Pearson Edexcel GCE In A Level Further Mathematics (9FM0) Paper 4B
Further Statistics QP & MS june 2024
, Number Number
Further Mathematics
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Advanced
PAPER 4B: Further Statistics 2
.
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P72801A
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,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,
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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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Question 1 continued
3
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Further Statistics QP & MS june 2024
, Number Number
Further Mathematics
■ ■
Advanced
PAPER 4B: Further Statistics 2
.
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)
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2
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,
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Question 1 continued
3
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