| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Find stationary point then sketch curve |
| Difficulty | Standard +0.3 This is a standard calculus question requiring differentiation to find stationary points, second derivative test for nature, and third derivative for inflection point. While it involves a quartic polynomial requiring some algebraic manipulation and factorization, the techniques are routine A-level methods with no novel problem-solving required. The 12-mark allocation reflects computational length rather than conceptual difficulty, placing it slightly above average. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.07n Stationary points: find maxima, minima using derivatives1.07p Points of inflection: using second derivative |
| Answer | Marks | Guidance |
|---|---|---|
| 16 | (b) | M1 |
| Answer | Marks |
|---|---|
| A1 | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | curve with a minimum in 3rd quadrant and stationary point of |
| Answer | Marks | Guidance |
|---|---|---|
| x | 0 | (½) |
| Answer | Marks | Guidance |
|---|---|---|
| 𝑑𝑥 | 12 | (0) |
| x | 0 | (½) |
| y | ‒6 | (−3.875) |
| x | 0 | (½) |
| Answer | Marks | Guidance |
|---|---|---|
| 𝑑𝑥² | ‒42 | (0) |
Question 16:
16 | (b) | M1
B1
A1 | 1.1
1.1
1.1 | curve with a minimum in 3rd quadrant and stationary point of
inflection in 4th quadrant and no other stationary points
(0, ‒6) identified as y-intercept (intercept must be below the x-axis
and above ‒20)
correct curve with intercepts at (‒a,0) and (b,0),
where ‒3 < a < ‒2.6 and 0.8 < b < 1.2;
minimum at (‒2, y) where ‒90 < y < ‒80 and
inflection for 0 < x < 1 and y is between the x-axis and the
y-intercept
[3]
x | 0 | (½) | 1
𝑑𝑦
𝑑𝑥 | 12 | (0) | 18
x | 0 | (½) | 1
y | ‒6 | (−3.875) | ‒1
x | 0 | (½) | 1
𝑑²𝑦
𝑑𝑥² | ‒42 | (0) | 78
PMT
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information using our Expression of Interest form.
Please get in touch if you want to discuss the accessibility of resources we offer to support you in delivering our qualifications.The equation of a curve is
$$y = 6x^4 + 8x^3 - 21x^2 + 12x - 6.$$
\begin{enumerate}[label=(\alph*)]
\item In this question you must show detailed reasoning.
Determine
\begin{itemize}
\item The coordinates of the stationary points on the curve.
\item The nature of the stationary points on the curve.
\item The $x$-coordinate of the non-stationary point of inflection on the curve.
\end{itemize}
[12]
\item On the axes in the Printed Answer Booklet, sketch the curve whose equation is
$$y = 6x^4 + 8x^3 - 21x^2 + 12x - 6.$$
[3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2022 Q16 [15]}}