| Exam Board | OCR |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Inverse function graphs and properties |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring verification of a given point by substitution, then differentiation of inverse trig functions using standard formulas. The derivatives of arcsin and arccos are bookwork, and evaluating them at the given point involves simple arithmetic with no conceptual challenges. |
| Spec | 1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs1.07l Derivative of ln(x): and related functions |
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The diagram shows parts of the curves with equations $y = \cos ^ { - 1 } x$ and $y = \frac { 1 } { 2 } \sin ^ { - 1 } x$, and their point of intersection $P$.\\
(i) Verify that the coordinates of $P$ are $\left( \frac { 1 } { 2 } \sqrt { 3 } , \frac { 1 } { 6 } \pi \right)$.\\
(ii) Find the gradient of each curve at $P$.
\hfill \mbox{\textit{OCR FP2 2008 Q2 [5]}}