Mathematics · Oct / Nov 2023 · Paper 41 · Question 2
YMA01
As printed in the paper
The question as text
2. x cm Figure 1 Figure 1 shows a cube which is increasing in size. At time t seconds, • the length of each edge of the cube is x cm 2 • the surface area of the cube is S cm 3 • the volume of the cube is V cm 2 s –1 Given that the surface area of the cube is increasing at a constant rate of 4 cm
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
2(a)[4]
or d
S
States or uses
S
=
6
x
2
t =
4
d
and d
S
States or uses
S
=
6
x
2
t =
4
d
Attempts to use d
S
d
S
d
x
d
x
d
x
4
12
...
=
×
=
x
×
=
d
t
d
x
d
t
d
t
d
t
d
x
1
oe
=
d
t
3
x
(a) Alt
or d
S
States or uses
S
=
6
x
2
t =
4
d
and d
S
States or uses
S
=
6
x
2
4
t =
d
d
S
d
x
d
x
=
4
S
=
4
t
+
c
S
=
6
x
2
6
x
2
=
4
t
+
c
12
x
=
4
=
...
d
t
d
t
d
t
or
d
t
d
x
S
6
x
2
6
x
2
4
t
c
12
x
4
...
=
=
+
=
=
d
x
d
t
d
x
1
oe
=
d
t
3
x
2(b)[3]
d
V
States or uses
3
x
2
x =
d
d
V
d
V
d
x
d
V
1
Attempts to use
=
×
=
3
x
2
×
=
x
d
t
d
x
d
t
d
t
3
x
1
d
V
=
V
3
d
t
(b) Alt
2
d
S
1
−
V
=
x
3
,
S
=
6
x
2
S
=
6
V
3
=
4
V
3
d
V
d
V
d
V
d
S
1
Attempts to use
=
×
=
×
4
d
t
d
S
d
t
1
−
4
V
3
d
V
1
=
V
3
d
t
This will most likely be the use of A rather than S for surface area.
or d
S
B1: States or uses
S
6
x
2
(ignore any units associated with either)
=
t =
4
d
may be implied by d
S
Note that
S
=
6
x
2
x =
12
x
d
and d
S
B1: States or uses
(ignore any units associated with either)
S
=
6
x
2
t =
4
d
may be implied by d
S
Note that
S
=
6
x
2
12
x
x =
d
M1: Attempts to use d
d
d
or equivalent with their d
x and d
t where d
and d
S
S
x
S
S
S
=
×
x =
kx
d
t
d
x
d
t
d
d
d
constant, in an attempt to find d
x
t . May be implied by their working.
d
1
A1: d
x
1
4
3 , 12
oe e.g.
x from correct work and apply isw once a correct answer is seen.
=
d
t
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