| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | 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 only basic power rule integration (rewriting surds as fractional powers) and finding a constant using a boundary condition. Part (a) is simple substitution/simplification. No problem-solving insight needed, just routine technique application. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits |
The curve $C$ with equation $y = f(x)$ is such that
$$\frac{dy}{dx} = 3\sqrt{x} + \frac{12}{\sqrt{x}}, \quad x > 0$$
(a) Show that, when $x = 8$, the exact value of $\frac{dy}{dx}$ is $9\sqrt{2}$.
(3)
The curve $C$ passes through the point $(4, 30)$.
(b) Using integration, find $f(x)$.
(6)\begin{enumerate}
\item The curve $C$ with equation $y = \mathrm { f } ( x )$ is such that
\end{enumerate}
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 \sqrt { } x + \frac { 12 } { \sqrt { } x } , \quad x > 0$$
(a) Show that, when $x = 8$, the exact value of $\frac { \mathrm { d } y } { \mathrm {~d} x }$ is $9 \sqrt { } 2$.
The curve $C$ passes through the point $( 4,30 )$.\\
(b) Using integration, find $\mathrm { f } ( x )$.\\
\hfill \mbox{\textit{Edexcel C1 Q4 [9]}}