| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Simpson's rule application |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard C3 techniques: integration of 1/x (routine), applying Simpson's rule formula (procedural), and simple algebraic manipulation to extract ln 2. All parts are textbook exercises with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.09f Trapezium rule: numerical integration |
\begin{enumerate}[label=(\roman*)]
\item Find, in simplified form, the exact value of $\int_{10}^{20} \frac{60}{x} \, dx$. [2]
\item Use Simpson's rule with two strips to find an approximation to $\int_{10}^{20} \frac{60}{x} \, dx$. [3]
\item Use your answers to parts (i) and (ii) to show that $\ln 2 \approx \frac{25}{36}$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 2010 Q3 [7]}}