Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
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)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P71776A0232*
,Question 1 continued
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(Total for Question 1 is 6 marks)
3
*P71776A0332* Turn over
, 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)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4
*P71776A0432*
Candidate surname Other names
Centre Number Candidate Number
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)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P71776A0232*
,Question 1 continued
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(Total for Question 1 is 6 marks)
3
*P71776A0332* Turn over
, 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)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4
*P71776A0432*
