AQA Further AS Paper 1 2020 June — Question 1 1 marks

Exam BoardAQA
ModuleFurther AS Paper 1 (Further AS Paper 1)
Year2020
SessionJune
Marks1
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex numbers 2
TypeConvert to exponential/polar form
DifficultyEasy -1.2 This is a straightforward conversion to modulus-argument form requiring only calculation of r = √(1² + 3) = 2 and identifying the argument in the fourth quadrant as -π/3. It's a routine recall question worth 1 mark with multiple choice format, making it easier than average even for Further Maths students.
Spec4.02b Express complex numbers: cartesian and modulus-argument forms
Express the complex number \(1 - i\sqrt{3}\) in modulus-argument form. Tick \((\checkmark)\) one box. [1 mark] \(2\left(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}\right)\) \(2\left(\cos\frac{2\pi}{3} + i\sin\frac{2\pi}{3}\right)\) \(2\left(\cos\left(-\frac{\pi}{3}\right) + i\sin\left(-\frac{\pi}{3}\right)\right)\) \(2\left(\cos\left(-\frac{2\pi}{3}\right) + i\sin\left(-\frac{2\pi}{3}\right)\right)\)
Question 1:
AnswerMarks Guidance
1Ticks correct box. 1.1b
Total1 2�cos�−3�+𝑖𝑖sin�−3��
QMarking instructions AO 
Question 1:
1 | Ticks correct box. | 1.1b | B1 | 𝜋𝜋 𝜋𝜋
Total | 1 | 2�cos�−3�+𝑖𝑖sin�−3��
Q | Marking instructions | AO | Marks | Typical solution
Express the complex number $1 - i\sqrt{3}$ in modulus-argument form.

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

$2\left(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}\right)$

$2\left(\cos\frac{2\pi}{3} + i\sin\frac{2\pi}{3}\right)$

$2\left(\cos\left(-\frac{\pi}{3}\right) + i\sin\left(-\frac{\pi}{3}\right)\right)$

$2\left(\cos\left(-\frac{2\pi}{3}\right) + i\sin\left(-\frac{2\pi}{3}\right)\right)$

\hfill \mbox{\textit{AQA Further AS Paper 1 2020 Q1 [1]}}
This paper (18 questions)
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Q1 1 Q2 1 Q3 1 Q4 5 Q5 4 Q6 2 Q7 4 Q8 8 Q9 8 Q10 8 Q11 3 Q12 2 Q13 9 Q14 7 Q15 4 Q16 4 Q17 4 Q18 5