| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find stationary points |
| Difficulty | Standard +0.8 This question requires implicit differentiation (a C4/FP1 topic), algebraic manipulation to find dy/dx, and then analysis of stationary points requiring setting dy/dx = 0 and proving a general result. Part (b) requires insight that numerator = 0 implies x = 0. More demanding than standard implicit differentiation exercises due to the proof element and multi-step reasoning. |
| Spec | 1.07s Parametric and implicit differentiation |
| Answer | Marks | Guidance |
|---|---|---|
| 12 | (a) | e |
| Answer | Marks |
|---|---|
| dx 7 | M1 |
| Answer | Marks |
|---|---|
| [4] | 1.1a |
| Answer | Marks |
|---|---|
| 2.1 | implicit differentation |
| Answer | Marks | Guidance |
|---|---|---|
| 12 | (b) | dy |
| Answer | Marks |
|---|---|
| x(cid:32)0 so all stationary points lie on y-axis | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.2 |
| 2.1 | dy |
Question 12:
12 | (a) | e
p
dy dy (cid:170) dy 6x2 (cid:186)
6x2 (cid:14)3y2 (cid:32)5 (cid:171)(cid:159) (cid:32) (cid:187)
dx dx dx 5(cid:16)3y2
(cid:172) (cid:188)
S
dy dy
when x = 1, y = 2, 6 (cid:14) 12 (cid:32) 5
dx dx
dy 6
(cid:159) (cid:32) (cid:16)
dx 7 | M1
A1
M1
A1
[4] | 1.1a
1.1
1.1
2.1 | implicit differentation
correct
substituting x = 1, y = 2
cao
12 | (b) | dy
(cid:32)0 so 6x2 (cid:32)0
dx
x(cid:32)0 so all stationary points lie on y-axis | B1
E1
[2] | 1.2
2.1 | dy
Substitute (cid:32)0 into their
dx
differentiated expression
Completion of argumentFig. 12 shows the curve $2x^3 + y^3 = 5y$.
\includegraphics{figure_12}
\begin{enumerate}[label=(\alph*)]
\item Find the gradient of the curve $2x^3 + y^3 = 5y$ at the point $(1,2)$, giving your answer in exact form. [4]
\item Show that all the stationary points of the curve lie on the $y$-axis. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 Q12 [6]}}