| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas Between Curves |
| Type | Two Curves Intersection Area |
| Difficulty | Moderate -0.3 This is a straightforward C2 integration question requiring verification of intersection points by substitution (routine algebra) and finding area between curves using a standard formula. The integration itself involves basic power rules (x^{-2} and x^2), and the limits are given. Slightly easier than average due to the verification part being trivial and the integration being mechanical with no tricky algebraic manipulation required. |
| Spec | 1.08e Area between curve and x-axis: using definite integrals1.08f Area between two curves: using integration |
4\\
\includegraphics[max width=\textwidth, alt={}, center]{608720b6-5b18-45e9-8838-c94b347ab3b7-2_547_511_1813_817}
The diagram shows a sketch of parts of the curves $y = \frac { 16 } { x ^ { 2 } }$ and $y = 17 - x ^ { 2 }$.\\
(i) Verify that these curves intersect at the points $( 1,16 )$ and $( 4,1 )$.\\
(ii) Calculate the exact area of the shaded region between the curves.
\hfill \mbox{\textit{OCR C2 2005 Q4 [8]}}