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 12 June 2026
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.
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill in the boxes at the top of this page with your name,
centre number and candidate number.
• clearly
Answer all questions and ensure that your answers to parts of questions are
labelled.
• – there may
Answer the questions in the spaces provided
be more space than you need.
• Answers without working
You should show sufficient working to make your methods clear.
may not gain full credit.
• the tables the value should beshould
Values from statistical tables be quoted in full. If a calculator is used instead of
given to an equivalent degree of accuracy.
•Information
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 7 questions in this question paper. The total mark for this paper is 75.
• The marks for each question are shown in brackets
– use this as a guide as to how much time to 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. Turn over
P75687RA
©2026 Pearson Education Ltd.
P:1/1/1/1/
*P75687RA0128*
,1. In a study, the type of foot arch of 400 athletes and their level of pronation (the amount
that the foot rolls inwards toward the arch) when running are recorded.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
The results are summarised in the table below.
Type of foot arch
Observed frequencies
Low Neutral High Total
Under 36 30 44 110
Level of
Normal 51 66 55 172
pronation
Over 53 34 31 118
Total 140 130 130 400
A podiatrist, Diogo, believes that there is an association between the type of foot arch
and the level of pronation when running.
Diogo decides to carry out a chi‑squared test to investigate this.
The lowest individual expected frequency is 35.75
(a) Calculate the expected frequencies for
(i) Low and Over
(ii) Neutral and Normal
(2)
The value of
(O E ) 2
E
for the other seven classes is 6.314 to 3 decimal places.
(b) Carry out a suitable test, at the 5% significance level, to determine whether or not
there is sufficient evidence to support Diogo’s belief.
You should state your hypotheses, test statistic, critical value and conclusion clearly.
(6)
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2
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, Question 1 continued
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*P75687RA0328* Turn over
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 12 June 2026
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.
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill in the boxes at the top of this page with your name,
centre number and candidate number.
• clearly
Answer all questions and ensure that your answers to parts of questions are
labelled.
• – there may
Answer the questions in the spaces provided
be more space than you need.
• Answers without working
You should show sufficient working to make your methods clear.
may not gain full credit.
• the tables the value should beshould
Values from statistical tables be quoted in full. If a calculator is used instead of
given to an equivalent degree of accuracy.
•Information
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 7 questions in this question paper. The total mark for this paper is 75.
• The marks for each question are shown in brackets
– use this as a guide as to how much time to 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. Turn over
P75687RA
©2026 Pearson Education Ltd.
P:1/1/1/1/
*P75687RA0128*
,1. In a study, the type of foot arch of 400 athletes and their level of pronation (the amount
that the foot rolls inwards toward the arch) when running are recorded.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
The results are summarised in the table below.
Type of foot arch
Observed frequencies
Low Neutral High Total
Under 36 30 44 110
Level of
Normal 51 66 55 172
pronation
Over 53 34 31 118
Total 140 130 130 400
A podiatrist, Diogo, believes that there is an association between the type of foot arch
and the level of pronation when running.
Diogo decides to carry out a chi‑squared test to investigate this.
The lowest individual expected frequency is 35.75
(a) Calculate the expected frequencies for
(i) Low and Over
(ii) Neutral and Normal
(2)
The value of
(O E ) 2
E
for the other seven classes is 6.314 to 3 decimal places.
(b) Carry out a suitable test, at the 5% significance level, to determine whether or not
there is sufficient evidence to support Diogo’s belief.
You should state your hypotheses, test statistic, critical value and conclusion clearly.
(6)
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_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P75687RA0228*
, Question 1 continued
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3
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