surname names
Number Number
Further Mathematics
🟐 🟐
Advanced
PAPER 3B: Further Statistics 1
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,
• 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.
• Values
Answers without working may not gain full credit.
from statistical tables should be quoted in full. If a calculator is used instead
• Inexact
of the tables the value should 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 as
question
to how are
muchshown
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.
2025 Pearson Edexcel A Level Further Mathematics Question Paper Option 3B June+ Mark
scheme
,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)
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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
, 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
DO NOT WRITE IN THIS AREA
4
■■■■
Number Number
Further Mathematics
🟐 🟐
Advanced
PAPER 3B: Further Statistics 1
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,
• 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.
• Values
Answers without working may not gain full credit.
from statistical tables should be quoted in full. If a calculator is used instead
• Inexact
of the tables the value should 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 as
question
to how are
muchshown
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.
2025 Pearson Edexcel A Level Further Mathematics Question Paper Option 3B June+ Mark
scheme
,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)
3
Turn over
, 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
DO NOT WRITE IN THIS AREA
4
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