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Core Pure Mathematics

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  • Core Pure Mathematics
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  • PEARSON (PEARSON)

Given that z1 = 3cos   π3 + isin   π3  z = 2cos12π  − isin12π  (a) write down the exact value of (i) | z1z2 | (ii) arg (z1z2) (2) Given that w = z1z2 and that arg (wn) = ...

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  • 3 mei 2022
  • 32
  • 2021/2022
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  • given that z1 3cos   π3 isin   π3  z 2cos12π  − isin12π  a write down the exact value of i | z1z2 | ii arg z1z2 2 given that w z1z2 and that

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  • PEARSON (PEARSON)
  • Core Pure Mathematics
  • Core Pure Mathematics
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Please check the examination details below before entering your candidate information
Candidate surname Other names


Centre Number Candidate Number
Pearson Edexcel
Level 3 GCE
Time 1 hour 30 minutes
Paper
reference 9FM0/02
Further Mathematics
Advanced
PAPER 2: Core Pure Mathematics 2


You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator


Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for algebraic manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball-point pen.
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill in the boxes at the top of this page with your name,
centre number and candidate number.
• labelled.
Answer all questions and ensure that your answers to parts of questions are clearly

• Answer the questions in the spaces provided
– there may be more space than you need.
• You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 9 questions in this question paper. The total mark for this paper is 75.
• – use this asfora guide
The marks each question are shown in brackets
as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
Try to answer every question.
• Check your answers if you have time at the end.
• Good luck with your examination. Turn over



*P66797A0132*
P66797A
©2021 Pearson Education Ltd.

1/1/1/1/1/

,1. Given that
  π  π
z1 = 3  cos   + isin   
  3  3 
 π  π 
z2 = 2  cos   − isin   
  12   12  

(a) write down the exact value of
(i) | z1z2 |
(ii) arg (z1z2)
(2)
Given that w = z1z2 and that arg (w n) = 0 , where n  +
(b) determine
(i) the smallest positive value of n
(ii) the corresponding value of | w n |
(3)
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2
*P66797A0232*

,Question 1 continued
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(Total for Question 1 is 5 marks)

3
*P66797A0332* Turn over

,  4 −2
2. A= 
5 3

The matrix A represents the linear transformation M.
Prove that, for the linear transformation M, there are no invariant lines.
(5)
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4
*P66797A0432*

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