| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Find curve equation from derivative (straightforward integration + point) |
| Difficulty | Moderate -0.8 This is a straightforward C1 integration question requiring basic manipulation of surds (part a) and standard integration of power functions (part b). The derivative is already in a form ready to integrate using x^(1/2) and x^(-1/2), requiring only knowledge of the power rule for integration and using a boundary condition to find the constant. This is easier than average as it's purely procedural with no problem-solving or insight required. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
The curve $C$ with equation $y = f(x)$ is such that
$$\frac{dy}{dx} = 3\sqrt{x} + \frac{12}{\sqrt{x}}, \quad x > 0.$$
\begin{enumerate}[label=(\alph*)]
\item Show that, when $x = 8$, the exact value of $\frac{dy}{dx}$ is $9\sqrt{2}$. [3]
\end{enumerate}
The curve $C$ passes through the point $(4, 30)$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Using integration, find $f(x)$. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q36 [9]}}