| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Find stationary point then sketch curve |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question on curve sketching requiring basic differentiation to find a stationary point, simple substitution for coordinates, and routine algebraic manipulation. While it covers multiple skills, each part uses standard techniques with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.02m Graphs of functions: difference between plotting and sketching1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives |
| Answer | Marks | Guidance |
|---|---|---|
| \((0, 0)\) | B1 | Coordinates, must have brackets |
| Answer | Marks | Guidance |
|---|---|---|
| \(0\) | B1 | B0 if more than 1 value given |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{dy}{dx} = 12 - 6\sqrt{x}\) | B1 | allow one coefficient error |
| their \(\frac{dy}{dx} = 0\) | M1 | Must be two terms |
| \(\sqrt{x} = 2\) | M1 | rearrange equation to make \(\sqrt{x}\) or \(x\) the subject |
| \(x = 4\) | A1 | www. A0 if more than one value of \(x\) |
| \((4, 16)\) | A1 | www. Must have brackets |
| Answer | Marks | Guidance |
|---|---|---|
| correct shape of curve | B1 | |
| curve passes through \((4,16)\) and \((9,0)\) and touches/passes through \((0,0)\); may be identified on or adjacent to graph | B1 | FT their stationary point |
| curve in 1st and 4th quadrants only with correct shape, no points in 2nd or 3rd quadrant | B1 |
## Question 9(a):
$(0, 0)$ | **B1** | Coordinates, must have brackets
## Question 9(b):
$0$ | **B1** | B0 if more than 1 value given
## Question 9(c):
$\frac{dy}{dx} = 12 - 6\sqrt{x}$ | B1 | allow one coefficient error
their $\frac{dy}{dx} = 0$ | M1 | Must be two terms
$\sqrt{x} = 2$ | M1 | rearrange equation to make $\sqrt{x}$ or $x$ the subject
$x = 4$ | A1 | www. A0 if more than one value of $x$
$(4, 16)$ | A1 | www. Must have brackets
---
## Question 9(d):
correct shape of curve | B1 |
curve passes through $(4,16)$ and $(9,0)$ and touches/passes through $(0,0)$; may be identified on or adjacent to graph | B1 | FT their stationary point
curve in 1st and 4th quadrants only with correct shape, no points in 2nd or 3rd quadrant | B1 |
---9 The equation of a curve is $y = 12 x - 4 x ^ { \frac { 3 } { 2 } }$.
\begin{enumerate}[label=(\alph*)]
\item State the coordinates of the intersection of the curve with the $y$-axis.
\item Find the value of $y$ when $x = 9$.
\item Determine the coordinates of the stationary point.
\item Sketch the curve, giving the coordinates of the stationary point and of any intercepts with the axes.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2022 Q9 [10]}}