2024 Pearson Edexcel GCE In A Level Further Mathematics (9FM0) Paper 02 Pure Mathematics question paper and marking scheme (merged)

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Centre Number Candidate Number




Pearson Edexcel Level 3 GCE
Monday 3 June 2024
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/02
Further Mathematics
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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.

• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,

• Answer
centre number and candidate number.
all questions and ensure that your answers to parts of questions are

• Answer
clearly labelled.
the questions in the spaces provided

• You
– there may be more space than you need.
should show sufficient working to make your methods clear.

•Information
Answers without working may not gain full credit.
Inexact answers should be given to three significant figures unless otherwise stated.

•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.

• – use this asfora guide
are 9 questions in this question paper. The total mark for this paper is 75.
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. Turn over

,1. (a) Using the definition of sinh x in terms of exponentials, prove that

4 sinh3 x  3sinh x  sinh 3x




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(2)
(b) Hence solve the equation

sinh 3x  19 sinh x

giving your answers as simplified natural logarithms where appropriate.
(5)




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Question 1 continued




(Total for Question 1 is 7 marks)



Turn over
3

, 3 x
2. f(x) = tanh1  6  x  x <3
  2
 




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(a) Show that

1
f ′(x) = –
2x  3
(4)
(b) Hence determine f ′′(x)
(1)
(c) Hence show that the Maclaurin series for f(x), up to and including the term in x2, is

ln p  qx  rx2

where p, q and r are constants to be determined.
(3)




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