A-level Pearson Edexcel Level 3 GCE AL Further Mathematics (9FM0) Paper 01 Core Pure Mathematics 1 SUMMER EXAM QUESTION PAPER (AUTHENTIC MARKING SCHEME ATTACHED)

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Pearson Edexcel Level 3 GCE
reference 9FM0/01
Paper
Time 1 hour 30 minutes
Further Mathematics  


Advanced
PAPER 1: Core Pure Mathematics 1

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



A-level Pearson Edexcel Level 3 GCE
AL Further Mathematics (9FM0)
Paper 01 Core Pure Mathematics 1 SUMMER EXAM
QUESTION PAPER
(AUTHENTIC MARKING SCHEME ATTACHED)


Turn over


P71776A *P71776A0132*
©2022 Pearson Education Ltd.
Q:1/1/1/1/

,1. f(z) = z3 + az + 52 where a is a real constant

Given that 2 – 3i is a root of the equation f(z) = 0

(a) write down the other complex root.
(1)

(b) Hence

(i) solve completely f(z) = 0
(ii) determine the value of a
(4)

(c) Show all the roots of the equation f(z) = 0 on a single Argand diagram.
(1)
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2
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,Question 1 continued
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(Total for Question 1 is 6 marks)
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, 2. In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.


Determine the values of x for which

64 cosh4 x – 64 cosh2 x – 9 = 0

Give your answers in the form q ln 2 where q is rational and in simplest form.
(4)
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4
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