| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Find curve from gradient |
| Difficulty | Moderate -0.8 This is a straightforward C1 integration question requiring algebraic manipulation (expanding and simplifying with fractional powers) followed by routine integration using the power rule and finding a constant using boundary conditions. All steps are standard textbook procedures with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.08b Integrate x^n: where n != -1 and sums1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx) |
\begin{enumerate}[label=(\alph*)]
\item Show that $\frac{(3 - \sqrt{x})^2}{\sqrt{x}}$ can be written as $9x^{-\frac{1}{2}} - 6 + x^{\frac{1}{2}}$. [2]
\end{enumerate}
Given that $\frac{dy}{dx} = \frac{(3 - \sqrt{x})^2}{\sqrt{x}}$, $x > 0$, and that $y = \frac{2}{3}$ at $x = 1$,
\begin{enumerate}[label=(\alph*)]
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\item find $y$ in terms of $x$. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q7 [8]}}