| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Find stationary points coordinates |
| Difficulty | Moderate -0.8 This is a straightforward application of basic differentiation and finding stationary points. Part (i) requires only routine polynomial differentiation using the power rule, and part (ii) involves setting the derivative equal to zero and solving a simple quadratic equation. Both steps are standard textbook exercises with no problem-solving insight required, making it easier than average. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(3x^2 - 12x - 15\) | 2 | M1 if one term incorrect or an extra term is included |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Their \(\frac{dy}{dx} = 0\) s.o.i. | M1 | |
| \(x = 5\) | B1 | |
| \(x = -1\) | B1 |
## Question 4:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $3x^2 - 12x - 15$ | **2** | **M1** if one term incorrect or an extra term is included |
---
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Their $\frac{dy}{dx} = 0$ s.o.i. | **M1** | |
| $x = 5$ | **B1** | |
| $x = -1$ | **B1** | |
---4 (i) Differentiate $x ^ { 3 } - 6 x ^ { 2 } - 15 x + 50$.\\
(ii) Hence find the $x$-coordinates of the stationary points on the curve $y = x ^ { 3 } - 6 x ^ { 2 } - 15 x + 50$.
\hfill \mbox{\textit{OCR MEI C2 Q4 [5]}}