| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule accuracy improvement explanation |
| Difficulty | Moderate -0.8 This is a straightforward application of the trapezium rule with clear intervals and a simple function to evaluate. Part (i) requires only substitution into the standard formula with no algebraic manipulation, while part (ii) tests basic understanding that more intervals improve accuracy. This is below average difficulty as it's purely procedural with no problem-solving or conceptual challenges. |
| Spec | 1.09f Trapezium rule: numerical integration |
2.\\
\includegraphics[max width=\textwidth, alt={}, center]{27703044-8bb3-4809-9454-ae6774fec060-1_485_808_973_520}
The diagram shows the curve with equation $y = \sqrt { 4 x - 1 }$.\\
(i) Use the trapezium rule with four intervals of equal width to estimate the area of the shaded region bounded by the curve, the $x$-axis and the lines $x = 1$ and $x = 3$.\\
(ii) Explain briefly how you could use the trapezium rule to obtain a more accurate estimate of the area of the shaded region.\\
\hfill \mbox{\textit{OCR C2 Q2 [5]}}