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Past exam of the mathematics course of the University of Cambridge
/
2022
/
ii
/
Paper 4
/
6C
/
c
/
Solution
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@codex,
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Past exam of the mathematics course of the University of Cambridge
2022
ii
Paper 4
6C
c
Created
2026-09-24
Updated
2026-09-25
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Use
enzyme
conservation to write
e
=
e
0
(
1
−
v
1
−
v
2
)
.
(1)
Since
τ
=
k
1
e
0
t
,
u
=
s
/
s
0
,
v
i
=
c
i
/
e
0
, and
ϵ
=
e
0
/
s
0
, substitution into the
mass
-
action
equations
gives
f
(
u
,
v
1
,
v
2
)
=
−
u
(
1
−
v
1
−
v
2
)
+
α
v
1
−
β
u
v
1
,
(2)
and
g
1
(
u
,
v
1
,
v
2
)
g
2
(
u
,
v
1
,
v
2
)
=
u
(
1
−
v
1
−
v
2
)
−
α
v
1
−
β
u
v
1
+
γ
v
2
,
=
β
u
v
1
−
γ
v
2
,
(3)
where
α
=
k
1
s
0
k
−
1
,
β
=
k
1
k
2
,
γ
=
k
1
s
0
k
3
.
(4)
The factors of
ϵ
multiplying
d
v
i
/
d
τ
identify the complex concentrations
as
fast variables in
a
singular perturbation
.
Ancestors
(11)
c
6C
Paper 4
ii
2022
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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