Mathematics · May / June 2021 · Paper 21 · Question 1
YMA01
As printed in the paper
The question as text
1. Adina is saving money to buy a new computer. She saves £5 in week 1, £5.25 in week 2, £5.50 in week 3 and so on until she has enough money, in total, to buy the computer. She decides to model her savings using either an arithmetic series or a geometric series. Using the information given,
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[3]
series should be used.
(ii) (
nu
)
=
5
+
(
n
−
1)" "
d
or
(
u
)
=
5
+
n d
" "
n
(
nu
)
=
5
+
0.25(
n
−
1)
oe
n
1(b)[4]
(
)
Need
S
=
2
× +
5
(
n
−
1) 0.25
×
3
50
n
2
⇒
0.25
n
2
+
9.75
n
700
⇒
(
n
+
19.5)
2
−
19.5
2
2800
⇒
n
=
...
So 37 weeks.
Notes:
(a)(i)
B1: Identifies that there is a common difference (e.g. goes up in equal amounts) between first and
second, and second and third terms, or that the ratio between first and second, and second and third
is not the same, and states arithmetic series/sequence to be used.
M1: Attempts general term for A.S. with n or n – 1 used and their d (which need not be correct).
A1: Correct expression for general term, accept equivalents, eg 4.75
0.25n
. May use another label
+
than un or no label at all.
(b)
M1: Uses the sum formula for A.S. with their a and d and equates to, or sets inequality with, 350.
Accept with any inequality symbol or equality between.
A1: Correct equation/inequality. Accept with any inequality symbol or equality between.
M1: Forms and solves a 3 term quadratic (need not be gathered to one side). Any valid method
(including calculator – you may need to check).
A1: 37 weeks selected as answer.
For attempts via listing, send to review.
For use of geometric series:
Case 1: If a student states arithmetic series but uses geometric series formulae, then only the B mark
can be scored in (a), but in (b) allow M0A0M1A0 if a correct method is used to solve their equation
n
5(" "
r
−
1)
35
0
(or with “=” or “<” etc) to find n (so
n
=
log
(70(" " 1) 1)
r
−
+
oe)
"
r
"
1
" "
r
−
Case 2: If a student states a geometric series and gives a common ratio, then allow B0M1A0 in (a)
5(" "
r
n
−
1)
for
(
u
)
=
5
" "k
r
with k = n or n – 1 and in (b) allow M1A0 for
35
0
and then M1A0 for
n
"
r
"
−
1
a correct method to solve this equation.
(i) Correct shape and
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