| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule with stated number of strips |
| Difficulty | Moderate -0.3 Part (a) is a standard trapezium rule application with clear ordinates and straightforward arithmetic—routine C2 content. Part (b) tests understanding of transformations but is direct recall of how horizontal stretches affect function notation. Both parts are textbook-standard with no problem-solving required, making this slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.09f Trapezium rule: numerical integration |
\begin{enumerate}[label=(\alph*)]
\item Use the trapezium rule with four ordinates (three strips) to find an approximate value for $\int_0^6 \sqrt{x^3 + 1} dx$, giving your answer to four significant figures. [4]
\item The curve with equation $y = \sqrt{x^3 + 1}$ is stretched parallel to the $x$-axis with scale factor $\frac{1}{2}$ to give the curve with equation $y = f(x)$. Write down an expression for $f(x)$. [2]
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2009 Q4 [6]}}