Mathematics · Oct / Nov 2025 · Paper 61 · Question 1

YMA01

As printed in the paper

The question as text

1. A biologist is studying horses. The biologist records the height, h cm, and the weight, w kg, of 8 horses. The table below shows the biologist’s results. Height 140 145 150 157 138 140 148 142 Weight 500 521 539 554 492 497 532 525 [You may use Σ h = 1160 Σ w = 4160 Σ hw = 604135 Σ w 2 = 2166 600 Shh = 286]

Read automatically from the paper; the printed page above is exact.

Show the answer and mark scheme

1(a)[3]
S
=
604135
−
S
ww =
2166600
−
hw
8
8
[
]
hw =
S
935
[
]
S
ww =
3400
"935"
r =
=
0.9481...
awrt 0.948
1(b)[2]
×
286 "3400"
"935"
[
]
b =
=
1(c)[3]
3.269...
286
4160
1160
[
]
a =
−
"3.269..."
×
=
45.96...
8
8
=
+
*
w
46.0 3.27
h
[On average] for each/1 [cm] increase in height/h the
1(d)[1]
weight/w increases by “3.27”[kg]
(e)(i)
546.31 awrt 546
(ii)
601.9 awrt 602
The 1st estimate is more reliable estimate since…
The 1st estimate is an interpolation/The 2nd is an
extrapolation
1(e)[2]
S
=
604135
−
S
ww =
2166600
−
hw
8
8
[
]
hw =
S
935
[
]
S
ww =
3400
"935"
r =
=
0.9481...
awrt 0.948
×
286 "3400"
"935"
[
]
b =
=
3.269...
286
4160
1160
[
]
a =
−
"3.269..."
×
=
45.96...
8
8
=
+
*
w
46.0 3.27
h
[On average] for each/1 [cm] increase in height/h the
weight/w increases by “3.27”[kg]
(e)(i)
546.31 awrt 546
(ii)
601.9 awrt 602
The 1st estimate is more reliable estimate since…
The 1st estimate is an interpolation/The 2nd is an
extrapolation
153(height) is within data range/170 is not within data
range
153 is closer to the mean(height)/170 is further from
the mean
Notes
for a correct expression for Shw or Sww implied by either correct
(a)
M1
A1
935 cao
A1
3400 cao
(b)
M1
for a valid attempt at r allow ft their values from (a)
A1
awrt 0.948 correct answer scores 2 out of 2
(c)
M1
for a correct numerical expression to find the value of b
for a correct method to find the value of a ft their b
M1
oe for this mark
Allow
w
−
520
=
"3.269..."(
h
−
145)
correct solution with both method marks and correct given
A1*
equation stated.
do not award this mark if there is incorrect working seen e.g. a =
45.85 rounding to a = 46.0 do not allow
=
+
w
46 3.27
for a correct numerical interpretation which includes height/h
(d)
B1
and weight/w
if units are stated then they must be correct
(e)(i)
B1
awrt 546
(ii)
B1
awrt 602
for 1st estimate oe and a correct supporting reason.
(f)
B1
ignore extraneous noncontradictory comments.
for 2nd/3rd reason, do not allow comments that refer to weights
1(f)[1]
153(height) is within data range/170 is not within data
range
153 is closer to the mean(height)/170 is further from
the mean
Notes
for a correct expression for Shw or Sww implied by either correct
(a)
M1
A1
935 cao
A1
3400 cao
(b)
M1
for a valid attempt at r allow ft their values from (a)
A1
awrt 0.948 correct answer scores 2 out of 2
(c)
M1
for a correct numerical expression to find the value of b
for a correct method to find the value of a ft their b
M1
oe for this mark
Allow
w
−
520
=
"3.269..."(
h
−
145)
correct solution with both method marks and correct given
A1*
equation stated.
do not award this mark if there is incorrect working seen e.g. a =
45.85 rounding to a = 46.0 do not allow
=
+
w
46 3.27
for a correct numerical interpretation which includes height/h
(d)
B1
and weight/w
if units are stated then they must be correct
(e)(i)
B1
awrt 546
(ii)
B1
awrt 602
for 1st estimate oe and a correct supporting reason.
(f)
B1
ignore extraneous noncontradictory comments.
for 2nd/3rd reason, do not allow comments that refer to weights

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