| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2004 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Polar coordinates |
| Type | Arc length of polar curve |
| Difficulty | Standard +0.8 This question requires knowledge of the polar arc length formula (a Further Maths topic), application to an exponential spiral, and integration involving √(1 + 1/25) as a constant factor. While the integration itself is straightforward once set up, the formula is non-standard at A-level and requires careful application. The sketching adds minimal difficulty. This is moderately challenging for Further Maths students but routine once the formula is known. |
| Spec | 4.09b Sketch polar curves: r = f(theta)4.09c Area enclosed: by polar curve |
4 The curve $C$ has polar equation
$$r = \mathrm { e } ^ { \frac { 1 } { 5 } \theta } , \quad 0 \leqslant \theta \leqslant \frac { 3 } { 2 } \pi$$
(i) Draw a sketch of $C$.\\
(ii) Find the length of $C$, correct to 3 significant figures.
\hfill \mbox{\textit{CAIE FP1 2004 Q4 [6]}}