AQA Further Paper 1 2022 June — Question 2 1 marks

Exam BoardAQA
ModuleFurther Paper 1 (Further Paper 1)
Year2022
SessionJune
Marks1
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex numbers 2
TypeComplex number arithmetic and simplification
DifficultyModerate -0.8 This is a straightforward application of De Moivre's theorem for division of complex numbers in polar form: divide moduli (both 1) and subtract arguments. The calculation is 6π/13 - (-2π/13) = 8π/13, making it a routine one-step problem with multiple choice format, easier than average but requiring knowledge of Further Maths content.
Spec4.02e Arithmetic of complex numbers: add, subtract, multiply, divide

Simplify $$\frac{\cos\left(\frac{6\pi}{13}\right) + i\sin\left(\frac{6\pi}{13}\right)}{\cos\left(\frac{2\pi}{13}\right) - i\sin\left(\frac{2\pi}{13}\right)}$$ Tick (\(\checkmark\)) one box. [1 mark] \(\cos\left(\frac{8\pi}{13}\right) + i\sin\left(\frac{8\pi}{13}\right)\) \(\square\) \(\cos\left(\frac{8\pi}{13}\right) - i\sin\left(\frac{8\pi}{13}\right)\) \(\square\) \(\cos\left(\frac{4\pi}{13}\right) + i\sin\left(\frac{4\pi}{13}\right)\) \(\square\) \(\cos\left(\frac{4\pi}{13}\right) - i\sin\left(\frac{4\pi}{13}\right)\) \(\square\)

Question 2:
AnswerMarks Guidance
2Ticks correct answer 1.1b
cos +i sin 
13 13
AnswerMarks Guidance
Total1
QMarking instructions AO
Question 2:
2 | Ticks correct answer | 1.1b | B1 | 8π 8π
cos +i sin 
13 13
Total | 1
Q | Marking instructions | AO | Marks | Typical solution
Simplify
$$\frac{\cos\left(\frac{6\pi}{13}\right) + i\sin\left(\frac{6\pi}{13}\right)}{\cos\left(\frac{2\pi}{13}\right) - i\sin\left(\frac{2\pi}{13}\right)}$$

Tick ($\checkmark$) one box.
[1 mark]

$\cos\left(\frac{8\pi}{13}\right) + i\sin\left(\frac{8\pi}{13}\right)$ $\square$

$\cos\left(\frac{8\pi}{13}\right) - i\sin\left(\frac{8\pi}{13}\right)$ $\square$

$\cos\left(\frac{4\pi}{13}\right) + i\sin\left(\frac{4\pi}{13}\right)$ $\square$

$\cos\left(\frac{4\pi}{13}\right) - i\sin\left(\frac{4\pi}{13}\right)$ $\square$

\hfill \mbox{\textit{AQA Further Paper 1 2022 Q2 [1]}}