2025 Pearson Edexcel Level 3 GCE Further Mathematics Advanced PAPER 3B: Further Statistics 1Combined Question Paper &
Final Marking Scheme
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
•• IfUse black ink or ball-point pen.
pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fillcentre
in the boxesand
number at the top of this
candidate page with your name,
number.
Answer all questions and ensure that your answers to parts of questions are
• clearly labelled.
• – there may
Answer the questions in the spaces provided
be more space than you need.
• Answers withoutsufficient
You should show working to make your methods clear.
working may not gain full credit.
• Values from statistical tables should be quoted in full. If a calculator is used instead
of the tables the value should be given to an equivalent degree of accuracy.
• Inexact answers should be given to three significant figures unless
otherwise stated.
Information
•• There
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 7 questions in this question paper. The total mark for this paper is 75.
• The
– use marks
this asfor eachas
a guide question
to how are shown
much timeintobrackets
spend on each question.
Advice
• Try
Read each question carefully before you start to answer it.
•• Checkto answer every question.
your answers if you have time at the end.
Turn over
P76380A
©2025 Pearson Education Ltd.
Y:1/1/1/
,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
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)
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)
Turn over
3
, 2. The discrete random variable X has probability distribution
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)
DO NOT WRITE IN THIS AREA
4
Final Marking Scheme
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
•• IfUse black ink or ball-point pen.
pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fillcentre
in the boxesand
number at the top of this
candidate page with your name,
number.
Answer all questions and ensure that your answers to parts of questions are
• clearly labelled.
• – there may
Answer the questions in the spaces provided
be more space than you need.
• Answers withoutsufficient
You should show working to make your methods clear.
working may not gain full credit.
• Values from statistical tables should be quoted in full. If a calculator is used instead
of the tables the value should be given to an equivalent degree of accuracy.
• Inexact answers should be given to three significant figures unless
otherwise stated.
Information
•• There
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 7 questions in this question paper. The total mark for this paper is 75.
• The
– use marks
this asfor eachas
a guide question
to how are shown
much timeintobrackets
spend on each question.
Advice
• Try
Read each question carefully before you start to answer it.
•• Checkto answer every question.
your answers if you have time at the end.
Turn over
P76380A
©2025 Pearson Education Ltd.
Y:1/1/1/
,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
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)
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)
Turn over
3
, 2. The discrete random variable X has probability distribution
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)
DO NOT WRITE IN THIS AREA
4
