Mathematics · Oct / Nov 2024 · Paper 41 · Question 1
YMA01
As printed in the paper
Show the answer and mark scheme
1(a)[4]
1
−
1
1
3
(
)
−
3
8
−
3
x
=
1
−
x
3
2
8
1
−
(
)
2
(
)(
)
3
3
3
−
1
−−
1
1
3
−
1
−−
1
1
−−
1
2
3
3
(
)
1
−
x
= + −
1
1
−
x
+
3
3
−
x
+
3
3
3
−
x
+
...
8
3
8
2!
8
3!
8
1
1
1
1
7
(
)
8
−
3
x
−
=
+
x
+
x
2
+
x
3
+
...
3
2
16
64
1536
1(b)[2]
2
3
1
1
2
1
2
7
2
2851
−
1
2851
+
+
+
+
...
=
3
6
=
=
...
2
16 3
64 3
1536 3
5184
5184
or 2333
5184
=
12851
2851
1
Note a misread of (
)
8 3x
−
can score a maximum of B1M1A0A0 M0A0
3
(a)
− must be evaluated. May be implied by further work e.g. 1
1
1 1 ...
1
B1: Obtains (
)
.
...
±
x
−
8
3
2 ±
3
2
provided this has not come from an incorrect method.
1
1
1
1
1
e.g. (
8
3
x
)
−
...
is B0.
−
=
=
+
+
+
3
1
(
)
2
2
1
3
3
x
(
)
1
3
3
x
8
−
3
x
3
2
2
M1: Attempts the binomial expansion of (1 + kx)n to get the third or fourth term unsimplified with
an acceptable structure.
The correct binomial coefficient must be combined with
2x or
3x which may be unsimplified.
(
)
(
)(
)
−
−−
1 ...
−
−−
1
−−
2 ...
1
1
1
1
1
Look for
3
3
x
2
or
3
3
3
x
3
o.e. (you do not need to be concerned
2!
3!
3
with their
which may be 1 or e.g. if they have a negative sign in front of the whole term)
−
8
1
1
−
−
Do not allow notation such as
3
,
3
unless interpreted correctly in further work.
1
2
May be implied by correct coefficients with
2x or
3x
1
1
7
1x for x for this mark) which
A1: For 2 correct simplified terms of
x
,
x
2
,
x (allow
3
16
64
1536
may be listed.
Condone if coefficients are given as decimals i.e.
0.0625 , 0.015625
x
x
2
, 0.004557...
x
3
1
−
3
1
1
7
3
Also allow for
1
−
x
= +
1
x
+
x
2
+
x
3
+
...
(Note B0M1A1A0 is possible)
8
8
32
768
1
1
1
7
A1:
+
x
+
x
2
+
x
3
. Isw following a correct answer.
Make a free account to save your answers and see your weak topics and ask the AI why a wrong answer is wrong.