2024 PEARSON EDEXCEL GCE A LEVEL RURTHER MATHEMATICS 9FMO/4B PAPER 4B MERGED QUESTION
PAPER AND MARKING SCHEME
surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 4B: Further Statistics 2
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 of
•Information
tables the value should be given to an equivalent degree of accuracy.
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• – use this asfora guide
are 8 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.
• Read each question carefully before you start to answer it.
Advice
•• Try to answer every question.
Check your answers if you have time at the end. Turn over
P72801A
©2024 Pearson Education Ltd.
F:1/1/1/1/1/1/
,1. Two students are experimenting with some water in a plastic bottle. The bottle is filled
with water and a hole is put in the bottom of the bottle. The students record the time,
t seconds, it takes for the water level to fall to each of 10 given values of the height,
DO NOT WRITE IN THIS AREA
h cm, above the hole.
Student A models the data with an equation of the form t = a + b h
The data is coded using v = t – 40 and w = h and the following information
is obtained.
v = 626 v 2
= 64678 w = 22.47 Sww = 4.52 S
vw
= − 338.83
(a) Find the equation of the regression line of t on h in the form t = a + b h
(4)
The time it takes the water level to fall to a height of 9 cm above the hole is 47 seconds.
(b) Calculate the residual for this data point.
Give your answer to 2 decimal places.
(2)
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Given that the residual sum of squares (RSS) for the model of t on h is the same as
the RSS for the model of v on w,
(c) calculate the RSS for these 10 data points.
(2)
Student B models the data with an equation of the form t = c + dh
The regression line of t on h is calculated and the residual sum of squares (RSS) is
found to be 980 to 3 significant figures.
(d) With reference to part (c) state, giving a reason, whether Student B’s model or
Student A’s model is the more suitable for these data.
(1)
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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
3
Turn over
, 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
4
PAPER AND MARKING SCHEME
surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 4B: Further Statistics 2
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 of
•Information
tables the value should be given to an equivalent degree of accuracy.
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• – use this asfora guide
are 8 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.
• Read each question carefully before you start to answer it.
Advice
•• Try to answer every question.
Check your answers if you have time at the end. Turn over
P72801A
©2024 Pearson Education Ltd.
F:1/1/1/1/1/1/
,1. Two students are experimenting with some water in a plastic bottle. The bottle is filled
with water and a hole is put in the bottom of the bottle. The students record the time,
t seconds, it takes for the water level to fall to each of 10 given values of the height,
DO NOT WRITE IN THIS AREA
h cm, above the hole.
Student A models the data with an equation of the form t = a + b h
The data is coded using v = t – 40 and w = h and the following information
is obtained.
v = 626 v 2
= 64678 w = 22.47 Sww = 4.52 S
vw
= − 338.83
(a) Find the equation of the regression line of t on h in the form t = a + b h
(4)
The time it takes the water level to fall to a height of 9 cm above the hole is 47 seconds.
(b) Calculate the residual for this data point.
Give your answer to 2 decimal places.
(2)
DO NOT WRITE IN THIS AREA
Given that the residual sum of squares (RSS) for the model of t on h is the same as
the RSS for the model of v on w,
(c) calculate the RSS for these 10 data points.
(2)
Student B models the data with an equation of the form t = c + dh
The regression line of t on h is calculated and the residual sum of squares (RSS) is
found to be 980 to 3 significant figures.
(d) With reference to part (c) state, giving a reason, whether Student B’s model or
Student A’s model is the more suitable for these data.
(1)
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
3
Turn over
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
4
