| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Find curve from gradient |
| Difficulty | Moderate -0.8 This is a straightforward C1 integration question requiring basic power rule application (rewriting 1/x² as x^(-2)), finding the constant using given conditions, and substituting x=2. It's easier than average as it involves only routine integration techniques with no problem-solving insight needed, though the two-part structure and constant determination add minimal complexity beyond pure recall. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx) |
| Answer | Marks |
|---|---|
| \(y = 5x - x^{-1} + C\) | M1 A2 (1,0) |
| Answer | Marks |
|---|---|
| \(7 = 5 - 1 + C\), \(C = 3\) | M1 A1 ft |
| \(x = 2\): \(y = 10 - \frac{1}{2} + 3 = 12\frac{1}{2}\) | M1 A1 |
## Part (a)
$y = 5x - x^{-1} + C$ | M1 A2 (1,0)
## Part (b)
$7 = 5 - 1 + C$, $C = 3$ | M1 A1 ft
$x = 2$: $y = 10 - \frac{1}{2} + 3 = 12\frac{1}{2}$ | M1 A1
**Total: 7 marks**
---$$\frac{dy}{dx} = 5 + \frac{1}{x^2}.$$
\begin{enumerate}[label=(\alph*)]
\item Use integration to find $y$ in terms of $x$. [3]
\item Given that $y = 7$ when $x = 1$, find the value of $y$ at $x = 2$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q6 [7]}}