OCR Further Pure Core 1 2021 November — Question 5 4 marks

Exam BoardOCR
ModuleFurther Pure Core 1 (Further Pure Core 1)
Year2021
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex numbers 2
TypeDe Moivre to derive trigonometric identities
DifficultyStandard +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.
Spec4.02q 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]

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]}}