| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Session | Specimen |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Arc length of parametric curve |
| Difficulty | Challenging +1.2 This is a standard arc length question for a cycloid using the parametric formula. While it requires knowing the arc length formula, computing dx/dt and dy/dt, and simplifying the resulting trigonometric expression using identities (notably the half-angle formula), these are well-practiced techniques in FP3. The integration itself is straightforward once simplified. It's moderately harder than average due to the algebraic manipulation required, but follows a predictable template for parametric arc length problems. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.08d Evaluate definite integrals: between limits |
\includegraphics{figure_1}
The parametric equations of the curve $C$ shown in Figure 1 are
$$x = a(t - \sin t), \quad y = a(1 - \cos t), \quad 0 \leq t \leq 2\pi$$
Find, by using integration, the length of $C$.
(Total 6 marks)
\hfill \mbox{\textit{Edexcel FP3 Q3}}