Pearson Edexcel Level 3 GCE Further Mathematics Advanced PAPER 2: Core Pure Mathematics 2 QP
JUNE 2024
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.
• The
are 9 questions in this question paper. The total mark for this paper is 75.
– use this asfor
marks each as
a guide question
to how are
muchshown
timeintobrackets
spend on each question.
• Read
Advice 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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2
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Question 1 continued
(Total for Question 1 is 7 marks)
3
Turn over
, 3 x
2. f(x) = tanh1 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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