Mathematics · May / June 2021 · Paper 11 · Question 5
YMA01
As printed in the paper
The question as text
5. P PA PB O t Figure 2 The share value of two companies, company A and company B, has been monitored over a 15-year period. The share value PA of company A, in millions of pounds, is modelled by the equation 2 t 0 PA = 53 – 0.4(t – 8) where t is the number of years after monitoring began. The share value PB of company B, in millions of pounds, is modelled by the equation PB = –1.6t + 44.2 t 0 where t is the number of years after monitoring began. Figure 2 shows a graph of both models. Use the equations of one or both models to answer parts (a) to (d).
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5(a)[2]
(
)
2
P
−
P
=
44.2
−
53
−
0.4 8
×
=
...
B
A
awrt (£) 16.8 million
5(b)[1]
(£) 53 (million)
5(c)[4]
2
−
1.6
t
+
44.2
=
53
−
0.4(
t
−
8)
84
⇒
0.4
t
2
−
8
t
+
=
0
⇒=
t
...
5
t =
10
−
58
=
awrt 2.38
(years)
(
)
"2.38"
<
t
15
5(d)[1]
“The share value would be negative” / “the model is known to hold for 15
years only (and 20 years is more than 15).”
(a)
M1 Substitutes
t =
0
into the equation for
P and finds the difference between 44.2 and
P .
A
A
A1 awrt (£) 16.8 million.
(b)
B1
(£) 53 million. Condone 53
(c)
1.6
44.2
53
0.4(
8)
2
M1
Sets
−
t
+
=
−
t
−
They may have already attempted to multiply out
so condone errors that may occur before setting
P
P
. Also may score for use of any
=
A
B
inequality sign.
M1
Rearranges the equation to form a 3TQ on one side of the equation (= 0) or inequality and
attempts to solve the quadratic. Condone slips in their working. See general rules for solving
a quadratic. They may use a calculator to state the root(s) which is acceptable.
A1
awrt 2.38 (years) o.e. isw after a correct answer
(
)
A1ft
"2.38"
<
t
oe from correct working. You may follow through on their value of t
15
provided
. Ignore any reference to an upper limit provided it is
15
t <
15
(d)
B1
“The share value (or P) would be negative” or “the model is known to hold for 15 years
only (and 20 is greater than 15)” or equivalent explanations.
Eg “P must be greater than (or equal to) zero”.
Note “ 4.6
< ” is insufficient (it does not refer to the model or the share value of P)
−
0
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