Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 13 June 2025
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/3B
Further Mathematics
Advanced
PAPER 3B: Further Statistics 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 algebra 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,
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
• – there may
labelled.
Answer the questions in the spaces provided
• Answers without working
be more space than you need.
You should show sufficient working to make your methods clear.
• of the tables the value shouldshould
may not gain full credit.
Values from statistical tables be quoted in full. If a calculator is used instead
• Inexact
be given to an equivalent degree of accuracy.
answers should be given to three significant figures unless
otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• – use this asfora guide
are 7 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.
• Check your answers if you have time at the end.
Try to answer every question. Turn over
P76380A
©2025 Pearson Education Ltd.
Y:1/1/1/
*P76380A0124*
,1. Irina is practising her serves in badminton and counts the number of her serves that are
faults. She finds that 15% of her serves are faults.
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Assuming that each serve is independent,
(a) find the probability that
(i) Irina’s 4th fault comes on her 20th serve,
(2)
(ii) in 18 serves, Irina has 4 faults.
(2)
With practice, Irina reduces her proportion of faults, p, so that the mean number of
serves until her 4th fault is at least 32
(b) Find the maximum value of p
(3)
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2
*P76380A0224*
, Question 1 continued
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(Total for Question 1 is 7 marks)
3
*P76380A0324* Turn over
, 2. The discrete random variable X has probability distribution
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x –1 a b
1 1 1
P(X = x)
2 4 4
where a and b are positive constants.
(a) Find an expression for E(X ) in terms of a and b
(2)
The discrete random variable Y is defined as Y = a + bX
1 5
Given that Var(Y ) = Var(X ) and E(Y ) =
4 16
(b) find the value of E(X )
(7)
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4
*P76380A0424*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 13 June 2025
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/3B
Further Mathematics
Advanced
PAPER 3B: Further Statistics 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 algebra 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,
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
• – there may
labelled.
Answer the questions in the spaces provided
• Answers without working
be more space than you need.
You should show sufficient working to make your methods clear.
• of the tables the value shouldshould
may not gain full credit.
Values from statistical tables be quoted in full. If a calculator is used instead
• Inexact
be given to an equivalent degree of accuracy.
answers should be given to three significant figures unless
otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• – use this asfora guide
are 7 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.
• Check your answers if you have time at the end.
Try to answer every question. Turn over
P76380A
©2025 Pearson Education Ltd.
Y:1/1/1/
*P76380A0124*
,1. Irina is practising her serves in badminton and counts the number of her serves that are
faults. She finds that 15% of her serves are faults.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
Assuming that each serve is independent,
(a) find the probability that
(i) Irina’s 4th fault comes on her 20th serve,
(2)
(ii) in 18 serves, Irina has 4 faults.
(2)
With practice, Irina reduces her proportion of faults, p, so that the mean number of
serves until her 4th fault is at least 32
(b) Find the maximum value of p
(3)
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2
*P76380A0224*
, Question 1 continued
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(Total for Question 1 is 7 marks)
3
*P76380A0324* Turn over
, 2. The discrete random variable X has probability distribution
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
x –1 a b
1 1 1
P(X = x)
2 4 4
where a and b are positive constants.
(a) Find an expression for E(X ) in terms of a and b
(2)
The discrete random variable Y is defined as Y = a + bX
1 5
Given that Var(Y ) = Var(X ) and E(Y ) =
4 16
(b) find the value of E(X )
(7)
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4
*P76380A0424*
