OCR C2 — Question 4 7 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNumerical integration
TypeTrapezium rule with stated number of strips
DifficultyModerate -0.8 This is a straightforward application of the trapezium rule with clearly specified strips (n=4, interval [0,2]), followed by a simple volume calculation using scaling. The function is easy to evaluate, and both parts require only routine procedural work with no problem-solving insight needed.
Spec1.09f Trapezium rule: numerical integration

4. \includegraphics[max width=\textwidth, alt={}, center]{e5d62032-84ad-4e0b-9b72-ccfd8f4dbac8-2_465_844_246_516} The diagram shows the curve with equation \(y = \frac { 1 } { x ^ { 2 } + 1 }\).
The shaded region \(R\) is bounded by the curve, the coordinate axes and the line \(x = 2\).
  1. Use the trapezium rule with four strips of equal width to estimate the area of \(R\). The cross-section of a support for a bookshelf is modelled by \(R\) with 1 unit on each axis representing 8 cm . Given that the support is 2 cm thick,
  2. find an estimate for the volume of the support.

4.\\
\includegraphics[max width=\textwidth, alt={}, center]{e5d62032-84ad-4e0b-9b72-ccfd8f4dbac8-2_465_844_246_516}

The diagram shows the curve with equation $y = \frac { 1 } { x ^ { 2 } + 1 }$.\\
The shaded region $R$ is bounded by the curve, the coordinate axes and the line $x = 2$.\\
(i) Use the trapezium rule with four strips of equal width to estimate the area of $R$.

The cross-section of a support for a bookshelf is modelled by $R$ with 1 unit on each axis representing 8 cm . Given that the support is 2 cm thick,\\
(ii) find an estimate for the volume of the support.\\

\hfill \mbox{\textit{OCR C2  Q4 [7]}}