Please check the examination details below before entering your candidate
information
Candidate surname Other names
Centre Candidate
Number Number
Pearson Edexcel Level 3
GCE
Monday 5 June 2023
Paper
Afternoon (Time: 1 hour 30
minutes) referenc
e
9FM0/02
Further Mathematics
Advanced
PAPER 2: Core Pure
Mathematics 2
You must have: Total
Mathematical Formulae and Statistical Tables (Green), Marks
calculator
Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for symbolic algebraic
manipulation, differentiation and integration, or have retrievable
mathematical formulae stored in them.
Instructions
•• Use black ink or ball-point
• 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
pen. number and candidate number.
• Answer
centre
all questions and ensure that your answers to parts of questions are
name, labelled.
clearly
• Answer the questions in the spaces
provided – there may be more space than
• you need.
You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
•Informatio
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
n booklet ‘Mathematical Formulae and Statistical Tables’ is
are 9 questions in this question paper. The total mark for this paper
• isThe – usefor
75.marks
provided.
question.
thiseach
as aquestion
guide asare shown
to how in time to spend on each
much
•e brackets
Advic
Read each question carefully before you start to answer it.
•• Try to answer every
Check your answers if you have time at the Turn over
end.
question.
1
,1.
AREA
DO NOT WRITE IN THIS
R
initial line
O
Figure 1
Figure 1 shows a sketch of the curve with polar equation
r = 2 sinh θ + cosh θ 0θπ
The region R, shown shaded in Figure 1, is bounded by the initial line, the curve and the
line with equation θ = π
Use algebraic integration to determine the exact area of R giving your answer in the
form peq – r where p, q and r are real numbers to be found.
(4)
AREA
DO NOT WRITE IN THIS
AREA
DO NOT WRITE IN THIS
2
, DO NOT WRITE IN THIS DO NOT WRITE IN THIS DO NOT WRITE IN THIS
AREA AREA AREA
Question 1 continued
(Total for Question 1 is 4 marks)
over
Turn
3
, 2. (a) Write down the Maclaurin series of ex, in ascending power of x, up to and including
the term in x3
(1)
AREA
DO NOT WRITE IN THIS
(b) Hence, without differentiating, determine the Maclaurin series of
e(e – 1)
x
in ascending powers of x, up to and including the term in x3, giving each coefficient
in simplest form.
(5)
AREA
DO NOT WRITE IN THIS
AREA
DO NOT WRITE IN THIS
4
information
Candidate surname Other names
Centre Candidate
Number Number
Pearson Edexcel Level 3
GCE
Monday 5 June 2023
Paper
Afternoon (Time: 1 hour 30
minutes) referenc
e
9FM0/02
Further Mathematics
Advanced
PAPER 2: Core Pure
Mathematics 2
You must have: Total
Mathematical Formulae and Statistical Tables (Green), Marks
calculator
Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for symbolic algebraic
manipulation, differentiation and integration, or have retrievable
mathematical formulae stored in them.
Instructions
•• Use black ink or ball-point
• 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
pen. number and candidate number.
• Answer
centre
all questions and ensure that your answers to parts of questions are
name, labelled.
clearly
• Answer the questions in the spaces
provided – there may be more space than
• you need.
You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
•Informatio
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
n booklet ‘Mathematical Formulae and Statistical Tables’ is
are 9 questions in this question paper. The total mark for this paper
• isThe – usefor
75.marks
provided.
question.
thiseach
as aquestion
guide asare shown
to how in time to spend on each
much
•e brackets
Advic
Read each question carefully before you start to answer it.
•• Try to answer every
Check your answers if you have time at the Turn over
end.
question.
1
,1.
AREA
DO NOT WRITE IN THIS
R
initial line
O
Figure 1
Figure 1 shows a sketch of the curve with polar equation
r = 2 sinh θ + cosh θ 0θπ
The region R, shown shaded in Figure 1, is bounded by the initial line, the curve and the
line with equation θ = π
Use algebraic integration to determine the exact area of R giving your answer in the
form peq – r where p, q and r are real numbers to be found.
(4)
AREA
DO NOT WRITE IN THIS
AREA
DO NOT WRITE IN THIS
2
, DO NOT WRITE IN THIS DO NOT WRITE IN THIS DO NOT WRITE IN THIS
AREA AREA AREA
Question 1 continued
(Total for Question 1 is 4 marks)
over
Turn
3
, 2. (a) Write down the Maclaurin series of ex, in ascending power of x, up to and including
the term in x3
(1)
AREA
DO NOT WRITE IN THIS
(b) Hence, without differentiating, determine the Maclaurin series of
e(e – 1)
x
in ascending powers of x, up to and including the term in x3, giving each coefficient
in simplest form.
(5)
AREA
DO NOT WRITE IN THIS
AREA
DO NOT WRITE IN THIS
4
