Mathematics · Oct / Nov 2024 · Paper 21 · Question 7
YMA01
As printed in the paper
The question as text
7. Jem pays money into a savings scheme, A, over a period of 300 months. Jem pays £20 into scheme A in month 1, £20.50 in month 2, £21 in month 3 and so on, so that the amounts Jem pays each month form an arithmetic sequence.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
7(a)[1]
(
)
(
)
( )
=
20 99 0.5
+
=
£ 69.50*
u
100
7(b)[2]
1 300
(
)
2 20
299 0.5
(
)
...
S
=
×
+
=
300
2
or
1 300
(
)
S
=
20 169.50
+
=
...
300
2
=
( )
£ 28425
7(c)[3]
299 250
(
)
20
×
r
299
=
250
r
=
=
1.008483032...
20
(
)
20 1
−
r
300
(
)
=
=
27362.948...
S
300
1
−
r
28425
27362.948...
−
(£)1060
(a)
(
)
B1*: Correct method shown e.g.
20
+
99 0.5
=
69.50
is sufficient.
Note that the £ symbol is not required but
(
)
scores B0
20
+
99 0.5
=
69.5
Condone attempts to work backwards e.g.
(
)
(
)
69.5
=
20
+
n
−
1
×
0.5
49.5
=
n
−
1
×
0.5
n
=
100
hence true
Note that 69.5 can be used in this case but a (minimal) conclusion is required.
(b)
1
(
)
(
)
M1:
Attempts
2 n
2
×
a
+
n
−
1
d
with n = 300, a = 20 and d = 0.5
1
(
)
or e.g.
+
with n = 300, a = 20 and l = 169.5(0) (or an attempt at 20 299 0.5
2 n a
l
A1:
Correct value. The £ symbol is not required.
(c)
Correct strategy to find r e.g. 299 250.
) 299 250
Award for e.g. (
M1:
r =
or e.g.
20
20
1
250
(
)
299
=
.
May be implied by awrt 1.01 if no incorrect work is seen e.g. clear
r
20
use of 300 250
which gives 1.008454636… is M0
20
1 log12.5
May be done via logs e.g.
r =
10
299
M1:
Uses their r with a correct GP sum formula with a = 20 and n = 300 and subtracts
from the answer to part (b) either way round.
Depends on having attempted the sum of an AP in (b).
May be implied by their working/value.
Note this has been seen more than once for the GP sum following 299 250
20
20 1 12.5
(
)
−
S
= −
300
1 1.008483032
(
)
1
−
1
a
−
r
n
and scores M0 as it suggests
S
=
has been used.
n
1
−
r
A1:
Cao not awrt with or without the “£” symbol.
Note that the accuracy being used for “r” varies considerably.
Some rounded values for reference are:
r
|Correct (b) −
|
S
S
300
300
1.01
37576.93252…
9151.932524…
1.008
24796.03972…
3628.960276…
1.0085
27458.42195…
966.5780531…
1.00848
27345.9295…
1079.070499…
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