| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | De Moivre to derive trigonometric identities |
| Difficulty | Standard +0.8 This is a Further Maths question requiring application of de Moivre's theorem to derive a multiple angle identity. While the technique is standard for FP1 students (expressing sin³θ using exponentials, expanding, and comparing coefficients), it involves several algebraic steps and careful manipulation of complex exponentials. The 4-mark allocation and need for systematic working place it moderately above average difficulty. |
| Spec | 4.02q De Moivre's theorem: multiple angle formulae |
Use de Moivre's theorem to find the constants $A$, $B$ and $C$ in the identity $\sin^3 \theta \equiv A \sin \theta + B \sin 3\theta + C \sin 5\theta$. [4]
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q5 [4]}}