| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule with stated number of strips |
| Difficulty | Moderate -0.3 This is a straightforward application of the trapezium rule with clearly specified intervals and ordinates, followed by a standard concavity reasoning question. The calculation is routine with no algebraic manipulation required, though it involves more arithmetic than the most basic questions. Slightly easier than average due to its mechanical nature. |
| Spec | 1.09f Trapezium rule: numerical integration |
3.\\
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The diagram shows the curve with equation $y = \frac { 4 x } { ( x + 1 ) ^ { 2 } }$.\\
The shaded region is bounded by the curve, the $x$-axis and the line $x = 1$.\\
(i) Use the trapezium rule with four intervals, each of width 0.25 , to find an estimate for the area of the shaded region.\\
(ii) State, with a reason, whether your answer to part (a) is an under-estimate or an over-estimate of the true area.\\
\hfill \mbox{\textit{OCR C2 Q3 [7]}}