| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Determine nature of stationary points |
| Difficulty | Moderate -0.8 This is a straightforward calculus question requiring standard differentiation of power functions, finding stationary points by setting dy/dx = 0, and using the second derivative test. All techniques are routine AS-level procedures with no problem-solving insight needed, making it easier than average but not trivial due to the algebraic manipulation required. |
| Spec | 1.07d Second derivatives: d^2y/dx^2 notation1.07l Derivative of ln(x): and related functions1.07n Stationary points: find maxima, minima using derivatives1.07p Points of inflection: using second derivative |
| Answer | Marks | Guidance |
|---|---|---|
| 10 | (i) | (A) |
| Answer | Marks |
|---|---|
| x3 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | One term correct |
| (B) | kx ‒ 3 ‒ 1 |
| Answer | Marks |
|---|---|
| x4 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | dy |
| Answer | Marks | Guidance |
|---|---|---|
| 10 | (ii) | dy |
| Answer | Marks |
|---|---|
| [96 ] which is positive so (½, 12) is a minimum | M1 |
| Answer | Marks |
|---|---|
| [5] | 2.1 |
| Answer | Marks |
|---|---|
| 2.4 | FT their x; dependent on (i)(B) |
Question 10:
10 | (i) | (A) | 2
16 oe
x3 | M1
A1
[2] | 1.1
1.1 | One term correct
(B) | kx ‒ 3 ‒ 1
6
6x ‒ 4 or
x4 | M1
A1
[2] | 1.1
1.1 | dy
FT their for M1
dx
10 | (ii) | dy
their = 0
dx
x = ½
y = 12
substitution of their x = ½ in their second
derivative
[96 ] which is positive so (½, 12) is a minimum | M1
A1
A1
M1
A1
[5] | 2.1
1.1
1.1
1.1
2.4 | FT their x; dependent on (i)(B)
involving x
www\begin{enumerate}[label=(\roman*)]
\item A curve has equation $y = 16x + \frac{1}{x}$. Find
\begin{enumerate}[label=(\Alph*)]
\item $\frac{dy}{dx}$, [2]
\item $\frac{d^2y}{dx^2}$. [2]
\end{enumerate}
\item Hence
\begin{itemize}
\item find the coordinates of the stationary point,
\item determine the nature of the stationary point. [5]
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2018 Q10 [9]}}