| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Integration with algebraic manipulation |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing basic index laws, algebraic expansion, and integration. Part (a) is trivial recall, part (b) is simple binomial expansion, and parts (c)-(d) follow directly from the expansion using standard integration rules. The 'hence' structure guides students through each step with minimal problem-solving required, making this easier than average for A-level. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits |
\begin{enumerate}[label=(\alph*)]
\item Write down the value of $n$ given that $\frac{1}{x^3} = x^n$. [1]
\item Expand $\left(1 + \frac{3}{x^2}\right)^2$. [2]
\item Hence find $\int \left(1 + \frac{3}{x^2}\right)^2 dx$. [3]
\item Hence find the exact value of $\int_1^3 \left(1 + \frac{3}{x^2}\right)^2 dx$. [2]
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2009 Q2 [8]}}