| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Addition & Double Angle Formulae |
| Type | Prove identity with double/compound angles |
| Difficulty | Challenging +1.2 This is a Further Maths question requiring expansion of a binomial, application of De Moivre's theorem, and algebraic manipulation to derive a trigonometric identity. While it involves multiple steps (binomial expansion, using z + 1/z = 2cos θ, equating real parts), the approach is methodical and follows standard techniques taught in FP1. The question guides students by specifying the expansion method, making it more accessible than an unstructured proof. It's harder than average A-level due to being Further Maths content, but straightforward for that level. |
| Spec | 4.02q De Moivre's theorem: multiple angle formulae |
3 By expanding $\left( z ^ { 2 } + \frac { 1 } { z ^ { 2 } } \right) ^ { 3 }$, where $z = \mathrm { e } ^ { \mathrm { i } \theta }$, show that $4 \cos ^ { 3 } 2 \theta = \cos 6 \theta + 3 \cos 2 \theta$.
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q3 [5]}}