| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2005 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Basic power rule differentiation |
| Difficulty | Easy -1.2 This is a straightforward C1 question requiring only basic differentiation and integration rules (power rule). Both parts are routine textbook exercises with no problem-solving required—students simply apply standard formulas to each term independently. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{dy}{dx} = 6 + 8x^{-3}\) | M1, A1 (2) | \(x^n \to x^{n-1}\); both terms correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\int(6x - 4x^{-2})dx = \frac{6x^2}{2} + 4x^{-1} + c\) | M1 A1 A1 (3) | 1st A1 for one correct term \(\frac{6x^2}{2}\) or \(4x^{-1}\); 2nd A1 for all 3 terms correct in one line |
## Question 2:
### Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{dy}{dx} = 6 + 8x^{-3}$ | M1, A1 (2) | $x^n \to x^{n-1}$; both terms correct |
### Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\int(6x - 4x^{-2})dx = \frac{6x^2}{2} + 4x^{-1} + c$ | M1 A1 A1 (3) | 1st A1 for one correct term $\frac{6x^2}{2}$ or $4x^{-1}$; 2nd A1 for all 3 terms correct in one line |
---Given that $y = 6 x - \frac { 4 } { x ^ { 2 } } , x \neq 0$,
\begin{enumerate}[label=(\alph*)]
\item find $\frac { \mathrm { d } y } { \mathrm {~d} x }$,
\item find $\int y \mathrm {~d} x$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2005 Q2 [5]}}