at A. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 Q9 [5]}}