| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Integration with algebraic manipulation |
| Difficulty | Standard +0.3 This is a straightforward C2 question testing expansion of brackets with fractional powers, algebraic manipulation, and integration using the power rule. Part (a) requires simple substitution and solving, part (b) is routine algebraic expansion, and part (c) applies standard integration techniques to the simplified form. All steps are mechanical with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
Given that $\text{f}(x) = (2x^{\frac{1}{3}} - 3x^{-\frac{1}{2}})^2 + 5$, $x > 0$,
\begin{enumerate}[label=(\alph*)]
\item find, to 3 significant figures, the value of x for which f(x) = 5. [3]
\item Show that f(x) may be written in the form $Ax^{\frac{2}{3}} + \frac{B}{x} + C$, where A, B and C are constants to be found. [3]
\item Hence evaluate $\int_1^2 \text{f}(x) \, \text{dx}$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [11]}}