| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Basic power rule differentiation |
| Difficulty | Easy -1.2 This is a straightforward differentiation and integration question requiring only basic power rule application with no chain rule despite the topic label. Both parts are routine A-level exercises with standard techniques—rewriting 5/x² as 5x⁻², applying power rule term-by-term, and reversing the process for integration. No problem-solving or conceptual insight required. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(3x^2 - 3 - \frac{10}{x^3}\) | M1 | Allow M1 for \(\pm\frac{k}{x^3}\) |
| B1 | B1 for either \(3x^2\) or \(-3\) | |
| A1 | A1 for all correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(2x^3 + \frac{1}{x^2}\) or \(2x^3 + x^{-2}\) | M1 | Allow M1 for \(ax^3\) or \(\pm\frac{b}{x^2}\) \((a,b \neq 0)\) |
| A1 | A1 for both terms correct. Allow unsimplified form, e.g. \(-\frac{2}{-2x^2}\) | |
| \(+ c\) | B1 |
## Question 1:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $3x^2 - 3 - \frac{10}{x^3}$ | M1 | Allow M1 for $\pm\frac{k}{x^3}$ |
| | B1 | B1 for either $3x^2$ or $-3$ |
| | A1 | A1 for all correct |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2x^3 + \frac{1}{x^2}$ or $2x^3 + x^{-2}$ | M1 | Allow M1 for $ax^3$ or $\pm\frac{b}{x^2}$ $(a,b \neq 0)$ |
| | A1 | A1 for both terms correct. Allow unsimplified form, e.g. $-\frac{2}{-2x^2}$ |
| $+ c$ | B1 | |
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\begin{enumerate}[label=(\alph*)]
\item Find $\frac { \mathrm { d } } { \mathrm { d } x } \left( x ^ { 3 } - 3 x + \frac { 5 } { x ^ { 2 } } \right)$.
\item Find $\int \left( 6 x ^ { 2 } - \frac { 2 } { x ^ { 3 } } \right) \mathrm { d } x$.
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q1 [6]}}