Mathematics · May / June 2024 · Paper 21 · Question 2
YMA01
As printed in the paper
The question as text
2. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. In an arithmetic series, • the sixth term is 2 • the sum of the first ten terms is –80 For this series,
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
2(a)[4]
a
+
d
=
a
d
2
Solves simultaneously
=
20,
= −
98
d
a
n
(
)
Attempts
2
×−
98
+
−
1
×
20 ...8000
2(b)[3]
n
2
2
5
−
54
−
4000...0
=
(34.2)
n
n
n
n =
35
(a)
10 2
+
9
= −
80
B1:
One of
a
+
5
d
=
2
or
a
d
2
B1:
Both equations correct. May be unsimplified (isw after correct equations seen).
M1:
Solves their two equations in a and d (one of which must be correct) and finds at least
a or d. There may be slips, but score for any attempt that reaches a value provided at
least one equation was correct and both attempted. Implied by correct answers
following correct equations stated.
A1:
For
d
=
20,
a
= −
98
Alt
10 (2
(
)
B1:
Correct formula in d only using 6th and 10th term
−
5 )
+
(2
+
4 )
d
d
2
B1:
d = 20
M1:
Attempts to find a using a + 5d = 2
A1:
Correct a
(b)
Note: allow all marks in (b) with any equality or inequality used throughout.
n
(
)
2
×−
98
+
−
1
×
20 ...8000
M1:
Attempts to use
n
with their a and d. Accept if set
2
equal to 8001. NB If 800 or 80000 is used, allow the M (misread).
dM1: Sets up and solves a 3 term quadratic equation in n. Accept if just the positive root is
given, but at least one positive root must be obtained.
Allow use of calculator /formulae (may need to check values if no method shown).
May be implied by a rounded or truncated positive integer value following a suitable
equation having been set up.
2
FYI the correct equation is
5
n
−
54
n
−
4000...0
(
)35
A1:
n =
stated following a correct equation formed (allowing for incorrect
inequality).
Alt by trial and improvement
n
(
)
2
×−
98
+
−
1
×
20
M1:
Attempts to use
n
with their a and d and integer values of n
2
either side of the sum being 8000
dM1: Two consecutive values for n giving results either side of 8000 attempted.
A1:
n =
35
stated following correct working with both n=34 and n= 35 having been seen.
(
)
(
)
2log
2
−
=
4
+
log
+
10
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