Mathematics · Oct / Nov 2022 · Paper 11 · Question 3
YMA01
As printed in the paper
The question as text
3. The share price of a company is monitored. Exactly 3 years after monitoring began, the share price was £1.05 Exactly 5 years after monitoring began, the share price was £1.65 The share price, £V, of the company is modelled by the equation V = pt + q where t is the number of years after monitoring began and p and q are constants.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
3(a)[3]
1.05
=
3p
+
q
1.65
=
5p
+
q
e.g. 2
p =
0.6
or 1.05
=
3
+
(1.65
−
5 )
or 1.65
5
(1.05
3 )
p
p
=
p
+
−
p
=
0.3
=
0.15
p
q
3(b)[2]
2.5
=
"0.3"
+
"0.15"
=
T
T
T =
7.8
(a)
M1
Forms two simultaneous equations (which may be in pence) and proceeds to find a value for
p or q
May be implied by a correct p or q (allow sight of 30 or 15).
Also score for an attempt to calculate 1.65 1.05
−
or equivalent.
5
3
−
A1
or
oe
p =
0.3
q =
0.15
A1
p =
0.3
and
q =
0.15
oe
(b)
M1
Uses their values for p and q with
V =
2.5
and rearranges to find a value for T. It must come
from 2.5
±
q
which you may need to check on your calculator, allowing for truncation or
p
rounding (eg 8 following correct values for V, p and q)
A1
7.8 cao isw after sight of the correct answer.
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