Mathematics · Oct / Nov 2021 · Paper 21 · Question 1
YMA01
As printed in the paper
The question as text
1. The first three terms, in ascending powers of x, of the binomial expansion of (1 + kx) 16 are 1, −4x and px2 where k and p are constants.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[3]
States/uses either 16
k = − or
4
=
2
1
(i)
k = −
4
15
(ii)
p =
2
16
(
)
16
g( )
x
=
2
+
1
+
kx
1(b)[3]
x
16 15 14
×
×
3
Attempts either 2''
p or
''
16
×
×
k
3!
16 15 14
×
×
3
Attempts sum of 2''
p and
''
16
×
×
k
3!
2x (
)
15 140
x
2
125
x
2
Term in
=
−
= −
(a)
16 15
×
2
M1: States or uses either 16
k = − or
4
k
=
p
. It may be implied by a correct value
2
for k or p if no incorrect working is seen.
(i)
1
k = −
A1:
or 0.25
−
4
(ii)
15
1
A1:
p =
or 7.5
Allow if this follows from
k = ±
2
4
.
(b)
( )
2p x
2
M1: Attempts one of the two relevant terms or coefficients. Either
or
( )
16 15 14
×
×
3
16
×
×
k
x
2
or exact equivalent. May be part of an attempt at a full
3!
expansion. May be in terms of p and k
dM1: Must have attempted at least one of the terms correctly. Attempts sum of their
( )
( )
"
16 15 14
×
×
"
2
3
2 " "
×
p
x
and their
16
×
×
k
x
2
which must be arising from correct
3!
combination of powers from the expanded brackets though the coefficients need not be
correct. Must be numerical terms. May be part of an attempt at a full expansion.
FYI If the k is not cubed in the second of these then you may see 2240x2 and can score the
dM.
−
125x
2
x . Do not allow as part of an expansion for this
2
A1:
Term in
. Must include the
mark.
(
)
3
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