Edexcel FP2 2003 June — Question 2 10 marks

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2003
SessionJune
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex numbers 2
TypeSolve equations using trigonometric identities
DifficultyChallenging +1.2 This is a standard Further Maths FP2 question testing de Moivre's theorem application. Part (a) requires expanding (cos θ + i sin θ)^5 using binomial theorem and equating real parts—a routine technique. Part (b) involves recognizing that cos 5θ = -1 leads to specific angles, then substituting back—methodical but not requiring novel insight. The multi-step nature and Further Maths content places it above average difficulty, but it's a textbook exercise type.
Spec4.02q De Moivre's theorem: multiple angle formulae

2. (a) Use de Moivre's theorem to show that $$\cos 5 \theta = 16 \cos ^ { 5 } \theta - 20 \cos ^ { 3 } \theta + 5 \cos \theta$$ (b) Hence find 3 distinct solutions of the equation \(16 x ^ { 5 } - 20 x ^ { 3 } + 5 x + 1 = 0\), giving your answers to 3 decimal places where appropriate.

2. (a) Use de Moivre's theorem to show that

$$\cos 5 \theta = 16 \cos ^ { 5 } \theta - 20 \cos ^ { 3 } \theta + 5 \cos \theta$$

(b) Hence find 3 distinct solutions of the equation $16 x ^ { 5 } - 20 x ^ { 3 } + 5 x + 1 = 0$, giving your answers to 3 decimal places where appropriate.\\

\hfill \mbox{\textit{Edexcel FP2 2003 Q2 [10]}}