Mathematics · May / June 2022 · Paper 41 · Question 1
YMA01
As printed in the paper
The question as text
1. The binomial expansion of –2 ½kx½ < 3 (3 + kx) where k is a non-zero constant, may be written in the form 2 + Dx 3 + ... A + Bx + Cx where A, B, C and D are constants.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[1]
1
A =
9
1(b)[3]
"3 "(1
−
2
+ −
( 2)( )
kx
+
( 2)( 3)
−
−
( )
kx
2
+
...)
or
3
2
3
k
2
k
2 ( 2)( 3)
−
−
k
2
k
2
=
3
−
x :
3 ( 2) 3
−
2
−
= −
and
2x :
27
2
3
27
( 2)( 3)
−
−
k
2
k
= ×−
3 ( 2)
...
k
2
=
...
k
2
3
3
k
2
+
6
k
=
0
*
(c)(i)
k = −
6
(ii)
2 ( 2)( 3)( 4) " 6"
−
−
−
−
3
32
=
3
−
3!
3
9
Notes
Mark parts (a) and (b) as a whole.
(a)
1
A =
B1:
9
(b)
kx −
B1: Correct unsimplified coefficients for x and
2x either in an expansion or separate for
(3
+
)
−
1(c)[3]
1
A =
9
"3 "(1
−
2
+ −
( 2)( )
kx
+
( 2)( 3)
−
−
( )
kx
2
+
...)
or
3
2
3
k
2
k
2 ( 2)( 3)
−
−
k
2
k
2
=
3
−
x :
3 ( 2) 3
−
2
−
= −
and
2x :
27
2
3
27
( 2)( 3)
−
−
k
2
k
= ×−
3 ( 2)
...
k
2
=
...
k
2
3
3
k
2
+
6
k
=
0
*
(c)(i)
k = −
6
(ii)
2 ( 2)( 3)( 4) " 6"
−
−
−
−
3
32
=
3
−
3!
3
9
Notes
Mark parts (a) and (b) as a whole.
(a)
1
A =
B1:
9
(b)
kx −
B1: Correct unsimplified coefficients for x and
2x either in an expansion or separate for
(3
+
)
−
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