PAPER 3: Themes in breadth with aspects in depth Option 39.1: Civil rights and race relations in the USA, 1850–2009 Option 39.2: Mass media and social change in Britain, 1882–2004 Combined Question Paper & Final Marking Scheme

2025 Pearson Edexcel Level 3 GCE Advanced PAPER 3A: Further Mathematics Advanced PAPER 3A: Further
Pure Mathematics 1 Combined Question Paper & Final Marking Scheme
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Pearson Edexcel Level 3 GCE
Wednesday 18 June 2025
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/3A
Further Mathematics
 


Advanced
PAPER 3A: Further Pure Mathematics 1

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 symbolic algebraic manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
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Answer all questions and ensure that your answers to parts of questions are
• clearly labelled.
• 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.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information

•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
There are 9 questions in this question paper. The total mark for this paper is 75.
• The this asfora each
– usemarks question
guide as to howare shown
much timeintobrackets
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.
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P76379A
©2025 Pearson Education Ltd.
Y:1/1/1/1/

,1. (a) Given that
2
y = ecosec x




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complete the table below with the value of y corresponding to x = 2, giving your
answer to 2 decimal places.


x 1.5 1.75 2 2.25 2.5

y 2.73 2.81 5.22 16.31

(1)

(b) Use Simpson’s rule, with all the values of y in the completed table, to estimate, to
one decimal place, the value of
2.5 2



cosec x
e dx
1.5
(3)




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(c) Using your answer to part (b) and making your method clear, estimate the value of
2.5 2



cot x
e dx
1.5
(2)




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2


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
Question 1 continued




(Total for Question 1 is 6 marks)



Turn over
3

, 2.  The Taylor series expansion of f(x) about x = a is given by 
 
 f(x) = f(a) + (x – a)f ′(a) + (x  a)2 (x  a)r (r) 
f ′′(a) + ... + f (a) + ...




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 r!

2!

Given that

d2 y dy
 3  2xy  4 (I)
dx 2 dx


(a) show that

d4 y dy d2 y d3 y
a  bx c
dx4 dx dx2 dx3

where a, b and c are integers to be determined.
(4)
dy
Hence, given that y = 1 and = 1 when x = 2
dx




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(b) determine a Taylor series solution, in ascending powers of (x – 2), up to and
including the term in (x – 2)4, of the differential equation (I), giving each coefficient
in simplest form.
(4)




4