Mathematics · Oct / Nov 2020 · Paper 21 · Question 5
YMA01
As printed in the paper
The question as text
5. Ben is saving for the deposit for a house over a period of 60 months. Ben saves £100 in the first month and in each subsequent month, he saves £5 more than the previous month, so that he saves £105 in the second month, £110 in the third month, and so on, forming an arithmetic sequence.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
5(a)[2]
Uses a + (n – 1)d with a = 100, d = 5 and n
(
)
t
=
100
+
40 1
−
×
5
= 40. This may be implied by a correct
40
expression e.g. 100 + 39´5
Cao. Correct answer with no working
= (£)295
scores both marks.
5(b)[3]
Uses a correct sum formula with a = 100,
d = 5 and n = 60 or n = 40. May be implied
by a correct numerical expression.
1 60
(
)
(
(
)
)
1
S
=
2 100
×
+
60 1
−
×
5
If using
(
)
with n = 40 you may see
2 n a
+
l
60
2
or
1 40
(
)(
)
100
+
295
using their result from
(
)
l =
100
+
60 1
−
×
5
=
395
2
1 60
(a) and this scores M1 also.
(
)(
)
S
=
100
+
395
60
2
Correct numerical expression with n = 60.
If there are any missing brackets then this
mark should be withheld unless the correct
expression is implied by their answer.
Cao. Correct answer with no working
scores 3 marks. Apply isw if necessary and
= (£)14 850
award this mark once a correct answer is
seen.
5(c)[3]
Attempts to use a correct sum formula with
a = 600, d = −10 and sets = 18 200.
1
(
)
(
)
2 n
2 600
×
+
n
−
1
×−
10
=
18200
Condone poor use of brackets.
Correct equation which may be implied by
subsequent work.
Obtains the printed answer with at least one
600
n
−
5
n
2
+
5
n
=
18200
intermediate line and no errors. Allow other
5
n
2
−
605
n
+
18200
=
0
variables to be used for n but the final
n
2
−
121
n
+
3640
=
0
*
answer must be as printed including “= 0”
5(d)[2]
Attempts to solve the given quadratic. This
may be implied by correct answers. Apply
(
)(
)
n
−
56
n
−
65
=
0
general guidance if necessary but must
reach at least one value for n. (Allow them
(
)56,65
⇒
n
=
to use x rather than n)
Correct values (ignore how they are
labelled e.g. allow x = …)
5(e)[1]
States (n =) 65 and gives a suitable reason –
E.g.
see below for examples of acceptable
(n =) 65 because e.g. the money has already
comments. There must be no contradictory
been saved after 56 months
statements and any calculations must be
correct.
Acceptable comments for 5(e):
n = 65 means t = 600 – 10´64 = –40 which is not possible/doesn’t make sense/etc.
n = 65 because Lina will have saved the money after 56 months
n = 65 because Lina will have saved the money before then
(
)
600
+
n
−
1
×−
10
=
0
⇒
n
=
61
so she will have paid off the loan before n = 65
Condone “because 65 > 60” or equivalent e.g. it is only over 60 months (or 5 years)
n = 65 means t = 600 – 10´64 = –40 so reject (but not just “it is negative”)
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