Mathematics · May / June 2021 · Paper 41 · Question 1
YMA01
As printed in the paper
The question as text
1. Given that k is a constant and the binomial expansion of 1 + kx | kx | < 1 in ascending powers of x up to the term in x3 is 1 + 1 8 x + Ax2 + Bx3
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[5]
1
2
2
2
2
2
1
2
3
2
(
)
(
)
(
)
(1
+
kx
)
= +
1
×
kx
+
×
kx
+
×
kx
...
2
2!
3!
1
1
1
(i)
k
=
⇒
k
=
2
8
4
1
1
1
1
3
× −
× −
× −
2
2
1
M1 A1 A1
2
2
2
2
1
A
'' ''
k
3
=
×
= −
B
=
×
'' ''
k
=
(ii)
2!
128
3!
1024
1
1
1
2
3
1(b)[2]
Substitutes
0.6
1.15
1
0.6
''
'' 0.6
''
'' 0.6
1.072398
x =
⇒
= +
×
−
×
+
×
=
8
128
1024
1
1
1
1
2
3
2
(
)
(
)
(
)
1(b) alt
(1
+
kx
)
= +
1
×
kx
−
×
kx
+
×
kx
2
8
16
Substitutes ''
kx =
''
0.15
1
1
1
2
3
⇒
1.15
= +
1
×
0.15
−
×
0.15
+
×
0.15
=
1.072398
2
8
16
(a)(i)
M1: Sets 1
1
or 1
1
k =
kx
=
x
and proceeds to find k. Implied by a correct value for k
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