Mathematics · Oct / Nov 2021 · Paper 21 · Question 5
YMA01
As printed in the paper
The question as text
5. A company that owned a silver mine • extracted 480 tonnes of silver from the mine in year 1 • extracted 465 tonnes of silver from the mine in year 2 • extracted 450 tonnes of silver from the mine in year 3 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]
+
×−
= 285 tonnes
N
{
}
5(b)[3]
2 480
×
+
(
N
−
1)
×−
15
=
7770
Sets
2
N
{
}
2
960 15
−
N
+
15
=
7770
⇒
N
−
65
N
+
1036
=
0
*
2
5(c)[1]
States 28 only
(a)
a
(
n
1
)
d
M1: Attempts to use
+
−
with at least two of a, d and n correct. (So allow with
a
nd
+
if both a and d are correct, bod.) They may have d > 0 for this mark.
A1:
285 tonnes. Condone the omission of the units
(b)
Note: Use of n instead of N is fine throughout part (b).
7770
M1: Attempts to use a correct sum formula with
S =
using their a and d, condoning
slips.
N
{
}
A1:
A correct equation for N. E.g.
2 480
×
+
(
N
−
1)
×−
15
=
7770
2
2
A1*: Achieves
N
−
65
N
+
1036
=
0
(including the “=0”) following a correct intermediate
line (see scheme) and with no errors, although “=0” may be implied in intermediate steps.
(c)
B1:
States 28 only. The 37 should be rejected if found. 29 is B0.
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