Mathematics · May / June 2024 · Paper 61 · Question 4
YMA01
As printed in the paper
The question as text
4. A biologist is studying bears. The biologist records the length, d cm, and the girth, g cm, of 8 bears. The biologist summarises the data as follows 2 d 1456 8 . g 713 2 . dg 141978 84 . g 72675 98 . Sdd = 16 769.78
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
4(a)[3]
S
=
141978.84
−
or
S
=
72675.98
−
dg
8
gg
8
S
dg =
12105.12
S
gg =
9094.2
"12105.12"
r =
4(b)[2]
16769.78 "9094.2"
×
= 0.9802…. awrt 0.98
"12105.12"
[
]
4(c)[3]
b =
=
0.7218...
16769.78
713.2
1456.8
[
]
a =
−
"0.7218..."
×
= −
42.297....
8
8
g = −42.3 + 0.722d *
4(d)[1]
for each 1 [cm] increase in length/d the girth/g increases by “0.722…”
(e)(i)
138.2 awrt 138
(ii)
[unreliable] as get a negative girth
4(e)[2]
S
=
141978.84
−
or
S
=
72675.98
−
dg
8
gg
8
S
dg =
12105.12
S
gg =
9094.2
"12105.12"
r =
16769.78 "9094.2"
×
= 0.9802…. awrt 0.98
"12105.12"
[
]
b =
=
0.7218...
16769.78
713.2
1456.8
[
]
a =
−
"0.7218..."
×
= −
42.297....
8
8
g = −42.3 + 0.722d *
for each 1 [cm] increase in length/d the girth/g increases by “0.722…”
(e)(i)
138.2 awrt 138
(ii)
[unreliable] as get a negative girth
0.722
x =
17.3
x =
23.96...
awrt 24
Notes
(a)
for a correct expression for Sdg or Sgg
M1
for 12105.12 Allow 302628
A1
25
for 9094.2 Allow 45471
A1
5
If exact answers are not seen then SC award M1A0A1 for both awrt 12100 and awrt 9090 if
correct methods are seen
If exact answers are not seen then SC award M1A0A0 for both awrt 12100 and awrt 9090 if no
working seen
for a valid attempt at r with their Sdg not equal to 141978.84
(b)
M1
awrt 0.98
A1
(c)
for a correct method to find the value of b May be implied by 0.7218 or better
M1
M1
for a correct method to find a ft their b May be implied by –42.29 or better
A1*
both method marks must be awarded with sight of 0.7218 or better or –42.29 or better
for a suitable contextual comment that mentions 0.722 (or better) If units are stated they must be
(d)
B1
correct.
(e)(i)
B1
awrt 138 Allow 1.38m
For a correct reason eg sd = 45.8 cm so girth is nearly 3sd below mean so likely outlier
(ii)
B1
Allow substitution of 50 leading to g = –6.2 and suitable reason e.g. this is not possible/this is
negative Do not allow substitution of 0.5 to imply the girth is negative
(f)
for a correct equation. implied by awrt 24
M1
awrt 24
A1
18 15
−
(
)
[
]
4(f)[2]
0.722
x =
17.3
x =
23.96...
awrt 24
Notes
(a)
for a correct expression for Sdg or Sgg
M1
for 12105.12 Allow 302628
A1
25
for 9094.2 Allow 45471
A1
5
If exact answers are not seen then SC award M1A0A1 for both awrt 12100 and awrt 9090 if
correct methods are seen
If exact answers are not seen then SC award M1A0A0 for both awrt 12100 and awrt 9090 if no
working seen
for a valid attempt at r with their Sdg not equal to 141978.84
(b)
M1
awrt 0.98
A1
(c)
for a correct method to find the value of b May be implied by 0.7218 or better
M1
M1
for a correct method to find a ft their b May be implied by –42.29 or better
A1*
both method marks must be awarded with sight of 0.7218 or better or –42.29 or better
for a suitable contextual comment that mentions 0.722 (or better) If units are stated they must be
(d)
B1
correct.
(e)(i)
B1
awrt 138 Allow 1.38m
For a correct reason eg sd = 45.8 cm so girth is nearly 3sd below mean so likely outlier
(ii)
B1
Allow substitution of 50 leading to g = –6.2 and suitable reason e.g. this is not possible/this is
negative Do not allow substitution of 0.5 to imply the girth is negative
(f)
for a correct equation. implied by awrt 24
M1
awrt 24
A1
18 15
−
(
)
[
]
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