2024 PEARSON EDEXCEL GCE A LEVEL FURTHER MATHEMATICS 9FMO/02 PAPER 2 MERGED QUESTION
PAPER AND MARKING SCHEME
surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 2: Core Pure Mathematics 2
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
P75683A
©2024 Pearson Education Ltd.
F:1/1/1/1/1/
,1. (a) Using the definition of sinh x in terms of exponentials, prove that
4 sinh3 x + 3sinh x sinh 3x
DO NOT WRITE IN THIS AREA
(2)
(b) Hence solve the equation
sinh 3x = 19 sinh x
giving your answers as simplified natural logarithms where appropriate.
(5)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
2
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, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
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Question 1 continued
(Total for Question 1 is 7 marks)
3
Turn over
, 3− x
2. f(x) = tanh−1 6 + x x <3
2
DO NOT WRITE IN THIS AREA
(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)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
■■■■
PAPER AND MARKING SCHEME
surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 2: Core Pure Mathematics 2
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
P75683A
©2024 Pearson Education Ltd.
F:1/1/1/1/1/
,1. (a) Using the definition of sinh x in terms of exponentials, prove that
4 sinh3 x + 3sinh x sinh 3x
DO NOT WRITE IN THIS AREA
(2)
(b) Hence solve the equation
sinh 3x = 19 sinh x
giving your answers as simplified natural logarithms where appropriate.
(5)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
2
■■■■
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
(Total for Question 1 is 7 marks)
3
Turn over
, 3− x
2. f(x) = tanh−1 6 + x x <3
2
DO NOT WRITE IN THIS AREA
(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)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
■■■■
